current research topics in mathematics education

Journal for Research in Mathematics Education

An official journal of the National Council of Teachers of Mathematics (NCTM), JRME is the premier research journal in mathematics education and is devoted to the interests of teachers and researchers at all levels--preschool through college.

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A Way to Consider Balance Among JRME Publications: Descriptive, Transformative, and Reflective Research

Looking inside the black box: measuring implementation and detecting group-level impact of cognitively guided instruction.

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of instructional practice to assess the extent to which observable features of mathematics instruction are consistent with the principles of CGI. We describe the conceptual foundations and first use of the instrument, which we call M-CLIPS. We found that teachers involved in the first 2 years of a CGI program were using methods consistent with the principles. In contrast, instructional practice in the comparison condition was mostly inconsistent with those principles.

Understanding Preservice Elementary Teachers as Mathematical Modelers and Their Perceptions of the Process

A growing consensus holds that preservice K–8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their models. We also explore their reflections on modeling as a pedagogical experience. We introduce Modeling Decision Maps as a tool to examine how PSTs construct and refine mathematical models, and we draw on reflective journal entries to capture PSTs’ perspectives on the process. Our findings indicate that realistic modeling tasks provide opportunities to foster PSTs’ understanding of modeling, grow their mathematical modeling skills, and attune them to important pedagogical practices.

The Journal for Research in Mathematics Education is published online five times a year—January, March, May, July, and November—at 1906 Association Dr., Reston, VA 20191-1502. Each volume’s index is in the November issue. JRME is indexed in Contents Pages in Education, Current Index to Journals in Education, Education Index, Psychological Abstracts, Social Sciences Citation Index, and MathEduc.

An official journal of the National Council of Teachers of Mathematics (NCTM), JRME is the premier research journal in mathematics education and is devoted to the interests of teachers and researchers at all levels--preschool through college. JRME presents a variety of viewpoints. The views expressed or implied in JRME are not the official position of the Council unless otherwise noted.

JRME is a forum for disciplined inquiry into the teaching and learning of mathematics. The editors encourage submissions including:

• Research reports, addressing important research questions and issues in mathematics education,
• Brief reports of research,
• Research commentaries on issues pertaining to mathematics education research.

More information about each type of submission is available here . If you have questions about the types of manuscripts JRME publishes, please contact [email protected].

Editorial Board

The  JRME  Editorial Board consists of the Editorial Team and Editorial Panel.  The Editorial team, led by JRME Editor Patricio Herbst, leads the review, decision and editorial/publication process for manuscripts.  The Editorial Panel reviews manuscripts, sets policy for the journal, and continually seeks feedback from readers. The following are members of the current JRME Editorial Board.

Editorial Staff   

Editorial Panel  

International Advisory Board   

Headquarters Journal Staff  

The editors of the  Journal for Research in Mathematics Education (JRME)  encourage the submission of a variety of manuscripts.

Manuscripts must be submitted through the JRME Online Submission and Review System . 

Research Reports

JRME publishes a wide variety of research reports that move the field of mathematics education forward. These include, but are not limited to, various genres and designs of empirical research; philosophical, methodological, and historical studies in mathematics education; and literature reviews, syntheses, and theoretical analyses of research in mathematics education. Papers that review well for JRME generally include these Characteristics of a High-Quality Manuscript . The editors strongly encourage all authors to consider these characteristics when preparing a submission to JRME. 

The maximum length for Research Reports is 13,000 words including abstract, references, tables, and figures.

Brief Reports

Brief reports of research are appropriate when a fuller report is available elsewhere or when a more comprehensive follow-up study is planned.

• A brief report of a first study on some topic might stress the rationale, hypotheses, and plans for further work.
• A brief report of a replication or extension of a previously reported study might contrast the results of the two studies, referring to the earlier study for methodological details.
• A brief report of a monograph or other lengthy nonjournal publication might summarize the key findings and implications or might highlight an unusual observation or methodological approach.
• A brief report might provide an executive summary of a large study.

The maximum length for Brief Reports is 5,000 words including abstract, references, tables, and figures. If source materials are needed to evaluate a brief report manuscript, a copy should be included.

Other correspondence regarding manuscripts for Research Reports or Brief Reports should be sent to

Ilana Seidel Horn, JRME Editor, [email protected] .

Research Commentaries

The journal publishes brief (5,000 word), peer-reviewed commentaries on issues that reflect on mathematics education research as a field and steward its development. Research Commentaries differ from Research Reports in that their focus is not to present new findings or empirical results, but rather to comment on issues of interest to the broader research community. 

Research Commentaries are intended to engage the community and increase the breadth of topics addressed in  JRME . Typically, Research Commentaries —

• address mathematics education research as a field and endeavor to move the field forward;
• speak to the readers of the journal as an audience of researchers; and
• speak in ways that have relevance to all mathematics education researchers, even when addressing a particular point or a particular subgroup.

Authors of Research Commentaries should share their perspectives while seeking to invite conversation and dialogue, rather than close off opportunities to learn from others, especially those whose work they might be critiquing. 

Foci of Research Commentaries vary widely. They may include, but are not restricted to the following:

• Discussion of connections between research and NCTM-produced documents
• Advances in research methods
• Discussions of connections among research, policy, and practice
• Analyses of trends in policies for funding research
• Examinations of evaluation studies
• Critical essays on research publications that have implications for the mathematics education research community
• Interpretations of previously published research in JRME that bring insights from an equity lens
• Exchanges among scholars holding contrasting views about research-related issues

Read more about Research Commentaries in our May 2023 editorial . 

The maximum length for Research Commentaries is 5,000 words, including abstract, references, tables, and figures.

Other correspondence regarding Research Commentary manuscripts should be sent to: 

Tesha Sengupta-Irving, JRME Research Commentary Editor, [email protected] .

Editorial Policies

Appeals Process Policy

Artificial Intelligence (AI) Policy

Tools for Authors

The forms below provide information to authors and help ensure that NCTM complies with all copyright laws: 

Student Work Release

Photographer Copyright Release

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Want to Review?

Find more information in this flyer  about how to become a reviewer for JRME . 

The  Journal for Research in Mathematics Education  is available to individuals as part of an  NCTM membership  or may be accessible through an  institutional subscription .

The  Journal for Research in Mathematics Education  ( JRME ), an official journal of the National Council of Teachers of Mathematics (NCTM), is the premier research journal in math education and devoted to the interests of teachers and researchers at all levels--preschool through college.

JRME is published five times a year—January, March, May, July, and November—and presents a variety of viewpoints.  Learn more about   JRME .

© 2024 National Council of Teachers of Mathematics (NCTM)

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Articles on Mathematics education

Displaying 1 - 20 of 40 articles.

The mystic and the mathematician: What the towering 20th-century thinkers Simone and André Weil can teach today’s math educators

Scott Taylor , Colby College

How counting by 10 helps children learn about the meaning of numbers

Helena Osana , Concordia University ; Jairo A. Navarrete-Ulloa , Universidad de O’Higgins (Chile) , and Vera Wagner , Concordia University

Heritage algorithms combine the rigors of science with the infinite possibilities of art and design

Audrey G. Bennett , University of Michigan and Ron Eglash , University of Michigan

The simple reason a viral math equation stumped the internet

Egan J Chernoff , University of Saskatchewan and Rina Zazkis , Simon Fraser University

4 things we’ve learned about math success that might surprise parents

Tina Rapke , York University, Canada and Cristina De Simone , York University, Canada

The key to fixing the gender gap in math and science: Boost women’s confidence

Lara Perez-Felkner , Florida State University

Celebrating Marion Walter – and other unsung female mathematicians

Jennifer Ruef , University of Oregon

These four easy steps can make you a math whiz

20% maths decree sets a dangerous precedent for schooling in South Africa

Clive Kronenberg , Cape Peninsula University of Technology

Why it doesn’t help – and may harm – to fail pupils with poor maths marks

Elizabeth Walton , University of the Witwatersrand

Boredom, alienation and anxiety in the maths classroom? Here’s why

Brian Hudson , University of Sussex

Mastery over mindset: the cost of rolling out a Chinese way of teaching maths

Alexei Vernitski , University of Essex and Sherria Hoskins , University of Portsmouth

What makes a mathematical genius?

David Pearson , Anglia Ruskin University

The rush to calculus is bad for students and their futures in STEM

Kevin Knudson , University of Florida

The Common Core is today’s New Math – which is actually a good thing

How to get children to want to do maths outside the classroom

Steve Humble , Newcastle University

Don’t freak if you can’t solve a math problem that’s gone viral

It’s often the puzzles that baffle that go viral

Jonathan Borwein (Jon) , University of Newcastle

More high school science and maths linked to more dropouts

Washington University in St. Louis

Better at reading than maths? Don’t blame it all on your genes

Kathryn Asbury , University of York

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Home > Computational, Mathematical, and Physical Sciences > Mathematics Education > Theses and Dissertations

Mathematics Education Theses and Dissertations

Theses/dissertations from 2024 2024.

Rigorous Verification of Stability of Ideal Gas Layers , Damian Anderson

Documentation of Norm Negotiation in a Secondary Mathematics Classroom , Michelle R. Bagley

New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting

Theses/Dissertations from 2023 2023

Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales

Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff

Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley

Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson

Theses/Dissertations from 2022 2022

Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll

Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon

Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena

The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper

Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby

Structural Reasoning with Rational Expressions , Dana Steinhorst

Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong

Theses/Dissertations from 2021 2021

Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams

You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer

Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens

Theses/Dissertations from 2020 2020

Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway

Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen

Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe

Theses/Dissertations from 2019 2019

Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson

Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson

Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis

“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross

Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark

Theses/Dissertations from 2018 2018

Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason

How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job

Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau

Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky

Theses/Dissertations from 2017 2017

Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard

Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard

Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville

Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga

Theses/Dissertations from 2016 2016

The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis

Insight into Student Conceptions of Proof , Steven Daniel Lauzon

Theses/Dissertations from 2015 2015

Teacher Participation and Motivation inProfessional Development , Krystal A. Hill

Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet

English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill

Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich

Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts

Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson

Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke

Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise

Theses/Dissertations from 2014 2014

The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams

Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch

Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd

Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton

An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen

Theses/Dissertations from 2013 2013

Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo

Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau

Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc

Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele

Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk

Theses/Dissertations from 2012 2012

Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call

Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons

Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson

Mathematics Teacher Time Allocation , Ashley Martin Jones

Theses/Dissertations from 2011 2011

How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell

Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce

A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams

Theses/Dissertations from 2010 2010

Growth in Students' Conceptions of Mathematical Induction , John David Gruver

Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart

Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon

Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams

Theses/Dissertations from 2009 2009

A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick

The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling

Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak

Theses/Dissertations from 2008 2008

Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon

How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks

Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill

Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson

Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb

Theses/Dissertations from 2007 2007

Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff

What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff

Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow

One Problem, Two Contexts , Danielle L. Gigger

The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry

Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer

Theses/Dissertations from 2006 2006

How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras

Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz

The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze

Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb

Theses/Dissertations from 2005 2005

Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff

An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen

Theses/Dissertations from 2004 2004

Reasoning About Motion: A Case Study , Tiffini Lynn Glaze

Theses/Dissertations from 2003 2003

An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford

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Exploring research trends of technology use in mathematics education: A scoping review using topic modeling

Sunghwan hwang.

1 Department of Mathematics Education, Chuncheon National University of Education, 126 Gongji-ro, Chuncheon, Gangwon-do, South Korea

Eunhye Flavin

2 Department of Education Studies, Stonehill College, 320 Washington St, North Easton, MA 02357 USA

3 Department of Teacher Development and Educational Studies, Oakland University, Rochester, MI USA

Associated Data

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

This study performed a scoping review of the literature concerning the use of technology in mathematics education published between January 1981 and March 2022 to explore research trends. After the defined filtering process, we retrieved 2,433 articles from Web of Science , ERIC , and PsycInfo databases and employed Latent Dirichlet Allocation (LDA) topic modeling to extract key terms and topics from the selected articles. The analysis focused on the four aspects: (a) evolution of research trends of technology use in mathematics education, (b) frequently used words, (c) latent research topics, and (d) research trends for particular topics. The findings revealed a steady increase in research interest, and the combination of frequently used words in the article abstracts suggests popular research topics that have been studied during the set period. The results of LDA identified seven research topics that were not precisely aligned with those identified in prior studies on mathematics education or educational technology. This implied technology integration into mathematics education as a distinctive research area. Over time, the seven topics showed different research trends (stable, fluctuating, increasing, and decreasing). We discussed plausible reasons for these varied patterns and proposed implications based on the research findings.

Introduction

Human life and society have changed as a result of technological development. Technological devices and apps have affected how people learn, communicate, work, and interact with each other (Chen et al., 2020 ; Kenski, 2008 ). In addition to these societal changes, especially the increase in distance education due to the COVID-19 pandemic, it would be safe to say that the use of technology in education is no longer a choice but an essential tool for suitable educational development (Kimmons, 2020 ). The introduction and expansion of technology in education have tremendously changed the educational environment. It has transformed not only curricula, educational resources, textbooks, and classroom environment but also teacher instructional practices and student learning styles (Akapame et al., 2019 ; Chen et al., 2020 ; Clements et al., 2013 ; Hoyles, 2018 ; Ozyurt & Ayaz, 2022 ; Roschelle et al., 2017 ), which led to different student achievement, motivation, and attitudes (Bicer & Capraro, 2016 ; Higgins et al., 2019 ).

Mathematics education is not an exception. In 1980, The National Council of Teachers of Mathematics (NCTM) proposed an agenda for the development of mathematics education and highlighted the importance of using technological tools (e.g., calculators and computers) in mathematics teaching and learning at all grade levels. Moreover, NCTM ( 2014 ) reported that the use of technology could improve teachers’ instructional quality and student mathematics learning, which assists in achieving educational equity. In this perspective, researchers in mathematics education have conducted various studies to examine features, opportunities, challenges, methods, resources, implementation, and outcomes of technology use in mathematics education. For example, the Third International Handbook of Mathematics Education (Clements et al., 2013 ) extensively explained how the use of technology influences mathematics curriculum, teaching, learning (e.g., modeling, reasoning, and algebra), and assessment. Such efforts have changed the entire landscape of mathematics education (Hoyles, 2018 ; Roschelle et al., 2017 ).

In response to the popularity and importance of technology use, diverse literature reviews were conducted in mathematics education. The topics covered both general educational technology, such as artificial intelligence (Hwang & Tu, 2021 ), educational robotics (Zhong & Xia, 2020 ), tablets (Svela et al., 2019 ), and mathematics-specific technology, such as GeoGebra (Yohannes & Chen, 2021 ) and graphing calculators. Furthermore, researchers have reviewed mathematics teachers’ technological pedagogical and content knowledge (TPACK; Zou et al., 2022 ) and the effectiveness of technology use in mathematics achievement (Cheung & Slavin, 2013 ).

These studies provided information on the current status of technology use in mathematics education and directions for future studies. However, most review studies have examined research trends on a particular topic. Thus, we still have limited information on overall research topics on technology use in mathematics education and how they have evolved. Previous studies have analyzed less than 100 articles with manual coding methods to synthesize previous studies, which might lead to inaccurate outcomes due to a prolonged process and an insufficient number of articles (Chen et al., 2020 ; Yin & Yuan, 2022 ). Kimmons ( 2020 ) emphasized the importance of reliable review studies revealing research trends of technology in education. However, only a few studies have extensively examined what research topics have been examined and how they evolved regarding technology use in mathematics education.

This study aims to fill this gap and synthesize relevant studies on the use of technology in mathematics education published in the last four decades (1981–2022) after the publication of the NCTM’s ( 1980 ) document. We employed topic modeling to automatically analyze a large corpus of text data to efficiently examine a large volume of articles (Blei, 2012 ). The findings of this study could provide information on past and present research trends of technology use in mathematics education and directions for future studies.

Literature review

To enlighten readers about what mathematics educators have researched, we first provided the research trends in mathematical education. Then, we discussed research trends of overall educational technology, which might provide insight regarding the research trends of technology use in mathematics education. Additionally, we reviewed literature that utilized topic modeling that informed the data analysis approach in our study.

Research trends in mathematics education

Researchers have synthesized peer-reviewed articles to identify research trends in mathematics education (e.g., Foster & Inglis, 2019 ; Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). These studies have found several domains consisting of dozens of topics. For example, Inglis and Foster ( 2018 ) examined articles published in two leading mathematics education journals ( Educational Studies in Mathematics and Journal for Research in Mathematics Education ) between 1968 and 2015 and employed topic modeling. They identified 28 topics across four domains. The domains included mathematical content (e.g., algebra and geometry), mathematical process (e.g., proof and argument), teaching and learning environments (e.g., teachers’ knowledge and beliefs, reform curriculum, and novel assessment), and hard cores and heuristics (e.g., research theory and methods). They reported that topics about algebra, proof and argumentation, teachers’ knowledge and beliefs, reform curriculum, classroom discussion, and sociocultural theory had received increasing attention. In contrast, the interest in geometry, constructivism, and experimental design topics has declined over time. Later, Foster and Inglis ( 2019 ) analyzed two mathematics education journals in the UK (Mathematics Teaching and Mathematics in School ). They again reported similar findings.

Similarly, Gökçe and Güner ( 2021 ) examined 1,021 mathematics education articles published between 1980 and 2019. They found the following four research domains: foundation (e.g., theory, perspective, and standard), implementation (e.g., effect, performance, and intervention), association (e.g., science, technology, and grade), and evaluation (e.g., success, policy, and program). They also reported that the research focus has shifted from individual student learning and generalization to curriculum and teacher-related factors, equity, and cognitive and affective skills (e.g., motivation, attitude, and self-efficacy).

These research trends can be explained by a paradigm shift in mathematics education (Bray & Tangney, 2017 ; Gökçe & Güner, 2021 ; Stinson & Bullock, 2012 ). In the early stage, mathematics education researchers focused on examining the effect of a certain program in predicting student achievement with quasi-experimental methods. However, with the demise of the process–product movement, researchers have paid more attention to examining individual students’ problem-solving. Various studies have been conducted to understand how students construct new knowledge and reorganize the existing knowledge (Bray & Tangney, 2017 ; Inglis & Foster, 2018 ). Moreover, with the effect of sociocultural theory (Vygotsky, 1986 ), researchers have examined the effects of sociocultural factors and classroom environments on mathematics teaching and learning processes (Inglis & Foster, 2018 ). The topic included classroom discourse and norms (Yackel & Cobb, 1996 ), curriculum materials (Remillard, 2005 ), teacher knowledge (Ball et al., 2008 ), student background and identity (Hand & Gresalfi, 2015 ), and technology (Drijvers, 2015 ).

The reform movement in mathematics education has also affected the research trends. The reform movement asked mathematics teachers to shift from traditional teacher-centered instructional practices into student-centered ones (Munter et al., 2015 ; Schoenfeld, 2004 ). Drills and exercises based on behaviorism were deemphasized in mathematics classrooms, whereas student autonomy, conceptual understanding, investigations, discussion, and cooperation were emphasized (Munter et al., 2015 ; NCTM, 2014 ; Schoenfeld, 2004 ). Therefore, teachers are expected to teach mathematical content and processes (e.g., problem-solving, reasoning and proof, communication, connections, and representations), which improve students’ mathematical competencies (NCTM, 2014 ). In this process, educational technologies were extensively introduced in mathematics education to support mathematics teaching and learning (Hoyles, 2018 ). For example, dynamic geometry software (e.g., Cabri and Sketchpad) and mathematical apps could support students’ investigation and help them examine and compare various mathematical ideas (Drijvers, 2015 ).

The roles of technology use in mathematics education

Mathematics educators have highlighted that mathematical technology should be integrated into mathematics education (Association of Mathematics Teacher Educators [AMTE], 2022 ; NCTM, 2014 ). Trends in International Mathematics and Science Study researchers have emphasized using various types of technology for mathematics teaching and learning, such as interactive whiteboards, internet, apps, calculators, computers, and smart tables (Mullis & Martin, 2017 ). Moreover, from a practical perspective, researchers in OECD countries ( 2019 ) reported that technology should be stressed in school mathematics as most workplaces are required to use technological tools.

The introduction of technology in mathematics education transforms mathematics teaching and learning environments (Clements et al., 2013 ; Roschelle et al., 2017 ). Students could investigate conceptual knowledge, practice problems, justify mathematical ideas, and communicate with their peers and teachers using various technology tools (Higgins et al., 2019 ; Roschelle et al., 2017 ). Thus, Cullen et al. ( 2020 ) proposed four roles of technology use in mathematics education, including supporting proof, presenting, and relating representations, enhancing reasoning, and working as a tutee.

Similarly, Drijverse ( 2015 ) examined student learning and proposed the following three didactical functions of technology use in mathematics education: doing mathematics, practicing skills, and developing conceptual understanding. Doing mathematics indicates using technology to outsource works that could be done by hand (e.g., drawing a figure and doing simple computation). The technology for practicing mathematics refers to using technology to improve speed, accuracy, and proficiency of mathematical skills and providing instructions and feedback to support mathematics learning (e.g., online-tutoring system). The technology for developing conceptual understanding provides students with more autonomy and flexibility in the construction of mathematical knowledge. Examples of this type of technology are dynamic geometry software, such as Cabri, Desmos, Geogebra, and Sketchpad. Later, Roschelle et al. ( 2017 ) proposed another category regarding the roles of technology in mathematics education: the context for interest-driven mathematics. This technology is designed to enhance students’ motivation and interest in mathematics learning, such as 3D printers, games, and Lego Mindstorms. However, using technology in the mathematics classroom is affected by technology type and knowledge, beliefs, and curriculum (Akapame et al., 2019 ; Gökçe & Güner, 2021 ; NCTM, 2014 ). Thus, researchers have also examined how those factors facilitate or hinder using technology in mathematics education (e.g., Hu et al., 2020 ; Radmehr & Goodchild, 2022 ).

Research trends in educational technology

The research trends of educational technology have shown a shift from studies on individual student learning and assessment to studies on collaboration and new learning strategies with emerging technology. Zawacki-Richter and Latchem ( 2018 ) examined articles published in  Computers and Education between 1976 and 2016. They reported that the research trends have changed across four stages: computer-assisted teaching, stand-alone multimedia learning, network computer use for collaboration, and online learning. Chen et al. ( 2020 ) examined the 50 years (1971–2018) of research trends in  the British Journal of Educational Technology (BJET) with topic modeling. They found that topics related to student collaboration (e.g., online social communication and socialized e-learning) and emerging technologies (e.g., mobile-assisted language learning and game-based learning) have received increasing attention over time.

Tatnall and Fluck ( 2022 ) examined articles published in  Education and the Information Technologies (EAIT). They reported the following research trends: evaluation and software (1996–2000), case study and pedagogy (2001–2005), collaboration and learning efficacy (2006–2010), the emergence of e‐learning (2011–2015), and mobile and blended learning (2015–2020). Similarly, Ozyurt and Ayaz ( 2022 ) analyzed research trends in the EAIT journal and reported that technology acceptance and social network-based learning were the most studied topics during the past 25 years. Additionally, the gamification topic showed the highest acceleration rate in popularity.

Unlike studies examining research trends in a journal, Kimmons ( 2020 ) analyzed 7,708 educational technology articles published between 2015 and 2019. Kimmons found that current studies have focused on three topics: (a) learning environments as modalities (e.g., mobile, flipped, and online learning), (b) achieving learning goals of school subjects (e.g., language learning and mathematics), and (c) using emerging technology for educational purposes (e.g., augmented reality [AR] and virtual reality [VR]). Similarly, Dağhan and Gündüz ( 2022 ) examined 10,386 articles in educational technology journals published during 2000–2018 and reported that interactive learning environments were the most frequently used keywords, followed by teaching/learning strategies, higher education, online learning, and e-learning. Moreover, flipped classroom, social media, and game-based learning keywords showed a considerable increase over time.

Topic modeling

Topic modeling is one of the analytical methods in text mining methodology. Computer scientists created this natural language processing technique, and social scientists have used topic models to understand certain phenomena in the world through the text people have written (Ramage et al., 2009 ). Topic modeling is a statistical model where topics are treated as latent variables. Each document includes multiple sets of words that have underlying topics. The topic modeling provides a set of words that frequently co-occur with each topic, and a topic represents a recurring pattern in which the words co-occur (Blei, 2012 ; Yin and Yuan, 2022 ). While topic modeling is an automated process, researchers label the topic names based on the results of data analysis. Thus, topic modeling is an amalgam of objective data analysis and subjective data labeling processes (Hwang & Cho,  2021 ). Latent Dirichlet Allocation (LDA) is one of the widely used methods for exploring topic models because LDA is a powerful method for generating a probabilistic model to discover a topic from the corpus (Blei, 2012 ; Yin & Yuan, 2022 ).

A scheme of the LDA algorithm with mathematical notations can be addressed as follows. First, creating a topic starts with choosing the collection of documents (i.e., corpus D ) to be analyzed. Each document ( d ) consists of words ( N ). The observed n th word in document d can be detected ( W d , n ). The LDA algorithms set two hyperparameters (α and η) that act as a prior to the posterior calculation. The α parameter is a Dirichlet parameter for a document-topic density specifying prior beliefs about topic uniformity and sparsity within documents. The η parameter is a representative of topic-word density. This parameter specifies prior beliefs about word uniformity and sparsity within topics. This LDA algorithm assumes that each document displays the topics in different proportions ( θ d ). Each word in the document is chosen from one of the topics ( Z d , n ) . After repeating this topic generation in each document, researchers obtain document-topic probability distributions ( β k ) and topic-per-word probability distributions ( θ d ). While these processes provide a probabilistic model, researchers need to determine how many numbers of topics are optimal to represent the dataset. Thus, researchers should decide the optimal number of topics ( k-number ) based on the perplexity value. The lower perplexity value indicates a better model fit (Blei, 2012 ; Nikita, 2020 ).

The current study

Several review studies have been conducted to examine the research trends of technology use in mathematics education (e.g., Zhong & Xia, 2020 ). However, these studies have examined the research trends of limited topics with a small number of articles. Therefore, as a scoping review, this study collected articles regarding the use of technology in mathematics education after the publication of the NCTM ( 1980 ) document and synthesized them. Scoping reviews refer to exploratory research that aims to “determine the scope or coverage of a body of literature on a given topic and give clear indications of the volume of literature and studies available” (Munn et al., 2018 , p. 2). Thus, scoping reviews address broad research questions and are helpful in systematically analyzing a wide range of extant work to assess the extent of the available evidence and highlight gaps (Arksey & O'Malley, 2005 ; Major et al., 2018 ; Munn et al., 2018 ). Arksey and O'Malley ( 2005 ) proposed a framework to conduct scoping reviews: (1) identifying research questions, (2) identifying related literature, (3) collecting studies, (4) charting the collected data, and (5) synthesizing, summarizing, and reporting the findings. Following this framework, the sections below describe how we collected, analyzed, charted, and synthesized data and what the major findings of this study were. Moreover, this study used topic modeling which helps us to identify latent research topics and examine how they evolve, which might not have been discussed in previous studies (Blei, 2012 ; Chen et al., 2020 ; Yin & Yuan, 2022 ). The research questions of this study are as follows:

• Q1. How did overall research trends of technology use in mathematics education evolve?
• Q2. Which words were frequently used in previous studies?
• Q3. What were the latent research topics?
• Q4. What were the research trends for individual topics?

Methodology

Data collection and retrieving process.

We implemented four steps to collect articles on technology use in mathematics education (Fig.  1 ). First, we used three research databases, Web of Science, ERIC, and PsycInfo, to search for relevant articles and selected articles containing “mathematics or math” and “technology or technologies” in the abstract and “education” in any field of the document. Second, we excluded dissertations and theses and only included peer-reviewed articles to ensure scholarly quality (Hwang & Cho, 2021 ). In addition, we excluded non-English written articles. As NCTM’s ( 1980 ) document that emphasizes technology use in mathematics education was first published in 1980, we only included articles published after 1980 (January 1981– March 2022). After this process, we obtained 13,886 research articles ( Web of Science: 4,861 , ERIC: 5,482, and PsycInfo: 3,543). Third, the EndNote 20 software was used to import articles obtained. After deleting the duplicated articles, we obtained 5,687 articles. Fourth, the titles, abstracts, and full texts of each article were reviewed, and the articles that were irrelevant to technology use in mathematics education (e.g., technology use in engineering education) were excluded. A total of 2,433 articles were retrieved through this filtering process.

Data retrieving process following the guidelines of the PRISMA group (Moher et al., 2009 ). Note. The data that support the findings of this study are available on request from the authors

Data analysis

Pre-processing.

We adopted the programming language R and conducted two pre-processing steps: stop words removal and stemming (Yin & Yuan, 2022 ). We first eliminated stop words (e.g., pronouns, conjunctions, and prepositions) that do not represent the topic of the research articles. We also eliminated the terms usually included in an abstract but contain low information about the article, such as ‘‘study,’’ ‘‘database,’’ ‘‘journal,’’ ‘‘paper,’’ and ‘‘author.’’ Second, we conducted a stemming process where it reduced a word to its word stem (e.g., the term “technologies” is transformed into “technology.”). This text normalization technique is necessary for the use of the LDA algorithm to enhance the efficiency and accuracy of the data analysis. Words such as “teacher” and “teachers” will be reduced to the word “teacher.” Figs.  3 , ​ ,5, 5 , and Table ​ Table3 3 technically show the word stems that were undertaken in the stemming process. For the stemming technique, we used a SnowballC package in R . Through these pre-processing steps, we retrieved 136,262 words.

A word cloud of topic 5 with the fifty highest term-topic probability words. Note . The bigger and bolder the word stem appears, the higher the word stem's term-topic probability

Frequently used words in the abstract. Note. The words shown in Fig. 5 are technically word stems. For example, ‘includ’ is a word stem of include, includes, included, and including that reduces the suffixes

Word Clouds of Each Topic with the Fifty Highest Term-Topic Probability Words

Note . The bigger and bolder the word stem appears, the higher the word stem's term-topic probability.

Perplexity analysis

To determine the optimal number of topics ( k ), we used a ldatuning package in R , which provides model fitness scores for the given topics (Nikita, 2020 ). We calculated a model fitness score using CaoJuan2009 , which provided the information on the optimal topic number. Cao et al. ( 2009 ) validated that the best k number of LDA is correlated with the distances between topics. This metric uses the average cosine distance between every pair of topics to measure the stability of the topic structure. A smaller average distance represents that the topic structure is more stable. Therefore, in the CaoJuan2009 metric, the lower value represents a better model fit. Figure  2 depicts that a line level falls off (the lowest value) when the number of topics is 7. This shows that the study data at hand had the best generalization performance with seven topics. Thus, we decided to categorize the collected articles into seven topics.

Perplexity of topic model

Determining research topic name

We used three types of information to determine the name of each topic: (a) top 15 characteristic words, (b) word clouds, and (c) top 20 representative articles. We first examined each topic’s top 15 characteristic words to initiate our idea around the possible topic names. The top 15 characteristic words refer to the words with the highest term-topic probability words ( β k ), which were frequently revealed in the abstract. Second, we created a word cloud of each topic with the top 50 words. The size of a term in a word cloud reflects the value of a term-topic probability, and a larger term indicates a higher term-topic probability. This visualization made it easier to see which terms (or research areas) are more representative than other terms within the topic. Third, we read the top 20 articles ( θ d ) with the highest proportion of words. This process helped us understand the narratives of each topic (e.g., research purpose and findings) and determine the research topic name.

For example, topic 5 was named “teacher instruction and TPACK” for the following reasons. First, the top 15 terms obtained by the LDA algorithm were ‘‘teacher,’’ ‘‘teach,’’ ‘‘integrate,’’ ‘‘classroom,’’ ‘‘practice,’’ ‘‘knowledge,’’ ‘‘preservice,’’ ‘‘content,’’ ‘‘lesson,’’ ‘‘pedagogy,’’ ‘‘participate,’’ ‘‘pd [professional development],’’ ‘‘train,’’ and ‘‘instruct.’’ The combination of these terms would be the name of the topic. Second, the word cloud analysis (see Fig.  3 ) revealed that ‘teacher’ took the larger proportion, followed by ‘‘teach,’’ ‘‘integrate,’’ ‘‘classroom,’’ ‘‘practice,’’ ‘‘knowledge,’’ ‘‘preservice,’’ and ‘‘content.’’ Third, the articles with the highest topic-article probability examined teachers’ technology use for mathematics instructions and their TPACK (e.g., Akapame et al., 2019 ).

Overall research trends and word frequency

This study examined 2,433 articles published between January 1981 and March 2022. Table ​ Table1 1 and Fig.  4 show the number of articles by 10-year period and a year. As the table and figure show, the number of articles has gradually increased over time, indicating the popularity of this field. In the 1980s, only 26 articles (1.1%) examined technology use in mathematics education. However, since 2009, more than 100 articles have been published every year. For example, in the 2010s, 1,408 articles were published (57.8%). These results were aligned with previous studies reporting that since the 1980s, educational technology has facilitated integration in mathematics education (Bray & Tangney, 2017 ; Roschelle et al., 2017 ).

The Number of Articles Over a 10-Year Period

The number of articles by a year

We also examined the most frequently used words in the collected data. Figure  5 depicts the words with more than 500 frequencies in abstracts. There were 53 words found, such as ‘‘student,’’ ‘‘teacher,’’ ‘‘learn,’’ ‘‘teach,’’ ‘‘school,’’ ‘‘develop,’’ ‘‘classroom,’’ ‘‘effect,’’ ‘‘design,’’ and ‘instruct.’’ Note that while ‘‘technology’’ and ‘‘mathematics’’ were not included in Fig.  5 , all articles included the two terms as we only selected articles that included them in abstracts. The combination of these words allowed us to build an idea of what research topics might have been studied. The words ‘‘student,’’ ‘‘classroom,’’ ‘‘effect,’’ and ‘‘learning’’ might represent a topic that examines the effect of technology use on student mathematics learning (e.g., Bicer & Capraro, 2016 ).

Determining research topics names

Tables ​ Tables2 2 and ​ and3 3 show the information on seven topics derived from the LDA algorithm. Table ​ Table2 2 presents topic names, top 15 words, and a sample representative article of each topic. Table ​ Table3 3 provides word clouds that visualized each topic with the top 50 frequently used words. Topic 1 (T1) was named “using technology to support mathematics learning.” The articles in T1 were concerned with using technology to foster student engagement, interaction, and investigations in mathematics learning (e.g., Cheng-Huan et al., 2017 ). Topic 2 (T2) was labeled “technology in K-12 curriculum.” The articles in T2 examined how technology resources in curriculum materials related to teacher instruction and student learning (e.g., Hu et al., 2020 ). Topic 3 (T3) was labeled as “computers and ICT (information and communication technology) use at school.” Articles in T3 examined mathematics students’ or teachers’ attitudes, perceptions, readiness of using computers and ICT, and factors affecting them (e.g., Birgin et al., 2020 ).

Topic Names, Characteristic Words, and a Sample Representative Article of Each Topic

Topic 4 (T4) was named “technology use at higher education.’’ The representative studies primarily concerned technology use in college and university environments, which utilized online mediation techniques or computer-assisted methods for teaching and learning mathematics (e.g., Radmehr & Goodchild, 2022 ). Topic 5 (T5) was labeled as “teacher instruction and TPACK.” Articles on this topic examined in-service and pre-service mathematics teachers’ instructional practices with technology and their TPACK (e.g., Akapame et al., 2019 ).

Topic 6 (T6) was named “using technology for conceptual understanding.” This topic discussed the use of technology for teaching and learning mathematical content and process, which improve students' conceptual understanding of solving mathematical tasks (e.g., Urban-Woldron, 2015 ). Topic 7 (T7) was labeled “examining the effect of technology on cognitive and affective development.” This topic mainly examined the effect of technology use on students' cognitive and affective development (e.g., Bicer & Capraro, 2016 ).

Research trend analysis

We analyzed the proportion of each topic by a 10-Year Period to understand the research trend (see Table ​ Table4 4 and Fig.  6 ). The greater topic proportion showed that the topic had received more attention from researchers in that period. According to the 2010s data, the difference between the highest (T5 and T6, 14.7%) and the lowest (T3, 13.7%) topic proportion was negligible (1%). However, different patterns were observed when we analyzed the topic proportion between January 1981 and March 2022. For example, the topic proportions of T5 have slightly decreased over time. In the 1980s, T5 took 16.5% of the total publication. However, in the 2010s and 2020–2022 March, T5 took 14.7% and 14.0%, respectively. Moreover, while the topic proportion of T6 has steadily increased over time (9.6% in the 1980s and 15.4% in 2020–2022 March), T2, T3, and T7 showed fluctuation patterns. For example, T7 took 13.3% in the 1980s, followed by 17.7% in the 1990s and 14.0% in the 2010s. The analysis of research trends of each topic by a year also revealed similar patterns (see Table ​ Table5). 5 ). Except for outliers, two topics (T1 and T4), showed a relatively stable change over time. However, other topics revealed decreasing (T5), increasing (T6), or fluctuating (T2, T3, and T7) patterns.

Topic Proportion by a 10-Year Period

Research trends of each topic by a 10-year period

Research Trends of Each Topic by a Year

To understand the research trends more closely, we calculated the Pearson correlation between the topics using the R package psych . Table ​ Table6 6 shows that T1 and T4 (0.36*, stable pattern) and T3 and T7 (0.39*, fluctuating pattern) had positive relationships, showing that they had similar research trends. However, T2 was negatively associated with T1 (-0.37*), T3 (-0.34*), T4 (-0.61***), and T7 (-0.38*), while T1 and T6 (-0.41**), and T5 and T7 (-0.51***) were negatively related, indicating opposite research interests over time.

The Correlation Between Research Topics

* p  < .05. ** p  < .01. *** p  < .001

Overall, the research trends analysis showed different emphases over time (see Fig.  6 ). In the 1980s, T2 and T5 were the most popular topics. However, during the 1990s and 2000s, T7 was the most popular topic while the trendline gradually decreased over time and interest diminished in the 2010s. In addition, T1 and T3 have received increasing attention in the 2000s. Since the 2010s, T2 and T6 have received increasing attention. In particular, the research interest on T6 has grown steadily from the 1980s until March 2022.

The study aimed to analyze research trends of technology use in mathematics education from 1981 to March 2022. The study has the following four research questions: (1) How did overall research trends of technology use in mathematics education evolve? (2) Which words were frequently used in previous studies? (3) What were the latent research topics? (4) What were the research trends for individual topics? To solve the research questions, we retrieved relevant articles from Web of Science, ERIC, and PsycInfo databases and selected 2,433 peer-review English-written articles published between January 1981 and March 2022. Then, we examined their abstracts using topic modeling (Blei, 2012 ).

The findings of the first research question revealed that research interest in technology use in mathematics education has steadily increased. During the 1980s, only 26 articles examined using technology in mathematics education, whereas more than 100 articles have been published yearly since 2007. These increasing research trends aligned with the arguments of NCTM ( 1980 , 2014 ) and the Programme for International Student Assessment (OECD, 2019 ) documents emphasizing the importance of technology use in mathematics education. This could be because researchers have found new opportunities and positive effects of technology use on teacher instruction (Hoyles, 2018 ; Hu et al., 2020 ) and student learning outcomes (Higgins et al., 2019 ). Consequently, other relevant studies, such as mathematics teachers’ perception of ICT (Birgin et al., 2020 ), professional development (Bicer & Capraro, 2016 ), TPACK (Akapame et al., 2019 ), and online teaching and learning (Radmehr & Goodchild, 2022 ), have been conducted.

To delve into the second research question, we identified 53 frequently used words with more than 500 frequencies. The words included ‘‘student,’’ ‘‘teacher,’’ ‘‘learn,’’ ‘‘teach,’’ ‘‘school,’’ ‘‘develop,’’ ‘‘classroom,’’ ‘‘effect,’’ ‘‘design,’’ and ‘‘instruct.’’ The combination of these words (e.g., the effects of teacher instruction with technology on student learning) can represent important research topics on technology use in mathematics education.

As for the third research question, we examined the major research topics and found seven topics: “Using technology to support mathematics learning” (T1), “technology in K-12 curriculum” (T2), “computers and ICT use in schools” (T3), “technology use in higher education” (T4), “teacher instruction and TPACK” (T5), “using technology for conceptual understanding” (T6), and “examining the effect of technology on cognitive and affective development” (T7). However, these topic classifications were not neatly aligned with the previous topic classification of mathematics education research (e.g., Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). Inglis and Foster ( 2018 ) classified research on mathematics education into the following four domains: mathematical content, mathematical process, teaching and learning environments, and hard cores and heuristics. However, our analysis did not show topics related to hard cores and heuristics examining research theories and methods. Moreover, some topics were linked to more than two domains. For example, T4 included calculus (mathematical content), discussion and communication (mathematical process), and course and online (teaching and learning environments) as top characteristic words (see Tables ​ Tables2 2 and ​ and3). 3 ). This result may stem from the difference in the scope of data used for the study. Our study includes articles examining technology use in mathematics education, while Inglis and Foster ( 2018 ) examined articles in two mathematics education journals only.

The seven topics found in this study were not aligned with previous literature reviews on educational technology (e.g., Chen et al., 2020 ; Ozyurt & Ayaz, 2022 ; Tatnall & Fluck, 2022 ). In a study examining research trends of BJET , Chen et al. ( 2020 ) identified 15 topics relating to a teacher (e.g., teacher education), learning strategies (e.g., problem-based learning, game-based learning, mobile-assisted language learning, socialized e-learning), learning environment (e.g., online social communities), evaluation (assessment and feedback), and other areas (e.g., early childhood education in the digital age and review studies). However, their analysis could not find topics related to conceptual understanding (T6) and K-12 curriculum (T2). Additionally, early childhood education, review studies, and learning strategies with emerging technologies were not identified in this study.

These differences are not unplausible because individual studies have analyzed different datasets according to different research purposes. However, these differences also indicate that research on technology use in mathematics education has distinctive research topics. While there are amalgams between mathematics education and educational technology, researchers have developed their distinctive research areas to enhance mathematics teaching and learning with technology use. Thus, researchers who are interested in technology use in mathematics education need to study mathematics education and educational technology and the integration of technology into mathematics education as a distinctive research area.

To delve into the fourth research question, we examined the number of publications on each topic over a year and a 10-year period. The findings revealed four different patterns, including stable (T1 and T4), decreasing (T5), increasing (T6), and fluctuating (T2, T3, and T7) patterns. The popular topics have changed from T2 and T5 (the 1980s) to T1, T3, and T7 (between the 1990s and the 2000s) to T2 and T6 (between the 2010s and March 2022). Interestingly, T6, the least studied topic in the 1980s, has received steadily increasing attention over four decades. Additionally, T2 has received the most research interest in the early (1980s) and later periods (since 2010).

These results are plausible. Since 1980, researchers have paid much more attention to enhancing student conceptual understanding by developing the reform-based curriculum and improving teacher instructional skills and knowledge (Bray & Tangney, 2017 ; Inglis & Foster, 2018 ). In this process, technological resources presented in mathematics curriculum (T2) and teachers’ technology use in mathematics classrooms and their TPACK (T5), which could facilitate or hinder the development of students’ conceptual understanding, were extensively analyzed. According to Remillard ( 2005 ), the curriculum included formal curriculum (e.g., printed documents) and teachers’ intended (e.g., teaching goals) and enacted curriculum (i.e., actually teaching in the classroom). Furthermore, mathematics teachers’ instruction and pedagogical content knowledge were related to teachers’ knowledge of curriculum (Ball et al., 2008 ). In sum, the similar research trends of T2 and T5 between the 1980s and 1990s were reasonable.

However, T2 and T5 have shown different research trends since the 2000s. T2 has revealed increasing research attention (13.3% in the 2000s, 14.3% 2010s, and 15.6% in 2020 – March 2022), whereas the research interest in T5 showed minimal change (14.6% in the 2000s and 14.7% 2010s) or slightly decreased (14.7% in 2010s and 14.0% in 2020–2022 March). Consequently, T2 and T5 showed a fluctuating and decreasing pattern. The revival of research attention on T2 might be affected by the publishment of curriculum documents. The curriculum documents emphasizing technology use in mathematics education have been steadily published. For example, NCTM published curriculum documents and standards emphasizing technology integration in mathematics education (AMTE, 2022 ; NCTM, 1980 , 2014 ). Similarly, Common Core State Standards for Mathematics highlighted technology's roles in mathematics education (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010 ). However, these documents were published by US mathematics educators. Therefore, further studies are needed to understand the research trends of T2 and T5.

The limited research attention on T6 before the 2000s implied that while researchers had focused on enhancing student conceptual understanding using technology, they were more concerned about examining technology integration into curriculum and teacher instruction than the direct relationship between technology use and students’ conceptual understanding. However, since the 2000s, researchers have paid more attention to the direct relationship between them, which indicated a steady increase in T6 over time (9.6% in the 1980s, 12.3% in the 2000s, and 15.4% in 2020–2022 March).

The popularity of T1, T3, and T7 between the 1990s and 2000s showed that researchers were interested in examining the effect of technology at school on student mathematics achievement, motivation, and overall learning experiences. These research trends were aligned with research trends in mathematics education and educational technology. In the early stage, mathematics researchers focused on examining student mathematics achievement using quasi-experimental methods (Bray & Tangney, 2017 ; Stinson & Bullock, 2012 ). They aimed to understand individual student learning processes and generalize teacher instructions (Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). Similarly, researchers examining educational technology have focused on evaluation and assessment at the early stage of research (Chen et al., 2020 ; Tatnall & Fluck, 2022 ).

However, there were some lags in research trends on the use of technology in mathematics education. Since 1990, as the sociocultural theory has grown in popularity, mathematics educators have placed more emphasis on student collaboration, teacher-student interactions, classroom environments, and student backgrounds than on evaluating student mathematics achievement (Inglis & Foster, 2018 ). As Table ​ Table4 4 shows, T7 was one of the most popular topics before the 2010s.

Since 2000, researchers studying educational technologies have become more concerned with new learning strategies with emerging technologies that could enhance student collaboration and autonomy, such as e-learning, mobile and blended learning, and social network-based learning (Ozyurt & Ayaz, 2022 ; Tatnall & Fluck, 2022 ). These topics, however, were not identified in our study. This implies that the research on technology use in mathematics education is relatively slow in adopting new theories and technologies than research on mathematics education and educational technology.

This study has four limitations. First, we retrieved the articles from three research databases ( Web of Science, ERIC, and PsycInfo ). Also, we included English-written articles published in peer-reviewed journals and excluded dissertations, theses, and non-English written articles. If we had included the excluded articles, our findings might be different. Second, we searched articles containing “mathematics or math” and “technology or technologies” in the abstract. Thus, articles that did not contain those words in abstracts were excluded from this study. For example, a study examining the calculator use for algebra learning might not be included in our data due to our search criteria. Readers should be cautious when interpreting our findings. Third, we only examined the articles’ abstracts. While examining abstracts to understand research trends is a common method (e.g., Chen et al., 2020 ), other important information presented in the different sections, such as findings and conclusions, was excluded during the data analysis process.

Fourth, labeling the topic names was a relatively subjective process. The LDA method is an entirely automatic, unsupervised algorithm (Blei, 2012 ). However, the topic names should be determined by researchers based on the information of the data, such as the most frequently occurring words and the articles with a high proportion on the topic. While this information enabled us to validate the topic names, other researchers might use different names even when analyzing the same data. Given the limitations of the present study, future studies may employ other research databases, including dissertations, theses, and non-English papers, and examine full texts of articles to verify the findings of this study.

Implications and conclusion

The development of technology has changed mathematics teaching and learning environments. Considering the expansion of technology use in mathematics education, this study synthesized previous studies published between January 1981 and March 2022 and examined research trends in the field using topic modeling.

We proposed three implications based on the research findings. First, it would be valuable to examine teaching and learning strategies with emerging technology in mathematics education. This study did not identify topics pertaining to utilizing new technology (e.g., AR, VR, and mobile, game-based, blended, and flipped learning). However, several researchers have emphasized the importance of using new technology in education (Kimmons, 2020 ; Tatnall & Fluck, 2022 ), where teachers serve as facilitators and students take the lead in their mathematical learning as investigators. Therefore, further studies on mathematics teachers' and students' use of emerging technology are needed. We can, for instance, examine mathematics teachers’ instructional strategies in the virtual environment (e.g., Hu et al., 2020 ) and AI-based mathematics learning systems (Hwang & Tu, 2021 ).

Second, it is suggested that researchers consider examining further studies based on sociocultural theory. This study identified topics focusing on individual student mathematics learning, such as examining cognitive and affective development (T7) and conceptual understanding (T6). While these topics are critical issues, it would be productive to examine how technology use affects social interaction in actual and virtual mathematics classrooms (e.g., student collaboration, classroom discourse and norms, and teacher-student interactions). Moreover, it would be innovative to analyze the effect of technology use on the construction of student mathematical identity. Researchers (Hand & Gresalfi, 2015 ; Yackel & Cobb, 1996 ) have documented that classroom activities, resources, and culture affect both student cognitive and affective development and their mathematical identity (i.e., how a student acts, engage, position, and interact in mathematics learning). Given that student mathematical identity affects their educational aspirations and future careers (Black et al., 2010 ), it is valuable to analyze how technology use in mathematics classrooms affects student mathematical identity. Therefore, further studies may examine such issues.

Third, it is important to investigate the relationship between technology use and equity and access in mathematics education. The United Nations (United Nations General Assembly, 2015 ) suggested quality education as one of the agendas for sustainable development of our society and emphasized the importance of accessing quality education, regardless of student background (e.g., race, gender, and socioeconomic status). Technology can help achieve these goals because all students could be provided opportunities to investigate mathematics problems, present ideas, learn needed instructions, and communicate with peers in technological learning environments (AMTE, 2022 ; Clements et al., 2013 ; Higgins et al., 2019 ; NCTM, 2014 ). For example, Crawford ( 2013 ) validated that a supplementary online mathematics curriculum improved the mathematics achievement of English language learners considerably. Crawford ( 2013 ) explained that because students could learn mathematics at their own pace with a web-based curriculum, they could accurately understand mathematical concepts and practice mathematical skills, which enhanced access and equity in mathematics education. Even though this study did not find equity-related topics, the relationship between access, equity, and technology use in mathematics education should be more thoroughly studied to achieve sustainable development.

This study has theoretical and practical significance. Theoretically, this study made a scientific contribution in two ways. First, it provided researchers with overall research trends of technology use in mathematics education. Second, it identified topics that did not precisely align with those identified in previous studies on mathematics education or educational technology (e.g., Chen et al., 2020 ; Inglis & Foster, 2018 ). Practically, the study findings have guided further studies and practices to increase the effects of technology use in mathematics teaching and learning.

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Ji-Eun Lee, Email: ude.dnalkao@5432eel .

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• Back Issues
• Letters Policy

Projects selected for dB-SERC Course Transformation Awards

The Discipline-Based Science Education Research Center (dB-SERC) has awarded 12 Course Transformation Awards to faculty in natural sciences.

Since 2014, dB-SERC has supported natural sciences faculty members in developing projects to transform the way classes are taught by adopting evidence-based teaching practice to improve student learning outcomes.

Award recipients receive funds for equipment, student support or summer salary for faculty. Two mentor-mentee awards also were given out to support classroom innovation projects conducted by students and faculty working together.

Course Transformation Awards

Young Ahn, Department of Biological Sciences: Designing a high-structure course combining frequent low-stakes assessments with inclusive teaching for a large-enrollment introductory biology class

This proposal aims to test the “heads and hearts” hypothesis which suggests that both students’ cognitive (heads) and affective (hearts) learning experiences must be purposefully constructed in classroom environments. This project will investigate whether a course structure that combines frequent low-stakes assessments (heads) and inclusive teaching (hearts) can improve student performance and reduce achievement gaps in a large-enrollment introductory biology course thereby promoting retention in STEM.

Anusha Balangoda, Department of Geology and Environmental Science : Use of a Collaborative Online Reading Platform for Pre-class Reading Assignments in a Large Enrollment First-Year Undergraduate Class

The proposed work seeks funding to implement pre-class reading assignments through a social annotation platform allowing active reading on assigned course materials outside the class. A free social platform, Perusall, provides an interactive experience for students to engage with peers asynchronously and facilitates a space to teach and learn from peers. This collaborative social platform allows students to work on assignments outside the classroom to promote productive discussions and produce high-quality peer interactions.

Seth Childers, Department of Chemistry: Development of Interdisciplinary Courses for a New Chemical Biology Major

In the Department of Chemistry, the PI is proposing a chemical biology major, including two new lecture courses and one laboratory course, proposed to launch in Fall 2025 or 2026. This timeline allows them to craft a curriculum while deploying evidence-based learning practices to enhance job readiness. Based on student surveys, the program aims to accommodate approximately 48 majors annually and engage non-majors as a desirable scientific elective campus wide.

Russell Clark and Aidan Payton, Department of Physics & Astronomy: Gender Equity in Introductory Physics Lab Group Roles

This is a continuation of a dB-SERC award from 2020 (Development of Teacher Guides and Rubrics for Introductory Physics Labs). The original plan for that award was to develop better rubrics and other materials to help the TA graders provide more valuable feedback to the students. However, the University was forced into quarantine midway through the first semester of the project, and so the character of it changed.  They know from a previous study that student groups tend to have gender bias in which men tend to work with the experimental apparatus and women are relegated to secretarial roles (recording data, writing the report, etc.). They attempted to mitigate this by asking the students to cycle through the roles week to week so that each student would get to participate in each role multiple times.

Erika Fanselow, Department of Neuroscience: Incorporating digital and physical 3D brain models into interactive online and in-class activities to enhance student engagement and mastery in neuroanatomy courses

The goal of this course transformation is to develop interactive, online and in-class exercises that incorporate digital and printed 3D models of nervous system structures. These 3D model-based exercises and in-class activities are intended to enhance students’ visualization and conceptualization of neuroanatomical structures. The rationale for this course transformation proposal is based on the fact that neuroanatomy students are commonly overwhelmed by the complexity of the nervous system, resulting in a condition Jozefowicz (1994) referred to as “neurophobia,” which he concluded actually keeps students from choosing fields such as neurology.

Sean Garrett-Roe, Department of Chemistry: Activity redesign and mindset intervention based on growth-oriented testing in Chem-0110 General Chemistry I

“Grading for Growth” is a movement to encourage students to embrace deeper intellectual engagement with their studies by revolutionizing the way that their learning is assessed. Student-focused active learning pedagogies, such as Process Oriented Guided Inquiry Learning (POGIL), are well-established; student-focused assessments, on the other hand, are a new frontier. The PIs have formulated, implemented and assessed a student-focused assessment system that they call “Growth-Oriented Testing.” As successful as the system has been, the assessment results have illuminated ways in which their in-class materials have not optimally supported students, and the student opinion surveys suggest ways in which they have not optimally framed the learning process. As a result, students may not get the full benefits of the learning environment. A long-range goal of their teaching is to help students embrace a life of growth and learning; they want the students to learn both Chemistry and the metacognitive and metaemotional skills they need to succeed beyond the Chemistry classroom.

Sean Gess, Department of Biological Sciences: Supporting richer class-wide discussion and promoting the use of scientific argumentation in Foundations of Biology laboratory courses

This project focuses on class-wide discussion in a guided, authentic research lab. In this course students engage in science education by performing authentic research science to address active research questions being investigated within the department. The course is designed to mimic the research process, including discussions of data to try and understand it better. These discussion-based activities often struggle to support the learning objectives due to low participation from students or students not really listening and engaging with others during the discussions. To improve these discussions, they have previously introduced an explicit framing to attempt to help students understand the norms around this activity, normalize it as a professional practice, and encourage engagement and participation. This approach to science learning has shown gains in critical thinking skills and supports epistemic learning of STEM content.

Burhan Gharaibeh, Natasha Baker and Bridget Deasy, Department of Biological Sciences: Enhancing student engagement in anatomy and physiology courses through regenerative medicine primary science literature

Students of anatomy and physiology in different majors often report difficulty in these courses due to the need for memorizing lists of structures and comprehending complex physiological processes. They have preliminary data demonstrating that adding discussions of current, clinically relevant therapies and biotechnology articles related to regenerative medicine studies were effective in enhancing the biology student’s engagement during anatomy lectures. More importantly, the addition of these discussions to the curriculum appeared to improve exam grades.

Melanie Good and Eric Swanson, Department of Physics & Astronomy: The Use of Comprehensive PACE (Pseudoscience and Conspiracy-theory Education) in Physics and Society

Phys0087: Physics and Society was a course developed by Eric Swanson to help students examine the conceptual foundations of modern science with the goal of understanding how science affects our daily lives and our impact on the environment. At the intersection of science and society lies the issue of popular belief in the claims of pseudoscience and conspiracy theories. These beliefs are fairly common and often can be difficult to dislodge with education in science alone. However, past work has shown that explicit instruction on topics related to pseudoscience and conspiracy theory beliefs may be effective in reducing endorsement of these beliefs. The PIs have seen this among their own students, based on pilot data and data from a previous dB-SERC Course Transformation Award. The success of their earlier work has captured the attention not only of our university media, but also the Lilienfeld Alliance, a group of higher education professionals across the nation that is committed to promoting critical thinking skills in the face of the claims of pseudoscience, who invited them to join their cause. With the momentum they have built, they are inspired to more comprehensively overhaul Phys0087: Physics and Society to expand upon their original transformation. Their new proposed course transformation would extend the pseudoscience module into a comprehensive PACE (Pseudoscience and Conspiracy-theory Education) curriculum in Phys0087–Physics and Society during the 2024-2025 school year.

Edison Hauptman and Jeffrey Wheeler, Department of Mathematics: Contract Grading in Calculus 2

In summer 2024, Edison Hauptman’s section of Analytic Geometry & Calculus 2 (Math 0230) was taught with a different set of assignments and grading structure. The grading structure for the class resembled a contract between the instructor and their students: the instructor provided many different assignments, and for a student to earn a desired grade, they had to score enough points on various assignments of their choice to reach that grade’s point threshold. This course structure can have many variations and is called a “grading contract.” Compared to the current (default) course structure for Calculus courses at the University of Pittsburgh, a grading contract is a more equitable way to evaluate a diverse set of students, allows the instructor to be more accommodating to students without sacrificing the course’s rigor, and encourages more student buy-in. This project develops and evaluates a set of assignments offered to students in  Hauptman’s Summer 2024 12-week section of Math 0230 and focuses on mathematical skills emphasized in each assignment.

Zuzana Swigonova, Department of Biological Sciences: Combining computer visualizations with 3D printed models to engage students in active study of molecular structure and function

All biological processes in a living system depend on proper functioning of molecules. Understanding the principles of molecular structure, the three-dimensional spatial arrangements of atoms and functional groups that allow for intra- and intermolecular interactions, is crucial for grasping the fundamentals of structure-function relationships. Despite the many benefits of physical 3D models, printing intricate biological molecules has several limitations, such as low level of atomic detail in complex structures, depiction of a single static molecular representation, and labor-intensive post-printing processing. Computer visualization allows for the development of abundant resources that complement physical models with no added material cost. They propose to develop teaching resources using computer visualization to supplement the physical 3D models.

Margaret Vines, Department of Chemistry: Learning to learn chemistry

The purpose of this project is to help students learn. Most students come to college with the desire to learn. They want to be successful and learn the material presented to them in their classes. Unfortunately, many of them engage in activities that do not help with their learning. The PI’s goal is to help students begin to learn how to learn. They will do this as part of their regular lecture and recitation in general Chemistry. They will educate them about learning techniques and explain why they will aid in their learning. They will then demonstrate these techniques in class, and the students will be given opportunities to use these techniques inside and outside the lecture and recitation. Finally, they will encourage their students to develop those techniques for use in their other classes.

Mentor/Mentee Award

Mentor: Anusha Balangoda / Mentee: Beth Ann Eberle. Department of Geology and Environmental Science: Use of Cooperative Learning Approach in Recitations to Untangle Pressing Environmental Issues in Introductory Environmental Science Class

Cooperative learning is a student-centered active learning strategy in which a small group of students is responsible for their own success and that of their team by holding themselves accountable for the process and outcomes of the activities. In this project, they propose to use a cooperative learning strategy in the GEOL 0840 Introductory Environmental Science course, which is a large enrollment three-credit class, and both lectures and recitations are required.

Mentor: Ben Rottman / Mentee: Rebecca McGregor. Department of Psychology; Learning Research and Development Center: Using a Consulting Model and Project-Based Learning to Teach Psychology Research Methods

In the field of psychology, research methods form the foundation of students’ knowledge during the remainder of their undergraduate degree and beyond. Students in PSY 0036: Research Methods Lecture at the University of Pittsburgh have three course objectives: learn how to read, interpret and discuss research design and conclusions, learn how to critique research, and learn how to design valid research. There are currently few opportunities for students to apply this knowledge to real-world experiences, as this is an introductory course in which students have not yet developed the skills to analyze and interpret their own data. Thus, this course design through the dB-SERC would provide a semester-long collaborative assignment in which students would develop a project proposal to investigate a real-world research problem for a fictional client.

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The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things

• Published: 27 April 2021
• Volume 108 , pages 385–400, ( 2021 )

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• Marcelo C. Borba 1  

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The COVID-19 pandemic has changed the agenda of mathematics education. This change will be analyzed by looking at three trends in mathematics education: the use of digital technology, philosophy of mathematics education, and critical mathematics education. Digital technology became a trend in mathematics education in response to the arrival of a different kind of artifact to the mathematics classroom. It was thrust into the spotlight as the pandemic suddenly moved classrooms online around the world. Challenges specific to mathematics education in this context must be addressed. The link between the COVID-19 pandemic and digital technology in education also raises epistemological issues highlighted by philosophy of mathematics education and critical mathematics education. Using the notion that the basic unit of knowledge production throughout history is humans-with-media, I discuss how humans are connected to the virus, how it has laid bare social inequality, and how it will change the agendas of these three trends in mathematics education. I highlight the urgent need to study how mathematics education happens online for children when the home environment and inequalities in access to digital technologies assume such significant roles as classes move on-line. We need to understand the political role of agency of artifacts such as home in collectives of humans-with-media-things, and finally we need to learn how to implement curricula that address social inequalities. This discussion is intertwined with examples.

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1 Introduction

It is not possible to predict the state of the COVID-19 crisis at the time this article reaches the reader. The effects of the pandemic, and the response to it, have been shocking—with lockdowns, masks, and respirators, etc.—and have left most people at a loss. Some “world leaders” say that the virus is “just a cold,” while others say we may take months or years to have things “back to normal.” There are even those who say that COVID-19 is just a test for a much more serious health crisis that may be still to come. What is certain is that throughout the world, things have changed dramatically and suddenly. The virus has hit all classes of society, though of course it has hit the poor harder. But what are the effects of the pandemic in mathematics education? One effect that was almost universal was a tendency to “go online”: shop online, meet friends online, and learn online.

We have moved online because COVID-19 is caused by an invisible virus; it has no cure; and, without a clear pattern, it can cause the death of one person in a few days and cause almost no symptoms in another. Moreover, one may be infected and transmitting but asymptomatic for several days and then become very ill all of a sudden. Though not all “leaders” have taken their advice, most experts and the World Health Organization (WHO) recommend social isolation as the main tool to control, slow down, and hopefully stop the pandemic. All of a sudden, teachers, professors, and educational managers at all levels were put under pressure to develop (mathematics) education online, as the virus can be transmitted through physical contact—both between humans and between humans and non-living things.

Since the beginning of the official history of the International Commission on Mathematical Instruction (ICMI) in 1908, only war has interrupted the International Meetings of Mathematics Education (ICME), according to Menghini et al. ( 2008 ). This year, the ICMI decided to suspend ICME-14 Footnote 1 for a different reason: due to the risk of spreading the coronavirus, traveling and gathering in groups would be unsafe. Some would say that ICME-14 was suspended due to a different kind of war: instead of generals in the background, and soldiers in the field, ready to kill or die, we have the whole of humanity trying to fight this non-living being, a virus. It is debatable whether the war metaphor is appropriate or not for this health crisis, but terminology aside, the crisis can lead us to some reflection on mathematics education. This essay will raise some questions to the mathematics education community that were caused by this non-living-thing: the virus SARS-CoV-2, which causes COVID-19.

Engelbrecht et al. ( 2020 ) reported that they had to change the conclusion of their survey paper on digital technology in March to April of this year, as it occurred to the authors that the paper could become dated even sooner than other digital technology survey papers. In normal times, such papers become old because digital technology changes so fast, and we rarely even have the time to implement a given technology in the classroom before a new one comes up. However, at this point, everything may become outdated, because we cannot predict the evolution of the COVID-19 crisis, nor whether a new crisis will follow it. The authors decided to include discussion about COVID-19 in the introduction and conclusion of the paper. At the end of the paper, they write:

The question is, what has this [COVID-19] to do with mathematics education and digital technology? Besides the impact on conferences and on the transforming mathematics classroom we may have to ask broader questions: Digital technology intensified traveling and our way of living, so it is also partly responsible for the present crisis. Is it possible that the use of digital technology can generate a similar crisis in mathematics education? Conversely, if the crisis lasts for a long period, would digital technologies be able to provide alternative ways to implement mathematics education? There is not much research on online mathematics education for young children, but if the crisis lasts for a long time, are we going to implement it without sufficient research? If the current crisis is over soon, are we going to develop research on mathematics education for a possible “COVID-2X” crisis? In this paper, among others, we have anthropomorphized media, talking about agency. The notion of humans-with-media as the collective that produces knowledge, may synthesize it, as we discussed in this paper. The COVID-19 virus (SARS-CoV-2) is a non-living being: can we talk about the impact (agency) of COVID-19 on mathematics education and on the world? Engelbrecht et al. ( 2020 , p.838)

This paper will deal with the questions from this excerpt in the following sense: I will discuss how new trends of mathematics education may arise or change with the ongoing crisis, and I will draft responses to some of these questions. Trends in mathematics education can be understood as a response, an answer, to some problem, as suggested by D'Ambrosio and Borba ( 2010 ). A working group, or a conference on a given trend within mathematics education, emerges as a response to new demands. I will use the theoretical construct of humans-with-media to connect the COVID-19 crisis to three different trends: the use of digital technology, philosophy of mathematics education, and critical mathematics education. In the context of the trend of digital technology, I will discuss the possibilities and drawbacks of having more and more online education, as well as the new demand for this trend. In doing so, I will revisit the notion of humans-with-media and its perspective of collective knowledge production involving humans and non-human actors such as computers and SARS-CoV-2. This will put new issues on the agenda for philosophy of mathematics education, focusing on the agency of “things” and humans’ relation to this virus thing. Finally, I will give a brief history of the trend of critical mathematics education, and I will raise an agenda provoked by COVID-19 for these three trends in mathematics education. I believe that these discussions may be important for us to understand the moment we are living in, beyond mathematics education itself. They can also help to set an agenda of research and action in the classroom for those interested in these trends and their connection to the pandemic.

2 Digital technology and mathematics education

Taking into consideration the notion of trends, presented above, the trend that studies the link of mathematics education and “new technologies”—informatics, communication and information digital technology, and alike—has been present in conferences for more than 30 years. At ERME Footnote 2 and SBEM Footnote 3 (Borba, 2018 ), at ICMEs (Menghini et al., 2008 ), and at PME Footnote 4 , there are always working groups, discussion groups, and panels on the subject, because, as authors such as Jim Kaput ( 1991 ,  1992 ,  1998 ) have pointed out, we need to understand how to use computers in mathematics education. Borba et al. ( 2016 ) prepared a survey that was presented at ICME-13 and put forward four phases for the use of digital technology in mathematics education. The four phases themselves show the strength and the length of this movement, which has involved many researchers, teachers, and students.

The first two phases, symbolized, respectively, by Logo and by curriculum-topic software (e.g., Cabri-Géomèetre), are not so important for the discussion in this paper, as the Internet became the big star during the pandemic. The third phase of the use of digital technology was characterized by the emergence of the Internet and online courses. This phenomenon became important around the turn of the century, depending on the country. Some so-called developed countries saw the Internet become popular in the mid-1990s and in some other countries, like Brazil, very early this century. Brazil was one of the first countries to start online courses at the graduate level, at a time when other countries were very protective of their face-to-face education.

The current fourth phase is characterized by the arrival of fast Internet, which reshaped the possibilities of online education. As this phase has developed, Engelbrecht et al. ( 2020 ) have pointed out that different forms of blended learning are important, in particular for teacher education. The term “hybrid” has become more important to express the combination of face-to-face mathematics education and online education:

A wide array of media and technology is available to create new hybrid forms of teaching. The integration of technology enables educators to create learning experiences that actively and meaningfully pull students into course content. “This technology may form thinking collectives (Lévy, 1993 ) with teachers that can break the walls of the regular “cubic” classroom that is associated with lecturing.” (Engelbrecht et al., 2020 , p.838)

If we consider a trend as an effort to find answers to a given issue, COVID-19 has pushed forward the agenda of the digital technology trend in mathematics education. With the need for social isolation, it became necessary to offer education to children and undergraduates at home. In most of the world, the first semester of education in 2020 was suspended or went online. Many are now discussing different kinds of hybrid education as health conditions allow students and teachers to go back to school and universities. But although we have plenty of research on implementing education online on undergraduate education (Engelbrecht & Harding, 2002 , 2004 , 2005 ), this is not the case for education for children. In the survey articles mentioned above, and in conference working groups, hardly any research has been presented on online education for children. As this theme develops, (mathematics) education will have to deal with structural issues, such as the participation of parents or responsible others in education.

In Brazil, newspapers say that teachers are “going crazy” with demands from students coming from WhatsApp and other social networks, as students and parents in their home cannot deal with school tasks. Grading is another problem: can we grade students so young online? Is help from parents allowed? This type of question has not yet been researched. In Brazil, some research groups such as GPIMEM Footnote 5 are trying to document what is happening in some state systems as a first step for research and understanding of online education for children. In the state of São Paulo, a new app, CMSP Footnote 6 , was created in less than 30 days for 200 thousand teachers and 3.5 million students to somehow have access to education. The app operates in conjunction with two preexisting TV channels, one operated by the state and another by a consortium of universities (Paz, 2020 ).

Teachers and administrators were able to supervise students through the app to some degree, and students were having three classes a day instead of five, as the state is trying to implement education through other platforms as well (Secretaria de Educação do Estado de São Paulo (São Paulo State Department of Education)—SEED, 2020 ). But this was a very complex moment: teachers had to go online without enough time to be prepared, and at the same time, they had to deal with their regular problems: São Paulo is the richest state in Brazil but pays its teachers a terribly low salary compared to other professionals, as pointed out to me in an online interview with a teacher who preferred to stay anonymous. Underpaid teachers now have to deal with students 24 h a day, 7 days a week, which includes dealing with students’ “personal” problems—including problems associated with the chronic social inequality in Brazil. Teachers with low salaries are not likely to have the best mobile phones, laptops, or Internet plans. Teachers who may teach fifty 50-min classes a week may deal with hundreds of students. It is likely that such problems are occurring in other countries as well, as differences between the “haves” and “have-nots” exist throughout the world, and are amplified by COVID-19, as described by the historian Walter Scheidel (Canzian, 2020 ).

Crisis is also a chance for change: teachers who teach 50 classes per week will not have time to learn to use digital technology for teaching. With many states and city educational systems forced to go online because of the pandemic crisis, the argument to use technology is very strong. It is likely that we will have a lot of research associated with this new reality. For the purposes of this article, I was not able to collect data systematically, but informal reports from teachers suggest that the reality of teaching young teenagers and children online will have to be investigated. As mentioned before, there is hardly any research on online education associated with levels below high school, which can be verified in many survey papers related to the theme (Engelbrecht et al., 2020 ). But the focus cannot only be on teachers. How do children experience this version of home schooling? There are also many jokes on social networks about parents losing control as they become home-teachers at the same time as they had to implement the home-office, so the role of parents in online mathematics education may be another area for research. Involvement of parents in mathematics education has been a theme of some research, including involvement associated with the use of digital technology (Ford, 2015 ; Wilson, 2013 ). However, this was in informal or blended settings, such as festivals (Domingues, 2020 ). Now we have new challenges, including to report and discuss how online assessment was developed (or not developed). Inviting students to produce mathematical videos was a research project developed before the pandemic. Having students expressing mathematical knowledge with videos, or doing research with videos, was not a solid trend in the literature. However, video production may be an alternative for education during and after the pandemic. Instead of focusing on test results, we can have students producing videos online to express what they have learned in conditions such as the pandemic. Videos can be produced collectively, with help of parents, friends, and different media. Differences in resources, including degree of parental aid received, can be considered by teachers and school systems in a “non-ranking” type of assessment.

Production of digital mathematical videos by students and teachers is growing in Brazil (see Fig. 1 for an example), and with the onset of the pandemic, an online “library” with more than 600 videos ( https://www.festivalvideomat.com/ ) has been used as a resource for teachers and students in their classes and as inspiration for the kind of task students and teacher may produce. Moreover, issues that have been the subject of previous research may gain new life: in a recent review paper (Engelbrecht et al., 2020 ), it became clear that different technologies used in a class, from the blackboard to the most modern mobile phone, are not necessarily only mediators but also actors. This is an epistemological issue, and it is part of a trend that has been discussed within the psychology of mathematics education and the philosophy of mathematics education.

Mud Sea: Modelling and Mathematics Education. Source: https://www.youtube.com/watch?v=YpCteGqjxd0&list=PLiBUAR5Cdi63gZoTSrJ9qXeiZQEH2wFBL

3 Philosophy of mathematics education and agency in the notion of humans-with-media

“Why do we have education? What are the relations between education and society? How do we know?” These are the basic questions of philosophy of education. For more than 20 years, there have been working groups on the philosophy of mathematics education (Bicudo & Garnica, 2001 ). “How do we learn?” is connected to “How do we know?,” and thus questions regarding epistemology, the theory of knowing, have also been debated by psychology of mathematics education discussion groups. Both domains of research may be seen as trends, as they seek foundations for mathematics education, and they discuss how mathematics education is articulated in the classroom, the research that is developed about it, and its “return” to practical settings: settings, like the classroom, which for many months have been on hold by the coronavirus pandemic. Several authors have discussed classrooms and schools and the artifacts produced there. For example, Villarreal and Borba ( 2010 ) have shown how mathematics is produced by collectives of humans-with-artifacts throughout the history of mathematics.

D'Ambrosio and Borba ( 2010 ), besides conceptualizing a “trend” as a response to a given problem, have argued that trends are intertwined, using the metaphor of a tapestry. It is unsurprising, then, that the discussion about who is the agent of knowledge is discussed in more than one trend: in digital technology working groups and in philosophy of mathematics education and psychology of mathematics education discussion groups or conferences. Different mathematics education authors (e.g., Faggiano et al., 2017 ) have claimed that computers, for instance, have agency. Inspired by the work of Lévy ( 1993 ) and on the phenomenological approach that humans are “being-with-others,” the notion of humans-with-media has been developed over the course of many years. The notion of reciprocal modeling was the first step (Borba, 1993 ). My early work on this showed not only that different media shape humans (an idea shared with many) but also gave some empirical evidence of how humans shape technology, specifically a piece of software about functions. Being part of the design software team and a mathematics educator developing research, I could see this “collaboration” between, on the one hand, a piece of software—full of the ideas of a multidisciplinary team, presented at meetings of developers, mathematics educators, teachers, and so on—and, on the other hand, how high school students would interact with the software (and with me, a teacher-researcher). A high school student, for instance, was influenced by what I said and by the design of the piece of software Function Probe (Confrey, 1991 ), and he also shaped the piece of software in ways that were not predicted by the multidisciplinary team that had developed the software. This student did not use the commands the design team had created but used the size of the computer screen and other measuring artifacts to coordinate algebra and graphs. Borba and Villarreal ( 2005 ) synthesized how the notion of humans-with-media could be understood based on the work of Lévy ( 1993 ), Lave ( 1988 ), and Tikhomirov ( 1981 ). This led to the notion that knowing was not social solely in the sense that it involves more than one person, but that it also involves things.

The notion of humans-with-media was proposed to emphasize that production of knowledge is a result of a collective of humans and things. From Tikhomirov and Lave came the idea that knowing was goal oriented and that values were involved. Later, in Borba ( 2012 ), discussions about the values, emotions, and media involved in knowing mathematics with GeoGebra (or whatever software was available) were extended to the idea that media and technology themselves change notions of what humans are. Media are therefore constitutive not only of what we know but also of what we are. Kaptelinin and Nardi ( 2006 ) also analyzed the idea of extending agency to non-humans. These authors compared the capacities to produce effects, act, and fulfill intentions of different agents: things (natural), things (cultural), non-human living beings (natural), non-human living beings (cultural), and human beings as social entities.

Agency, therefore, should not be seen as binary, as either present or absent, but having different levels. I see this notion of agency as a “fuzzy” one, as in fuzzy mathematics, in which we may have degrees of agency. In such a mathematics, for instance, my jeans are not just blue or not (zero or one), but they are, for instance, 0.6 blue. Kaptelinin and Nardi ( 2006 ) suggest three dimensions of agency: based on necessity (action is taken based on biological and cultural reasons), delegated (things or living beings act as the perceived intentions that are delegated by other humans and things), and conditional (actions of things or people which result in unintended effects).

The notion of humans-with-media, which is consistent with a more complex view of agency, has been challenged, in many instances, by arguments that want to preserve the power of a human as the center of any action. In these views, intentionality and action come from somewhere that is not social. Much of mathematics education, cognitivist or not, is based on such a “one-knower” view. From such a perspective, the agent of knowing is a single person, or collective of humans, even though most researchers would recognize the influence of artifacts, environment, and social cultural factors.

The notion that both humans and non-humans have agency is part of an effort to model artifacts—in particular, pieces of software, hardware, and the Internet of Things (i.e., things that are connected to the Internet)—as the historical, social, and cultural factors in the collective that produces knowledge. It stresses a view that knowledge is produced (both from a philosophical and a psychological perspective) by humans-with-artifacts. With a perspective in which things have agency, artifacts are labeled media as they are thought to communicate. This argument was more easily applied for technologies of intelligence (Lévy, 1993 ): humans-with-graphing-calculators were easier to accept as having agency than humans-with-libraries or humans-with-classrooms.

Regardless of whether readers value online mathematics education or not, they may at some point use their memory of a regular classroom to claim that face-to-face interaction is fundamental to any learning that occurs in mathematics education. Alternatively, one may use the notion of a “distributed classroom”: an office for one student, the bedroom for another, and some kind of computer center for others. But everyone would recognize that classrooms are changing. We have described this as a classroom in movement (Borba et al., 2014 ).

What constitutes the unit of knowing is an endless, philosophical discussion: is it a single person? Is it social because it involves more than one person? Is it social because it has a goal and it involves humans and non-human actors? It is an endless discussion, like most philosophical discussions. However, it seems that the emergence of SARS-CoV-2 gives strength to one perspective on knowing because, according to authors such as Racaniello ( 2004 , p.1), “Viruses are not living things. Viruses are complicated assemblies of molecules, including proteins, nucleic acids, lipids, and carbohydrates, but on their own they can do nothing until they enter a living cell. Without cells, viruses would not be able to multiply. Therefore, viruses are not living things.” Yet despite being non-living, the virus has dramatically changed the way humans live. Viruses are closely connected to us: they cannot exist for long apart from living things, like humans, who have cells; the symptoms of COVID-19 arise under certain conditions when the virus is inside human cells. We can say that the virus has agency in the sense that it has changed the way we have to do things. This analogy helps us to understand how certain things are much more likely to happen if certain actors are present. To use the metaphor of the virus, software also needs humans to “survive.” Software, and later on the Internet, has changed the environment of educational settings, in a similar way to how SARS-CoV-2 has suddenly turned children’s bedrooms into classrooms.

Latour ( 2020a , b ), another inspiration for the notion of humans-with-media, presents his concern with the virus crisis in a way that relates to the discussion in this paper:

But there is another reason why the figure of the “war against the virus” is so unjustified: in the health crisis, it may be true that humans as a whole are “fighting” against viruses — even if they have no interest in us and go their way from throat to throat killing us without meaning to. The situation is tragically reversed in ecological change: this time, the pathogen whose terrible virulence has changed the living conditions of all the inhabitants of the planet is not the virus at all, it is humanity! But this does not apply to all humans, just those who make war on us without declaring war on us. For this war, the national state is as ill-prepared, as badly calibrated, as badly designed as possible because the battle fronts are multiple and cross each one of us. It is in this sense that the “general mobilization” against the virus does not prove in any way that we will be ready for the next one. It is not only the military that is always one war behind. (Latour, 2020a , b , para.8)

Latour, without saying so explicitly, foregrounds the agency of this virus: SARS-CoV-2 spreads through humans to survive and reproduce, and this action provokes reaction—agency—from humans. Of course, every comparison or metaphor has its limits. But the coronavirus has transformed our lives—we still do not know for how long—in a dramatic way. Computers—now represented by mobile phones, which are much more potent computers than the ones used at the end of the last century by the minority of students who had access to them—have changed the way we can experience mathematics, in particular the way we can “experiment” with mathematics. The Internet has become a community, an agent, and an artifact. Videos that are produced and shared by students with digital technology soon themselves become a part of new collectives of humans and media that are involved in producing knowledge. Souto and Borba (Souto & Borba, 2016 , 2018 ) have discussed how the notion of humans-with-media, which had its origins in activity theory (Tikhomirov, 1981 ), is now about to change the third generation of activity theory, breaking the rigidity of the triangles espoused by Engeström ( 2002 ) and Sannino and Engeström ( 2018 ) (Fig. 2 ).

This version of the humans-with-media construction has been called system-of-humans-with-media (Souto & Borba, 2018 ) to emphasize even more the notion that the collective of humans and non-humans is goal oriented and embedded in a community that has rules (Fig. 2 ). Considering media as agent has made it possible to think of the rigid triangles of the third generation of activity theory as dancing triangles, or as a GIF, in which the Internet, for instance, could be jumping from the instrument corner to the subject corner and/or to the community corner. Such an animation can be found on the GPIMEM website, in order to overcome the limits of the printed text ( https://igce.rc.unesp.br/#!/pesquisa/gpimem---pesq-em-informatica-outras-midias-e-educacao-matematica/animacoes/triangulo-sannino--engestrom/ ).

The structure of an activity system. Source: Sannino & Engeström, 2018

It is hard to know, as mentioned before, where the developments of the current health crisis will take us, but it seems that thinking about agency of non-living things as discussed in this section will be part of it. Questioning what the definition of “living things” is may be another consequence, which, of course, goes beyond what has been called the psychology of mathematics education or philosophy of mathematics education. But it will be relevant to some questions that perhaps were put aside or never asked before, questions such as: What are the specific roles of spaces/artifacts such as the classroom, face-to-face environments made for the intense use of Internet in education, and the “online classroom?” If the pandemic lasts even longer, what do we really mean by “face-to-face?” What does it mean to discuss affection in mathematics education without physical contact (e.g., hand shaking, hugging, kissing the cheek), so important in many parts of the world? The whole discussion about humans-with-media may gain a new dimension, as suggested in this section, related to some of the basic questions of philosophy of (mathematics) education. The pandemic foregrounds the role of home and the role of different parents and different social conditions in collectives that construct knowledge, in activity systems that produce knowledge. The idea of seeing fuzzy agency in non-humans should be developed further to include not only good access to internet, but to housing, which is a site of brutal inequality in Brazil and elsewhere. This famous photo (Fig. 3 ) illustrates the extent of inequality in Brazil, which, from the educational point of view, suggests that different housing may have different agency in constructions of knowledge, in particular in situations such as the one we lived during the pandemic. Housing matters in knowledge construction. Trying to solve a mathematics problem in a crowded house in a slum is very different than doing so in a spacious, luxurious apartment with a veranda.

Social inequality. Source: Of “Com 1% do país concentrando 28% da renda, Brasil não tem como dar certo...” L. Sakamoto, 2020. Recovered from https://noticias.uol.com.br/colunas/leonardo-sakamoto/2020/12/15/com-1-do-pais-concentrando-28-da-renda-brasil-nao-tem-como-dar-certo.htm?fbclid=IwAR3cAed7k9bb4qhHWhi7uAtZVhgCLFz9J-yx1dPuoW5rAS1xqVfgey6YrOc

In this sense, SARS-CoV-2 has pushed homes into the center of a collective that produces knowledge. Once again, we ask all the basic questions of the philosophy of mathematics education and psychology of mathematics education. What is the role of mathematics education? What is the role of the different education of parents in mathematics education? What is the role of non-living things, such as viruses, pieces of software, and homes, in the way we know and learn mathematics? A question that may be more critical is: What is the role of mathematics education for resisting inequality in the world?

4 Critical mathematics education and coronavirus

The trend of critical mathematics education (CME) responds to the main problem of social inequality in (mathematics) education and struggles against the view that mathematics is a branch of science that is separate from social, cultural, and political issues. CME’s role in the community of mathematics education is to remind us all about social inequality and other types of inequalities. CME may be said to have been officially born in 1990, in a meeting at the Cornell University in the USA (Powell, 2012 ; Torisu, 2017 ). There, the Critical Mathematics Educators Group was founded, with several members Footnote 7 , focusing on the key phrase “social justice.” Powell ( 2012 ) reports on how at ICME 6, in Budapest, Hungary, there was a meeting of researchers and how after the Cornell meeting, the group began to meet regularly, starting at ICME 7, in Quebec, Canada.

Present at the Quebec meeting was Skovsmose ( 1994 ), who also wrote about the development of critical mathematics education in Europe. Skovsmose shows the connection of this branch of CME in Europe to the Frankfurt School of Critical Education, one of the main representatives of which was Adorno, whose main issue was seeking an education that would prevent Nazism from occurring again. Today, critical mathematics education is more than important, in a moment in which countries such as the USA, Brazil, and Italy have far-right or fascist leaders, who have praised some of the fascist leaders of the twentieth century.

In the Cornell meeting, issues of social inequality, the role of mathematics in society, the ideology of certainty, and research methodologies appropriate to CME were presented (Borba, 1991 ; Borba & Skovsmose, 1996 ; Skovsmose & Borba, 2004 ). Since the 1990s, in Africa, authors such as Paulus Gerdes, from Mozambique, developed curricula and research about African traditions in mathematics and how to incorporate them into mathematics education (Gerdes, 2010 ; Torisu, 2017 ).

Development of curricula and pedagogical perspectives that highlight social inequality, gender and racial inequity, and the ideology of certainty was the initial focus of CME. More recently, environmental issues, and issues that were treated in other trends (e.g., mathematics education to the deaf or the blind), were brought into the agenda of CME. In sum, CME is a trend that shows that education is not neutral: it can promote equality or inequality. There are indicators already from Forbes that social inequality is growing during this pandemic: the billionaires are becoming even richer (Gavioli, 2020 ). The owners of Facebook and Amazon are among them! There is no need to be a mathematician to understand that this concentration of wealth upward means that the rest of the people have less. The owners of tech companies stand to gain as people move more and more online: their companies run online social networks, run online shopping services, and store digital data in online systems worldwide.

As I have already illustrated, social inequality is also growing in schools. As most schools and universities suspend face-to-face classes and go online one way or another, the issue of access has been a barrier to some and a trampoline to even more social inequality. Some universities in Brazil even opted not to resume education online because of inequitable access; but of course, as the university is not the only source of knowledge, online education also may have caused more social inequality. Here is an example from (mathematics) education in Brazil of a Catholic school located on the outskirts of a midtown city in the state of Sao Paulo: the school does not charge tuition for students, as parents do not earn enough income to feed their families; violence is also part of the daily experiences of these children. Teachers are paid above average (considering Brazilian standards), and from interviews with them, it is easy to see their engagement in fighting social inequality. Classes were first suspended in mid-March 2020 and resumed online afterwards, at different moments of April, depending on the school. Two teachers, Luiz Felipe Trovão (mathematics educator) and Karla Cristina Stropa Goulart (science educator), who were asked to answer an open question about their experience with teaching during the pandemic, reported how hard it was to communicate with students. Most students did not have access to the Internet. When they had access, they did not have the money to buy credits to operate the Internet Footnote 8 . The school tried to overcome this problem by providing chips with credits or sending printed didactical material to the children. But with less interaction with teachers, and without an environment to study in poor homes, through no fault of the teachers or the school, very little mathematics education or science education occurred. Trovão said that it is almost impossible to teach geometry online without proper interaction: homes, Internet access, etc.

The billionaires are becoming even richer; the poor are having even more difficulty accessing mathematics education: this may foreground the need that children will have, after the pandemic, to understand what happened. Mathematics educators may have to explore some tough topics: exponential functions to explain the spread of the coronavirus and how the richest grew even richer. Mathematics will not be enough, but a new agenda will be generated. Freire’s ( 1968 ) work about the pedagogy of the oppressed will be even more important. Putting together the agenda for the three trends, one should consider, for example, the role that home, as a physical and emotional “thing,” has in the pandemic school. We have collectives of home-parents-internet-student-teacher as the minimal unit of the collective agent who produces knowledge. Home and parents, things and humans, have added more to social inequality and to discussions about how to use digital technology in mathematics education.

Humans-with-media, seen as an activity system, provides a dynamic epistemological view that we can use to understand the different social aspects (in the micro- and macrolevels) of the research of digital technology. Simultaneously, in acknowledging agency in a wide variety of things, not only computers, it will be possible to structurally show social inequality: homes equipped differently cannot be assessed the same way. Children will suffer even more injustice than they suffer in school, if differences in Internet access, the comfort of home, etc., are not considered in assessment and teaching. Research under this frame, in digital technology, critical mathematics education, assessment, ethnomathematics, and other trends, may help to bring light to more epistemological discussion that is not value-free.

5 The three trends interacting

During the pandemic, “Lives” have become a craze in Brazil: presentations streamed over the Internet by artists, educators, and others. First, artists began holding Live presentations to incentivize people to stay at home. Soon after, other types of workers, such as mathematics educators, started holding our own Live presentations. During this pandemic, I have given many Lives produced by collectives that included Geogebra, the Internet, my home, and various broadcast software. The discussions of the mathematics of the pandemic and the sigmoid curve and its derivative were used in possibly thirty Lives. Figure 4 is a screenshot from a short video that shows this curve dynamically: https://igce.rc.unesp.br/#!/pesquisa/gpimem---pesq-em-informatica-outras-midias-e-educacao-matematica/animacoes/curva-epidemica-no-geogebra/ .

COVID-19 flattening curve. Source: https://www.youtube.com/watch?v=XYNMuaPm654&list=PLiBUAR5Cdi60qXjrzAVdhOgufWVuWTdl2&index=16

The derivative of the sigmoid was used to explain why it was both possible and important to “flatten the curve.” Different curves, with faster or slower growth, were associated to the roles of prevention, social status, and different kinds of homes. Examples of this type of “virtual classroom,” outside of the school/university context, illustrate how much the three trends analyzed in this paper can be powerfully intertwined. This calls for research to understand what kind of mathematics education is being experienced by those who synchronously or asynchronously viewed the Lives.

6 Discussion and conclusion

Most of mathematics education is supported by empirical papers. In the 1970s, most research was quantitative, and data was used to “prove” that a given method of teaching was better than another. Empirical data had the same role it plays to this day in a good part of what is considered science: there were control groups and experimental groups, and the methodology was based on (or reduced to) statistical treatment and conclusions. Later last century, and earlier this century, qualitative research has swung the pendulum in another direction. Qualitative research sees data as a voice, as a complement that should be added to other evidence in order to make (“prove”) a point (Borba et al., 2018 ). Truth was assumed to be explicitly contingent and subject to change long before the COVID-19 pandemic brought so many instabilities to our beliefs. As arguments grew apart from data, a wide set of reactions, including some from powerful funding agencies, emerged. For example, there were funding agencies that require quantitative data in a project. Now the notion of mixed methods is prevalent, even though it is not clear what the role of the data or the view of “truth” is in much of the research published.

Essays such as this paper serve the purpose of discussing ideas and presenting bases for research papers, so that we can know (in the different directions briefly presented above) about mathematics education, in the different epistemological positions that characterize our community. In this sense, this paper is a result of a reflection on how three trends could have their agendas transformed by SARS-CoV-2. Of course, other trends, such as ethnomathematics or early-grades mathematics education, will also be affected. The issues raised throughout this paper should be transformed by readers and should themselves become the objects of research. In this paper, I choose to deal with digital technology, philosophy of mathematics education, and critical mathematics education because the pandemic seems to have played a significant role in the changes of the agendas of these three trends. It seems important to raise new issues in these trends.

Digital technology is now a theme of concern (or research) for everyone (Engelbrecht et al., 2020a , b ). The amplification of the starkness of inequality under the pandemic cannot be ignored (except for those who believe that the Earth is flat and that hydroxychloroquine is a miracle cure for COVID-19), and the rise of the home office, associated with home schooling, confinement, and lockdown, may help many to think about philosophical issues regarding the role of “place” in knowing/learning and notions such as humans-with-media.

In the paragraphs above, I have pointed at my choices in identifying important trends. Why did I say “I” instead of “we,” which would refer to a collective of humans-with-media? It is a good question, and a tentative answer, in another domain of discussion (qualitative research and its influence in the classroom), was given in Borba et al. ( 2018 ). The authorship of a paper or a book may be individual, but it is a result of a collective endeavor of “endless” humans-with-media. This paper Footnote 9 has one author, but it involved the active participation of one doctoral student (Juliana Çar Stal), three teachers who lent me their speech (Karla Cristina Stropa Gourlart, Luiz Felipe Trovão, and one who wanted to remain anonymous), the reviewers, the editors of this special issue, members of the research group I belong to, the more than 100 members of the graduate program in mathematics education at UNESP Footnote 10 , Rio Claro, friends, the computer, the word processor, the home, the office, and, of course, the pandemic, COVID-19. We hope we can discuss this at the next ICME and that it does take place in 2021!

https://www.icme14.org/static/en/index.html

European Society for Research in Mathematics Education

Brazilian Society of Mathematics Education

Psychology of Mathematics Education Annual Meeting

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Alan Bishop, Arthur Powell, Claudia Zaslavsky, David Henderson, Dorothy Buerk, Europe Sign, George Gheverghese Joseph, Kelly Gaddis, Marcelo Borba, Marilyn Frankenstein, Marty Hoffman, Munir Fasheh, Paul Ernest, and Sam Anderson

In Brazil, most people will not have unlimited access to Internet in their cell phone. Especially if you are poor, you typically buy credits for Internet and pay as you go.

The content of this article is partially financed by the research Grants by CNPq, 400590-2016-6 and 303326-2015.

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Borba, M.C. The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things. Educ Stud Math 108 , 385–400 (2021). https://doi.org/10.1007/s10649-021-10043-2

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Accepted : 16 February 2021

Published : 27 April 2021

Issue Date : October 2021

DOI : https://doi.org/10.1007/s10649-021-10043-2

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