From teaching for war to acknowledging vulnerability: a cartography of gender and mistake-handling in mathematics education

Mathematics Curriculum Evaluation

From a traditional perspective, induction and deduction have been discussed as key ways to generate new knowledge. On the other hand, Charles Sanders Peirce introduced the notion of abduction, distinct from deduction and induction, to avoid the pitfalls of empiricism and rationalism. Abduction is the process of forming an explanatory hypothesis on an observed surprising result (C.P. 5.171). Peirce emphasized that abductive reasoning is the only way of creating new ideas, and both epistemologists and educational researchers have attempted to tackle this notorious problem, the so-called learning paradox, from a Peircean perspective on knowledge generation (Prawat, 1999). With mathematics educators’ recent interests in semiotic approaches, there has been growing attention to the importance of investigating abductive reasoning in mathematics education research. Studies have attempted to clarify the forms and uses of abductive reasoning in students’ mathematical inquiries in order to identify how students generate new mathematical ideas. Researchers also consider that investigating students’ abductive reasoning may help to interpret and understand what occurs in mathematics classrooms. Thus, exploring abductive reasoning in mathematics education may provide a more helpful cornerstone in understanding how mathematics teaching and learning progresses. This special issue of EURASIA Journal of Mathematics, Science and Technology Education aims to share current and future issues on abductive reasoning in mathematics education. In inviting the contributions for this special issue, we intend to offer the reader, original elements of reflection from a wide range of issues on abductive reasoning in mathematics education. David Reid gives an overview of the discussion of abductive reasoning in mathematics education researches based on a meta-analysis of the state-of-the-art literature. He presents the origins of the concept of abductive reasoning and identifies the most significant approaches in mathematics education literature that refers to abductive reasoning. He then proposes a framework in which the different approaches taken in the research literature can be placed and compared. Michael Hoffmann presents very fundamental issues regarding abductive reasoning. Hoffmann tackles two crucial questions related to knowledge creation from a Peircean perspective: Can diagrammatic reasoning indeed be conceived as a foundation of abductive creativity? What is the relationship between abduction and diagrammatic reasoning? To answer these questions, he clarifies the Peircean concept of diagram and diagrammatic reasoning and analyzes the significance of a consistent system of representation for diagrammatic reasoning. He then examines how diagrammatic reasoning and creation of abduction are related. Three further contributions address how abduction is related to various contexts of mathematics learning. Bettina Pedemonte presents the role of abduction in the proving process of students solving a geometrical problem. She focuses on two types of rules in problem solving: strategic rules and definitory rules. She then compares two types of abductions that are related to these two rules, and analyzes the relationship between these two types of abductions and the deductive proof. Ferdinand Rivera examines elementary students’ pattern generalization. He focuses on identifying multiple abductive actions in their pattern generalization, and shows how multiple abductions can be coordinated and how this coordination is related to pattern generalization. He also analyzes the relationship between elementary children’s structural incipient generalizations and the natural emergence of their understanding of functions, especially the central role of abduction in such an understanding. JinHyeong Park and Kyeong-Hwa Lee investigate the abductive nature of mathematical modeling and the characteristics of mathematical inquiries triggered by mathematical modeling. They identify four characteristics of mathematical inquiries triggered by mathematical modeling based on an analysis of didactical and historical cases: abductive, recursive, analogical, and context-dependent. Michael Meyer presents various task-design options that can be used to support students in discovering mathematical properties that refer to abductive reasoning. These task-design options are identified using intense scrutiny of the processes of discovering and verifying mathematical properties from a Peircean perspective on learning and knowledge creation. He also presents concrete examples of task design and empirical findings on the implementation of tasks. From theoretical issues to more practical issues, these contributions in this special issue present state-of-the-art issues in abductive reasoning in the mathematics education research community. We hope that these offer an informative insight into the lively research on abductive reasoning in mathematics education.

Preface.- Section I - Theoretical Perspectives. 1. Mathematical Literacy and Globalisation.- 2. Epistemological Issues in the Internationalization and Globalization of Mathematics Education .- 3. All around the World: Science Education, Constructivism, and Globalization.- 4. Geophilosophy, Rhizomes and Mosquitoes: Becoming Nomadic in Global Science Education Research. 5. Science Education and Contemporary Times: Finding Our Way through the Challenges.- 6. Social (In)Justice and International Collaborations in Mathematics Education.- 7. Globalisation, Ethics and Mathematics Education.- 8. The Politics and Practices of Equity, (E)quality and Globalisation in Science Education: Experiences from Both Sides of the Indian Ocean.- Section II - Issues in Globalisation and Internationalisation 9. Context or Culture: Can TIMSS and PISA Teach Us about What Determines Educational Achievement in Science?.- 10. Quixote's Science: Public Heresy/Private Apostasy.- 11. The Potentialities of (ethno) Mathematics Education: An Interview with Ubiratan D' Ambrosio.- 12. Ethnomathematics in the Global Episteme: Quo Vadis?.- 13. POP: A Study of the Ethnomathematics of Globalisation Using the Sacred.- 14. Internationalisation as an Orientation for Learning and Teaching in Mathematics.- 15. Contributions from Cross-National Comparative Studies to the Internationalization of Mathematics Education: Studies of Chinese and U.S. Classrooms.- 16. International Professional Development as a Form of Globalisation.- 17. Doing Surveys in Different Cultures: Difficulties and Differences - A Case from China and Australia.- 18. The Benefits and Challenges for Social Justice in International Exchanges in Mathematics and Science Education.- 19. Globalisation, Technology, and the Adult Learner of Mathematics.- Section III - Perspectives from Different Countries. 20. Balancing Globalisation and Local Identity in the Reform of Education in Romania.- 21. Voices from theSouth: Dialogical Relationships and Collaboration in Mathematics Education.- 22. Globalization and its Effects in Mathematics and Science Education in Mexico: Implications and Challenges for Diverse Populations.- 23. In between the Global and the Local: The Politics of Mathematics Education Reform in a Globalized Society.- 24. Singapore and Brunei Darussalam: Internationalisation and Globalisation through Practices and a Bilateral Mathematics Study.- 25. Lesson Study (JYUGYO KENKYU), from Japan to South Africa: A Science and Mathematics Intervention Program for Secondary School Teachers.- 26. The Post-Mao Junior Secondary School Chemistry Curriculum in the People's Republic of China: A Case Study in the Internationalization of Science Education.- 27. Globalisation/Localisation in Mathematics Education: Perception, Realism and Outcomes of an Australian Presence in Asia.- Biographical Notes.

This article describes a laboratory supplementary program that was integrated into a traditional mining engineering mathematics unit. The practical classes consisted of computer investigations designed to help develop mathematical concepts. The program described here was mainly web based and did not directly rely on a computer algebra system for its implementation. An evaluation of the program is included. References S. Cunningham. The visualization environment for mathematics education. In Visualization in Teaching and Learning Mathematics , ed. W. Zimmermann and S. Cunningham, 67--76. USA, Mathematical Association of America, 1991. A. Franco, P. Franco, A. Garcia, F. Garcia, F. J.Gonzalez, S. Hoya, G. Rodriguez, and A. de la Villa. Learning calculus of several variables with new technologies. The International Journal of Computer Algebra in Mathematics Education , 7 (4), 295--309, 2000. B. E. Garner and L. E. Garner. Retention of concepts and skills in traditional and reformed applied calculus. Mathematics Education Research Journal , 13 (3), 165--184, 2001 S. Habre. Visualization enhanced by technology in the learning of multivariate calculus. The International Journal of Computer Algebra in Mathematics Education , 8 (2), 115--130, 2001. B. H. Hallet. Visualization and calculus reform. In Visualization in Teaching and learning Mathematics , ed. W. Zimmermann and S. Cunningham, 121--126, 1991. USA, Mathematical Association of America F. Marton and R. Saljo. Approaches to learning. In eds. F. Marton, D. Hounsell and N. Entwistle, The Experience of Learning , 36--55, 1984. Scottish Academic Press, Edinburgh. R. Moreno and R. Mayer. Verbal redundancy in multimedia learning; When reading helps listening. Journal of Educational Psychology , 94 (1), 153--163, 2002. L. D. Murphy. Computer algebra systems in calculus reform, MSTE, University of Illinois at Urbana-Champaign, 1999. http://mste.illinois.edu/users/Murphy/Papers/CalcReformPaper.html M. Pemberton. Integrating web-based maple with a first year calculus and linear algebra course. Proceedings of the 2nd International Conference on the Teaching of Mathematics , Hersonissos, Greece, July 2002. http://www.math.uoc.gr/ ictm2/Proceedings/pap316.pdf R. Pierce and K. Stacey. Observations on students' responses to learning in a cas environment. Mathematics Education Research Journal , 13 (1), 28--46, 2001. M. D. Roblyer. Integrating Educational Technology Into Teaching (4th Ed.), 2006. Pearson, New Jersey, USA. J. Stewart. Calculus (5th Ed.), 2003. Brooks/Cole, Belmont, USA. E. J. Tonkes, B. I. Loch and A. W. Stace. An innovative learning model for computation in first year mathematics. International Journal of Mathematical Education in Science and Technology , 36 (7), 751--759, 2005. L. M. Villarreal. A step in the positive direction: Integrating a computer laboratory component into developmental algebra courses. Mathematics and Computer Education , 37 (1), 72--78, 2003. S. Vinner. The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics , 34 (2), 97--129, 1997. P. Vlachos and A.K. Kehagias. A computer algebra system and a new approach for teaching business calculus. The International Journal of Computer Algebra in Mathematics Education . 7 (2), 87--104, 2000.

The National Council of Teachers Mathematics (NCTM) has had the most profound influence on reform in mathematics education with the publications of its curriculum, professional teaching, and assessment documents in 1989, 1991, 1995, and 2000. The documents recommend standards for the mathematics curriculum in grades pre-K to12, professional standards for mathematics educators, and assessment standards for evaluating the quality of both student achievement and curriculum. The NCTM documents acknowledge that cultural experiences, social background, and gender of students have been ignored in mathematics education and that differences among students are not taken into account in the teaching and learning of mathematics. The Principles and Standards for School Mathematics (PSSM) (NCTM, 2000) highlighted equity by making it the first principle for reform of school mathematics: Excellence in mathematics education requires equity--... raising expectations for students' learning, developing effective methods of supporting the learning of mathematics by all students, and providing students and teachers the resources they need (p. 12). The PSSM offers a broad view of what it takes to accomplish equity that includes having high expectations for all students, accommodating for differences, and equitable allocation of human and material resources. The PSSM captures the essence of some conditions that lead to inequities in a school context by acknowledging that 1) low expectations negatively impact marginalized students in mathematics, 2) access to quality mathematics is not always equitable, and 3) allocation of material and human resources in not always equitable (NCTM, 2000). The PSSM addresses equity as it relates to curriculum, instruction, and assessment neither situates equity within the larger societal context nor offers suggestions for building an infrastructure for equity in mathematics education. Like the PSSM, other NCTM Standards documents the Assessment Standards for School Mathematics (NCTM, 1995), Professional Standards for Teaching Mathematics (NCTM, 1991), and Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) situates equity only within the context of curriculum, instruction, and assessment. These Standards documents also recognize that inequities exist in mathematics education but they fail to address the causes and roots of inequities. Martin (2003) criticizes NCTM for not taking a stronger position on equity. Martin's criticism focuses on the fact that the Equity Principle does not mention race, racism, and social justice. He states: the Standards contains no explicit or particular references to African American, Latino, Native American and poor students or the conditions they face in their lives outside of school, including the inequitable arrangement of mathematical opportunities in these out of school contexts. I would argue that blanket statements about all students signals an uneasiness or unwillingness to grapple with the complexities and particularities of race, minority/marginalized status, differential treatment, underachievement in deference to the assumption that teaching, curriculum, learning, and assessment are all that matter (p. 10). Martin's criticism provides the basis for examining the complexities that race, racism, and social justice have in mathematics education. According to PSSM (NCTM, 2000), equity is should be a goal for mathematics education. If equity is a goal in mathematics education, then mathematics educators must develop an infrastructure for equity comparable to the infrastructure developed that guided reform in curriculum materials, assessment, and pedagogy (Weissglass, 2000). Too often, race, racism, and social justice are relegated as issues not appropriate for mathematics education when actually these issues are central to the learning and teaching of mathematics for all students. …

Selected Regular Lectures from the 12th International Congress on Mathematical Education

Student character education is an education system that aims to instill certain character values ​​in students in which there are components of knowledge, awareness or will, as well as actions to carry out these values, for this review, teachers are able to carry out quality learning in every learning activity is included in learning mathematics. Student character education can be developed in learning mathematics that is oriented towards moral values. This study aims to implement the role of character education in mathematics education that is oriented towards moral values. This study uses SLR (Systematic Literature Review) research, where the data source is obtained from existing articles published by OJS (Online Journal System). Articles obtained through Google searches were grouped and tabulated based on the similarity of results/conclusions in the article results. After being tabulated, further analysis was carried out and finally reduced and conclusions drawn. Based on research data, the results obtained regarding the implementation of character education in learning mathematics that are oriented to moral values ​​find that: increasing moral values, developing moral values ​​and creativity, building character, problem solving processes, arousing curiosity, mathematical developments, logical thinking, being able to improve learning achievement, character education improves student learning outcomes. Based on these findings, it is hoped that educators, especially mathematics teachers, will always implement character education in learning mathematics that is oriented towards moral values. Keywords: Implementation, Character Education, Moral Values, Learning Mathematics

Previous articleNext article No AccessAttitudes of Prospective Teachers toward ArithmeticWilbur H. DuttonWilbur H. Dutton Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 52, Number 2Oct., 1951 Article DOIhttps://doi.org/10.1086/459310 Views: 8Total views on this site Citations: 32Citations are reported from Crossref Copyright 1951 The University of ChicagoPDF download Crossref reports the following articles citing this article:Rosetta Zan, Pietro Di Martino Students’ Attitude in Mathematics Education, (Feb 2020): 813–817.https://doi.org/10.1007/978-3-030-15789-0_146Kyoung Whan Choe, Jalisha B. Jenifer, Christopher S. Rozek, Marc G. Berman, Sian L. Beilock Calculated avoidance: Math anxiety predicts math avoidance in effort-based decision-making, Science Advances 5, no.1111 (Nov 2019).https://doi.org/10.1126/sciadv.aay1062Mairéad Hourigan, Aisling M. Leavy The influence of entry route to teaching on Irish pre-service primary teachers’ attitudes towards mathematics, Journal of Further and Higher Education 43, no.77 (Jan 2018): 869–883.https://doi.org/10.1080/0309877X.2017.1420148Menekşe ESKİCİ, Gökhan ILGAZ Lise Öğrencileri ve Matematik: Tutum, Başarı ve Cinsiyet Işığında, Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi (Feb 2019).https://doi.org/10.18506/anemon.422161Rosetta Zan, Pietro Di Martino Students’ Attitude in Mathematics Education, (Feb 2019): 1–5.https://doi.org/10.1007/978-3-319-77487-9_146-4Gülçin Oflaz CEBİRE YÖNELİK TUTUM ÖLÇEĞİ GELİŞTİRME ÇALIŞMASI, Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi (Dec 2018).https://doi.org/10.17218/hititsosbil.444718Aisling Leavy, Mairead Hourigan The beliefs of ‘Tomorrow's Teachers’ about mathematics: precipitating change in beliefs as a result of participation in an Initial Teacher Education programme, International Journal of Mathematical Education in Science and Technology 49, no.55 (Jan 2018): 759–777.https://doi.org/10.1080/0020739X.2017.1418916Aisling Leavy, Mairead Hourigan, Claire Carroll Exploring the Impact of Reform Mathematics on Entry-Level Pre-service Primary Teachers Attitudes Towards Mathematics, International Journal of Science and Mathematics Education 15, no.33 (Nov 2015): 509–526.https://doi.org/10.1007/s10763-015-9699-1Mairéad Hourigan, Aisling M. Leavy, Claire Carroll ‘Come in with an open mind’: changing attitudes towards mathematics in primary teacher education, Educational Research 58, no.33 (Jul 2016): 319–346.https://doi.org/10.1080/00131881.2016.1200340Markku S. Hannula, Pietro Di Martino, Marilena Pantziara, Qiaoping Zhang, Francesca Morselli, Einat Heyd-Metzuyanim, Sonja Lutovac, Raimo Kaasila, James A. Middleton, Amanda Jansen, Gerald A. Goldin Attitudes, Beliefs, Motivation, and Identity in Mathematics Education, (Jun 2016): 1–35.https://doi.org/10.1007/978-3-319-32811-9_1Pietro Di Martino, Rosetta Zan The Construct of Attitude in Mathematics Education, (Aug 2014): 51–72.https://doi.org/10.1007/978-3-319-06808-4_3Rosetta Zan, Pietro Di Martino Students’ Attitude in Mathematics Education, (Jul 2014): 572–577.https://doi.org/10.1007/978-94-007-4978-8_146Norma Wynn Harper, C. J. Daane Causes and Reduction of Math Anxiety in Preservice Elementary Teachers, Action in Teacher Education 19, no.44 (Jan 1998): 29–38.https://doi.org/10.1080/01626620.1998.10462889Dorothy R. Bleyer STUDENTS’ ATTITUDES TOWARD MATHEMATICS AND THEIR RELATIONSHIP TO LEARNING IN REQUIRED MATHEMATICS COURSES IN SELECTED POSTSECONDARY INSTITUTIONS, Community Junior College Research Quarterly 4, no.44 (Jul 2006): 331–347.https://doi.org/10.1080/0361697800040403Dennis M. Roberts, Edward W. Bilderback Reliability and Validity of a Statistics Attitude Survey, Educational and Psychological Measurement 40, no.11 (Apr 1980): 235–238.https://doi.org/10.1177/001316448004000138 Grace M. Burton Getting Comfortable with Mathematics, The Elementary School Journal 79, no.33 (Oct 2015): 129–135.https://doi.org/10.1086/461142Hilary L. Schofield, K. B. Start Mathematics Attitudes and Achievement among Student Teachers, Australian Journal of Education 22, no.11 (Mar 1978): 72–82.https://doi.org/10.1177/000494417802200106Ralph D. Norman Sex Differences in Attitudes toward Arithmetic-Mathematics from Early Elementary School to College Levels, The Journal of Psychology 97, no.22 (Jul 2010): 247–256.https://doi.org/10.1080/00223980.1977.9923970Lewis R. Aiken Update on Attitudes and Other Affective Variables in Learning Mathematics, Review of Educational Research 46, no.22 (Jun 2016): 293–311.https://doi.org/10.3102/00346543046002293Seymour Metzner The Elementary Teacher and the Teaching of Arithmetic: A Study in Paradox, School Science and Mathematics 71, no.66 (Jun 1971): 479–482.https://doi.org/10.1111/j.1949-8594.1971.tb08778.xLewis R. Aiken Attitudes Toward Mathematics, Review of Educational Research 40, no.44 (Jun 2016): 551–596.https://doi.org/10.3102/00346543040004551Bonnie H. Litwiller Enrichment: A Method of Changing the Attitudes of Prospective Elementary Teachers Toward Mathematics, School Science and Mathematics 70, no.44 (Apr 1970): 345–350.https://doi.org/10.1111/j.1949-8594.1970.tb08636.xLewis H. Coon Attitude: A Rating Scale for Calculus, The Journal of Educational Research 63, no.44 (Jan 2015): 173–177.https://doi.org/10.1080/00220671.1969.10883972Ralph G. Anttonen A Longitudinal Study in Mathematics Attitude, The Journal of Educational Research 62, no.1010 (Jan 2015): 467–471.https://doi.org/10.1080/00220671.1969.10883904Ingvar Werdelin FACTOR ANALYSES OF QUESTIONNAIRES OF ATTITUDES TOWARDS SCHOOL WORK, Scandinavian Journal of Psychology 9, no.11 (Sep 1968): 117–128.https://doi.org/10.1111/j.1467-9450.1968.tb00524.x Wilbur H. Dutton Another Look at Attitudes of Junior High School Pupils toward Arithmetic, The Elementary School Journal 68, no.55 (Oct 2015): 265–268.https://doi.org/10.1086/460444Wilbur H. Dutton Prospective Elementary School Teachers’ Understanding of Arithmetical Concepts, The Journal of Educational Research 58, no.88 (Dec 2014): 362–365.https://doi.org/10.1080/00220671.1965.10883245J. B. Biggs The Teaching of Mathematics‐‐II ATTITUDES TO ARITHMETIC‐NUMBER ANXIETY, Educational Research 1, no.33 (Jun 1959): 6–21.https://doi.org/10.1080/0013188590010301David Rappaport Preparation of Teachers of Arithmetic, School Science and Mathematics 58, no.88 (Nov 1958): 636–643.https://doi.org/10.1111/j.1949-8594.1958.tb08095.xE Glenadine Gibb, H. Van Engen Chapter II: Mathematics in the Elementary Grades, Review of Educational Research 27, no.44 (Jun 2016): 329–342.https://doi.org/10.3102/00346543027004329Bruce E. Meserve, John A. 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The aim of this chapter is to contribute to the debate about the trends, objects of study, and theoretical and methodological assumptions that have marked and constituted the current identity of working group Cognitive and Linguistic Processes in Mathematics Education of the Brazilian Society of Mathematics Education. The considerations presented bring together a range of investigations that explore the cognitive and linguistic aspects involved in the teaching and learning of mathematics in different learning contexts and different levels of schooling. The work developed by the group has been characterised by investigations conducted on language and communication in the classroom and their sociocultural aspects, alongside studies into the cognitive processes involved in mathematical reasoning. The discussion about the theoretical-methodological questions underlying the reflections on the cognitive and linguistic processes in the Brazilian scenario has been divided into two parts. In the first, we present a historical review of the main trends considered during the first 10 years of working group’s history. In the second, explore the more recent objects of study. We describe how this development indicates a convergence of Brazilian researchers with different theoretical and methodological affiliations, as they search for theoretical models that can explain the role of language, cognition and cultural aspects in the teaching and learning of mathematics. The advances made in terms of knowledge of cognitive and linguistic processes in mathematics education within Brazil are also presented.

I suggest a simple thought experiment. Science fiction books occasionally mention an imaginary device: a replicator. It consists of two boxes; you put an object in a box, close the lid, and instantly get its undistinguishable fully functional copy in the second box. In particular, a replicator can replicate smaller replicators. Now imagine the economy based on replicators. It needs two groups of producers: a very small group of engineers who build and maintain the biggest replicator and a very diverse, but still small, group of artisans, designers, and scientists who produce a single original prototype of each object. This hypothetical economy also needs service sector, mostly waste disposal. Next, try, if you can, imagine a sustainable, stable, equal, and democratic model of education that supports this lopsided economy. But this apocalyptic future is already upon us – in the information sector of economy, where computers act as replicators of information. Mathematics, due to its special role in the information technology, is the most affected part of human culture. The new patterns of division of labour split mathematics for makers from mathematics for users and trigger a crisis of mathematics education. The latter increasingly focuses on mathematics for users and undermines itself because sustainable reproduction of mathematics requires teachers educated as makers.

A challenge of teacher education is to produce graduate primary school teachers who are confident and competent teachers of mathematics. Various approaches to primary school teacher education in mathematics have been investigated, but primary teacher education graduates still tend to be diffident in their teaching of mathematics. In an age where personal use of mobile technologies is becoming ubiquitous, such technologies could provide a conduit into making mathematics teaching and learning more accessible to primary teacher education students. This paper introduces the use of a pedagogical framework which can scaffold mobile learning in mathematics teacher education programs. The paper discusses ways in which this framework, the Mobile Pedagogical Framework, can contribute to enhanced primary teacher education in mathematics, using mobile technologies. The Framework has three major dimensions: authenticity, collaboration and personalisation. Each of these will be discussed in terms of their alignment with current ideas about quality teaching in mathematics.

Preface and Acknowledgements.- Introduction.- Mathematics and Mathematics Education: Searching for common ground: Michael N. Fried.- Chapter 1. A Dialogue on a Dialogue.- Mathematics and Mathematics Education: Beginning a Dialogue in an Atmosphere of Increasing Estrangement: Michael N. Fried.- Some of my pet-peeves with mathematics education: Ted Eisenberg.- Mathematics at the Center of Distinct Fields: A Response to michael and Ted: Norma Presmeg.- Chapter 2. Mutual Expectations.- Mutual Expectations between Mathematicians and Mathematics Educators : Tommy Dreyfus.-With contributions by:Uri Onn, Joanna Mamona-Downs, Stephen Lerman.- Chapter 3. History of Mathematics, Mathematics Education, and Mathematics.- History in mathematics education. A hermeneutic approach: Hans Niels Jahnke.- Reflections on History of Mathematics: History of Mathematics and Mathematics Education: Luis Radford.- With contributions by:Alain Bernard, Michael N. Fried , Fulvia Furinghetti, Nathalie Sinclair.- Chapter 4. Problem-Solving: A Problem for Both Mathematics and Mathematics Education.- Reflections on Problem-Solving: Problem solving in mathematics and in mathematics education: Boris Koichu.- With contributions by: Gerald A. Goldin, A. Israel Weinzweig, Shlomo Vinner, Roza Leikin.- Chapter 5. Mathematical What Is It and How is It Determined?.-Mathematical Literacy: An Inadequate Metaphor: E. Paul Goldenberg.- Reflections on Mathematical literacy : What's new, why should we care, and what can we do about it? : Anna Sfard.- With contributions by:Abraham Arcavi, Ron Livne, Iddo Gal, Anna Sfard, Hannah Perl.- Chapter 6. Visualization in Mathematics and Mathematics Education: Visualization in Mathematics and Mathematics Education: A Historical Overview : M. A. (Ken) Clements.- Visualization in mathematics and mathematics education: Elena Nardi (University of East Anglia).- With contributions by: Rina Hershkowitz, Raz Kupferman , Norma Presmeg, Michal Yerushalmy.- Chapter 7. Justification and Proof.- Making Sense of Mathematical Reasoning and Proof: David Tall.- Reflections on Justification and Proof: Justification and Proof in Mathematics and Mathematics Education: Keith Weber.- With contributions by: Gila Hanna, Guershon Harel, Ivy Kidron, Annie Selden and John Selden.- Chapter 8. Policy: What Should We Do, and Who Decides?.- Mathematics and mathematics education policy: Mogens Niss.- Reflections on Policy: Mathematics and Mathematics Education Policy-Searching for Common Ground : Nitsa Movshovitz-Hadar.- With contributions by:Jonas Emanuelsson, Davida Fischman, Azriel Levy, Zalman Usiskin.- Chapter 9. Collaboration.- Mathematics and Education: Collaboration in Practice: Hyman Bass.- Deborah Loewenberg Ball.- Reflections on Collaboration between Mathematics and Mathematics Education: Patrick W. Thompson.- With contributions by: Michele Artigue, Gunter Torner, Ehud de Shalit.- Postscript.- We Must Cultivate Our Common Ground: Jeremy Kilpatrick.- Appendix 1. Ted Eisenberg, Teacher, Colleague, and Friend.- Ted as advisor and colleague: Tommy Dreyfus.- Thank you, Ted!: Francis Lowenthal.- Annotated bibliography of Ted Eisenberg's Major Publications: Tommy Dreyfus.- Appendix 2. Reprints of the Dialogues between Presmeg, Eisenberg, and Fried from ZDM 41(1-2).-Index

Mathematics teaching and learning are critical aspects of education that impact our world. There are implications for the mathematics education research community that should push us to have critical conversations about our research and how it informs mathematics education. I present a brief overview of research in mathematics education through the lens of Investigations in Mathematics Learning, the official journal of the Research Council on Mathematics Learning, using issues from 2017-2021. Included are findings from qualitative analyses and ideas calling on the mathematics education community to consider that provide a positioning for mathematics education researchers (MERs). I challenge us to consider multiple questions with regard to our research: What does it add to the field of mathematics education? How does it contribute to broadening and deepening our understandings? How does it inform practice to further effective equitable teaching and learning of mathematics? Are we being inclusive? Are we a leading voice in mathematics education research and are we being effective curators and stewards of this work? As MERs, as a field, as professional organizations, what could and should we do? We have a unique opportunity at this juncture to work together to inform and impact mathematics learning in profound ways.

Children's Mathematics Learning: The Struggle to Link Form and Understanding

ScratchJr design in practice: Low floor, high ceiling