Mathematics Education

Tracing the Development of Pedagogical Reasoning in Teachers' Conversations

by Ilana Horn

Presented at annual meeting of the American Educational Research Association, Vancouver, BC. Co-authored with Britnie Kane.

Increasingly, school improvement efforts include teacher communities as part of their overall strategy, yet the... more Increasingly, school improvement efforts include teacher communities as part of their overall strategy, yet the relationship between teachers’ talk and professional learning remains underspecified. Using a situative perspective on learning, this paper examines the development of pedagogical reasoning in teachers’ collaborative conversations. In the context of a larger design experiment, which sought to improve high school mathematics instruction in a large urban school district, we analyzed 17 hours of videotaped meetings from Beginning, Emergent, and Sophisticated teacher workgroups comprised of 13 teachers. Focusing on the resources for learning in teachers’ pedagogical reasoning, we used quantitative and qualitative analyses to uncover differences in conversational processes and content across the three groups. In addition to differences in time spent engaged in collaborative problem solving, teaching principles –– propositions that serve as the foundation for pedagogical reasoning –– proved to be the distinguishing characteristic across the three groups. Not only did principles differentiate teachers’ stances on issues of practice, but they also operated differently in the process of conversation. We propose a model of teacher workgroup development that accounts for the differences in conversational process and content and consider its implications for theory and practice.

Learning on the Job: A Situated Account of Teacher Learning in High School Mathematics Departments

by Ilana Horn

Lessons Learned From Detracked Mathematics Departments

by Ilana Horn

Turnaround Students in High School Mathematics: Constructing Identities of Competence Through Mathematical Worlds

by Ilana Horn

Fast Kids, Slow Kids, Lazy Kids: Framing the Mismatch Problem in Mathematics Teachers� Conversations

by Ilana Horn

Horn & Campbell Mediated Field Experience as a Pedagogy for Teacher Education

by Ilana Horn

Division K Interactive Poster Session from AERA 2012 in Vancouver, BC

Only connect: troubling oppositions in gender and mathematics

by Heather Mendick

Originally published in 2005 in the International Journal of Inclusive Education, 9(2), 161-180. (Reprinted in the online Philosophy of Mathematics Education journal)
In 2012 I read this in Jeanette Winterson's book 'Why be happy when you can be normal?' which expresses, more eloquently and succinctly, what I was trying to say in this paper:
"There is still a popular fantasy, long since disproved by both psychoanalysis and science, and never believed by any poet of mystic, that is possible to have a thought without a feeling. It isn't.
"When we are objective we are subjective too. When we are neutral we are involved. When we say 'I think' we don't leave our emotions outside the door. To tell something not to be emotional is to tell them to be dead."

This paper focuses on the ways in which many researchers working in the area of gender and mathematics make sense of... more This paper focuses on the ways in which many researchers working in the area of gender and mathematics make sense of their data. In particular, it is argued that their use of the oppositional framing, separation versus connection (and others, such as cognition versus affect and objective versus subjective), operates to fix difference, and so to fix gender and mathematics within a structure of binary thinking that ultimately serves to re/produce gender inequalities. The aim is to suggest a more productive approach to understanding the continued gendering of participation in mathematics. This approach is based in deconstructing these oppositional patterns. This theoretical approach is illustrated using readings of interviews with two young mathematics students, Analia and Phil, talking about their relationships with the subject. The paper ends by looking at what this unfixing of difference means for mathematics pedagogy.

Tay, L.Y., Lim, S.K., Lim, C.P. & Koh, J.H.L. (2012). Pedagogical approaches for ICT integration into primary school English and Mathematics: A Singapore case study. Australasia Journal of Educational Technology, 28(4), 740-754.

by Cher Ping LIM

This case study research attempts to examine the pedagogical approaches for the teaching of English and Mathematics... more This case study research attempts to examine the pedagogical approaches for the teaching of English and Mathematics with information communication technology (ICT) in a primary school in Singapore. The study uses the learning with and learning from ICT framework in reporting and analysing how ICT has been used in the teaching of English and Mathematics. This framework also looks into the level of production (i.e., students’ creation of digital work) and collaboration when learning with and/or from ICT. From the review of documents and lesson plans; interviews with teachers; group interviews with students; and questionnaire survey of the students on their frequency of ICT use, the findings seem to suggest a difference in the pedagogical approach adopted by the English and Mathematics teachers. The frequency of ICT use was also reported to be significantly higher in English lessons as compared to the Mathematics lessons. Mathematics teachers primarily adopted the learning from ICT pedagogy with occasional learning with ICT approach. However, English teachers facilitated the students to learn from and also with technology with production and also with elements of collaboration. This case study illuminates the usefulness of the learning with and from ICT as a conceptual framework in guiding both researchers and teachers to be more aware of the pedagogical implications when ICT is added in the teaching and learning process. This case study also once again suggests the pivotal role of the teacher.

Tangrams and Area Dissection: A Epistemological and Didactical Perpsective

by Raymond Falcon

This paper will look at how tangrams can be a part of the curriculum of mathematics today.  Tangrams have a... more This paper will look at how tangrams can be a part of the curriculum of mathematics today.  Tangrams have a history as far back as the Chinese and from Archimedes himself.  The Seven Clever Piece Chinese Tangrams are comprised of seven pieces comprising of a parallelogram, a square, and five isosceles triangles of various sizes.  Archimedes’ puzzle is similar but instead is constructed by fourteen pieces in creating a square.  Tangrams and the Archimedes puzzle can be essential in investigating properties of algebra and geometry specifically area dissection, measurement, length, area, ratios, spatial reasoning, and spatial visualization.  This paper will examine the history of area dissection, epistemology, and didactics of tangrams and area dissection in order to better understand the pedagogy implications of tangrams in the mathematics classroom. 

The gestures ASL signers use tell us when they are ready to learn math

by Daniel Lenzen

The development of children's understanding of mathematical patterns through mathematical activities

by Taro Fujita

Research in Mathematics Education Vol. 13. No. 3, 249-267

In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on... more In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns.

Constructions of mathematicians in popular culture and learners’ narratives: a study or mathematical and non-mathematical subjectivities

by Heather Mendick

This paper was co-authored with Marie-Pierre Moreau and Debbie Epstein. This paper was published in the Cambridge Journal of Education in 2010, volume 40, issue 1, pages 25-38. If your library subscribes then the hyperlink will take you to where you can access the paper. If not, then email me and I'll send you a copy.

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people... more In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular cultural texts, we argue that popular discourses overwhelmingly construct mathematicians as white, heterosexual, middle-class men, yet also construct them as 'other' through systems of binary oppositions between those doing and those not doing mathematics. Turning to the analysis of a corpus of 27 focus groups with school and university students in England and Wales, we explore how such images are deployed by learners. We argue that while learners' views of mathematicians parallel in key ways popular discourses, they are not passively absorbing these as they are simultaneously aware of the clichd nature of popular cultural images.

Imagining the mathematician: young people talking about popular representations of maths

by Heather Mendick

This paper was co-authored with Debbie Epstein and Marie-Pierre Moreau. This paper was published in Discourse: Studies in the Cultural Politics of Education in 2010, volume 31, issue 1, pages 45-60. If your library subscribes then the hyperlink will take you to where you can access the paper. If not, then email me and I'll send you a copy.

This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and... more This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and explores the ways in which young people deploy the discourses produced in these texts. We argue that there are particular (and sometimes contradictory) meanings and discourses about mathematics that circulate in popular culture, that young people use these as resources in identity making as (non-)mathematicians, negotiating their meaning in ways that are not always predictable, and that their influence on young people is diffuse and nevertheless important. The paper discusses the discourses that prevail in some of the popular cultural images of mathematics and mathematicians that came up in our research. We show how mathematics is represented as a secret language, while mathematicians are often mad, mostly male and almost invariably white. We then explore how young people negotiate these discourses, positioning themselves in relation to mathematics. Here we draw attention to the fact that both those who continue with mathematics after it ceases to be compulsory and those who do not, deploy similar images of mathematics and mathematicians. What is different is how they respond to and negotiate these images.

Mathematical stories: why do more boys than girls choose to study mathematics at AS-level in England?

by Heather Mendick

This paper was published in 2005 in British Journal of Sociology of Education, 26(2), 225-241. The hyperlink will give you access to the paper if your library subscribes to the journal - otherwise the version that I've uploaded is virtually the same as the one that was published.

In this paper I address the question: How is it that people come to choose mathematics and in what ways is this... more In this paper I address the question: How is it that people come to choose mathematics and in what ways is this process gendered? I draw on the findings of a qualitative research study involving interviews with 43 young people all studying mathematics in post-compulsory education in England. Working within a post-structuralist framework, I argue that gender is a project and one that is achieved in interaction with others. Through a detailed reading of Toni and Claudia's stories I explore the tensions for young women who are engaging in mathematics, something that is discursively inscribed as masculine, while (understandably) being invested in producing themselves as female. I conclude by arguing that seeing 'doing mathematics' as 'doing masculinity' is a productive way of understanding why mathematics is so male dominated and by looking at the implications of this understanding for gender and mathematics reform work.

Commentary: Translating as Nudging Teachers toward “Best Practice.” ZDM Mathematics Education 42 (3-4), 2012.

by Kathryn Anderson-Levitt

This commentary is a response to five articles appearing in the same issue: “Assessing elemental validity: the... more This commentary is a response to five articles appearing in the same issue: “Assessing elemental validity: the transfer and use of mathematical knowledge for teaching measures in Ghana,” by Yaa Cole; “A validation study of the use of mathematical knowledge for teaching measures in Ireland,” by Seán Delaney; “Analysis of psychometric properties as part of an ongoing adaptation process of MKT items for use in other countries,” by Janne Fauskanger, Arne Jakobsen, Reidar Mosvold and Raymond Bjuland; “To change or not to change: Adapting Mathematical Knowledge for Teaching (MKT) measures for use in Korea”, by Minsung Kwon, Mark Hoover Thames and JeongSuk Pang; and “Using the MKT measures to reveal Indonesian teachers’ mathematical knowledge: challenges and potentials,” by Dicky Ng.

You’re it! Body, Action, and Object in STEM Learning (ICLS 2012 Symposium)

by Dor Abrahamson

FOREWORD:
I organized this symposium to encourage dialogue among design-based researchers of STEM learning whose work is grounded in an embodied-cognition epistemological perspective on what it means to know. My sense is that we're working in parallel, and that we could avail a great deal by beginning to reflect collectively. The proceedings paper, written in advance of the conference gathering, captures the sense of inviting this collective reflection among the variety of embodied-cognition "flavors." I hope you find it interesting.

CITATION:
Abrahamson, D. (Chair & Organizer). You’re it! Body, action, and object in STEM learning (M. Eisenberg, Discussant). In P. Freebody, T. de Jong, E. Kyza & P. Reimann (Eds.), Proceedings of the International Conference of the Learning Sciences: Future of Learning (ICLS 2012). Sydney: University of Sydney / ISLS.

ABSTRACT:
In this special double symposium, sixteen established and emerging scholars from seven US universities,... more ABSTRACT:
In this special double symposium, sixteen established and emerging scholars from seven US universities, who share theoretical perspectives of grounded cognition, empirical contexts of design for STEM content domains, and analytic attention to nuances of multimodal expression, all gather to explore synergy and coherence across their diverging research questions, methodologies, and conclusions in light of the conference theme “Future of Learning.” Jointly we ask, What are the relations among embodiment, action, artifacts, and discourse in the development of mathematical, scientific, engineering, or computer-sciences concepts? The session offers emerging answers as well as implications for theory and practice.

Ten years of reform in primary mathematics education in England: A review of Effectiveness

by Richard Bowman

Co-author of US-based portion

The UK National Audit Office (NAO) commissioned RAND Europe to look at the evidence showing the effectiveness of... more The UK National Audit Office (NAO) commissioned RAND Europe to look at the evidence showing the effectiveness of reform of mathematics teaching in primary schools in England. This study looked at government-sponsored evaluations of mathematics reform in England, independent evaluations of the educational outcomes of mathematics reforms in England, and the international evidence regarding some of the main components of government policy aimed at improving educational outcomes. The study presents the results of the evaluations and the international literature and discusses the robustness of their findings.

How Middle School Mathematics Teachers Use Interim and Benchmark Assessment Data

by Richard Bowman

Coauthored with Lorrie A. Shepard and Kristen L. Davidson

In 2001, the enactment of the No Child Left Behind Act intensified the pressure on school districts to raise test... more In 2001, the enactment of the No Child Left Behind Act intensified the pressure on school districts to raise test scores, close achievement gaps, and turn around low-performing schools. In response, a large number of school districts have adopted interim or benchmark assessments to be administered periodically throughout the school year in anticipation of annual state tests. This report focuses on middle-school mathematics teachers‘ uses of interim and benchmark assessment results. We present findings from two-stage interviews with 30 teachers in seven districts across two states. While teachers' uses of assessment information varied, few gained substantive insights about students' mathematical understanding. Instead, teachers most frequently retaught standards or items with the lowest scores and focused on procedural competence. Although many teachers expressed an interest in using assessment results to inform instruction, they reported minimal professional development to this end, and often had a different understanding regarding the intended use of the assessments than did district leaders.

Pythagoras in China, or the Gou Gu Procedure

by Iolanda Guevara

Differences in learning geometry among high and low spatial ability pre-service mathematics teachers

by Darryl Corey