While reading the articles assembled in this volume, one cannot help asking Why gestures? What’s all the fuss about them? In the last few years, the fuss is, indeed, considerable, and not just here, in this special issue, but also in research on learning and teaching at large. What changed? After all, gestures have been around ever since the birth of humanity, if not much longer, but until recently, not many students of human cognition seemed to care. In this commentary, while reporting on what I saw while scrutinizing this volume for an answer, I will share some thoughts on the relationship between gesturing and speaking and about their relative roles in mathematical thinking.
journal-articles
Measuring quality of mathematics teaching in early childhood
The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics education, so too does the focus on teaching quality. This paper reviews nine instruments designed to measure mathematics teaching quality—their theoretical bases, foci, and psychometrics—and examines their appropriateness for administration in early childhood settings. Three of the nine measures are identified as having highly desirable characteristics, with one of them specifically designed for early childhood administration. The measures, our review process, and our recommendations for practice are presented. As school divisions and teacher educators examine teaching quality, they will be better able to support their teachers’ practice, and better able to reap the benefits in improved child outcomes.
ZDM, November 2008
- Mathematics education: new perspectives on gender, by Gilah Leder and Helen Forgasz
- Moving towards a feminist epistemology of mathematics, by Leone Burton†
- The emergence of women on the international stage of mathematics education, by Fulvia Furinghetti
- Israeli Jewish and Arab students’ gendering of mathematics, by Helen J. Forgasz and David Mittelberg
- Gender, technology and attitude towards mathematics: a comparative longitudinal study with Mexican students, by Sonia Ursini and Gabriel Sánchez
- On the role of computers and complementary situations for gendering in mathematics classrooms, by Helga Jungwirth
- Exploring gender factors related to PISA 2003 results in Iceland: a youth interview study, by Olof Bjorg Steinthorsdottir and Bharath Sriraman
- Gender differences in the mathematics achievements of German primary school students: results from a German large-scale study, by Henrik Winkelmann, Marja van den Heuvel-Panhuizen and Alexander Robitzsch
- Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom, by Jae Hoon Lim
- Images of mathematicians: a new perspective on the shortage of women in mathematical careers, by Katrina Piatek-Jimenez
- Equity in mathematics education: unions and intersections of feminist and social justice literature, by Laura Jacobsen Spielman
- Progress and stagnation of gender equity: contradictory trends within mathematics research and education in Sweden, by Gerd Brandell
- Gender in mathematics relationality: counseling underprepared college students, by Jillian M. Knowles
- Stepping beyond high school mathematics: a case study of high school women, by Charlene Morrow and Inga Schowengerdt
- Goos, Stillman and Vale: teaching secondary mathematics: research and practice for the 21st century, by Gaye Williams
The theme of this issue is: Mathematics Education: New Perspectives on Gender.
JMTE, November 2008
- Education for the knowledge to teach mathematics: it all has to come together, by Peter Sullivan
- Teachers’ perceptions of assessments of their mathematical knowledge in a professional development course, by Michelle T. Chamberlin, Jeff D. Farmer and Jodie D. Novak
- Learning mathematics for teaching in the student teaching experience: two contrasting cases, by Blake E. Peterson and Steven R. Williams
- Mathematical belief change in prospective primary teachers, by Peter Grootenboer
- Toward a framework for the development of mathematical knowledge for teaching, by Jason Silverman and Patrick W. Thompson
Personally, I find this issue particularly interesting, as it has a strong focus on mathematical content knowledge as well as beliefs. These are the main focus areas of my own research as well. I especially find the article by Silverman and Thompson interesting, and their attempt to approach a framework for the development of mathematical knowledge for teaching provides a nice overview of the research that has been done after Lee Shulman presented his ideas about Pedagogical Content Knowledge.
ESM, November issue
- Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks, by Ivy Kidron
- Students’ images and their understanding of definitions of the limit of a sequence, by Kyeong Hah Roh
- Deductive reasoning: in the eye of the beholder, by Michal Ayalon and Ruhama Even
- Signifying “students”, “teachers” and “mathematics”: a reading of a special issue, by Tony Brown
- On semiotics and subjectivity: a response to Tony Brown’s “signifying ‘students’, ‘teachers’, and ‘mathematics’: a reading of a special issue”, by Norma Presmeg and Luis Radford
- Review of the proceedings of the 2001, 2003 and 2005 French summer schools in Didactics of Mathematics, by Rudolf Sträßer
- Brian Griffiths (1927–2008) – his pioneering contributions to mathematics and education, by Keith Jones and Joanna Mamona-Downs
Estimating Iraqi deaths
In this paper, I present an account of attempts to quantify deaths of Iraqis during the occupation by US and other forces since the invasion of March 2003, and of the reactions to these attempts. This story illuminates many aspects of current socio-political reality, particularly, but by no means exclusively, in the United States. Here, these aspects are selectively discussed in relation to the overarching themes of what the story illuminates about the uses of statistical information in society and about shortcomings in mathematics education.
Knowledge and confidence of pre-service mathematics teachers
To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers’ knowledge as well as teachers’ own perceptions about their needs. By focusing on pre-service teachers’ knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers’ knowledge in mathematics and pedagogy for teaching as containing both teachers’ perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers’ own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers’ general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study’s findings indicate the feasibility and importance of conceptualizing the notion of teachers’ knowledge in mathematics and pedagogy for teaching to include teachers’ perceptions. The applicability and implications of this expanded notion of teachers’ knowledge is then discussed.
MTL, Volume 10 Issue 4 2008
- Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell, by Mary Kay Stein, Randi A. Engle, Margaret S. Smith and Elizabeth K. Hughes
- Picture Books as an Impetus for Kindergartners’ Mathematical Thinking, Marja van den Heuvel-Panhuizen and Sylvia van den Boogaard
- Mathematics Teaching and Learning as a Mediating Process: The Case of Tape Diagrams, by Aki Murata
IEJME, October 2008
- Do You Want Me to Do It with Probability or with My Normal Thinking? Horizontal and Vertical Views on the Formation of Stochastic Conceptions, by Susanne Prediger, Germany
- Teachers’ Perceptions of Mathematics Content Knowledge Assessments in Professional Development Courses, by Michelle T. Chamberlin, Robert A. Powers and Jodie D. Novak, USA
- Mathematics Anxiety Among 4th And 5th Grade Turkish Elementary School Students, by Fulya Yüksel-Şahin, Türkiye
- A Comparison of Placement in First-Year University Mathematics Courses Using Paper and Online Administration of a Placement Test, by Phyllis A. Schumacher and Richard M. Smith, USA
- Senior Student Teachers’ Understanding of Relations Between Function, Equation, and Polynomial Concepts as Conceptual Knowledge, Danyal Soybas, Yılmaz Aksoy and Hayri Akay, Türkiye
From arithmetical thought to algebraic thought
The introduction of the concept of the variable represents a critical point in the arithmetic–algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of “unknown” interferes with the interpretation of the variable “in functional relation” and the kinds of languages used by the students in problem-solving. We also wanted to study the concept of the variable in the process of translation from algebraic language into natural language. We present two experimental studies. In the first one, we administered a questionnaire to 111 students aged 16–19 years. Drawing on the conclusions of this research we carried out the second study with two pairs of students aged 16–17 years.