- Judith Grabiner, "Why should historical truth matter to math teachers?"
- David Hammer, "Attending and responding to students' epistemologies in physics instruction"
- Anna Sierpinska, "Institutional perspective in research in mathematics education"
Based on the notions of social and socio-mathematical norms we
investigate how these are established during the interactions of
pre-service teachers who solve mathematical problems. Norms identified
in relevant studies are found in our case too; moreover, we have found
norms related to particular aspects of the problems posed. Our results
show that most of these norms, once established, enhance the
problem-solving process. However, exceptions do exist, but they have a
local orientation and a relatively small influence.
- Heinz Steinbring wrote an article in ZDM, called: "Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?" In this article he shows how the didactical tradition in Germany has evolved in order to respond to new ideas and approaches in mathematics education.
- Jeff C. Marshall et al. wrote an article in International Journal of Science and Mathematics Education, called "K-12 Science and Mathematics Teachers’ Beliefs About and Use of Inquiry in the Classroom". Here they describe how they made and used a survey instrument in order to measure mathematics and science teachers' beliefs about and use of
inquiry in the classroom.
- Vanessa Ramos-Christian et al. wrote an article in Early Childhood Education Journal, called "Math Fluency: Accuracy Versus Speed in Preoperational and Concrete Operational First and Second Grade Children". They present a study that aims to investigate the relationship between cognitive ability and math fluency with 38 first and second grade
elementary aged children.
- Ana Isabel Sacristán and Richard Noss wrote an article in International Journal of Computers for Mathematical Learning, called "Computational Construction as a Means to Coordinate Representations of Infinity". They describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects.
Article discusses the value of problem solving in setting the stage for future math studies and thoroughly discusses three problems that can be solved verbally and algebraically.
- A congruence challenge, by Francis Lopez-Real
- Farewell coursework! by Loraine Rigglesford
- Learning about primes, by Alec McEachran (this is the centre feature, and is freely available!)
- The city of mathematics, by Adrian Watts and Class 4A
- Functioning with geometry and fractions, by Dereck Ball and Barbara Ball
Yesterday, the CMEG-5 conference started. The 5th International Conference on Creativity in Mathematics and the Education of Gifted Students is held in Israel, and it closes on Thursday. One of the interesting plenary lectures is held by Gerald Goldin of Rutgers University, USA. The title of his presentation is "The Affective Dimension of Mathematical Inventiveness", and here is the abstract with references:
Recent research points to the fundamental importance of affect in mathematical learning and problem solving. Some aspects of the structure of mathematics, as a disciplined way of generating knowledge and as a traditional school subject, can raise high affective barriers to students’ curiosity and inventiveness.
In this talk I shall first highlight some theoretical ideas important in current research, including: affect as an internal, interactive representational system; affective pathways; meta-affect; mathematical intimacy, integrity, and personal identity; and archetypal affective structures. I shall then discuss how we can develop affective processes and structures – in our students and in ourselves – that foster mathematical ability and mathematical creativity.
DeBellis, V. A. & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63 (2), 131-147.
Epstein, Y., Schorr, R. Y., Goldin, G. A., Warner, L., Arias, C., Sanchez, L., Dunn, M., & Cain, T. R. (in press). Studying the affective/social dimension of an inner-city mathematics class. Proceedings of the 29th Annual Conference of PME-NA (Lake Tahoe, Nevada, November 2007).
Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2, 209-219.
Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. InLeder, G., Pehkonen, E., & Törner, G. (Eds.), Beliefs: A Hidden Variable in Mathematics Education? Dordrecht: Kluwer (pp. 59-72).
P.S. Goldin's article can be read in its entirety in the conference proceedings, which is freely available as a downloadable PDF!
International Electronic Journal of Mathematics Education has delivered its first of three issues this year. The list of contents displays the following articles:
Examining “Mathematics For Teaching” Through An Analysis Of Teachers’ Perceptions Of Student “Learning Paths”
Donna Kotsopoulos and Susan Lavigne, Canada
Revisiting the Influence of Numerical Language Characteristics on Mathematics Achievement: Comparison among China, Romania, and U.S.
Jian Wang, Emily Lin, Madalina Tanase, and Midena Sas, USA
The Effects Of Grade Level, Gender, And Ethnicity On Attitude And Learning Environment In Mathematics In High School
Thienhuong N. Hoang , USA
Teacher Instructional Methods and Student Attitudes towards Mathematics
M. K. Akinsola, Botswana and F.b. Olowojaiye, Nigeria
The download links don't appear to work at the time of writing this, but that will hopefully be fixed soon!
- Chun-Yi Lee and Ming-Puu Chen
- Bridging the gap between mathematical conjecture and proof through computer-supported cognitive conflicts
Teaching Mathematics and its Applications Advance Access published on October 1, 2007
Teaching Mathematics Applications 2008 27: 1-10; doi:10.1093/teamat/hrm014
[Abstract] [PDF] [Request Permissions]
- Kris Green and Allen Emerson
- Reorganizing freshman business mathematics I: background and philosophy
Teaching Mathematics and its Applications Advance Access published on November 21, 2007
Teaching Mathematics Applications 2008 27: 11-23; doi:10.1093/teamat/hrm017
[Abstract] [PDF] [Request Permissions]
- Bulent Guven
- Using dynamic geometry software to convey real-world situations into the classroom: the experience of student mathematics teachers with a minimum network problem
Teaching Mathematics and its Applications Advance Access published on December 11, 2007
Teaching Mathematics Applications 2008 27: 24-37; doi:10.1093/teamat/hrm018
[Abstract] [PDF] [Request Permissions]
- Billy J. Duke, Jerry F. Dwyer, Jennifer Wilhelm, and Barbara Moskal
- Complex variables in junior high school: the role and potential impact of an outreach mathematician
Teaching Mathematics and its Applications Advance Access published on December 3, 2007
Teaching Mathematics Applications 2008 27: 38-47; doi:10.1093/teamat/hrm019
[Abstract] [PDF] [Request Permissions]
Getting the best out of Excel
Teaching Mathematics and its Applications Advance Access published on August 6, 2007
Teaching Mathematics Applications 2008 27: 48-52; doi:10.1093/teamat/hrm013
Studying the Effects of Professional Development: The Case of the NSF's Local Systemic Change Through Teacher Enhancement Initiative
Daniel J. Heck, Eric R. Banilower, Iris R. Weiss and Sharyn L. Rosenberg
First-Grade Basic Facts: An Investigation Into Teaching and Learning of an Accelerated, High-Demand Memorization Standard
Valerie J. Henry and Richard S. Brown
Standards-based Mathematics Curricula and Middle-Grades Students' Performance on Standardized Achievement Tests
Thomas R. Post, Michael R. Harwell, Jon D. Davis, Yukiko Maeda, Arnie Cutler, Edwin Andersen, Jeremy A. Kahan and Ke Wu Norman
BOOK REVIEW: Looking Inside Chinese Mathematics Education: A Review of How Chinese Learn Mathematics: Perspectives from Insiders
Jon R. Star and Kuo-Liang Chang
In this interesting article, the researchers describe an examination of strategies and misconceptions regarding number sense with 280 pre-service elementary teachers from Taiwan. In the test, these pre-service teachers responded to a series of real-life problems. In the following, I quote the abstract:
About one-fifth of the pre-service teachers applied number sense-based
strategies (such as using benchmarks appropriately or recognizing the
number magnitude) while a majority of pre-service teachers relied on
rule-based methods. This finding is consistent with earlier studies in
Taiwan that fifth, sixth, and eighth grade students tended to rely
heavily on written methods rather than using number sense-based
strategies. This study documents that the performance of pre-service
elementary teachers on number sense is low. If we want to improve
elementary students’ knowledge and use of number sense, then action
should be taken to improve the level of their future teachers’ number
Comparing theoretical frameworks enacted in experimental research: TELMA experience. The article is written by M. Cerulli, J. Trgalova, M. Maracci, G. Psycharis and J.-P. Georget. In the article, they present a methodology developed by six European research teams. The methodology is:
based on a cross-experimentation, showing how it gave insight to the
understanding of each team’s research and on the relationship between
theoretical frameworks and experimental research (from the abstract).
(...) that the later Wittgenstein presents us with an unreservedly social interpretation of mathematics that favours a certain direction for our research on mathematics education. According to this interpretation, mathematics could be considered to be constituted exclusively in complex social processes, in which case any conception of it mirroring a pre-existing world of mathematical objects is rejected. To contrast with the Wittgensteinian position, a Platonist position is presented and the two philosophical positions are discussed in relation to their significance for mathematics education (from the abstract).
The results indicate that educational investments are an important mediator of socioeconomic and racial/ethnic disparaties, completely explaining the black-white reading gap at kindergarten entry and consistently explaining 20 percent to 60 percent and 30 percent to 50 percent of the black-white and Hispanic-white disparities in the growth parameters, respectively, and approximately 20 percent of the socioeconomic gradients.The assessments in the study included mathematics areas such as number sense, properties, operations, measurement, geometry and spatial sense, data analysis, statistics, probability, patterns, algebra, and functions (p. 7).
Cheadle, Jacob, E. (2008). Educational investment, family context, and children's math and reading growth from kindergarten through the third grade. Sociology of Education, 81(1):1-31.
Educational Researcher has released their first issue of the year, and the list of contents can be found online. Although not a journal within our field precisely, the articles herein focus on issues that are at least indirectly related to research in mathematics education. The feature article in this issue is:
Robert E. Slavin
Educational Researcher 2008 37: 5-1
These findings provide evidence that children are, in fact, creating
and recreating ideas about different aspects of written numbers such as
the role of punctuation marks before necessarily being able to fully
articulate how written numbers work and before being formally taught,
though they have obviously been exposed from an early age to these
particular aspects of written numbers.
The report is available as downloadable pdf. I have copied the description of the report below:
This report documents and examines the relationship between the number
and types of math courses taken in the 11th and 12th grade and growth
in mathematics proficiency over the same time period. Using data from
the Education Longitudinal Study of 2002 (ELS:2002), the analysis
identifies the coursetaking sequences most prevalent among contemporary
high school students in their junior and senior years, sociodemographic
characteristics of the students who follow these course sequences, and
the association between specific courses and course sequences and
mathematics gains over the last two years of high school. Because most
students (94 percent) entered the second half of high school with a
mastery of basic mathematics skills such as simple arithmetic and
operations, most learning during this time was in intermediate-level
mathematics skills and concepts. For example, the percentage of
students with an understanding of simple problem solving skills grew
from 53 to 65 percentage points over the two year period. In terms of
learning in specific content areas, the largest gains in intermediate
skills such as simple operations and problem solving were made by those
who followed the geometry–algebra II sequence. The largest gains in
advanced skills such as derivations and making inferences from
algebraic expressions were made by students who took precalculus paired
with another course. The smallest gains were made by students who took
one mathematics course or no mathematics courses during their last 2
Hans Freudenthal was born into a Jewish family, September 17, 1905. He was born in Germany (Luckenwalde), and in 1930 he defended a thesis on topological groups at the University of Berlin. The same year, he was invited to Amsterdam as the assistant of LEJ Brouwer.
Early in his career, Freudenthal was involved with topology and algebra, and he also worked on Lie groups for a few years. In his later years, though, he became more and more interested in mathematics education. He wrote several important books and numerous scientific articles in this field.
The Freudenthal Institute in Utrecht, Netherlands, is named after him, and his theories have strongly influenced the Dutch tradition called Realistic Mathematics Edcuation.
- The Wikipedia article about Hans Freudenthal (feel free to contribute to this - it might use some improvement!)
- The biography at the MacTutor History of Mathematics archive
- Mathematics as an educational task (1973)
- Weeding and Sowing: Preface to a Science of Mathematical Education (1977)
- Didactical Phenomenology of Mathematical Structures (1983)
- Revisiting Mathematics Education: China Lectures (1991)
- The politics of mathematics education
- Cultural and social aspects of mathematics teaching and learning
- The sociology of mathematics and mathematics education
- Alternative research methodologies in mathematics education
The plenary lectures are:
- "Reinventing" Freire: Mathematics Education for Social Transformation (Eric Gutstein, University of Illinois-Chicago, USA)
- Describing teacher change: Interactions between teacher
moves and learner contributions (Karin Brodie, University of Witswatersrand, South Africa)
- Equity-in-Quality: Towards a Theoretical Framework (Murad Jurdak, American University of Beirut, Lebanon)
- Order of the World or Order of the Social. Conceptions of
Mathematics and Their Importance to Mathematics Education (Ole Ravn Christensen, Aalborg University, Denmark)
The February issue of Teaching Children Mathematics presents the following articles:
Tiering and Scaffolding: Two Strategies for Providing Access to Important Mathematics
Why Math Blogs?
Shirley M. Pyon
Design of Activities on Numerical Representations Based on Cognitive Research
Eleftheria R. Kalifatidou
Heather McLeay discusses a visual representation to aid the multiplication of fractions.
In the third of a series of four articles, Ian Thompson deconstructs the primary national strategy’s approach to written multiplication. The first two articles in this series were published in MT202 and MT204.
Tony Harries and Patrick Barmby explore the use of visual representations, in particular the array, in the teaching of multiplication in the primary school.
Pre-Service Elementary School Teachers’ Learning Styles and Attitudes towards Mathematics
Murat Peker and Seref Mirasyedioglu
[Full Text in PDF] (Size: 244 KB)
The Effects of Mathematics Anxiety on Matriculation Students as Related to Motivation and Achievement
Effandi Zakaria and Norazah Mohd Nordin
[Full Text in PDF] (Size: 158 KB)
Science and Mathematics Teachers’ Experiences, Needs, and Expectations Regarding Professional Development
Kathryn Chval, Sandra Abell, Enrique Pareja, Kusalin Musikul and Gerard Ritzka
[Full Text in PDF] (Size: 291 KB)
The article is about prospective teachers' beliefs and views about teaching and learning, and the way these beliefs and views affect their teaching once they have finished their studies. The aim of this particular project is to explore the effects of learning via computerised project-based learning. In order to assess the prospective teachers' change in views, the following data was gathered: two open questionnaires, written portfolios, and transcripts of class discussions.
Mathematics Teacher has released their February issue, with the following headlines:
Optimization of Cubic Polynomial Functions without Calculus
Ronald D. Taylor Jr. and Ryan Hansen
Are You Connected? Fostering Exploration with Unexpected Graphs
Michael Todd Edwards and Jeffrey A. Reinhardt
Explorations with 142857: Connecting the Elementary with the Advanced
Randall E. Groth
Analyzing Online Discourse to Assess Students’ Thinking
Randall E. Groth
Connecting Students’ Informal Language to More Formal Definitions
Jon D. Davis
Reading Texts and Writing Problems to Improve Problem Solving
Ariana Stanca P. Vacaretu
Poverty: Teaching Mathematics and Social Justice
Leah P. McCoy
Building Intuitive Arguments for the Triangle Congruence Conditions
Beyond Teachers’ Sight Lines: Using Video Modeling to Examine Peer Discourse
The last article is a Free preview article. This is an interesting article on discourse analysis and video models. Check it out!
The March issue of International Journal of Science and Mathematics Education is out, and it displays nine articles:
|Authors||Isabel Escudero and Victoria SÁnchez|
|Text||PDF (272 kb)|
|Authors||Jennifer Anne Wilhelm, Walter S. Smith, Kendra L. Walters, Sonya E. Sherrod and Judith Mulholland|
|Text||PDF (348 kb)|
|Text||PDF (286 kb)|
|Authors||Hsin-Kai Wu, Ying-Shao Hsu and Fu-Kwun Hwang|
|Text||PDF (288 kb)|
|Author||Gabriel J. Stylianides|
|Text||PDF (335 kb) HTML|
|Authors||Catherine Martin-Dunlop and Barry J. Fraser|
|Text||PDF (359 kb)|
|Authors||Susan A. Everett, Gail R. Luera and Charlotte A. Otto|
|Text||PDF (207 kb)|
|Authors||Chia-Ju Liu, Brady Michael Jack and Houn-Lin Chiu|
|Text||PDF (232 kb)|
|Authors||Vicente Mellado, María Luisa Bermejo, Lorenzo J. Blanco and Constantino Ruiz|
|Text||PDF (298 kb)|
Educational Studies in Mathematics has already published the March issue of this year, with the following articles:
|Text||PDF (420 kb) HTML|
|Authors||Matthew Inglis and Adrian Simpson|
|Text||PDF (378 kb) HTML|
|Text||PDF (246 kb) HTML|
|Authors||Sean Larsen and Michelle Zandieh|
|Text||PDF (164 kb) HTML|
|Text||PDF (240 kb) HTML|
Journal of Mathematics Teacher Education is arguably one of the most prestigious journals within our field, and it has just published the first issue of this year. There are five interesting articles in this issue:
|Authors||Plinio C. Moreira and Maria M. David|
|Text||PDF (257 kb) HTML|
|Authors||Jane-Jane Lo, Theresa J. Grant and Judith Flowers|
|Text||PDF (259 kb) HTML|
|Authors||Merrilyn E. Goos and Anne Bennison|
|Text||PDF (202 kb) HTML|
|Authors||Thuy Nguyen Thanh, Rijkje Dekker and Martin J. Goedhart|
|Text||PDF (323 kb) HTML|
|Text||PDF (95 kb) HTML|
ZDM - The International Journal on Mathematics Education (formerly known as Zentralblatt für Didaktik der Mathematik) has released their first issue of this year, with the theme: "From Patterns to Generalization: Development of Algebraic Thinking". The issue has the following contents (only the titles are displayed here - click on the links to investigate further!):
- Generalization in algebra: the foundation of algebraic thinking and reasoning across the grades
- Algebraic thinking with and without algebraic representation: a three-year longitudinal study
- Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns
- Seventh-grade students’ representations for pictorial growth and change problems
- The role of examples in forming and refuting generalizations
International Journal of Mathematics Education in Science and Technology has published their first issue this year, and it has the following original articles:
Authors: T. Bergqvist; J. Lithner; L. Sumpter
Authors: Carryn Bellomo; Remy Strapp
Authors: B. Divjak; Z. Erjavec
A simple yet accurate method for students to determine asteroid rotation periods from fragmented light curve data
Author: R. A. Beare
Author: K. Tarvainen
The evaluation of the error term in some Gauss-type formulae for the approximation of Cauchy Principal Value integrals
Author: H. V. Smith
Author: H. K. Pathak
The first issue of The Montana Mathematics Enthusiast this year includes a forum for "ethics and values in mathematics, teaching and learning". There are also a number of interesting feature articles:
9. Murad Jurdak (Lebanon)
|The Action Map as a Tool for Assessing Situated Mathematical Problem Solving Performance||pp.67-78|
10. M.K Akinsola (Botswana)
|Relationship of some psychological variables in predicting problem solving ability of in-service mathematics teachers||pp.79-100|
11. Kristin Umland (New Mexico, USA)
|A reflection on mathematical cognition: how far have we come and where are we going?||pp.101-116|
12. Yuichi Handa (California, USA)
|Reflections upon Teaching a Poorly-Conceived Lesson||pp.117-124|
13. Jaehoon Yim, Sanghun Song, Jiwon Kim (South Korea)
|Mathematically gifted elementary students' revisiting of Euler's polyhedron theorem||pp.125-142|
MONTANA FEATURE ARTICLE
14. David M. Davison and Johanna E. Mitchell (Montana, USA)
|How is Mathematics Education Philosophy Reflected in the Math Wars?||pp.143-154|
- A BRIEF REPORT: An Existence Proof: Successful Joint Implementation of
the IMP Curriculum and a 4 x 4 Block Schedule at a Suburban U.S. High
Steven L. Kramer and Regina Keller
- What Students Notice as Different Between Reform and Traditional Mathematics Programs
Jon R. Star, John P. Smith III and Amanda Jansen
- Teaching and Learning Fraction Addition on Number Lines
Andrew Izsák, Erik Tillema and Zelha Tunç-Pekkan
- Curriculum Use While Learning to Teach: One Student Teacher’s Appropriation of Mathematics Curriculum Materials
Gwendolyn M. Lloyd
- BOOK REVIEW: The Three Rs of Social Justice: A Review of Reading and Writing the World with Mathematics: Toward a Pedagogy for Social Justice
Tonya Gau Bartell and Thomas P. Carpenter
I know, this sounds like a huge challenge, and it is! I will, however, do my best to follow up on it, and if anyone else is interested in joining this attempt, I would like to invite you to contribute. This starts off as something I find interesting for myself, but I hope that several colleague researchers and educators will find this attempt interesting as well.