Mathematics education research links 03/31/2008

ATM • Conference 2008 - Keele University

tags: conference, education, mathematics, research


Essential skills for a math teacher

Education Week has an interesting article about the uncertainties about the skills that are needed to be a successful mathematics teacher. The point of departure for the article is the recent report by the National Mathematics Advisory Panel in the U.S. The report has several suggestions about the curriculum, cognition, instruction, etc. When it comes to the skills that are needed to become a good mathematics teacher, though, the answers were fewer:

Research does not show conclusively which professional credentials demonstrate whether math teachers are effective in the classroom, the report found. It does not show what college math content and coursework are most essential for teachers. Nor does it show what kinds of preservice, professional-development, or alternative education programs best prepare them to teach.
One of the panel members, Deborah Loewenberg Ball, was interviewed in the article, and she believed that it was in the area of improving teaching that the emphasis should be set in the years to come:
“We should put a lot of careful effort over the next decade into this issue so that we can be in a much different place 10 years from now.”
There appears to be a lot of work and research to do within this area. There is much agreement that the teacher is important, and the quality of the math teacher has an impact on the students' results.
But the 90-page report also says it is hard to determine what credentials and training have the strongest effect on preparing math teachers to teach, and teach well. Research has not provided “consistent or convincing” evidence, for instance, that students of certified math teachers benefit more than those whose teachers do not have that licensure, it found.
So, the question that Ball and her team has focused a lot on in their research still remains important for researchers in the future: What kind of knowledge is it that teachers need?

The role of scaling up research

A new article has been published online at Educational Studies in Mathematics. The article is entitled: "The role of scaling up research in designing for and evaluating robustness", and it is written by J. Roschelle, D. Tatar, N. Shechtman and J. Knudsen. Here is the abstract of the article:

One of the great strengths of Jim Kaput’s research program was his relentless drive towards scaling up his innovative approach to teaching the mathematics of change and variation. The SimCalc mission, “democratizing access to the mathematics of change,” was enacted by deliberate efforts to reach an increasing number of teachers and students each year. Further, Kaput asked: What can we learn from research at the next level of scale (e.g., beyond a few classrooms at a time) that we cannot learn from other sources? In this article, we develop an argument that scaling up research can contribute important new knowledge by focusing researchers’ attention on the robustness of an innovation when used by varied students, teachers, classrooms, schools, and regions. The concept of robustness requires additional discipline both in the design process and in the conduct of valid research. By examining a progression of three studies in the Scaling Up SimCalc program, we articulate how scaling up research can contribute to designing for and evaluating robustness.


When, how, and why prove theorems?

The full title of this new ZDM article is: "When, how, and why prove theorems? A methodology for studying the perspective of geometry", and it is written by P. Herbst and T. Miyakawa.

Every theorem has a proof, but not every theorem presented in schools (not only in the U.S., although this is the focus of the article). Why is that? Here is the abstract of the article, which truly raises some important questions:

While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.
Blogged with the Flock Browser

Promoting student collaboration

Megan E. Staples wrote an article called: "Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom". The article was published online in Journal of Mathematics Teacher Education on Wednesday. Here is the abstract of the article:

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.

Several researchers have addressed the issue of collaboration and group work, and Staples analyzes the role of one teacher in this respect. Staples observed 39 lessons in the study, and data was collected through field notes, reflective memos, and 26 lessons were also video-taped. She also conducted interviews with most of the students and the teacher, and she collected curriculum documents, etc. During the data analysis, four categories emerged that were critical for understanding the teacher's role (p. 8):
  1. Promoting individual and group accountability
  2. Promoting positive sentiment among group members
  3. Supporting student–student exchanges with tools and resources
  4. Supporting student mathematical inquiry in direct interaction with groups
These categories are used as point of departure for the organization and presentations of the results in the article.

The classroom is a complex system, and this is something Staples discuss a lot in the article. Understanding this complexity and being able to analyze it, is something she emphasizes as being important for both future and current teachers.

And interesting article. In the theoretical foundations, she refers (among others) to the works of researchers like E. Cohen and J. Boaler.


Norma 08 - final program

The final program of the Norma 08 conference has arrived (download as pdf). I am not going to repeat the entire program here, but I will point at the plenary lectures that will be presented at the conference:

  1. Monday, April 21, 16:30-17:30 - Jeppe Skott (Theme B)
  2. Tuesday, April 22, 11:00-12:00 - Paul Drijvers (Theme C)
  3. Wednesday, April 23, 11:00-12:00 - Eva Jablonka (Theme D)
  4. Thursday, April 24, 11:00-12.00 - Michèle Artigue (Theme A)

JMTE, April 2008

The April issue of Journal of Mathematics Teacher Education has been published. The following articles are enclosed:

This is an interesting collection of articles, addressing a multitude of perspectives from the use of video in teacher education in the article by Jon R. Star and Sharon K. Strickland to Jesse L.M. Wilkins' focus on the relationship between content knowledge, attitudes, beliefs and practices by elementary teachers. I find the latter article especially interesting, since it aims at analyzing relationships between knowledge, beliefs, attitudes and practices at the same time. All four are large fields of research, and this is therefore a brave attempt. I would like to question the choice of investigating the teachers' practice through self-reporting in a survey though.


National Mathematics Advisory Panel

In the U.S., the National Mathematics Advisory Panel (on request from the President himself) has delivered a report to the President and the U.S. Secretary of Education. This final report was delivered on March 13, and is freely available for anyone to download (pdf or Word document). I know this is old news already, but I will still present some of the highlights from the report here. Be also aware that there will be a live video webcast of a discussion of the key findings and principle messages in the report. The webcast will be held tomorrow, Thursday March 26, 10-11.30 a.m. Eastern Time. This discussion will be lead by Larry R. Faulkner (Chair of the Panel) and Raymond Simon (U.S. Deputy Secretary of Education).

A key element of the report is a set of "Principal Messages" for mathematics education. This set of messages consists of six main elements (quoted from pp. xiii-xiv):

  • The mathematics curriculum in Grades PreK-8 should be streamlined and should emphasize a well-defined set of the most critical topics in the early grades.
  • Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical achievement.
  • Our citizens and their educational leadership should recognize mathematically knowledgeable classroom teachers as having a central role in mathematics education and should encourage rigorously evaluated initiatives for attracting and appropriately preparing prospective teachers, and for evaluating and retaining effective teachers.
  • Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely "student centered" or "teacher directed." Research indicates that some forms of particular instructional practices can have a positive impact under specified conditions.
  • NAEP and state assessments should be improved in quality and should carry increased emphasis on the most critical knowledge and skills leading to Algebra.
  • The nation must continue to build capacity for more rigorous research in education so that it can inform policy and practice more effectively.
During their 20 month long work, the Panel split in five task groups, where they analyzed the available evidence in the following areas:
  • Conceptual knowledge and skills
  • Learning processes
  • Instructional practices
  • Teachers and teacher education
  • Assessment
These groups are visible in the main chapter headings of the report.

After having presented their principle messages, the panel present 45 main findings and recommendations for the further development of mathematics education in the U.S. These 45 findings and recommendations are split in the following main groups (strongly resembling the list of task groups above):
  • Curricular content
  • Lesson processes
  • Teachers and teacher education
  • Instructional practices
  • Instructional materials
  • Assessment
  • Research policies and mechanisms
These are the main issues in the forthcoming video webcast. All in all, it is an interesting report, so go ahead and read it!


Mathematics Teacher, April 2008

The April issue of Mathematics Teacher has arrived, and it contains the following three articles:

The last article is a free preview article, and is downloadable for everyone. The author has a focus on women in mathematics, and she discusses her use of cooperative groups, Blackboard (a course managment system) and the internet as means to facilitate meaningful mathematical discourse. The venue for examining these types of mathematical discourse is a course called "Women in Mathematics", which the author developed in her university. They studied the following women mathematicians in the course:
All in all, this is an interesting description of an interesting university course. At a meta-level, this article also address issues of how to use history of mathematics in your teaching. At the end of the article, the writer proposes that anecdotes and activities about women mathematicians can be used in "ordinary" mathematics courses, and this indicates a certain "direct" use of history.

Useless arithmetic

Linda Pilkey-Jarvis and Orrin H. Pilkey have written an article in Public Administration Review about the use of mathematical models in environmental decision making. Mathematical models are used extensively in the context of environmental issues and natural resources, and when these methods were first used, they were thought to represent a bridge to a better and more foreseeable future. There has also been much controversy in this respect, and the authors pose the question whether the optimism about the use of these models were ever realistic. In this article, they review the two main types of such models: quantitative and qualitative.

Although both present us with a generalized perspective on a natural problem, they are not equal in terms of predictive power. The first type—quantitative models—can be used as a surrogate for nature, whereas the second—qualitative models—do the same but with less accuracy.

After a review of these types of models, they provide a list of ten lessons that policy makers should learn when it comes to quantitative mathematical modeling:
  1. The outcome of natural processes on the earth’s surface cannot be absolutely predicted.
  2. Examine the excuses for predictive model failures with great care and skepticism.
  3. Did the model really work? Examine claims of past "successes" with the same level of care and skepticism that "excuses" are given.
  4. Calibration of models doesn’t work either.
  5. Constants in the equations may be coefficients or fudge factors.
  6. Describing nature mathematically is linking a natural flexible, dynamic system with a wooden, inflexible one.
  7. Models may be used as "fig leaves" for politicians, refuges for scoundrels, and ways for consultants to find the truth according to their clients’ needs.
  8. The only show in town may not be a good one.
  9. The mathematically challenged need not fear models and can learn how to talk with a modeler.
  10. When humans interact with the natural system, accurate predictive mathematical modeling is even more impossible.
These points are directed at policy makers, but I think several of them are also relevant for students at university level (and perhaps also upper secondary). In a simplified form, I think some of these points might even be relevant for younger pupils.
In the wrapping up of the article, they clarify their main argument:

Our argument in this article has been that mathematical models are wooden and inflexible next to the beautifully complex and dynamic nature of our earth. Quantitative models can condense large amounts of difficult data into simple representations, but they cannot give an accurate answer, predict correct scenario consequences, or accommodate all possible confounding variables, especially human behavior.

Pilkey-Jarvis, L. & Pilkey, O.H. (2008). Useless Arithmetic: Ten Points to Ponder When Using Mathematical Models in Environmental Decision Making. Public Administration Review 68 (3) , 470–479 doi:10.1111/j.1540-6210.2008.00883_2.x


NCME Annual Meeting

Yesterday, NCME (National Council on Measurement in Education) started their annual meeting. NCME's mission is among other things to "Advance the science of measurement in the field of education", so the focus is not on mathematics education solely. There are, however several presentations that deal with mathematics in the program. Here are the ones that I could find:

  • Shelley Ragland, James Madison University, Christina Schneider, CTB/McGraw- Hill, Ching Ching Yap, University of South Carolina, Pamela Kaliski, James Madison University: The Effect of Classroom Assessment Professional Development on English Language Arts and Mathematics Student Achievement: Year 2 Results
  • Carol Parke, Duquesne University, Gibbs Kanyongo, Duquesne University, Steven Kachmar, Duquesne University: Examining Relationships among Large-Scale Mathematics Assessment Performance, Grade Point Average, and Coursework in Urban High Schools
  • Michelle Boyer, CTB/McGraw-Hill, Enrique Froemel, Office of Student Assessment, Evaluation Institute, Supreme Education Council, State of Qatar, Richard Schwarz, CTB/McGraw-Hill: Obtaining Comparable Scores for Arabic and English Tests of Mathematics and Science Administered under the Qatar Comprehensive Educational Assessment Program
  • Catherine Taylor, University of Washington, Yoonsun Lee, Washington State Department of Education: Analyses of Gender DIF in Reading and Mathematics Items from Tests with Mixed Item Formats
  • Saw Lan Ong, Universiti Sains Malaysia: Effects of Test Language on Students’ Mathematics Performance
  • Bryce Pride, University of South Florida, Yi-Hsin Chen, University of South Florida, Teresa Chavez, University of South Florida, Corina Owens, University of South Florida, Yuh-Chyn Leu, National Taipei University of Education: An Exploration of Cognitive Skills and Knowledge underlying the TIMSS-2003 Fourth Grade Mathematics Items
  • Richard Sudweeks, Brigham Young University, Maria Assunta Forgione, Brigham Young University, Robert Bullough, Brigham Young University, Damon Bahr, Brigham Young University, Eula Monroe, Brigham Young University, Scott Thayn, Brigham Young University: Constructing Vertically Scaled Mathematics Tests for Tracking Student Growth in Value-Added Studies of Teacher Effectiveness
  • Samantha Burg, Metametrics, Inc.: An Investigation of Dimensionality across Grade Levels for Grades 3-8 Mathematics Achievement Tests

AERA 2008 - Annual meeting

Yesterday, the 2008 annual meeting of AERA started. Although this is not only a mathematics education conference, it has a lot of interesting presentations for our field as well. A brief search through the searchable program gave 353 hits on individual presentations with the word "math" in the title. There are also several paper sessions with themes related to mathematics education. Today, for instance, there is a session entitled "Addressing Mathematics Education in Special Education", which has the following participants:

Beyond Either/Or: Enhancing the Computation and Problem-Solving Skills of Low-Achieving Adolescents

*Brian A. Bottge (University of Kentucky), Jorge Enrique Rueda-Sarmiento (University of Wisconsin - Madison), Ana C. Stephens (University of Wisconsin - Madison)
Calculators, Friend or Foe? Calculators as Assessment Accommodations for Students With Disabilities
*Emily C. Bouck (Purdue University)
Interventions to Enhance Math Problem Solving and Number Combinations Fluency for Third-Grade Students With Math Difficulties: A Field-Based Randomized Control Trial
*Lynn S. Fuchs (Vanderbilt University), *Sarah Rannells Powell (Vanderbilt University), *Pamela M. Seethaler (Vanderbilt University), *Rebecca O'Rand Zumeta (Vanderbilt University), Douglas Fuchs (Vanderbilt University)
The Effects of Conceptual Model-Based Instruction on Solving Word-Problems With Various Contexts: “Transfer in Pieces”
*Yanping Xin (Purdue University), *Dake Zhang (Perdue University)
The Effects of Two Manipulative Devices on Hundreds Place-Value Instruction
*Amy Scheuermann (Bowling Green State Univeristy)


Two didactic approaches

Ferdinando Arzarello, Marianna Bosch, Josep Gascón and Cristina Sabena have written an article called "The ostensive dimension through the lenses of two didactical approaches", that has recently been published (online first) in ZDM. Here is the abstract.

The paper presents how two different theories—the APC-space and the ATD—can frame in a complementary way the semiotic (or ostensive) dimension of mathematical activity in the way they approach teaching and learning phenomena. The two perspectives coincide in the same subject: the importance given to ostensive objects (gestures, discourses, written symbols, etc.) not only as signs but also as essential tools of mathematical practices. On the one hand, APC-space starts from a general semiotic analysis in terms of “semiotic bundles” that is to be integrated into a more specific epistemological analysis of mathematical activity. On the other hand, ATD proposes a general model of mathematical knowledge and practice in terms of “praxeologies” that has to include a more specific analysis of the role of ostensive objects in the development of mathematical activities in the classroom. The articulation of both theoretical perspectives is proposed as a contribution to the development of suitable frames for Networking Theories in mathematics education.


Proofs as bearers of mathematical knowledge

This article by Gila Hanna and Ed Barbeau was published online two days ago in ZDM. The article examines a main idea from an article by Yehuda Rav in Philosophia Mathematica, that it is “proofs rather than theorems that are the bearers of mathematical knowledge”. An interesting theme of an article, with strong implications. Here is the entire abstract:

Yehuda Rav’s inspiring paper “Why do we prove theorems?” published in Philosophia Mathematica (1999, 7, pp. 5–41) has interesting implications for mathematics education. We examine Rav’s central ideas on proof—that proofs convey important elements of mathematics such as strategies and methods, that it is “proofs rather than theorems that are the bearers of mathematical knowledge”and thus that proofs should be the primary focus of mathematical interestand then discuss their significance for mathematics education in general and for the teaching of proof in particular.


New doctoral thesis from Sweden

Eva Riesbeck from Linköping University is defending her thesis on April 11. The thesis is written in Swedish, with an English summary, and the title is "På tal om matematik: matematiken, vardagen och den matematikdidaktiska diskursen". The main aim of the thesis is to analyze how discourse can be used as a theoretical and didactical concept to help advance knowledge about the teaching of mathematics. Riesbeck has used a socio-cultural perspective, and discourse analysis has been a theoretical point of departure. The thesis is freely available in PDF format. Here is the abstract in its entirety:
The aim of this dissertation is to describe and analyze how discourse as a theoretical and didactical concept can help in advancing knowledge about the teaching of mathematics in school. The dissertation has been written within a socio-cultural perspective where active participation and support from artefacts and mediation are viewed as important contributions to the development of understanding. Discourse analysis was used as a theoretical point of departure to grasp language use, knowledge construction and mathematical content in the teaching practises. The collection of empirical data was made up of video and audio tape recordings of the interaction of teachers and pupils in mathematics classrooms when they deal with problem-solving tasks, as well as discussions between student teachers as they engage in planning a teaching situation in mathematics. Discourse analysis was used as a tool to shed light upon how pupils learn and develop understanding of mathematics.

The results of my studies demonstrate that discussions very often are located in either a mathematical or in an every-day discourse. Furthermore, the results demonstrate how change between every-day and mathematical language often takes place unknowingly. Also the results underline that a specific and precise dialogue can contribute towards teachers’ and pupils’ conscious participation in the learning process. Translated into common vocabulary such as speak, think, write, listen and read teachers and pupils would be able to interact over concepts, signs, words, symbols, situations and phenomena in every-day discourse and its mathematical counterpart. When teachers and pupils become aware of discursive boundary crossing in mathematics an understanding of mathematical phenomena can start to develop. Teachers and pupils can construct a meta-language leading to new knowledge and new learning in mathematics.

The influence of theory

Christer Bergsten has wrote an article called "On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions", which was recently published (online first) by ZDM. Here is the abstract of the article:

After an introduction on approaches, research frameworks and theories in mathematics education research, three didactical research studies on limits of functions with different research frameworks are analysed and compared with respect to their theoretical perspectives. It is shown how a chosen research framework defines the world in which the research lives, pointing to the difficult but necessary task to compare research results within a common field of study but conducted within different frameworks.


NORMA 08 - online publications

The Norma-08 conference is approaching, and all accepted papers are now published online. Below is an overview of the regular papers in theme B. The reason for displaying the papers in this particular group is a selfish one of course, as it contains an article a colleague and I have written:

Regular papers theme B: Education and identity of mathematics teachers

IS THERE ALWAYS TRUTH IN EQUATION? Iiris Attorps and Timo Tossavainen











Mathematical knowledge for teaching

Journal of Mathematics Teacher Education (JMTE) recently published an (online first) article by A.J. Stylianides and Deborah L. Ball entitled "Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving". The article has a particular focus on knowledge about proof:

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof (quoted from the abstract).

Mathematical knowledge constituted in the classroom

M. Kaldrimidou, H. Sakonidis and M. Tzekaki have written an article that has recently been published online in ZDM. The article is entitled "Comparative readings of the nature of the mathematical knowledge under construction in the classroom", and it makes an attempt to:

(...) empirically identify the epistemological status of mathematical knowledge interactively constituted in the classroom. To this purpose, three relevant theoretical constructs are employed in order to analyze two lessons provided by two secondary school teachers. The aim of these analyses was to enable a comparative reading of the nature of the mathematical knowledge under construction. The results show that each of these three perspectives allows access to specific features of this knowledge, which do not coincide. Moreover, when considered simultaneously, the three perspectives offer a rather informed view of the status of the knowledge at hand (from the abstract).


Mathematics education research links 03/13/2008


tags: adults, education, mathematics, research

RME, issue 1, 2008

Research in Mathematics Education is the official journal of the British Society for Research into Learning Mathematics. As of this year, the journal is included in the Routledge system, and it is quite easy to track the latest news from the journal. It has now published the first issue of 2008, which includes several interesting papers. Here is a list of the research papers in issue 1, 2008:


Articles at IEJME are finally there!

International Electronic Journal of Mathematics Education published their first issue this year a while ago (see my post about it). Now, the articles and abstracts are finally available as well! The abstracts are available in plain HTML format, whereas the articles can be freely downloaded in PDF format. I find one of the articles particularly interesting, as it concerns the same area of research as I am involved in myself (teacher thinking and teacher knowledge). The article was written by Donna Kotsopoulos and Susan Lavigne, and it is entitled: Examining “Mathematics For Teaching” Through An Analysis Of Teachers’ Perceptions Of Student “Learning Paths”
I enclose a copy of the abstract here:

Abstract: How teachers think about student thinking informs the ways in which teachers teach. By examining teachers’ anticipation of student thinking we can begin to unpack the assumptions teachers make about teaching and learning. Using a “mathematics for teaching” framework, this research examines and compares the sorts of assumptions teachers make in relation to “student content knowledge” versus actual “learning paths” taken by students. Groups of teachers, who have advanced degrees in mathematics, education, and mathematics education, and tenth grade students engaged in a common mathematical task. Teachers were asked to model, in their completion of the task, possible learning paths students might take. Our findings suggest that teachers, in general, had difficulty anticipating student learning paths. Furthermore, this difficulty might be attributed to their significant “specialized content knowledge” of mathematics. We propose, through this work, that examining student learning paths may be a fruitful locus of inquiry for developing both pre-service and in-service teachers’ knowledge about mathematics for teaching.


Mathematics Teacher, March 2008

The March issue of Mathematics Teacher is out, with several interesting articles:


What counts as algebra?

"What counts as algebra in the eyes of preservice elementary teachers?" is the title of an article written by Ana C. Stephens for the Journal of Mathematical Behavior. The abstract describes an interesting article, and is enclosed below:
This study examined conceptions of algebra held by 30 preservice
elementary teachers. In addition to exploring participants’ general
“definitions” of algebra, this study examined, in particular, their
analyses of tasks designed to engage students in relational thinking or
a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary
teachers’ conceptions of algebra as subject matter are rather narrow.
Most preservice teachers equated algebra with the manipulation of
symbols. Very few identified other forms of reasoning – in particular,
relational thinking – with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional
symbol manipulation might be valued more than those that demonstrate
relational thinking, suggesting that what is viewed as algebra is what
will be valued in the classroom. This possibility, along with
implications for mathematics teacher education, will be discussed.

Sketchpad in Topogeometry

A. Hawkins and N. Sinclair have written an article that has been published (online first) by International Journal of Computers for Mathematical Learning. The article is entitled "Explorations with Sketchpad in Topogeometry", and the authors describe how they created several microworlds of topological surfaces using The Geometer's Sketchpad. Among the surfaces described are: the Moebius strip, the torus and the Klein bottle. The article contain lots of interesting examples and information about topological geometry, as well as about using this particular software.

(See also this list of interactive geometry software!)


Appropriating mathematical tools through problem solving in collaborative small-group settings

This is the title of a new PhD thesis in mathematics education, written by Martin Carlsen, University of Agder. Carlsen defended his thesis last Friday (February 29).

A main element in this thesis is the perspectives on learning mathematics through collaborative problem solving. This perspective has received attention by several of Carlsen's colleagues in Agder in the past (see e.g. Bjuland, 2004; Borgersen, 1994; Borgersen, 2004). Carlsen presents an analysis of how upper secondary students engage in problem-solving processes in order to achieve mathematical understanding, and he presents four separate studies within this field.

Bjuland, R. (2004). Student teachers' reflections on their learning process through collaborative problem solving in geometry. Educational Studies in Mathematics, 55(1):199-225.
Borgersen, H. E. (1994). Open ended problem solving in geometry. Nordisk Matematikkdidaktikk, 2(2): 6-35.
Borgersen, H. E. (2004). Open ended problem solving in geometry re-visited. Nordisk Matematikkdidaktikk, 9(3), 35-65.
Carlsen, M. (2008). Appropriating mathematical tools through problem solving in collaborative small-group settings. PhD thesis, University of Agder, Faculty of Engineering and Science, Kristiansand, Norway.

New articles from JMTE and ZDM

Journal of Mathematics Teacher Education (JMTE) and ZDM have published some new and interesting online articles:


RCML Annual conference

The annual conference of Research Council on Mathematics Learning (RCML) starts tomorrow in Oklahoma. The keynote speaker tomorrow is Anne Reynolds from Kent State University, and the theme for her lecture is "Meaningful mathematics for all students: The place of imagery". See the program (pdf) for more information about the conference. The overall theme of the conference is "Math for all", and the conference description links this to the slogan "No child left behind".

Mental representations of inferential statistics

The Journal of Mathematical Behavior has published an online article called "Exploring college students' mental representations of inferential statistics". The article is written by N.C. Lavigne, S.J. Salkind and J. Yan, and it reports a case study of how three college students made mental representations of their knowledge about inferential statistics. In the article, they discuss how this knowledge was connected and how it was applied in two problem solving situations. The researchers found that the representations of the students were based on incomplete statistical understanding, and their findings suggest that it could be useful as a diagnostic tool to modify the task format in certain ways.


Symposium in Rome

Celebrating the 100th anniversary of ICMI, a symposium will be held in Rome under the title: "The First Century of the International Commission on Mathematical Instruction (1908-2008) Reflecting and Shaping the World of Mathematics Education". This symposium is addressed to a selected group of participants, including many of the "big" names in our field. The International Programme Committee is chaired by Ferdinando Arzarello (Italy), and also includes names like Michèle Artigue, Hyman Bass, Jo Boaler, Fulvia Furinghetti, Jeremy Kilpatrik, Mogens Niss and Gert Schubring, to mention some.

A core component of the program of the symposium is five work groups, where several of the participants have posted interesting articles for download. The themes of the working groups are:
The symposium also includes nine plenary sessions:
The conference starts tomorrow, and it is closing on Saturday. So if you don't have the opportunity to be there, take a look at the webpage! There are lots of interesting material there.


Some new (online first) articles

Three of the big Springer journals have published new (online first) articles: