Elementary prospective teachers' mathematical beliefs

Susan L. Swars, Stephanie Z. Smith, Marvin E. Smith and Lynn C. Hart have written an article called A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. The article was published online in Journal of Mathematics Teacher Education on Thursday. Here is the abstract of their article:

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.

Belief enactment

Danish colleague Jeppe Skott has written an interesting article about research concerning teachers' beliefs. The article is entitled Contextualising the notion of ‘belief enactment’, and it was published online in Journal of Mathematics Teacher Education on Wednesday. Skott is a prominent researcher within the field of mathematics education research in the Nordic countries, and he has a critical view on the notion of research on teachers' beliefs, as well as the approach to this area of research. Here is the abstract of his article:

For more than 20 years, belief research has been based on the premise that teachers’ beliefs may serve as an explanatory principle for classroom practice. This is a highly individual perspective on belief–practice relationships, one that does not seem to have been influenced by the increasingly social emphases in other parts of mathematics education research. In this article, I use the notions of context and practice to develop a locally social approach to understanding the belief–practice relationships. It is a corollary of the approach taken that the high hopes for belief research with regard to its potential impact on mathematics instruction need to be modified.

Method, certainty and trust

David Pimm has written an article called Method, certainty and trust across disciplinary boundaries. This article was published online in ZDM earlier this week. Here is the abstract of his article:

This paper starts from some observations about Presmeg’s paper ‘Mathematics education research embracing arts and sciences’ also published in this issue. The main topics discussed here are disciplinary boundaries, method and, briefly, certainty and trust. Specific interdisciplinary examples of work come from the history of mathematics (Diophantus’s Arithmetica), from linguistics (hedging, in relation to Toulmin’s argumentation scheme and Peirce’s notion of abduction) and from contemporary poetry and poetics.

New IJMTL articles

Five new articles were published in International Journal for Mathematics Teaching and Learning on Tuesday:

How Does the Problem Based Learning Approach Compare to the Model-Eliciting Activity Approach in Mathematics? by Scott A. Chamberlin and Sidney M. Moon. Abstract: The purpose of this article is to discuss the similarities and differences in the two approaches referred to in the article title with an emphasis on implementation and outcomes.

Seeds of Professional Growth Nurture Students’ Deeper Mathematical Understanding, by Ji-Eun Lee and Dyanne Tracy. Abstract: This manuscript describes a group of middle school age students' exploration of virtual mathematics manipulatives and the authors' professional development process. In the manuscript, the authors share the experiences they had with middle school students and the process that they, as mathematics teachers, used to refine their own learning and teaching alongside the middle school students.

The State of Balance Between Procedural Knowledge and Conceptual Understanding in Mathematics Teacher Education, By Michael J. Bossé and Damon L. Bahr. Abstract: In this paper, we present the results of a survey-based study of the perspectives of mathematics teacher educators in the United States regarding the effects of the conceptual/procedural balance upon four concerns: the type of mathematics that should be learned in school, preservice teacher preparation, instructional conceptualization and design, and assessment.

An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers, by Damon L. Bahr and Eula Ewing Monroe. Abstract: Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University.

What is Good College Mathematics Teaching? by Carmen M. Latterell. Abstract: This article attempts to answer the question “What is good college mathematics teaching?” by examining three sources of information: research, student course evaluations, and responses on the website RateMyProfessors.com.

This is the journal where I published my own article about Real-life Connections in Japan and the Netherlands: National Teaching Patterns and Cultural Beliefs, in July, and as always, all articles are freely available in pdf format.

Pearson's correlation between three variables

Pauline Vos has written an article called Pearson's correlation between three variables; using students' basic knowledge of geometry for an exercise in mathematical statistics. The article was recently published in International Journal of Mathematical Education in Science and Technology. Here is a copy of the article abstract:

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras' theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.

Book review: "Algebra in the Early Grades"

The latest issue of Teachers College Record includes a book review of "Algebra in the Early Grades". This important book was edited by late James J. Kaput together with David W. Carraher and Maria L. Blanton, and it was published by Lawrence Erlbaum Associates in 2007. David Slavit provides a thorough review, which gives a nice insight into the main parts of the book.

If you are interested, you might want to check out the information about the book in Google Books (which includes links to where you can buy the book), and you might also be interested in taking a look at this page about Early Algebra.

Activating mathematical competencies

César Sáenz from the Autonomous University of Madrid, Spain, has written an article called The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). This article describes and analyzes the difficulties that Spanish student teachers had when attempting to solve the released items from PISA 2003. The student teachers (n=140) were first-year students, and they had not taken any mathematics courses in their teacher training at the time of the study. They didn't have any experience with the PISA tests, and they had no more than secondary-level mathematics studies before they started their teacher education. The test they took was made from a collection of 39 released items from PISA 2003.

The article was published in Educational Studies in Mathematics on Sunday. Here is the article abstract:

This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In this way, the school knowledge variable becomes a variable associated with the PISA competence variable.

Prospective elementary teachers' motivation

Amanda Jansen has written an article entitled Prospective elementary teachers’ motivation to participate in whole-class discussions during mathematics content courses for teachers. This article was published on Sunday in Educational Studies in Mathematics. Here is the abstract of her article:

Prospective elementary teachers’ (N = 148) motivation to participate in whole-class discussions during mathematics content courses for teachers, as expressed in their own words on an open-ended questionnaire, were studied. Results indicated that prospective teachers were motivated by positive utility values for participating (to achieve a short-term goal of learning mathematics or a long-term goal of becoming a teacher), to demonstrate competence (to achieve performance-approach goals), or to help others (to achieve social goals). Negative utility values for participating were expressed by those who preferred to learn through actively listening. Five motivational profiles, as composed of interactions among motivational values, beliefs, goals and self-reported participation practices, were prevalent in this sample. Self-reported variations among participants’ utility values and participation practices suggested that prospective teachers engaged differentially in opportunities to learn to communicate mathematically. Results provide pedagogical learner knowledge for mathematics teacher educators.

Gestures as semiotic resources

Ferdinando Arzarello, Domingo Paola, Ornella Robutti and Cristina Sabena have written an article called Gestures as semiotic resources in the mathematics classroom. The article was published online in Educational Studies in Mathematics a while ago. Here is the abstract of their paper:

In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching–learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.

Research fellow at University of Agder!

University of Agder, Norway, arguably has one of the strongest research groups in mathematics education. They have a strong Master programme, a PhD programme, and five international professors in mathematics education. Now, they have announced a free position/appointment as research fellow for a period of three years. So, if you want to become a PhD student in Norway, this might be your lucky day :-)

Some of the research areas within the field of mathematics education in Agder include:

• Developmental research in the teaching and learning of mathematics (from day-care centres to the university level)
• Mathematics classroom research
• Pupils' and students' understanding, attitudes and motivation for mathematics
• Problem solving and modelling in mathematics
• History of mathematics
• Mathematics teacher education and professional development

If you are interested, you can read the entire announcement from the link above, or you can contact Professor Simon Goodchild (simon.goodchild@uia.no).

ZDM, No 5, 2008

For some reason, ZDM has published two December issues this year. I have already covered one of them, which is actually No 6, but I have not covered No 5 (both are December issues). ZDM, No 5 has a focus on Empirical Research on Mathematics Teachers and their Education, and it is a very interesting issue (for me at least), with 14 articles:

• Introduction to the issue on Empirical research on mathematics teachers and their education, by Sigrid Blömeke, Gabriele Kaiser, Rainer Lehmann and William H. Schmidt
• Effectiveness of teacher education - State of research, measurement issues and consequences for future studies, by Sigrid Blömeke, Anja Felbrich, Christiane Müller, Gabriele Kaiser and Rainer Lehmann
• Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries, by William H. Schmidt, Richard T. Houang, Leland Cogan, Sigrid Blömeke, Maria Teresa Tatto, Feng Jui Hsieh, Marcella Santillan, Kiril Bankov, Shin Il Han, Tenoch Cedillo, John Schwille and Lynn Paine
• Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education, by Sigrid Blömeke, Lynn Paine, Richard T. Houang, Feng-Jui Hsieh, William H. Schmidt, M. Teresa Tatto, Kiril Bankov, Tenoch Cedilllo, Leland Cogan, Shin Il Han, Marcella Santillan and John Schwille
• Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics, by Anja Felbrich, Christiane Müller and Sigrid Blömeke
• “Last curves not quite correct”: diagnostic competences of future teachers with regard to modelling and graphical representations, by Björn Schwarz, Björn Wissmach and Gabriele Kaiser
• Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries, by Björn Schwarz, Issic K. C. Leung, Nils Buchholtz, Gabriele Kaiser, Gloria Stillman, Jill Brown and Colleen Vale
• Content and pedagogical content knowledge in argumentation and proof of future teachers: a comparative case study in Germany and Hong Kong, by Alexandra Corleis, Björn Schwarz, Gabriele Kaiser and Issic K. C. Leung
• Knowledge and confidence of pre-service mathematics teachers: the case of fraction division, by Yeping Li and Gerald Kulm
• Chinese elementary mathematics teachers’ knowledge in mathematics and pedagogy for teaching: the case of fraction division, by Yeping Li and Rongjin Huang
• Combining theories in research in mathematics teacher education, by Pessia Tsamir and Dina Tirosh
• Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs, by Stefan Krauss, Jürgen Baumert and Werner Blum
• A DNR perspective on mathematics curriculum and instruction. Part II: with reference to teacher’s knowledge base, by Guershon Harel
• Theories, context and values to understand learning with digital media: book review of ‘humans-with-media and the reorganization of mathematical thinking’, by M. Borba and M. Villareal, by Chronis Kynigos

So, if you (like me) you are interested in research related to mathematics teachers and/or mathematics teacher education, this would certainly be an issue to take a closer look at!

A large part of the articles in this issue are related to the international comparative study: "Mathematics Teaching in the 21st Century (MT21)". This study, according to the editorial, is the first study that has a focus on "how teachers are trained and how they perform at the end of their education".

NOMAD, No 3, 2008

Finally, the October issue of NOMAD is available! It contains the following articles:

• Nordic mathematics education research in the world and in the region (Editorial)
• Analyzing mathematical classroom discourse – initiating elaborations on the usefulness of the dialogical approach, by Andreas Ryve
• Learning mathematics through inquiry, by Ole Skovsmose and Roger Säljö
• Do students need to learn how to use their mathematics textbooks? The case of reading comprehension, by Magnus Österholm
  

Mathematics teachers' observable learning objectives

Paul Andrews has written an article entitled Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes. The article was published online in Educational Studies in Mathematics on Wednesday. Here is a copy of the article abstract:

Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

Mathematical enculturation

Jacob Perrenet and Ruurd Taconis have written an article called Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme. The article was published online in Educational Studies in Mathematics on Tuesday, and it is an Open Access article, so it is freely available to anyone! Here is the article abstract:

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.

ZDM, December 2008

The December issue of ZDM is out, and it contains 12 interesting articles. The theme of the issue is "An Asia Pacific focus on Mathematics Classrooms:

• Editorial to the issue “An Asia Pacific focus on mathematics classrooms”, by Chap Sam Lim, Allan White and Berinderjeet Kaur
• Lesson study in Asia Pacific classrooms: local responses to a global movement, by Allan Leslie White and Chap Sam Lim
• Reforming mathematics learning in Indonesian classrooms through RME, by Robert K. Sembiring, Sutarto Hadi and Maarten Dolk (Freely available Open Access article!)
• Exploring Japanese teachers’ conception of mathematics lesson structure: similarities and differences between pre-service and in-service teachers’ lesson plans, by Yoshinori Shimizu
• Teaching and learning of mathematics: what really matters to teachers and students?, by Berinderjeet Kaur
• Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation: public oral interactivity and mathematical orality, by David Clarke and Li Hua Xu
• Confucian heritage culture learner’s phenomenon: from “exploring the middle zone” to “constructing a bridge”, by Ngai-Ying Wong
• In the books there are golden houses: mathematics assessment in East Asia, by Frederick K. S. Leung
• An overview of the gender factor in mathematics in TIMSS-2003 for the Asia-Pacific region, by Jaguthsing Dindyal
• Teaching and learning of inclusive and transitive properties among quadrilaterals by deductive reasoning with the aid of SmartBoard, by Issic K. C. Leung
• A Sino-German semi-virtual seminar in mathematics education, by Matthias Ludwig, Wolfgang Müller and Binyan Xu
• U. D’Ambrosio (2006). Ethnomathematics: Link between traditions and modernity (A. Kepple, Trans.), by Hugh Burkhardt (Book review)
  

Embodied multi-modal communication

Julian Williams from University of Manchester (UK) has written an article entitled Embodied multi-modal communication from the perspective of activity theory. This article was published online in Educational Studies in Mathematics last week. Here is the abstract of the article:

I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in ‘grasping’ the meaning of mathematics if the whole object-orientated ‘activity’ is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a ‘threshold’ moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning.

IJSME, December 2008

The December issue of International Journal of Science and Mathematics Education has been published. This peer-reviewed journal is sponsored by the National Science Council in Taiwan, and has a particular emphasis on articles "that explore science and mathematics education from different cultural perspectives". The journal also encourages articles written by authors who do not have English as their first language. This is, in my opinion, a very nice focus from a scientific journal! The issue contains the following articles:

• Two Dimensions of Student Ownership of Learning During Small-Group Work in Physics, by Margareta Enghag and Hans Niedderer
• Issues in Implementing a Structured Problem-based Learning Strategy in a Volcano Unit: A Case Study, by Hyunju Lee and Sungah Bae
• Gender and Performance in Mathematical Tasks: Does the Context Make a Difference? by Anat Zohar and Anna Gershikov
• Exploring the phase space of a system of differential equations: different mathematical registers, by Thierry Dana-Picard and Ivy Kidron
• The Force Concept Inventory as a Measure of Students Conceptual Coherence, by Antti Savinainen and Jouni Viiri
• Sample, Random and Variation: The Vocabulary of Statistical Literacy, by Jane M. Watson and Ben A. Kelly
• Chinese High-School Students in Physics Classroom as Active, Self-Regulated Learners: Cognitive, Motivational and Environmental Aspects, by Heinz Neber, Jing He, Bang-Xiang Liu and Neville Schofield
• A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics, by Der-Ching Yang, Mao-neng Li and Chih-I Lin
  

Playing with representations

Tom Satwicz and Reed Stevens have written an article called Playing with Representations: How Do Kids Make Use of Quantitative Representations in Video Games? The article was published online in International Journal of Computers for Mathematical Learning on Tuesday. Here is a copy of the abstract of their article:

This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own games at home. The data set is composed of video recordings and artifact-based interviews. The concept of disciplined perception is used to understand how quantities are coordinated during game play. The current study shows young people using quantities in games to make predictions and organize their actions based on those predictions. Some ideas based on the study’s findings for using video games in school are discussed.

New journal: Educational Designer

A new journal for educational research has seen the light of day: Educational Designer! The journal is an online journal, and it was established by the International Society for Design and Development in Education. One of the articles in the first issue is written by Malcolm Swan, mathematics education researcher from the University of Nottingham. The article is concerned with Designing a Multiple Representation Learning Experience in Secondary Algebra. Here is the abstract of Swan's article (but the entire article is available online!):

This paper describes some of the research-based principles that I use when designing learning experiences to foster conceptual understanding. These principles are illustrated through the discussion of one type of experience: that of sorting multiple representations. I refer to learning experiences rather than tasks, because tasks are only one component of the design. Close attention is also paid to the role of the teacher in creating an appropriate climate for learning to take place.

After a brief excursion into my own theoretical framework, I describe the educational objectives behind my design and provide a detailed explanation of it in one topic, that of algebraic notation.  This is followed with an explanation of the principles that informed the design and the evolution of the task. Finally, I briefly indicate how the design might be generalised to include other topics.

ICMI newsletter, No 6, 2008

The October version of the ICMI newsletter has been sent to the subscribers' mailboxes. If you do not subscribe to the newsletter, you can find a complete archive here. Here is a copy of the table of contents:

CONTENTS
1. Editorial: About the ICMI Studies --- and a Call For Proposals
2. Symposium Celebrating the Centennial of the ICMI
3. Proceedings of the Symposium Celebrating the Centennial of the ICMI
4. ICTMA 14
5. New e-journal: Educational Designer
6. Calendar of Events of Interest to the ICMI Community
7. Subscribing to ICMI News

Interdisciplinary instruction

Claus Michelsen and Bharath Sriraman have written an article called Does interdisciplinary instruction raise students’ interest in mathematics and the subjects of the natural sciences? The article was published online in ZDM on Sunday. Here is the abstract of their article:

This article presents the research project IFUN (the acronym IFUN refers to Interesse og Fagoverskrindende Undervisning i Naturvidenskab and Interesse und Fächerübergreifender Unterricht in den Naturwisseschaften which is Danish and German, respectively, for Interest and Interdisciplinary Instruction in Science and Mathematics)—Interest and Interdisciplinary Instruction in Science (we use the term science as a common denominator for the subjects of physics, chemistry and biology) and Mathematics. The aim of the project was to investigate on how upper secondary students’ interest in the subjects of mathematics, physics, chemistry and biology might be improved by increased instructional interplay and integration between the subjects. The individual student’s interests in interdisciplinary domains of mathematics and science are studied within a three-dimensional framework: (1) the student’s interest in a particular interdisciplinary domain of mathematics and science. (2) The characteristics of a specific learning setting that causes a situational interest in the topic and promotes and supports a shift from catching interest to holding interest. (3) The student’s affiliation with and valuation of mathematics and science. We present the main results from an interest study conducted with a 147 item Likert questionnaire administered to 255 grade 11 students. The results of the study show that students have a high interest in mathematics and are positive towards interdisciplinary instruction. When it comes to the individual student’s affiliation with and valuation of mathematics and science, the study shows that future studies and careers play an important role. We conclude that the results indicate it is possible to expand interest in one subject to another subject through interdisciplinary instruction.

Diagnostic competentces of future teachers

Björn Schwarz, Björn Wissmach and Gabriele Kaiser have written an article entitled “Last curves not quite correct”: diagnostic competences of future teachers with regard to modelling and graphical representations. The article was published online in ZDM last week. Here is the abstract of their article:

The article describes the results of a national enrichment to the six-country study Mathematics Teaching in the 21st century (MT21)—an international comparative study about the efficiency of teacher education. The enrichment focuses on the diagnostic competence of future mathematics teachers as sub-component of teachers’ professional competence for which the evaluation of students’ solutions of a modelling task about the course of a racetrack is demanded. In connection with two sub-facets of the diagnostic competence, namely the competence to recognise students’ misconceptions and the competence of criteria-guided assessment of students’ solutions, typical answer patterns are distinguished as well as the frequency of their occurrence with regard to future teachers’ phase of teacher education and the level of school teaching they are going to teach in.

Future teachers' professional knowledge on argumentation and proof

Björn Schwarz, Issic K.C. Leung, Nils Buchholtz, Gabriele Kaiser, Gloria Stillman, Jill Brown and Colleen Vale have written an article about Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries, which was also published online in ZDM last week. It appears that a forthcoming issue of ZDM will have a strong focus on teacher education and teachers' mathematical content knowledge!

Here is the abstract of the article:

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.

Content and pedagogical content knowledge in Germany and Hong Kong

Alexandra Corleis, Björn Schwarz, Gabriele Kaiser and Issic K.C. Leung have written an article called Content and pedagogical content knowledge in argumentation and proof of future teachers: a comparative case study in Germany and Hong Kong. The article was published in ZDM last week, and it provides an interesting comparison between teachers in Germany and Hong Kong. Here is the article abstract:

The results of a comparative case study on mathematical and pedagogical content knowledge in the area of argumentation and proof of future teachers in Germany and Hong Kong are reported in this article. The study forms part of a qualitatively oriented comparative study on future teachers in Australia, Germany, and Hong Kong. Six case studies based on interviews and written questionnaires are described. These case studies show the strengths of the Hong Kong future teachers in mathematical knowledge in the area of argumentation and proof, whereas the three German future teachers perform stronger in the related pedagogical content domain. Furthermore, regarding the German future teachers, it seems that the two domains of knowledge are more strongly connected to each other. The results are interpreted in the light of related research, such as the MT21 study.

PME 33

The next annual conference for the International Group of Psychology of Mathematics Education (PME) is going to be held in Thessaloniki, Greece. The conference will take place between July 19-24, 2009. The conference venues will be the Aristotle University of Thessaloniki and the University of Macedonia. The theme of the conference has been chosen to be: "In search for theories in Mathematics Education". Be sure to check the list of important dates, if you plan to attend. The next deadline to look out for is January 12, for those who plan to submit research reports.

Interdisciplinarity in mathematics education

Bharath Sriraman (the editor of The Montana Mathematics Enthusiast) has written the editorial to a forthcoming issue of ZDM. The leading idea of this special issue is that of interdisciplinarity, and Sriraman's editorial is entitled: Interdisciplinarity in mathematics education: psychology, philosophy, aesthetics, modelling and curriculum. This special issue (ZDM, vol. 41, nos 1 and 2) will be a double issue with 22 articles! Sriraman presents some interesting numbers about the issue in his editorial, indicating that this is a somewhat special issue:

ZDM, vol 41, nos 1 and 2 = 3 International Symposia + 5 years of collaboration + 22 months of planning + 44 reviewers + 3 rounds of reviews, revisions, commentaries, re-revisions + 24 authors + 1 idiosyncratic guest editor + 1,123 e-mail communications = 22 articles.

The decorative impulse

Swapna Mukhopadhyay has written an article entitled The decorative impulse: ethnomathematics and Tlingit basketry. The article was published online in ZDM earlier this week. Here is the article abstract:

Pattern is a key element in both the esthetics of design and mathematics, one definition of which is “the study of all possible patterns”. Thus, the geometric patterns that adorn cultural artifacts manifest mathematical thinking in the artisans who create them, albeit their lack of “formal” mathematics learning. In describing human constructions, Franz Boas affirmed that people, regardless of their economic conditions, always have been engaged in activities that reveal their deeply held esthetic sense. The Tlingit Indians from Sitka, Alaska, are known for their artistic endeavors. Art aficionados and museum collectors revere their baskets and other artifacts. Taking the approach of ethnomathematics, I report my analysis of the complex geometrical patterns in Tlingit basketry.

Creativity and interdisciplinarity

Johathan Plucker and Dasha Zabelina have written an article in ZDM called: Creativity and interdisciplinarity: one creativity or many creativities? The article was published online on Tuesday. Here is the abstract of the article:

Psychologists and educators frequently debate whether creativity and problem solving are domain-general—applicable to all disciplines and tasks—or domain-specific—tailored to specific disciplines and tasks. In this paper, we briefly review the major arguments for both positions, identify conceptual and empirical weaknesses of both perspectives, and describe two relatively new hybrid models that attempt to address ways in which creativity and innovation are both domain-general and domain-specific.

Exploring Japanese teachers' conception of mathematics lesson structure

Yoshinori Shimizu has written an article called Exploring Japanese teachers’ conception of mathematics lesson structure: similarities and differences between pre-service and in-service teachers’ lesson plans. The article was published online in ZDM on Saturday, and it will be one of the articles in a forthcoming issue on An Asia Pacific focus on mathematics classrooms. Japanese Lesson Study has been known in the Western world for years. It is normally recognized that the book of Jim Stigler and James Hiebert: The teaching gap, first introduced the idea of lesson study to the West.

In this article, Shimizu analyzes the teachers' conception of structure in mathematics lessons by focusing on their lesson plans. Here is the abstract of the article:

The research reported in this paper explores teachers’ conception of what mathematics lesson structure is like by analyzing the lesson plans they wrote. Japanese in-service and pre-service teachers (n = 246) were asked to produce a lesson plan for teaching the formula for finding the area of a parallelogram. Organizations of planned lessons were analyzed in terms of the form and content of steps/phases descriptions of them. Also, the multiplicity was analyzed of anticipated students’ responses to the problem posed in the plans. The analysis revealed both similarities and differences between lesson plans produced by the two groups of teachers. In particular, it was found that in-service teachers tended to retain the description of the problem to be posed and the anticipation of student responses in their lesson plans, while they abandoned other elements that they were trained to write when they were pre-service teachers. The results suggest that these two elements constitute the “core” of Japanese teachers’ conception of lesson structure. Origins of these core elements are discussed with a focus on the role of lesson plans as vehicles for examining and improving lessons in Lesson Study.

JRME, November 2008

The November issue of Journal for Research in Mathematics Education has been published, with the following main articles:

• Access to Upper-Level Mathematics: The Stories of Successful African American Middle School Boys, by Robert Q. Berry III
• Mapping Mathematics Classroom Discourse and Its Implications for Models of Teaching, by Mary P. Truxaw and Thomas C. DeFranco
• The Effect of Schema-Based Instruction in Solving Mathematics Word Problems: An Emphasis on Prealgebraic Conceptualization of Multiplicative Relations, by Yan Ping Xin
• Review: A Trio of Strategies for Success: A Review of Mathematics Education at Highly Effective Schools That Serve the Poor: Strategies for Change, by Joanne Rossi Becker

Using SmartBoard

Issic K.C. Leung has written an article about using SmartBoard. The article is entitled Teaching and learning of inclusive and transitive properties among quadrilaterals by deductive reasoning with the aid of SmartBoard, and it was published online in ZDM on Friday. Here is the abstract of the article:

Learning to identify Euclidean figures is an essential content of many elementary school geometry curricula. Students often learn to distinguish among quadrilaterals, for example, by categorizing their geometric properties according to two attributes, namely the length of the edges and the size of the interior angles. But knowing how to differentiate them based on their geometric properties does not necessarily help students to develop the abstract concepts of the inclusive and transitive properties among the quadrilaterals. With the aid of dynamic geometry multimedia software in SmartBoard (SB), a kind of digital whiteboard (DWB), we enhanced the teaching and learning effectiveness by the effect of “animation-on-demand” in classrooms. This is basically a dual delivery of geometric concepts by texts, narrations and words accompanied by pictures, illustrations and animations. The preliminary results of our study on 9-year-old students’ performance in tests given after three such lessons show that those students could differentiate with reasons why a square is a rhombus (inclusion) as well as a parallelogram (transitivity).

Creating optimal mathematics learning environments

Dionne I. Cross has written an article entitled Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. The article was recently published online in International Journal of Science and Mathematics Education. Here is a copy of the article's abstract:

The issue of mathematics underachievement among students has been an increasing international concern over the last few decades. Research suggests that academic success can be achieved by focusing on both the individual and social aspects of learning. Within the area of mathematics education, the development of metacognitive skills and the incorporation of discourse in classroom instruction has resulted in students having deeper conceptual understandings of the content and increased mathematical achievement. However, studies in this field tend to focus on the effects of these practices separately, making research that seeks to harness the potential of both quite rare. This paper reports on a study that was aimed at addressing this gap in the literature by examining the effects of writing and argumentation on achievement. Two hundred and eleven students and five teachers participated in this multimethod study that investigated the effects of three treatment conditions on mathematical achievement. These conditions were writing alone, argumentation alone, and writing and argumentation combined. Analysis of covariance revealed significant differences between the groups, and tests of the contrasts showed that students who engaged in both argumentation and writing had greater knowledge gains than students who engaged in argumentation alone or neither activity.