Anderson Norton, Andrea McCloskey and Rick A. Hudson have written an interesting article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Here is the abstract of their article:

In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.

Today is the second day of the CERME7 conference in Rzeszow, Poland. I am attending (and enjoying!) the conference, and I’ll try and share some of the highlights. A lot of our time on this conference is devoted to working group sessions, and it is really a working conference! I am very much in favor of such a format for a conference, and I think it adds some beneficial things to it. The disadvantage, of course, is that you don’t really learn a lot about what is going on in the other working groups. The plenary lecture of today was very interesting, partially because it presented us with an overview of the results from the efforts of one particular working group over the last couple of years.

The lecture was held by Markku Hannula from the University of Helsinki, Finland. He held a very interesting lecture on “Structure and dynamics of affect in mathematical thinking and learning”. In this lecture, he presented us with an overview of research on affects in mathematics education over the last decades. He started off with a focus on the influential article (or handbook chapter) from 1992 by my good friend Douglas McLeod. Since the early 90s, this research area has developed quite a lot, although, in many respects, researchers still struggle with the same issues. This is very much related to the concepts in use, the relationships between the concepts as well as the dynamics involved. Hannula provided a structured and well presented overview of this development, and he also presented us with a nice three-dimensional model of the issues at hand. His presentation also included a nice overview of how the CERME working group on affects had developed over the years. I will look out for his paper when it arrives, and I am sure that it will be of great interest!

Below is the abstract of his lecture:

In this presentation, I will review the development of research on affect in mathematics education since the late 1990s and forecast some directions for future development. One trend in the development has been the elaboration of the theoretical foundation. I will suggest that a useful description of the affective domain can be based on distinctions in three dimensions: 1. rapidly changing affective states vs. relatively stable affective traits; 2. cognitive, motivational and emotional aspects of affect; and 3. the social, the psychological and the physiological nature of affect. Another direction of development has been to explore the structural nature of affect empirically. I will review some instruments that have been developed to measure different dimensions of beliefs, motivation and emotional traits. Moreover, I will look at some empirical results concerning how the different dimensions are related to each other, and how they develop over time.

A new special issue of ZDM has appeared, and it is a theme issue on Creating and using representations of mathematics teaching in research and teacher development. This one is a quite huge issue, containing 16 articles altogether. Here is an overview of all the articles:

• On creating and using representations of mathematics teaching in research and teacher development
• Introduction to this issue, by Patricio Herbst and Daniel Chazan
• Representing context in video records of practice for urban mathematics teacher education, by Ann R. Edwards
• Opening the closed text: the poetics of representations of teaching, by Michael Kevin Weiss
• Tacitation and implicitation: the construction of semiotic tools for representing mathematics teaching, by Jean-Philippe Maitre, Christian Dépret, Erica de Vries and Jacques Baillé
• Designing representations of trigonometry instruction to study the rationality of community college teaching, by Vilma Mesa and Patricio Herbst
• Co-facilitation of study groups around animated scenes: the discourse of a moderator and a researcher, by Talli Nachlieli
• Who does what? A linguistic approach to analyzing teachers’ reactions to videos, by Gloriana González
• Representation of the notion “learning-as-participation” in everyday situations of mathematics classes, by Götz Krummheuer
• Using comics-based representations of teaching, and technology, to bring practice to teacher education courses, by Patricio Herbst, Daniel Chazan, Chia-Ling Chen, Vu-Minh Chieu and Michael Weiss
• Designing an intelligent teaching simulator for learning to teach by practicing, by Vu Minh Chieu and Patricio Herbst
• Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion, by Sandra Crespo, Joy Ann Oslund and Amy Noelle Parks
• Using video to teach future teachers to learn from teaching, by Rossella Santagata and Jody Guarino
• Making practice studyable, by Hala Ghousseini and Laurie Sleep
• Teachers’ reactions to animations as representations of geometry instruction, by Deborah Moore-Russo and Janine M. Viglietti
• Using video representations of teaching in practice-based professional development programs, by Hilda Borko, Karen Koellner, Jennifer Jacobs and Nanette Seago

Readers of this blog are probably familiar with The Montana Mathematics Enthusiast already. TMME is an international peer-reviewed journal with a main focus on mathematics education research. The journal has both print and electronic versions. Over the past two years, the main editor of the journal, Professor Bharath Sriraman, has been kind enough to let me print information about new issues (along with his editorials) here before they are printed. This tradition continues, and I am now happy to announce the next issue of TMME, which is going to be a huge double-issue: volume 8, Numbers 1 & 2. Here is a brief overview of the contents of this forthcoming issue

0.      Editorial: Opening 2011’s  journal treasure chest, by Bharath Sriraman (Montana, USA)
1.      Vignette of Doing Mathematics:  A Meta-cognitive Tour of the Production of Some Elementary Mathematics, by Hyman Bass (USA)
2.      Mathematical Intuition (Poincare, Polya, Dewey), by Reuben Hersh (USA)
3.      Transcriptions, Mathematical Cognition, and Epistemology, by Wolff-Michael Roth & Alfredo Bautista (Canada)
4.      Seeking more than nothing: Two elementary teachers conceptions of zero, by Gale Russell & Egan J Chernoff  (Canada)
5.      Revisiting Tatjana Ehrenfest-Afanassjewa’s (1931) “Uebungensammlung zu einer geometrischen Propädeuse”: A Translation and Interpretation, by Klaus Hoechsmann (Canada)
6.      Problem-Based Learning in Mathematics, by Thomas C. O’Brien (posthumously),Chris Wallach, Carla Mash-Duncan (USA)
 
Special Section: New perspectives on identification and fostering mathematically gifted students: matching research and practice
Guest Editors: Viktor Freiman (Canada) & Ali Rejali (Iran)
7.      New perspectives on identification and fostering mathematically gifted students: matching research and practice, by Viktor Freiman  (Canada) & Ali Rejali (Iran)
8.      The education of mathematically gifted students: Some complexities and questions, by Roza Leikin (Israel)
9.      Historical perspectives on a program for mathematically talented students, by Harvey B. Keynes and Jonathan Rogness (USA)
10.  The proficiency challenge: An action research program on teaching of gifted math students in grades 1-9, by Arne Mogensen (Denmark)
11.  Designing and teaching an elementary school enrichment program: What the students were taught and what I learned, by Angela M. Smart (Canada)
12.  An overview of the gifted education portfolio for the John Templeton Foundation, by Mark Saul (USA)
13.  Prospective teachers’ conceptions about teaching mathematically talented students: Comparative examples from Canada and Israel, by Mark Applebaum (Israel), Viktor Freiman (Canada), Roza Leikin (Israel)
14.  Mathematical and Didactical Enrichment for Pre-service Teachers: Mentoring Online Problem Solving in the CASMI project, by Manon LeBlanc & Viktor Freiman (Canada)
15.  Gifted Students and Advanced Mathematics, by Edward J. Barbeau (Canada)
16.  Disrupting gifted teenager’s mathematical identity with epistemological messiness, by Paul Betts & Laura McMaster (Canada)
17.  The promise of interconnecting problems for enriching students’ experiences in mathematics, by Margo Kondratieva (Canada)
18.  Creativity assessment in school settings through problem posing tasks, by Ildikó Pelczer & Fernando Gamboa Rodríguez(Mexico)

Below is the editorial for you to read:

The title is meant to be a joke. Educational Studies in Mathematics always publish their issues early (at least the release dates don’t correspond to the numbers of the issues). Anyhow, the journal has now released the January issue of 2011 (Volume 76, Number 1). The issue contains five interesting articles (along with a couple of book reviews and an editorial):

• Can slope be negative in 3-space? Studying concept image of slope through collective definition construction, by Deborah Moore-Russo, Anna Marie Conner and Kristina I. Rugg
• The effect of using a video clip presenting a contextual story on low-achieving students’ mathematical discourse, by Yifat Ben-David Kolikant and Orit Broza
• Understanding mathematics textbooks through reader-oriented theory, by Aaron Weinberg and Emilie Wiesner
• “Variation problems” and their roles in the topic of fraction division in Chinese mathematics textbook examples, by Xuhua Sun
• Young workers and their dispositions towards mathematics: tensions of a mathematical habitus in the retail industry, by Robyn Jorgensen Zevenbergen

The December issue of Educational Studies in Mathematics has appeared (at least online), and it contains seven interesting articles. Several articles in this issue relate to affective issues like teachers’ conceptions (Thanheiser’s article), perspectives (Hemmi’s article), motivation and motivational profiles (Phelps’ article), anxiety (Bekdemir’s article), etc. Here is a complete list of the articles that appear in this issue:

• Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework, by Eva Thanheiser.
• So we decided to call “straight line” (…): Mathematics students’ interaction and negotiation of meaning in constructing a model of elliptic geometry, by Maria Kaisari and Tasos Patronis.
• Three styles characterising mathematicians’ pedagogical perspectives on proof, Kirsti Hemmi.
• Factors that pre-service elementary teachers perceive as affecting their motivational profiles in mathematics, by Christine M. Phelps.
• The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students, by Mehmet Bekdemir.
• Truth and the renewal of knowledge: the case of mathematics education, by Tony Brown.
• Discussing a philosophical background for the ethnomathematical program, by Denise Silva Vilela.

Thanheiser, in her article, describes a study where she administered a survey to 33 pre-service teachers. The topic of the survey was related to addition and subtraction of multidigit whole numbers, and the respondents were students in an elementary mathematics methods course in the U.S. Apparently, these students were struggling when it came to explaining the mathematics that is underlying the algorithms they use.

The article by Kaisari and Patronis presents us with a glimpse in to the interesting field of elliptic geometry in the context of a university course. The article provides a nice introduction to the mathematical field of non-euclidean geometry, and the authors present and discuss data concerning students’ interaction concerning certain problems within this area of mathematics.

Hemmi’s article presents a very interesting (to me at least) focus on the pedagogical perspectives of mathematicians who teach mathematics at a Swedish university. The conceptual framework for the study builds upon the ideas of Lave and Wenger, but Säljö’s theories concerning artefacts and mediational tools are also included. Naturally, quite a lot of attention is also paid to mathematical proof. In the article, Hemmi presents a theoretical model of three teacher styles when it comes to perspectives on proof.

Like many of the other articles in this issue, Phelps also has a focus on pre-service teachers. Her focus is on their self-efficacy beliefs and learning goals. These beliefs and goals compose the motivational profiles of the pre-service teachers, and Phelps has interviewed 22 such pre-service teachers.

Many students have bad experiences with mathematics in school, and Bekdemir’s aim is to “examine whether the worst experiences and most troublesome mathematics classroom experience affect mathematics anxiety in pre-service elementary teachers” (quoted from the abstract). 167 senior elementary pre-service teachers participated in a study where three different instruments were used. The article provides a nice overview of previous research concerning mathematics anxiety, so if this is something you are interested in, you should check it out!

The article by Tony Brown is more of a theoretical article, and he provides a very interesting discussion of issues related to truth, objectivity and knowledge in mathematics education. One of the theories he introduces and makes use of in his discussion is that of Alain Badiou. This and other interesting theories are presented and discussed, and he ends up concluding/arguing that “the task of education is to ensure that people do not think that they should settle”.

Finally, Vilela’s article provides a discussion of Wittgenstein’s analytical framework, and whether such a framework might be relevant for a philosophical reflection concerning ethnomathematics. This article, which is also a theoretical article, provides interesting insight into the philosophical theories of Wittgenstein, and it might be seen as an attempt to build a philosophical basis for ethnomathematics based on these theories.

So, this issue of ESM should indeed have something of interest – if not for everyone, so at least for many researchers with different interests 🙂

Next week (starting on Monday), The Global Education Conference 2010 is coming up. Maria Droujkova has done an excellent job in collecting (and providing a presentation) of all the mathematics related sessions in this online conference. Many of these sessions might be interesting to the readers of this blog as well, so make sure to check out her blog post on this!

Christopher R. Rakes, Jeffrey C. Valentine, Maggie B. McGatha and Robert N. Ronau have written a very interesting article where they provide a systematic review of research regarding improvement strategies in algebra instruction. Their article is entitled Methods of Instructional Improvement in Algebra: A Systematic Review and Meta-Analysis, and it was published in the latest issue of AERA journal Review of Educational Research. Algebra, they claim, is considered to be “the backbone of secondary mathematics education in the United States” (p. 372), but quite a low proportion of students pass their Algebra II exam. The National Mathematics Advisory Panel were therefore concerned that traditional algebra instruction was not as effective as it should be. In their article, Rakes and colleagues discuss what algebra is, what the main challenges for algebra instruction are, and they present a systematic review of literature based on the following questions:

• What methods for improving algebra instruction have been studied?
• How effective have these methods been at improving student achievement scores?
• Which characteristics of teaching interventions in algebra are the most important for determining the effectiveness of the intervention on student achievement?

Their impressive review consisted of 82 studies that were selected from a time span of 40 years. The results of their study “indicate that a wide variety of reforms effectively improve student achievement in algebra. The degree to which these efforts focus on the development of conceptual understanding also influences the magnitude of effects” (p. 391). If you are interested in algebra instruction, you should definitely take the time to read this interesting 30 page article!

Here is the abstract of their article:

This systematic review of algebra instructional improvement strategies identified 82 relevant studies with 109 independent effect sizes representing a sample of 22,424 students. Five categories of improvement strategies emerged: technology curricula, nontechnology curricula, instructional strategies, manipulatives, and technology tools. All five of these strategies yielded positive, statistically significant results. Furthermore, the learning focus of these strategies moderated their effects on student achievement. Interventions focusing on the development of conceptual understanding produced an average effect size almost double that of interventions focusing on procedural understanding.

Reference

Rakes, C.R., Valentine, J.C., McGatha, M.B., & Ronau, R.N. (2010). Methods of Instructional Improvement in Algebra – A Systematic Review and Meta-Analysis. Review of Educational Research, 80(3), 372-400.