Video-based assessment

March 16, 2011 / Reidar Mosvold / Leave a comment

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.

Research on affect at CERME7

February 10, 2011February 10, 2011 / Reidar Mosvold / 3 Comments

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.

Creating and using representations, ZDM theme issue

February 8, 2011 / Reidar Mosvold / Leave a comment

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

… and it has appeared!

January 11, 2011 / Reidar Mosvold / Leave a comment

Just before Christmas, I wrote about a forthcoming issue of TMME. This issue has now appeared, and (as usual) all the articles are freely available for anyone! I am not going to repeat the rather impressive list of authors and titles for this issue, since you can easily find that for yourself. I would only like to point you to the excellent editorial by the main editor (Professor Bharath Sriraman), entitled: Opening 2011’s Journal Treasure Chest. And this issue truly is a treasure chest! So, point your cursor towards the journal’s home page, and dig into the chest!

New issue of TMME soon to appear

December 20, 2010 / Reidar Mosvold / 1 Comment

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:

View this document on Scribd

2011 is already here (at least in Educational Studies in Mathematics)

December 13, 2010 / Reidar Mosvold / Leave a comment

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

Argumentation and proofs in elementary calculus

November 30, 2010 / Reidar Mosvold / Leave a comment

Ferdinando Arzarello and Cristina Sabena have written an article entitled Semiotic and theoretic control in argumentation and proof activities. This article was recently published online in Educational Studies in Mathematics. Here is an abstract of their article:

We present a model to analyze the students’ activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin’s structural description of arguments, Peirce’s notions of sign, diagrammatic reasoning and abduction, and Habermas’ model for rational behavior. Based on empirical qualitative analysis we identify three different kinds of semiotic actions featuring the organization of the argumentations, and related to different epistemological status of the arguments. In such semiotic actions, the students’ argumentation and proof activities are managed and guided according to two intertwined modalities of control, which we call semiotic and theoretic control. The former refers to decisions concerning the selection and implementation of semiotic resources; the latter refers to decisions concerning the selection and implementation of a more or less explicit theory or parts of it. The structure of the model allows us to pinpoint a dialectical dynamics between the two.

Imagining mathematics teaching practice

November 29, 2010 / Reidar Mosvold / Leave a comment

Sandra Crespo, Joy Ann Oslund and Amy Noelle Parks have written an article that was recently published online in ZDM – The international journal on mathematics education. The article is heading towards an interesting topic: that of mathematics teaching practice. The title of their article is Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion. Here is the abstract:

Prospective teachers work with a variety of representations of mathematics teaching (i.e., narrative cases, transcripts, video clips) in teacher preparation courses. Generally, they are considered the audience, not producers, of those artifacts. In this article, however, we focus on representations produced by prospective teachers when they were asked to generate a hypothetical classroom dialogue for the equality task: “What goes in the box: 8+4=[ ]+5?” We discuss the nature and quality of the representations produced by four different cohorts of teacher preparation students—prior to admission, at the beginning, middle, and end of their program. Prospective teachers within and across all cohorts produced an unexpected diversity of representations of class discussions. Of special interest to us were their hybrid representations, those that combined multiple images of mathematics teaching practices. These representations not only provide a lens into prospective teachers’ development as mathematics teachers but could also become tools to support novices as they learn more complex forms of mathematics teaching.

Two interesting articles on teachers’ knowledge

November 25, 2010November 25, 2010 / Reidar Mosvold / Leave a comment

In the recent issue of Journal for Research in Mathematics Education, two interesting articles about teachers’ mathematical knowledge for teaching are published. One of these articles, “The nature and predictors of elementary teachers’ mathematical knowledge for teaching“, was written by Heather C. Hill. Here is the abstract of her article:

This article explores elementary school teachers’ mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.

The other article was written by Courtney A. Bell, Suzanne Wilson, Traci Higgins and D. Betsy McCoach, and this article is entitled “Measuring the effects of professional development on teacher knowledge: the case of developing mathematical ideas“. The abstract of their article can be found below:

This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers’ specialized knowledge for teaching mathematics and illustrates how such research could be conducted. This study adds to our understanding of the ways in which professional development program features, facilitators, and issues of scale interact in the development of teachers’ mathematical knowledge for teaching. Study limitations and challenges are discussed.

Preschoolers’ notion of chance and probability

November 24, 2010November 24, 2010 / Reidar Mosvold / Leave a comment

Zoi Nikiforidou and Jenny Pange have written an article about The notions of change and probabilities in preschoolers, which was published in the most recent issue of Early Childhood Education Journal. Here is the abstract of their article:

Chance, randomness and probability constitute statistical notions that are interrelated and characterize the logicomathematical thinking of children. Traditional theories support that probabilistic thinking evolves after the age of 7. However, recent research has underlined that children, as young as 4, may possess and develop basic notions, through mental mechanisms and/or through intuitive processes. In the current study, preschoolers (N = 200) aged 4–6, participated in two diverse probability tasks related to the likelihood of events and the graphical representation of randomness. The aim of this study was to test whether children, at this young age, have the ability to predict the most probable outcome in a probabilistic game with animal cards and whether they can mark symbols randomly distributed in a 5 × 5 matrix. Preschoolers infered correctly the most likely outcome and showed a minimal understanding of randomness by preferring the uniform rather than random distribution of items. Such findings have both methodological and educational implications for further research as already the notions of chance and probabilities are integrated in Preschool Mathematics Curricula worldwide.