Author: Reidar Mosvold

Sociocultural complexity in mathematics teaching

/ Reidar Mosvold / Leave a comment
Barbara Jaworski and Despina Potari have written an article called Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. The article was published in Educational Studies in Mathematics a few days ago. Here is a copy of their abstract:

This paper is methodologically based, addressing the study of mathematics teaching by linking micro- and macro-perspectives. Considering teaching as activity, it uses Activity Theory and, in particular, the Expanded Mediational Triangle (EMT) to consider the role of the broader social frame in which classroom teaching is situated. Theoretical and methodological approaches are illustrated through episodes from a study of the mathematics teaching and learning in a Year-10 class in a UK secondary school where students were considered as “lower achievers” in their year group. We show how a number of questions about mathematics teaching and learning emerging from microanalysis were investigated by the use of the EMT. This framework provided a way to address complexity in the activity of teaching and its development based on recognition of central social factors in mathematics teaching–learning.

Exemplary mathematics instruction in Japanese classrooms

/ Reidar Mosvold / Leave a comment
Yoshinori Shimizu has written an article that I think will be of great interest to many: Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective. For more than a decade, researchers have had a focus on teaching practice in East-Asia, and in particular in Japan. Shimizu aims at examining some key characteristics of exemplary mathematics instruction in Japanese eigth-grade classrooms. The article was published online in ZDM on Wednesday. Here is the abstract:

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.

Conditional inference and advanced mathematical study

/ Reidar Mosvold / Leave a comment

Matthew Inglis and Adrian Simpson have written an article that was recently published online in Educational Studies in Mathematics. The article is entitled Conditional inference and advanced mathematical study: further evidence. Here is the article abstract:

In this paper, we examine the support given for the ‘theory of formal discipline’ by Inglis and Simpson (Educational Studies Mathematics 67:187–204, 2008). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional reasoning skills. We further examine the idea that the differences between the conditional reasoning behaviour of mathematics and arts undergraduates reported by Inglis and Simpson may be put down to different levels of general intelligence in the two groups. The studies reported in this paper call into question this suggestion, but they also cast doubt on a straightforward version of the theory of formal discipline itself (at least with respect to university study). The paper concludes by suggesting that either a pre-university formal discipline effect or a filtering effect on ‘thinking dispositions’ may give a better account for the findings.

Teaching contests

/ Reidar Mosvold / Leave a comment

Yeping Li and Jun Li have written an interesting article called Mathematics classroom instruction excellence through the platform of teaching contests. The article was published online in ZDM on Tuesday. Here is a copy of their abstract:

In this study, we aimed to examine features of mathematics classroom instruction excellence identified and valued through teaching contests in the Chinese mainland. By taking a case study approach, we focused on a prize-winning lesson as an exemplary lesson that was awarded the top prize in teaching contests at both the district and the city level. The analyses of the exemplary lesson itself revealed important features on the lesson’s content treatment, students’ engagement, and the use of multiple methods to facilitate students’ learning. These features are consistent with what the contest evaluation committees valued and what seven other mathematics expert teachers focused in their comments. The Chinese teaching culture in identifying and promoting classroom instruction excellence is then discussed in a broader context.

Didactical designs

/ Reidar Mosvold / Leave a comment
Takeshi Miyakawa and Carl Winsløw have written an article called Didactical designs for students’ proportional reasoning: an “open approach” lesson and a “fundamental situation”. The article was published online in Educational Studies in Mathematics on Saturday. Here is their abstrac:

In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from different cultural and intellectual environments: lesson study in Japan (implicitly based on the “open approach method”) and “didactical engineering” in France (based on the theory of didactical situations). The general aim of our paper is to compare these two environments and their approaches to didactical design, basing our discussion on the concrete designs mentioned above. Clear differences among them are presented, while we also identify links which hold potential for integrating research and practice.

Teaching research groups in China

/ Reidar Mosvold / Leave a comment
Yudong Yang has written an interesting article that was recently published online in ZDM. The article has been entitled How a Chinese teacher improved classroom teaching in Teaching Research Group: a case study on Pythagoras theorem teaching in Shanghai. The Teaching Research Group system seems to be somewhat similar to the Japanese Lesson Study approach, and I find this very interesting. Here is the article abstract:

In China, a school-based teaching research system was built since 1952 and Teaching Research Group (TRG) exists in every school. In the paper, a teacher’s three lessons and the changes in each lesson were described, which might show a track of how lessons were continuously developed in TRG. The Mathematical Tasks Framework, The Task Analysis Guide, and Factors Associated with the Maintenance and the Decline of High-level Cognitive Demands developed in the Quantitative Understanding: Amplifying Student Achievement and Reasoning project (Stein and Smith in Math Teach Middle School 3(4):268–275, 1998; Stein et al. in Implementing stardards-based mathematics instruction. Teachers College Press, NY, pp. 1–33, 2000), were employed in this study. Based on the perspective of Mathematical Task Analysis, changes of three lessons were described and the author provided a snapshot for understanding how a Chinese teacher gradually improved his/her lessons in TRG activities.

Black-white gap in mathematics course taking

/ Reidar Mosvold / Leave a comment
Sean Kelly has written an article about The Black-White Gap in Mathematics Course Taking. This article has been published in a recent issue of the journal Sociology of Education. Here is the abstract of Kelly’s article:

Using data from the National Education Longitudinal Study, this study investigated differences in the mathematics course taking of white and black students. Because of lower levels of achievement, prior course taking, and lower socioeconomic status, black students are much more likely than are white students to be enrolled in low-track mathematics courses by the 10th grade. Using multilevel models for categorical outcomes, the study found that the black-white gap in mathematics course taking is the greatest in integrated schools where black students are in the minority and cannot be entirely accounted for by individual-level differences in the course-taking qualifications or family backgrounds of white and black students. This finding was obscured in prior research by the failure to model course taking adequately between and within schools. Course placement policies and enrollment patterns should be monitored to ensure effective schooling for all students.

Good mathematics instruction in South Korea

/ Reidar Mosvold / Leave a comment
JeongSuk Pang has written an article called Good mathematics instruction in South Korea. The article has recently been published online in ZDM. Here is the article abstract:

There have been only a few studies of Korean mathematics instruction in international contexts. Given this, this paper describes in detail a sixth grade teacher’s mathematics instruction in order to investigate closely what may be counted as high-quality teaching and learning in Korea. This paper then discusses several key characteristics of good mathematics instruction along with some background information on Korean educational practice. This paper concludes with remarks that good mathematics instruction may be perceived differently with regard to underlying social and cultural norms.

Teaching Mathematics and its Applications, issue 1, 2009

/ Reidar Mosvold / Leave a comment

The first issue (of 2009) of Teaching Mathematics and its Applications has been published. Here is an overview of the contents:

Section A Back

Adnan Baki and Bulent Guven
Khayyam with Cabri: experiences of pre-service mathematics teachers with Khayyam’s solution of cubic equations in dynamic geometry environment
Teaching Mathematics and its Applications Advance Access published on February 17, 2009
Teaching Mathematics Applications 2009 28: 1-9; doi:10.1093/teamat/hrp001 [Abstract] [PDF] [Request Permissions]

Paul Glaister and Elizabeth M. Glaister
HMS—harmonic motion by shadows
Teaching Mathematics and its Applications Advance Access published on November 3, 2008
Teaching Mathematics Applications 2009 28: 10-15; doi:10.1093/teamat/hrn022 [Abstract] [PDF] [Request Permissions]

Yiu-Kwong Man
On Feynman’s Triangle problem and the Routh Theorem
Teaching Mathematics and its Applications Advance Access published on January 30, 2009
Teaching Mathematics Applications 2009 28: 16-20; doi:10.1093/teamat/hrn024 [Abstract] [PDF] [Request Permissions]

John Monaghan, Peter Pool, Tom Roper, and John Threlfall
Open-start mathematics problems: an approach to assessing problem solving
Teaching Mathematics and its Applications Advance Access published on January 30, 2009
Teaching Mathematics Applications 2009 28: 21-31; doi:10.1093/teamat/hrn023 [Abstract] [PDF] [Request Permissions]

Keith Parramore
Enlisting excel—again
Teaching Mathematics Applications 2009 28: 32-37; doi:10.1093/teamat/hrp004 [Abstract] [PDF] [Request Permissions]

Tanja Van Hecke
Minimizing the delay at traffic lights
Teaching Mathematics and its Applications Advance Access published on February 17, 2009
Teaching Mathematics Applications 2009 28: 38-42; doi:10.1093/teamat/hrp002 [Abstract] [PDF] [Request Permissions]

Section B Back

Yiu-Kwong Man
A study of two-term unit fraction expansions via geometric approach
Teaching Mathematics and its Applications Advance Access published on October 19, 2008
Teaching Mathematics Applications 2009 28: 43-47; doi:10.1093/teamat/hrn020 [Abstract] [PDF] [Request Permissions]

Chris Sangwin
The wonky trammel of Archimedes
Teaching Mathematics and its Applications Advance Access published on November 28, 2008
Teaching Mathematics Applications 2009 28: 48-52; doi:10.1093/teamat/hrn019 [Abstract] [PDF] [Request Permissions]