The September issue of Educational Studies in Mathematics was published last week, and – as always – it contains a number of interesting articles.

• Re-mythologizing mathematics through attention to classroom positioning, by David Wagner and Beth Herbel-Eisenmann
• Encrypted objects and decryption processes: problem-solving with functions in a learning environment based on cryptography, by Tobin White
• Using diagrams as tools for the solution of non-routine mathematical problems, by Marilena Pantziara, Athanasios Gagatsis and Iliada Elia
• Social representations as mediators of practice in mathematics classrooms with immigrant students, by Núria Gorgorió and Guida de Abreu
• Success in mathematics within a challenged minority: the case of students of Ethiopian origin in Israel (SEO), by Tiruwork Mulat and Abraham Arcavi
• Examining the supervision of mathematics student teachers through analysis of conference communications, by Maria Lorelei Fernandez and Evrim Erbilgin
• Approach to mathematical problem solving and students’ belief systems: two case studies, by María Luz Callejo and Antoni Vila
• Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction, by Doug M. Clarke and Anne Roche

I would like to point your interest to Tobin White’s article in particular, since this is an Open Access article. So, regardless of whether you are a subscriber or not, this article is freely available to all!

Esther Levenson has written an article called Fifth-grade students’ use and preferences for mathematically and practically based explanations. The article was published online in Educational Studies in Mathematics a few days ago. What Levenson refers to as “practice based explanations” are related to what others refer to as real-life connections, students’ informal knowledge, etc. Practice based explanations do not rely on mathematical notions only, and include explanations that use manipulatives and explanations that are based on real-life contexts. Obviously, this implies that there is a variety of explanations to consider, and Levenson provides a nice overview of some relevant literature within this field. She also discusses students’ evaluations of explanations, and she thereby enters a discussion of the different types of knowledge you need to have.

The study she reports from is a combination of quantitative and qualitative analysis of data from a total of 105 students in 5th grade (in Israel). Data were collected from two questionnaires, in addition to follow-up interviews with some of the students.

Here is the abstract of Levenson’s article:

This paper focuses on fifth-grade students’ use and preference for mathematically (MB) and practically based (PB) explanations within two mathematical contexts: parity and equivalent fractions. Preference was evaluated based on three parameters: the explanation (1) was convincing, (2) would be used by the student in class, and (3) was one that the student wanted the teacher to use. Results showed that students generated more MB explanations than PB explanations for both contexts. However, when given a choice between various explanations, PB explanations were preferred in the context of parity, and no preference was shown for either type of explanation in the context of equivalent fractions. Possible bases for students’ preferences are discussed.

Jaehoon Yim (South Korea) has written an article entitled Children’s strategies for division by fractions in the context of the area of a rectangle. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of the article:

This study investigated how children tackled a task on division by fractions, and how they formulated numerical algorithms from their strategies. The task assigned to the students was to find the length of a rectangle given its area and width. The investigation was carried out as follows: First, the strategies invented by eight 10- or 11-year-old students, all identified as capable and having positive attitudes towards mathematics, were categorised. Second, the formulation of numerical algorithms from the strategies constructed by nine students with similar abilities and attitudes towards mathematics was investigated. The participants developed three types of strategies (making the width equal to 1, making the area equal to 1, and changing both area and width to natural numbers) and showed the possibility of formulating numerical algorithms for division by fractions referring to their strategies.

The latest issue of American Educational Research Journal contains several articles that are interesting for the mathematics education research community. Here are three that I find particularly interesting:

• National Income, Income Inequality, and the Importance of Schools: A Hierarchical Cross-National Comparison, by Amita Chudgar and Thomas F. Luschei. Abstract: The international and comparative education literature is not in agreement over the role of schools in student learning. The authors reexamine this debate across 25 diverse countries participating in the fourth-grade application of the 2003 Trends in International Mathematics and Science Study. The authors find the following: (a) In most cases, family background is more important than schools in understanding variations in student performance; (b) schools are nonetheless a significant source of variation in student performance, especially in poor and unequal countries; (c) in some cases, schools may bridge the achievement gap between high and low socioeconomic status children. However, schools’ ability to do so is not systematically related to a country’s economic or inequality status.
• Assessing the Contribution of Distributed Leadership to School Improvement and Growth in Math Achievement, by Ronald H. Heck and Philip Hallinger. Abstract: Although there has been sizable growth in the number of empirical studies of shared forms of leadership over the past decade, the bulk of this research has been descriptive. Relatively few published studies have investigated the impact of shared leadership on school improvement. This longitudinal study examines the effects of distributed leadership on school improvement and growth in student math achievement in 195 elementary schools in one state over a 4-year period. Using multilevel latent change analysis, the research found significant direct effects of distributed leadership on change in the schools’ academic capacity and indirect effects on student growth rates in math. The study supports a perspective on distributed leadership that aims at building the academic capacity of schools as a means of improving student learning outcomes.
• The Hispanic-White Achievement Gap in Math and Reading in the Elementary Grades, by Sean F. Reardon and Claudia Galindo. Abstract: This article describes the developmental patterns of Hispanic-White math and reading achievement gaps in elementary school, paying attention to variation in these patterns among Hispanic subgroups. Compared to non-Hispanic White students, Hispanic students enter kindergarten with much lower average math and reading skills. The gaps narrow by roughly a third in the first 2 years of schooling but remain relatively stable for the next 4 years. The development of achievement gaps varies considerably among Hispanic subgroups. Students with Mexican and Central American origins—particularly first- and second-generation immigrants—and those from homes where English is not spoken have the lowest math and reading skill levels at kindergarten entry but show the greatest achievement gains in the early years of schooling.

Eirini Geraniou has written an article called The transitional stages in the PhD degree in mathematics in terms of students’ motivation. This article was published online in Educational Studies in Mathematics on Friday. Here is the abstract of Geraniou’s article:

This paper presents results of a longitudinal study in the transition to independent graduate studies in mathematics. The analysis of the data collected from 24 students doing a PhD in mathematics revealed the existence of three transitional stages within the PhD degree, namely Adjustment, Expertise and Articulation. The focus is on the first two transitional stages, since the data collection focused mainly on these. Based on the first two transitional stages and the students’ ways of dealing with them, which were called ‘survival strategies’, three types of students were identified. The importance of motivation for each transitional stage and the successful transition overall are considered as well.

Summer is over, and I am back at work (and blogging)! I am not going to try and catch up with everything that has been published and done during my vacation, but rather start with what is new now.

One of the major journals – ZDM – has recently released a new issue: Volume 41, Number 4. This issue contains 11 articles, in addition to the introduction by Stephen J. Hegedus and Luis Moreno-Armella.

• Intersecting representation and communication infrastructures, by Stephen J. Hegedus and Luis Moreno-Armella
• Sounds and pictures: dynamism and dualism in Dynamic Geometry, by Nicholas Jackiw and Nathalie Sinclair
• Artifacts and signs after a Vygotskian perspective: the role of the teacher, by Maria Alessandra Mariotti
• Time for telling stories: narrative thinking with dynamic geometry, by Nathalie Sinclair, Lulu Healy and Cassia Osorio Reis Sales
• Potential scenarios for Internet use in the mathematics classroom, by Marcelo C. Borba
• “No! He starts walking backwards!”: interpreting motion graphs and the question of space, place and distance, by Luis Radford
• Dynamic mathematics and the blending of knowledge structures in the calculus, by David O. Tall
• Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation, by Richard Noss, Celia Hoyles, Manolis Mavrikis, Eirini Geraniou, Sergio Gutierrez-Santos and Darren Pearce
• Co-action with digital technologies, by Luis Moreno-Armella and Stephen J. Hegedus
• Book review: Menghini, M., Furinghetti, F., Giacardi, L. and Azarello, F. (eds.): The first century of the International Commission on Mathematical Instruction (1908–2008): reflecting and shaping the world of mathematics education, by Michael N. Fried
• ICMI Study 20: educational interfaces between mathematics and industry, by Alain Damlamian and Rudolf Sträßer