An article called Prospective elementary teachers use of representation to reason algebraically has recently been published online in The Journal of Mathematical Behavior. The article was written by Kerri Richardson, Sarah Berenson and Katrina Staley. Here is the abstract of their article:

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment. The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks. Based on critical events in the teaching experiment, we developed a scale to map changes in preservice teachers’ understanding. Features of the tasks emerged that contributed to this understanding.

Esther Levenson, Dina Tirosh and Pessia Tsamir (all from Tel Aviv University in Israel) have written an article that was recently published in The Journal of Mathematical Behavior. The article is entitled Students’ perceived sociomathematical norms: The missing paradigm. Here is the article abstract:

This study proposes a framework for research which takes into account three aspects of sociomathematical norms: teachers’ endorsed norms, teachers’ and students’ enacted norms, and students’ perceived norms. We investigate these aspects of sociomathematical norms in two elementary school classrooms in relation to mathematically based and practically based explanations. Results indicate that even when the observed enacted norms are in agreement with the teachers’ endorsed norms, the students may not perceive these same norms. These results highlight the need to consider the students’ perspective when investigating sociomathematical norms.

Russel Gersten and colleagues have written an article called Mathematics Instruction for Students With Learning Disabilities: A Meta-Analysis of Instructional Components. This article was published in the recent issue of Review of Educational Research. Here is the abstract of their article:

The purpose of this meta-analysis was to synthesize findings from 42 interventions (randomized control trials and quasi-experimental studies) on instructional approaches that enhance the mathematics proficiency of students with learning disabilities. We examined the impact of four categories of instructional components: (a) approaches to instruction and/or curriculum design, (b) formative assessment data and feedback to teachers on students’ mathematics performance, (c) formative data and feedback to students with LD on their performance, and (d) peer-assisted mathematics instruction. All instructional components except for student feedback with goal-setting and peer-assisted learning within a class resulted in significant mean effects ranging from 0.21 to 1.56. We also examined the effectiveness of these components conditionally, using hierarchical multiple regressions. Two instructional components provided practically and statistically important increases in effect size–teaching students to use heuristics and explicit instruction. Limitations of the study, suggestions for future research, and applications for improvement of current practice are discussed.

Pessia Tsamir, Dina Tirosh, Michal Tabach and Esther Levenson have written an article about Multiple solution methods and multiple outcomes—is it a task for kindergarten children? This article was recently published online in Educational Studies in Mathematics. Here is a copy of their article abstract:

Engaging students with multiple solution problems is considered good practice. Solutions to problems consist of the outcomes of the problem as well as the methods employed to reach these outcomes. In this study we analyze the results obtained from two groups of kindergarten children who engaged in one task, the Create an Equal Number Task. This task had five possible outcomes and five different methods which may be employed in reaching these outcomes. Children, whose teachers had attended the program Starting Right: Mathematics in Kindergartens, found more outcomes and employed more methods than children whose teachers did not attend this program. Results suggest that the habit of mind of searching for more than one outcome and employing more than one method may be promoted in kindergarten.

Keith Weber has written an article that was recently published in The Journal of Mathematical Behavior. The article is entitled How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics. Here is the abstract of Weber’s article:

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes exercises about it. The paper focuses on how Isaac developed an understanding of this concept, how he evaluated whether a mathematical assertion is true or false, how he generated counterexamples to disprove a statement, and the general role examples play for him in concept development and understanding.