Jon R. Star and Kristie J. Newton have written an article about The nature and development of experts’ strategy flexibility for solving equations. The article was published online in ZDM last week. Algebra is an area of mathematics in which many pupils struggle. There is also an agreement among many researchers that proficiency in algebra includes understanding as well as skills. This study aims at investigating the flexibility of experts’ strategies when solving algebraic equations. Eight experts in school algebra were participating in the study, and their flexibility was measured using a researcher-designed algebra test as well as semi-structured interviews. These interviews were conducted immediately after the participants had completed the test.

Here is the abstract of their article:

Largely absent from the emerging literature on flexibility is a consideration of experts’ flexibility. Do experts exhibit strategy flexibility, as one might assume? If so, how do experts perceive that this capacity developed in themselves? Do experts feel that flexibility is an important instructional outcome in school mathematics? In this paper, we describe results from several interviews with experts to explore strategy flexibility for solving equations. We conducted interviews with eight content experts, where we asked a number of questions about flexibility and also engaged the experts in problem solving. Our analysis indicates that the experts that were interviewed did exhibit strategy flexibility in the domain of linear equation solving, but they did not consistently select the most efficient method for solving a given equation. However, regardless of whether these experts used the best method on a given problem, they nevertheless showed an awareness of and an appreciation of efficient and elegant problem solutions. The experts that we spoke to were capable of making subtle judgments about the most appropriate strategy for a given problem, based on factors including mental and rapid testing of strategies, the problem solver’s goals (e.g., efficiency, error-free execution, elegance) and familiarity with a given problem type. Implications for future research on flexibility and on mathematics instruction are discussed.

I like the title of a new article written by Jeanne Tunks and Kirk Weller, especially the first part of it! Here is the entire title: Changing practice, changing minds, from arithmetical to algebraic thinking: an application of the concerns-based adoption model (CBAM). This article was published online in Educational Studies in Mathematics on Saturday, and it discusses the results of a yearlong innovation program called “Teacher Quality Grant”. And, just to avoid any misunderstandings: it is not only the title of the article I find interesting. The article itself is very interesting, and the program described also appears to be quite interesting. Here is the abstract of the article:

This study examines the process of change among grade 4 teachers (students aged 9–10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the investigation: (1) How did teachers’ concerns about and levels of use of the innovation evolve during the course of the project? (2) What changes in teachers’ perceptions and practices arose as a result of the innovation? Results showed that several of the teachers’ concerns evolved from self/task toward impact. With continued support, several participants achieved routine levels of use, which they sustained beyond the project.

Mashooque Ali Samo has written an article called Students’ Perceptions Abouth the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Govenrment Girls’ Secondary School, Karachi. This article pays attention to misconceptions that arise in Algebra, and it has been published in International Journal for Mathematics Teaching and Learning. Here is the article abstract:

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students‟ difficulties in understanding letters in Algebra, the overall image that emerges from the literature is that students have misconceptions of the use of letters and signs in Algebra. My empirical research done through this study has revealed that the students have many misconceptions in the use of symbols in Algebra which have bearings on their learning of Algebra. It appears that the problems encountered by the students appeared to have connection with their lack of conceptual knowledge and might have been result of teaching they experience in learning Algebra at the secondary schooling level. Some of the findings also suggest that teachers appeared to have difficulties with their own content knowledge. Here one can also see that textbooks are also not presenting content in such an elaborate way that these could have provided sufficient room for students to develop their relational knowledge and conceptual understanding of Algebra. Moreover, this study investigates students‟ difficulty in translating word problems in algebraic and symbolic form. They usually follow phrase- to- phrase strategy in translating word problem from English to Urdu. This process of translating the word problem from English to their own language appears to have hindered in the correct use of symbols in Algebra. The findings have some important implications for the teaching of Algebra that might help to develop symbol sense in both students and teachers. By the help of symbol sense, they can use symbols properly; understand the nature of symbols in different situations, like, in functions, in variables and in relationships between algebraic representations. This study will contribute to future research on similar topics.