Experts' strategy flexibility for solving equations

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.