A naturalistic study of executive function and mathematical problem-solving

Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of eighth-grade students’ mathematical problem-solving were conducted. A fine-grained coding of the students’ talking-aloud during problem-solving in mathematics involved isolating the challenges students faced in each one of the four problem-solving phases, and then making a functional link to one of the executive functions of shifting, updating, and inhibiting. In total, 344 episodes were analyzed. Our results show that updating proved to be most challenging during the understanding the problem phase, inhibiting during the carrying out the plan phase, and shifting during the looking back and evaluation phase. Furthermore, students are more likely to make progress with the problem-solving if they are able to engage in a conscious appraisal of the problem at the onset of the problem-solving. Assisting students in establishing what the problem requires through the cognitive clues presented in the problem may necessitate explicit instructional on behalf of the teacher.

► Middle-school students’ mathematical problem-solving was explored using a naturalistic design.
► Executive function of working memory was used as a functional construct for the analysis.
► Different aspects of executive function implicated at different phases of problem-solving.
► Explicit instruction may be necessary to assist students to identify cognitive clues in the problem.