Journal of Mathematical Behavior 31 (2012) 196–208 Contents lists available at SciVerse ScienceDirect The Journal of Mathematical Behavior j ourna l ho me pag e: w ww.elsevier.com/locate/jmathb A naturalistic study of executive function and mathematical problem-solving Donna Kotsopoulos a,∗ , Joanne Lee b,1 a Faculty of Education, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2C 3L5 b Faculty of Science, Department of Psychology, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2C 3L5 a r t i c l e i n f o Article history: Available online 24 January 2012 Keywords: Executive function Instruction Mathematics Problem-solving a b s t r a c t Our goal in this research was to understand the specific challenges middle-school stu- dents 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 chal- lenging during the understanding the problem phase, inhibiting during the carrying out the plan phase, and shifting during the looking back and evaluation phase. Furthermore, stu- dents 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 stu- dents in establishing what the problem requires through the cognitive clues presented in the problem may necessitate explicit instructional on behalf of the teacher. © 2012 Elsevier Inc. All rights reserved. 1. Introduction According to the National Council of Teachers of Mathematics (2000, 2006), problem-solving is both the cornerstone of mathematics and a primary pedagogical tool through which mathematical learning ought to and does occur. Studies of mathematics instruction across international settings suggest that up to 40% of classroom time is devoted to problem- solving (Mullis, Martin, & Foy, 2008). Numerous studies suggest that problem-solving in mathematics improves learning outcomes and facilitates deeper and more meaningful understanding for students (Callejo & Vila, 2009; Cobb, Yackel, Wood, & Wheatley, 1988; Montague & Dietz, 2009; Mousoulides, Christou, & Sriraman, 2008; Schoenfeld, 1994; Stice, 1987). Perhaps the most enduring problem-solving model in mathematics emerged from Polya (1957). His 4-step problem- solving model includes understanding the problem, devising a plan, carrying out the plan, and looking back and evaluating the plan. Understanding the problem involves determining what the mathematical problem requires in terms of the mathe- matical concepts and procedures, accessing prior knowledge, and isolating pertinent information (rather than irrelevant or extraneous contexts). Devising a plan involves selecting appropriate mathematical processes and operations, and establish- ing procedures which are then executed to solve the problem. Carrying out the plan requires that mathematical processes ∗ Corresponding author. Tel.: +1 519 884 1970. E-mail addresses: dkotsopo@wlu.ca (D. Kotsopoulos), jlee@wlu.ca (J. Lee). 1 Tel.: +1 519 884 1970. 0732-3123/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jmathb.2011.12.005