Attempts to Solve the Problem at Hand: The Dynamic Relations Between the Presentation of Math Problems, Individual Cognitive Factors, and Problem-Solving Strategies
The strategies used during problem-solving are often considered an important indicator of mathematical cognition. These strategies range from observable gestures, like finger counting, to implicit memory strategies like direct retrieval (Geary et al., 1991). Across development, strategy use changes in frequency and type (Siegler, 1987). However, numerous factors can influence both strategy use and accuracy for children and adults alike. The four studies in this international symposium highlight how individual differences in cognitive factors interact with mathematical content, such as variations in problem presentation, as well as how this interaction, in turn, shapes strategy implementation and ultimate math performance.
In the first paper, Raychel Gordon (Doctoral Student, University of Maryland - College Park) and her collaborators will present work on the relations between school-aged children’s working memory, and differences in both strategy and explanation modality used during arithmetic problem-solving. Results will be discussed as to how individual differences in working memory, math knowledge, age, and gender may play a role in children’s use of gesture, verbal, or other strategies.
The second paper, presented by Fanny Ollivier (Doctoral Student, Université Rennes 2) and her colleagues, considers how variations in visual working memory (VWM) for adolescents with intellectual disability (ID) are related to their gesture strategies during calculation. Their findings suggest that individual differences in VWM may impact the efficacy of gesture as a problem-solving strategy. Specifically, for those in the sample with low VWM, the use of gestures improved their calculation, whereas for those with high VWM the use of gestures negatively impacted their calculation.
In the third paper, Venera Gashaj (Postdoctoral researcher, Learning Sciences & Higher Education, ETH Zürich) and her collaborators will discuss relations between domain-specific cognitive abilities, and how this relates to differences in mathematical stimuli. Specifically, adult math novices and experts were shown both symbolic and nonsymbolic proofs and then were asked to explain a randomly chosen proof. During this time, they were also either encouraged to gesture or prohibited from doing so. These findings help to unpack the relations between problem representation, math knowledge, and gesture as a strategy.
In the fourth paper, Avery Closser (Doctoral student, Worcester Polytechnic Institute) and her colleagues will present work regarding how differences in perceptual manipulation of math notation (e.g., 3+4*2 versus 3 + 4*2) interact with differences in cognitive abilities. Specifically, they assess whether college students’ inhibition abilities moderates the effect of spacing of the problem presentation on students’ accuracy and response time. This study provides key insight into how inhibition shapes the perception of and response to differences in problem representations.
Together, these papers continue to unpack how differences in domain-general and domain-specific cognitive abilities can interact with various types of math problems, leading to observable differences in both strategy use and accuracy. These studies include a variety of age groups and diverse methodologies. Overall, findings from these papers highlight the dynamic relations between how math problems are presented, individuals’ cognitive abilities, and problem-solving strategies.