Individual differences and change relationships between algebraic ability, working memory, and worry

© 2015 Dr. Kelly TreziseThe effects of emotion on cognition and of cognition on emotion are commonly examined separately. Anxiety-performance theorists, for example, claim that anxiety reduces available working memory (WM) capacity, and emotion regulation theorists claim that good working memory capacity allows emotions (e.g., anxiety) to be controlled. Since WM and anxiety have been implicated in math problem solving abilities, an explicit understanding of the reciprocal relationship between WM and anxiety would be beneficial for theories of math cognition. Currently, little is known whether the reciprocal interactions between WM and anxiety remain stable over time, are similar or different across individuals, are affected by contextual goals (studying for an exam), or different patterns of stability and/or change affect complex math problem solving differentially. To investigate these issues three studies examined the impact of WM-worry interactions on 14 year-olds’ algebraic problem solving. In Study 1, 80 students completed algebraic worry, algebraic WM, algebraic problem solving, non-verbal IQ and general math ability tasks. Worry level and WM capacity were subjected a latent profile analysis; four subgroups that differed in worry level and WM capacity were identified. Subgroup membership predicted algebraic problem solving accuracy: High WM/Low Worry > Moderate WM/Low Worry = Moderate WM/High Worry > Low WM/High Worry. The findings suggest a non-linear relationship between WM and worry relationship, and that WM-worry relationships predict algebraic problem solving abilities. The study suggests that individual differences in WM and worry interact, but indicate a different approach is required to separate the effects of WM and worry to identify their effects on each other, and their respective effects on algebraic problem solving. In Study 2, 137 students completed WM and algebraic worry tasks several times in a single day. A latent change model analysis examined the reciprocal influences of WM and worry over time, as well as their conjoint effects on an algebraic problem solving performance test. The findings showed WM decreased when worry was high, and worry increased when WM was low and WM and worry conjointly independently affected algebraic problem solving ability. The findings suggest that worry reduces WM capacity, and a good WM capacity helps to regulate worry, and that WM supports problem solving, while worry impairs problem solving ability. In Study 3, 126 students’ algebraic WM and algebraic worry were assessed twice in a single day. Latent transition analysis identified different patterns of WM/worry relationships. Subgroups differed in the degree to which WM and worry remained stable and/or changed across the two assessment occasions. For some subgroups, WM and worry remained stable across occasions and, for others, WM/worry relations changed. Moreover, subgroup membership predicted algebraic problem solving accuracy and response times. Overall, the findings show that individual differences in the stability/change patterns of WM/worry relationships are important predictors of math problem solving abilities. The pattern of findings suggests contemporary anxiety-cognition theories need to be amended to better account for individual differences in WM and anxiety. It is proposed that future research examine profiles of cognition-emotion relationships and their transitions over time, in order to characterise the cumulative effects of individual differences