Exploring Strategy Use for Multiplication Problem Solving in College Students

Abstract

This study investigated whether strategy accuracy and flexibility on various types of complex multiplication problems could predict college GPA concurrently and longitudinally in 164 college engineering students.  Additionally, it sought to answer whether low- and high-achieving students would show unique patterns of strategy flexibility, accuracy, and recognition of strategies on a complex multiplication task.  Strategy recognition significantly predicted variance in GPA at Time 1 and Time 2; the higher performing students were better at recognizing and executing problems in a forced-strategy format, highlighting the importance of the ability to recognize strategies as an important math skill. Group differences accounted for variance on total recognition, total correct strategy associative property, and total correct strategy distributive property.  Specifically, low- and average-achieving students were relatively similar in their ability to employ strategies, but high-achieving students were significantly better than the other two groups at executing the correct strategies. A significantly higher portion of students was more accurate on problems that incorporated a multiple of 10, which is consistent with the problem-difficulty effect.  Moreover, students of all abilities were more likely to spontaneously use strategies in a non-forced strategy format, suggesting that students had at least some ability to understand the mechanisms behind strategies. Educational implications are discussed.