Investigating children’s use of derived-fact strategies for addition and subtraction within 20

It is well established that children need to learn to solve addition and subtraction problems using fast, efficient and accurate strategies. However, it is unclear if derived-fact strategies represent such strategies for solving basic problems. In this study we individually interviewed 132 students in Years 3 and 4 (9 and 10 years of age) to investigate the strategies they used to solve addition and subtraction problems within 20. The problems the students solved were carefully planned to represent different problem sets within 20 and an elaborate coding scheme was used to distinguish different types of derived-fact strategies, along with the known fact that was applied. Our findings challenge commonly held assumptions relating to expectations of retrieval and highlight the prevalence of derived-fact strategies. Suggested implications are discussed in terms of, (i) how the teaching of subtraction might be improved, (ii) the number facts children should know, and (iii) the importance of defining terms like proficiency and fluency with basic additive problems to represent the reality of children’s solution strategies. Possible directions for future research are shared.