Exploring the relationship between multiplicative double counting stage and multiplication fluency level: A mixed methods study

Teachers spend a considerable amount of time and effort teaching students the basic combinations for multiplication facts, however, learning these facts continues to be a major stumbling block for many elementary students. Student’s fluency with multiplication facts is perhaps one of the most important objectives of teachers in grades three through five because of the impact it has on their comprehension of mathematics concepts introduced in these grade levels, such as fractions. Students continue to leave fourth and fifth grade with little to no multiplicative reasoning or understanding and this impacts them for years to come. The purpose of this study was to (1) examine fourth and fifth grade students’ stages of multiplicative double counting (mDC), (2) examine fourth and fifth grade students’ multiplication fluency levels, (3) determine if there was a correlation between mDC stage and multiplication fluency level, (4) determine the reasoning strategies used by students at each mDC stage, and (5) understand how the mental operations available to students at each stage support their fluency with multiplication facts. To address the questions, 28 fourth grade students and 31 fifth grade students from a rural midwestern elementary school were assessed on mDC stage and multiplication fluency level and then 13 students from each mDC stage were interviewed. The results demonstrated that there was a positive correlation between mDC stage and multiplication fluency level. Second, a student’s mDC stage was moderately related to the fluency strategy they chose when solving multiplication problems. Lastly, the mental operations of the anticipatory mDC students allowed them to demonstrate more efficiency and flexibility when solving multiplication problems, therefore increasing their fluency level. These findings suggest that a student’s ability to reason multiplicatively is positively associated with their ability to be fluent with multiplication facts and that increasing students’ multiplicative reasoning will likely increase multiplication fluency.