Abstract

This dissertation sought to investigate the effects of a mental mathematics intervention on seventh graders’ relational thinking in mathematics, an important topic as relational thinking is a precursor to algebraic reasoning. In this dissertation, improvements in students’ understanding of the equal sign, reasoning about true-false number sentences, mental mathematics, and working memory were addressed over the course of the three studies. The topic is important because there is lack of empirically-validated instructional methods to support students’ relational thinking beyond an understanding of the equal sign. Moreover, the majority of studies investigating ways to improve relational thinking have been conducted at the primary level. All three studies examined the relational thinking of seventh-graders before and after a mental mathematics intervention. In Study 1, students were assessed at three time points on their ability to solve equivalence problems and their reasoning about true-false number sentences. Study 2 replicated Study 1 but also extended it by examining long-term effects and including a measure of students’ mental computation. Study 3 examined whether the effects on relational thinking of a mental mathematics intervention could be augmented beyond what was observed in Studies 1 and 2 if students were permitted to write down parts of their mental computation strategies, thereby reducing their cognitive load. Overall, mean mental mathematics, equivalence, and reasoning about true-false number sentences scores improved following the intervention, suggesting an important link between mental computation and relational thinking. Reducing the cognitive load during mental computational did not have an effect on students’ relational thinking in Study 3. More research is needed on how mental mathematics instruction can serve as an effective tool at the primary and senior high school levels to improve relational thinking. Further studies are also needed to determine the role of working memory in mental mathematics related to relational thinking. Educators can learn from the present studies that mental mathematics contributes positively to students’ relational thinking in the seventh-grade, and that even short mental computation interventions may be effective. Limitations of this dissertation include the focus on only one grade level, as well as possible experimental bias.