Abstract
Relational thinking involves understanding equivalence and numerical relationships. The present study examined the relational thinking of seventh graders before and after a 15-day mental mathematics intervention in the context of whole number arithmetic. Using two intact seventh-grade classes and a staggered treatment design, students were assessed at three time points on their (a) ability to solve equivalence problems, and (b) reasoning abilities about true–false number sentences. The results indicated that the students in the class that received the intervention first (the Intervention First group) improved their performance on both measures after the intervention, and a similar pattern was found for the second class (the Intervention Second group), indicating that each group improved immediately following the mental mathematics intervention. Students in the Intervention First group were able to maintain their scores on the test of equivalence problems 4 weeks after the conclusion of the intervention. As the results suggest a link between mental mathematics and relational thinking, it is recommended that mental mathematics play a more prominent role in the seventh-grade mathematics classroom.
Highlights
Among the many concepts included in the middle- and secondary-school curricula is algebra, a topic that often causes much difficulty for many students [8, 17, 33]
That choosing a mental computation strategy is an act of relational thinking because it relies on creating implicit transformations that rely squarely on both “sameness” and substitution principles of mathematical equivalence [18]
Suitable comparisons were those not affected by the intervention, namely between Time 2 and Time 3 for the Intervention First group and between Time 1 and Time 2 for the Intervention Second group
Summary
Among the many concepts included in the middle- and secondary-school curricula is algebra, a topic that often causes much difficulty for many students [8, 17, 33]. As algebra is known to be a gatekeeper to students’ future academic and professional opportunities [22, 41], alleviating their struggles in algebra is of critical importance. While algebra allows for mathematical generalizations and solving for unknown quantities, critical to its success is its precursor, algebraic reasoning. Algebraic reasoning has been conceptualized as attending to patterns and rules in creating mathematical generalizations [8], and is important because it allows for an understanding of the structure of mathematics. Individuals who are successful in algebraic reasoning are able to discover patterns in a variety of mathematical expressions, and further generalize these patterns from familiar to unfamiliar situations.
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