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Educators can infer from this study that mental mathematics may serve as an effective way to enhance relational thinking at the middle-school level (e.g., the seventh and the eighth grades).
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These results suggest, in line with our hypothesis, that improvements in mental mathematics may be related to students' relational thinking.
Because of apparent overlap in cognitive processes required for relational thinking and mental computation, one might hypothesize that instruction that targets fluency in mental computation would enhance children's conceptions of the equal sign and their relational thinking more generally.
In our study, on the contrary, almost 50% of the students used relational strategies rather than computation on at least two of the problems on the relational thinking test following the mental mathematics intervention, providing further support for the role of mental computation in enhancing students' relational thinking.
relational thinking test.
Fig. 2 Relational thinking coding examples.
In sum, fostering relational thinking is critical because it gives meaning to arithmetic, leads to conceptual understanding of number and number properties, and enhances students' thinking about mathematical generalizations [17, 32, 43].
Refinements could be based on existing assessments of relational thinking.
Relational thinking involves understanding equivalence and numerical relationships.
As such, without viewing the equal sign symbol as a relational one, further relational thinking can be impeded.
Despite the apparent relationship between algebraic reasoning and relational thinking, the literature on teaching for algebraic reasoning through relational thinking is incomplete.
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Justyna Jupowicz-Kozak
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