The overarching goal of this 2-phase study was to investigate the contributions of relational reasoning to mathematical thinking and performance for 790 primary and middle-school Chinese students. Phase I of the study was undertaken to establish the reliability and validity of the Test of Relational Reasoning-Junior (TORRjr), a 32-item measure developed to assess children's and young adolescents' ability to reason analogically, anomalously, antinomously, and antithetically. The range of analyses from item difficulties to the overall structural model showed the TORRjr to be a psychometrically sound measure for study participants. There was also evidence of development in students' relational reasoning ability. In Phase II, the contributions of TORRjr performance to results of a novel measure of quantitative relations (QRTC 2 ), a traditional measure of mathematical ability (MAT), and a fluid measure of mental rotation (MRT) were examined. Relational reasoning was significantly associated with performance on all 3 measures to a moderate or moderately strong level. Relational reasoning was also found to partially mediate the association between the QRTC 2 and MAT and fully mediate the relation between MRT and MAT. Multiple-group regression analyses revealed a stronger association between relational reasoning and mathematical performance for middle-school students than for primary students. Theoretical and practical implications of the outcomes from both phases are forwarded. Educational Impact and Implications StatementRelational reasoning is a foundational cognitive ability that allows children, youth, and adults to extract meaningful patterns from the stream of seemingly unrelated information they encounter. In this study, the contributions that relational reasoning made to performance on traditional mathematics or mathematicsrelated measures was investigated for 790 Chinese elementary and middle-school students. Relational reasoning was assessed using the Test of Relational Reasoning-Junior (TORRjr), which was found to be a reliable and valid measure for these third-to seventh-grade students. Three mathematics or mathematicsrelated tests were administered: Mathematics Ability Test, a traditional measure composed of arithmetic, geometry, and algebra problems; Quantitative Relations Test for Chinese Children that gauged students' awareness of quantitative, numeric, mathematical, and featural changes in a novel task; and the Mental Rotations Test, which involved identifying identical but rotated figures within a given array. Results showed that TORRjr performance was significantly associated with all three measures at a moderate to moderately strong level. This outcome points to the importance of promoting and assessing elementary and middle-school students' analogical, anomalous, antinomous, and antithetical reasoning within the context of mathematics learning and instruction.

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In this article, we share what we learned about undergraduates’ struggles in writing quality summaries, comparison texts, and argumentative essays that were components of a unique course, Learning How to Learn. This course was designed to address core psychological issues that impede optimal learning for students from all majors, many of whom are preparing to attend professional or graduate school. Although never intended to be a course devoted to academic writing, the struggles we uncovered made it apparent that without addressing these students’ writing difficulties, especially with argumentation, optimal learning was not achievable. For each form of writing central to the course (i.e., summaries, comparisons, and argumentation), we not only describe the challenges we have documented over the past six years, but also the instructional responses we instituted to counter those challenges. We conclude by sharing insights we have garnered from this experience that may serve others who are confronting similar issues in their students’ writing abilities.

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