Relational reasoning’s contributions to mathematical thinking and performance in Chinese elementary and middle-school students.

Abstract

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.

The Development of Relational Reasoning in South Korean Elementary and Middle-School Students: A Cross-Sectional Investigation

“…In contrast, the measurement invariance seems little to do with their gender. This invariance by gender opens up more discussions due to its inconsistency with previous investigation (Zhao et al, 2020) although the measurement invariance captured in this study is more promising for the use of TORRjr in the field. Only according to the current study result, we can conclude TORRjr is a fair measure for relational reasoning in any gender.…”

“…No items in anomaly, antithesis, and antinomy were indicated as being extremely easy to students at every grade. These item difficulties indicated that the TORRjr was a little easier for this sample of South Korean children than had been reported for the norming sample of Chinese children in grades 3 to 7 (Zhao et al, 2020). The analogy scale, followed by the anomaly scale, appeared to be the easiest for students at every grade level.…”

“…On the one hand, the TORR has been found to be invariant with regard to age, gender, and ethnicity for college-age students (Dumas and Alexander, 2018). On the other hand, Zhao et al (2020) found a difference in TORRjr performance, with girls scoring higher than boys at grade 7. Thus, the findings from the current investigation may serve to corroborate or disconfirm the gender effect reported by Zhao et al for Chinese children. 3.…”

“…We expected that grade level is a determinant of students' relational reasoning performance. In prior investigations involving populations of primary, elementary, and middleschool students and using various research methodologies and data sources, evidence emerged that certain forms of relational reasoning are earlier developing, specifically analogical and anomalous reasoning (Jablansky et al, 2016(Jablansky et al, , 2019Zhao et al, 2020).…”

“…The four scales were presented in a fixed order (i.e., analogy, antinomy, antinomy, and antithesis), and each scale began with two sample items. No order effects were reported in previous studies based on random-ordered versions (Dumas and Alexander, 2016;Zhao et al, 2020). These sample items, which were not scored, were included to help students understand the directions and to reorient them as they moved to different scales.…”