Classroom Strategy Diversity and Children’s Early Mathematical Growth

• In Event: Effects of District Efforts to Improve Quality and Coherence of Pre-K–2 Math Instruction

Abstract

In their efforts to improve the quality and coherence of math instruction districts asked teachers to emphasize developing children's problem-solving skills rather than using a learned procedure. We needed an assessment that examined problem-solving strategies as well as correctness, so we used the research-based early mathematics assessment-short form (REMA-SF; Clements et al., 2017). The strategies students used to solve math problems were coded into sophistication levels. Both correctness and strategies were incorporated into the scoring process.

The collection of strategies allows novel analyses. Although considerable research has focused on intra-individual strategy variability and its benefits, we do not know whether classrooms that evince a wider variety of strategies across children (presumably because their teachers encourage students to develop their own strategies) are related to higher mathematics achievement. We created a unique methodology to measure the diversity of strategies within classrooms. In two previous studies, we classified strategy-related ecologies into three categories using a gardening metaphor: unchecked development (children using diverse strategies at all grade levels, shearing (more sophisticated strategies, such as using counting on or derived facts rather than counting all), and pruning (early diversity followed by predominant use of sophisticated strategies). We found that children moving from preschool to kindergarten and first grade showed that preschool strategy diversity within a classroom was strongly related to achievement, but in kindergarten and first grade, less classroom diversity was related to achievement, supporting the pruning ecology (Clements et al., 2020). A second study confirmed these results but revealed that for children who received an effective preK math curriculum, strategy diversity was beneficial at subsequent ages – unchecked development (Dong, 2023, under review).

For this presentation we analyzed longitudinal mathematical scores of 527 students from kindergarten to second grade to examine children’s math growth and its relationship to strategy diversity. A multilevel latent growth model relating children’s learning to the inter-individual strategy diversity in their classrooms revealed that early (preK) diversity of student-generated strategies followed by the next year’s (K) use of fewer and predominantly sophisticated strategies best predicted mathematical growth. The findings thus confirmed that, absent a strong preK intervention, the pruning ecology is most predictive of student growth in math. Apparently, children who first invent their own strategies and then learn over time that some strategies are more effective than others make the most progress in their math skills.

The same data set was analyzed with latent growth modeling to relate the scores (a combination of correctness and strategy sophistication) to classroom practices (Dong et al., 2023b). After controlling math assessment pre-scores and demographic variables in kindergarten, classroom student discussion practices (e.g., students taking with peers; explaining their reasoning) predicted children’s math post-scores, B = 10.61, SE = 3.91, t =2.72, p =.014.

In brief, the findings suggest that variation in student strategy use within classrooms, likely affected by teaching strategies, predicts overall student math achievement and is therefore valuable to examine in studies of math teaching and learning.

Authors

• Crystal A Day-Hess, University of Denver

• Douglas H. Clements, University of Denver

• Dale C. Farran, Vanderbilt University

• Kelley Durkin, Vanderbilt University

• Yixiao Dong, University of California - Santa Barbara

• Julie Sarama, University of Denver