A Replication Study to Evaluate the Effects of Schema-Based Instruction on Middle School Students' Proportional Problem-Solving Performance
Author: Jitendra, Asha K.
Date: 2016-00-00
Type: Reports - Research
Subjects: Replication (Evaluation),Schemata (Cognition),Problem Solving,Teaching Methods,Middle School Students,Grade 7,Urban Schools,Mathematics Instruction,Mathematics Tests,Pretests Posttests,Standardized Tests,Hierarchical Linear Modeling,Fidelity,Scores,Validity,Retention (Psychology),Multivariate Analysis

Ratio and proportional relationships are of primary importance during the upper elementary and middle school grades (Kilpatrick, Swafford, &amp; Findell, 2001; National Council of Teachers of Mathematics, 1989, 2000; National Mathematics Advisory Panel [NMAP], 2008). These relationships, along with the interrelated topics of fractions, decimals, and percent provide a critical foundation for algebra (NMAP, 2008). Proportionality involves the concept of ratio and is central to topics in mathematics such as linear functions, scale drawings, similarity, trigonometry, and probability. Proportionality is also at the core of many important concepts in the physical and social sciences. Solving even simple proportion problems is challenging for many children and adolescents when they lack understanding of the problem situation and whether a solution strategy is applicable (Adjiage &amp; Pluvinage, 2007; Fujimura, 2001; Lamon, 2007; Lobato et al., 2010; Miyakawa &amp; Winslow, 2009; NMAP, 2008; Tourniaire &amp; Pulos, 1985; Weinberg, 2002). Although students require instruction that supports the development of underlying concepts and flexible procedures to solve proportion problems (NMAP, 2008; Tourniaire &amp; Pulos, 1985), few intervention studies have been conducted to improve students' learning of ratios and proportions. The purpose of this study was to replicate and extend the study of the schema based instruction (SBI) intervention conducted by Jitendra et al. (in press) that demonstrated impact in proportional problem solving for a homogeneous sample. The following research questions were examined: (1) What are the effects of the SBI intervention on seventh-grade students' proportional problem solving immediately following the intervention and eight weeks following treatment; (2) What are the effects of the SBI intervention on problem solving immediately following the intervention and eight weeks following treatment for students receiving special education services; (3) What are the effects of the SBI intervention on seventh-grade students' general mathematical problem solving; (4) What are the effects of the SBI intervention on general mathematical problem solving for students receiving special education services; and (5) Does the treatment moderate students' learning trajectory over time? The consistent effects in previous randomized studies suggest confidence in the positive effects of SBI in enhancing proportional problem solving (PPS) for all students. This study replicated and extended earlier findings thus enhancing external validity. An SBI effect emerged for the immediate PPS test but unlike the original study (Jitendra et al., in press), participants did not maintain this learning over time for the PPS delayed posttest and the GMADE test. Future research, including a larger sample, is needed to confirm for whom and under what conditions the SBI intervention has positive effects. Tables are appended.