Perceptual Learning in Early Mathematics: Interacting with Problem Structure Improves Mapping, Solving and Fluency
Author: Thai, Khanh-Phuong
Date: 2014-00-00
Type: Reports - Research
Subjects: Mathematics Instruction,Problem Solving,Word Problems (Mathematics),Intervention,Elementary School Students,Elementary School Mathematics,Grade 3,Pretests Posttests,Statistical Analysis,Perceptual Development,Teaching Methods

Mathematics is the study of structure but students think of math as solving problems according to rules. Students can learn procedures, but they often have trouble knowing when to apply learned procedures, especially to problems unlike those they trained with. In this study, the authors rely on the psychological mechanism of perceptual learning (PL), the natural ability to extract invariant information across multiple learning experiences, to bring about this early appreciation of structure. In two studies, the authors examined the effectiveness of a PL approach to word problems, and to explore the relationship between understanding structure and solving. We designed and tested a PL based intervention called Math Problem Insight (MPI). In MPI, elementary school students practice solving and representing the structure of many word problems that varied along contextual and mathematical dimensions. The goal of MPI is to encourage the learner's own attentional system to highlight and extract invariant structure from varied contexts, by providing variations of verbal structures that map onto related abstract representations. The main research questions were: (1) Can PL interventions in which representation is the goal (rather than computing) help students make better generalization and use symbols to represent situations?; and (2) Are students who are proficient at solving are equally proficient in structure representation? In Study 1, the authors measured students' improvements in solving and representing the structure of word problems from solving and mapping practice with a PL intervention. The study also examined whether students were equally adept at solving and representing equivalent problems. In Study 2, they randomly assigned students to have only either representing experience (the Mapping condition) or solving experience (the Solving condition) during the PL intervention, to examine whether these particular short exercises led to task specific or general improvements with word problems. In Study 1, third-grade homeschoolers enrolled in an online school in Idaho completed the study from home, as part of typical online math assignments. Each student was individually assigned login names and passwords so that they could complete the assignment at their own pace. In Study 2, third-graders from an elementary school in a Midwestern town logged in from their school computers to complete the study. This school expressed interest in the MPI intervention because they had a decrease in the percentage of students passing mathematics. Although Studies 1 and 2 are difficult to compare directly due to different participant groups, the results were consistent with the possibility that the strongest PLM intervention effects occurred when mapping problems, requiring interactions with problem structures across representational formats, were mixed with solving practice also specifically designed to enhance PL. Tables and figures are appended.