Co-Principal Investigator: Levine, Susan

Purpose: In this project, researchers will explore malleable factors related to elementary students' use of spatial tools, such as diagrams, charts, and sketches, during mathematics problem solving. Despite research showing strong relations between spatial skill and mathematics, research also indicates learners do not always benefit from spatial supports, and numerous pedagogical considerations can impact their effectiveness (. Student factors such as working memory or fluid reasoning also can moderate the effectiveness of spatial tools, though the moderating effects of spatial skill itself have not been studied previously. In this Exploration project, the researchers will complete two studies designed to (1) determine which cognitive skills have the greatest moderating effects on student responses to mathematics instruction utilizing spatial tools and (2) iteratively test instructional strategies that incorporate spatial and relational thinking to help children deploy spatial tools strategically, incorporating the student factors that were found to be moderators in Study 1. The results from the study will yield a clearer view of the mechanisms underlying students' comprehension of spatial tools and will help teachers use these tools more effectively in elementary mathematics instruction.

Project Activities: In Study 1, the researchers will test student responses to a commonly used visuospatial instructional approach—providing diagrams to students while they are solving word problems— but will incorporate a set of known and hypothesized moderator variables (e.g., spatial visualization skill, working memory, fluid reasoning) to see whether students' responses to this training depend on individual differences in these cognitive skills. In Study 2, the researchers will use findings from research on the psychology of learning to design and test simple modifications to current visuospatial instructional approaches that are predicted to improve students' responses and will explore whether particular modifications are helpful depending on student factors.

Products: This project will generate data that indicate how a range of student and instructional factors combine to produce different student outcomes in mathematics problem solving. The researchers will publish journal articles and book chapters reporting the results, the instructional materials will be freely available, and a publicly accessible final dataset will be made available.

Structured Abstract

Setting: Data collection will take place in elementary schools in the Washington, D.C. and Chicago areas.

Sample: The sample includes a total of 580 3rd grade students, recruited from suburban and urban schools. The research team will use demographic questionnaires to ensure economic and racial/ethnic diversity, with the goal of recruiting a sample that has the same distribution of family income, education, and ethnicity as the national population. The researchers will aim for an equal number of boys and girls.

Factors: The researchers will test both student and instructional factors. The student factors include spatial skill, perceived problem difficulty, working memory, fluid reasoning, and mathematics fluency. Previous research indicates that the latter three factors can affect use of spatial tools during mathematics problem solving. This project will introduce spatial skill and perceived problem difficulty as additional factors, test their contributions relative to the others, and extend these findings to a younger age group than has been tested previously. This is an important advance because younger students tend to be understudied in this area and are more likely to show weak competence in the use of spatial tools. The instructional factors include use of meta-cognitive scaffolding, problem difficulty, and visualization source (self-generated vs. teacher-generated).

Research Design and Methods: Study 1 uses a pretest-training-posttest design. At pretest, the researchers will collect data on five student factors (spatial skill, perceived problem difficulty, working memory, fluid reasoning, mathematics fluency) as well as word problem performance using challenging and grade-appropriate problems. Thus, the researchers can test whether these student factors are related to students' pretest performance on word problems, as well as their propensity to generate visualizations, and whether these effects change based on problem difficulty. During the training phase, the researchers will offer either word problems with a diagram, as has been used in previous research, or word problems with no spatial supports. At posttest, performance on challenging and grade-appropriate word problems will again be measured to both attempt to replicate previous findings using this instructional approach, but also to see whether responses to this training are moderated by the five student factors measured at pretest.

Study 2 is a series of three pretest-training-posttest experiments that pit one instructional approach against another. These contrasts will include (1) whether students are given guided metacognitive scaffolding that explains how to use spatial visualizations strategically; (2) whether problems are challenging or easy; and (3) whether students generate visualizations themselves or are given a visualization to use.

Control Condition: Both studies use active controls that include direct instruction in mathematics. In Study 1, the control differs from the experimental condition only in that it does not include a visuospatial support. In Study 2, each training experiment pits one instructional approach against the other to see which approach is more effective.

Key Measures: Spatial skill will be assessed with the Woodcock-Johnson IV (WJ-IV) Spatial Relations subtest and the Visual Patterns Test (Pickering & Gathercole, 2001). Mathematics fluency will be assessed with the WJ-IV Math Facts Fluency subtest and the KeyMath3 Numeration subtest. Fluid reasoning will be assessed with the WJ-IV Concept Formation and Analysis-Synthesis subtests. Working memory will be assessed with Wechsler's Letter Span task. Listening comprehension will be assessed with the WJ-IV Listening Comprehension subtest. The pretest and posttest measures include the Word Problem Solving Test and an experimenter made test of challenging word problems which will be constructed and pilot-tested prior to use in Study 1.

Data Analytic Strategy: The research team will use multiple linear regression analyses to assess the influence of the hypothesized factors on students' problem-solving scores, their propensity to generate visualizations, and the quality of these visualizations. They will use general linear models with condition (treatment vs. control) as a fixed factor, pretest scores as a covariate, and posttest scores as the dependent variable to test the effects of the iterative training contrasts in Study 2. For the primary analysis, the pre- and posttests will be children's word problem test scores—both accuracy and response time. As a supplemental latent variable analysis, potentially increasing power, all of the above models will be emulated but using all items as factor indicators. The researchers will also consider whether any of these factors combine to yield unique patterns of student outcomes using parameter moderation methods adapted from methodological work by Bauer (2017).

Related IES Projects: Making Sense of Concrete Models for Mathematics (R305A080287); Spatial Ability as a Malleable Factor for Math Learning (R305A150588)