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.
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.
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.
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.
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).
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
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.
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Questions about this project?
To answer additional questions about this project or provide feedback, please contact the program officer.
