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IES Grant

Title: A Longitudinal Study of 3-D Spatial Skills and Mathematics Development in Elementary School Children
Center: NCER Year: 2011
Principal Investigator: Carr, Martha Awardee: University of Georgia Research Foundation
Program: Cognition and Student Learning      [Program Details]
Award Period: 3 years Award Amount: $588,847
Goal: Exploration Award Number: R305A110920
Description:

Co-Principal Investigator: Natalia Alexeev

Purpose: Researchers know little about the relationship between spatial skills and mathematics skills in elementary school populations. The research to date on the relationship between mathematics skills and spatial skills has primarily focused on older students and adults. The goal of this project is to explore the development of mathematics and spatial skills in early elementary school students. Specifically, the study will examine: (1) how spatial skills develop and change over the early elementary school years; (2) how the development of spatial skills is linked to the development of mathematics number sense; (3) whether gender and income moderate the relation between spatial skills and mathematics competency and between number sense and mathematics competency; (4) whether verbal working memory and inhibition moderate the relation between spatial skills and mathematics competency and between number sense and mathematics competency; (5) how the pattern of development of spatial skills and number sense influence performance on 4th grade state mandated mathematics competency test; and (6) whether development trajectories vary as a function of gender, income status, inhibition and verbal working memory. If so, the researchers will study what relations these variable trajectories have to mathematics competency.

Project Activities: The project will include a 3-year longitudinal study beginning in the second grade and ending in the fourth grade. The purpose of the longitudinal study is to examine how spatial skills develop and change over the elementary school years and to examine the relationship between the development of spatial skills and the development of mathematics number sense and competency. A battery of assessments intended to measure spatial skills and mathematics knowledge will be completed by students in the fall and spring of both second and third grade and in the spring of fourth grade. In addition, an experiment designed to determine whether a 5-week training program will improve second and fourth grade students' spatial skills will be conducted. The experimental study will help determine wither spatial skills are malleable in early elementary school students.

Products: The products of this project will include preliminary evidence of how mathematics and spatial skills develop in early elementary school students and the malleability of spatial skills in early elementary school students. Peer-reviewed publications will also be produced.

Structured Abstract

Setting: This study will take place in elementary schools in Georgia.

Population: For the experimental study, 60 second and 60 fourth grade students will participate. For the longitudinal study, 300 second grade students (150 boys and 150 girls) will be recruited and followed longitudinally through the fourth grade. Students with a range of abilities and mixed ethnic groups will be included (25 percent African-American, 10 percent Hispanic, 2 percent Asian and 63 percent Caucasian). Half of the children are eligible for free or reduced lunches.

Intervention: The proposed work will include an experiment designed to determine whether a 5-week training program can improve second and fourth grade students' spatial skills. The training program will be implemented during students' afterschool program and will include exercises to improve students' spatial skills through use of isometric drawings, orthographic drawings, flat patterns, rotation of objects about single and multiple axes, and cutting planes. Each topic will be trained for two half-hour sessions a week for a total of 5 weeks. For each session, the spatial manipulations will be described to the students using three dimensional objects and two dimensional diagrams. The instructor will describe and map the relationships between the three dimensional objects and the two dimensional diagrams. The students will be given the exercises to complete and feedback and instruction will be provided by the instructor as the students complete the exercises.

Research Design and Methods: The 3-year longitudinal study will include 300 second grade students followed through fourth grade. Assessment of spatial skills, number sense in the form of assessments of number magnitude, place value, the ability to decompose number, to solve complex word problems, and cognitive strategy use will occur at five points in time during the 3 year period(fall/spring of second grade; fall/spring of third grade; and fall of fourth grade). Students' scores from the state mandated mathematics test during the spring of fourth grade will be used as an outcome measure. In addition, during Year 2, an experiment will be conducted to determine whether spatial skills are malleable. The experiment will include 60 second grade and 60 fourth grade students participating in afterschool programs. All students will be pretested on verbal working memory, inhibition, and spatial measures. Students will be matched on the spatial measures and then randomly assigned in pairs to the treatment or control condition. Students in the treatment group will receive 5 weeks of instruction (twice a week for 30 minutes each session) for a total of 10 hours of instruction designed to improve spatial visualization and perception. The researchers will compare the treatment and control post-test means on the individual spatial measures controlling for pretest spatial scores, verbal working memory, and inhibition. All data collection will be done individually outside of the classroom.

Control Condition: For the experimental study, students in the control condition will receive the instruction and activities they typically receive as part of their afterschool program.

Key Measures: Spatial skills will be measured using a two-dimensional mental rotation task, a water level task, and a matching parts visualization task. To assess number sense, students will be given mathematics problems focusing on place value, decomposition, number magnitude, and solving complex word problems. Students' mathematics competency will be measured using the scores from the mathematics portion of the Georgia Criterion Referenced Competency Test administered to students at the end of fourth grade. Assessments of students' verbal working memory and inhibition will also be collected.

Data Analytic Strategy: Growth mixture modeling will be used to analyze the longitudinal data. In preparation for the growth mixture modeling, researchers will use factor analysis to determine whether the spatial measures and the number sense measures possess underlying constructs. To determine whether spatial skills are malleable, researchers will compare treatment and control posttest means on the individual spatial measures controlling for pretest spatial scores, verbal working memory and inhibition. Researchers will examine the impact of instruction on each of the three measures of spatial skills.


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