DOI: 10.5061/dryad.sn02v6xh8
title: Algebra equation solving performance by LD and non-LD students using hands-on equations (grades 6-8)

description: This dataset contains quantitative student performance data from a study
 investigating the effectiveness of the Hands-On Equations program, Level
 1, a balance model-based manipulative approach, for teaching algebraic
 equations to middle school students. The dataset captures pre- and
 post-instructional scores on algebra tests administered to a diverse
 sample of students, including those in regular and Learning Disabled (LD)
 classrooms. The dataset is structured with individual student records,
 containing scores from three distinct assessment points. Data from a total
 of 167 students (Grades 6-8) across three LD classes (n=46) and five
 regular classes (n=121) from a middle school in the Northeastern United
 States. The dataset consists of students' numerical scores across the
 three assessment time points. The dataset is designed to facilitate
 comparisons of student performance: within-grade gains (pre-test vs.
 post-tests; differences in performance between LD and regular classrooms;
 and relative improvements between LD and regular student groups. The
 analysis of this dataset showed considerable score enhancements from
 pre-tests to post-tests for all participating classes (both regular and
 LD), with LD students exhibiting significantly greater average gains than
 regular students. This dataset holds reuse potential for researchers
 interested in mathematics education (particularly algebra instruction at
 the middle school level), the efficacy of concrete manipulatives in
 teaching abstract mathematical concepts, and instructional strategies for
 students with learning disabilities (LD). It may be particularly useful to
 researchers who want to compare other educational interventions to the
 Hands-On Equation program and to researchers who desire to compare
 learning gains that can be obtained with the same educational intervention
 across different student populations. The anonymized student-level scores
 make it valuable for various statistical re-analyses or meta-analyses. The
 data set includes the six equations presented on each test, and any
 further information can be obtained from the author. Concerning ethical
 considerations, the data was collected anonymously via forms where
 teachers recorded scores without personal identifiers. Number codes
 replaced personal names during data processing to ensure
 de-identification. Research Domain (OECD Fields of Science and Technology
 classification): 5.3 Educational sciences Keywords: Algebra Education,
 Mathematics Manipulatives, Learning Disabilities, Middle School, Hands-On
 Equations, Equation Solving, Educational Interventions
description: # Algebra equation solving performance using hands-on equations for
 students with learning disabilities and their peers (grades 6-8) Dataset
 DOI: [10.5061/dryad.sn02v6xh8](10.5061/dryad.sn02v6xh8) ## **File list** *
 Algebra_Equation_Solving_Performance_Using_Hands-On_Equations_Manipulatives_(Grades_6-8).csv * LD_Study_SAV_File.sav * Borenson_LD_Study_Output_File.pdf ## **File descriptions** **Algebra_Equation_Solving_Performance_Using_Hands-On_Equations_Manipulatives_(Grades_6-8).csv–** the data in unformatted form. **LD_Study_SAV_File.sav–** the data for direct use in SPSS. **Borenson_LD_Study_Output_File.pdf**- results from statistical analysis (see Output file description under Usage Notes for further information). ## **Usage Notes** **Datafile Description** * **Variables/Columns:** * Nr: Anonymized unique identifier for each student. * pretest: Score (0-6 points) on the initial algebra assessment administered before instruction. * posttestM: Score (0-6 points) on the post-instructional algebra assessment administered after six lessons using manipulatives. * posttestWM: Score (0-6 points) on the final post-instructional algebra assessment administered after the seventh lesson (paper and pencil solution). * Grade: Student's grade level (6, 7, or 8). * LD: Categorical variable indicating class type (Regular =0 or LD=1). * Classroom: Anonymized unique identifier for each classroom. * dif1:  posttestM-pretest. * dif2: posttestWM-pretest. * filter_$ = Categorical variable that can be used to select Grade 7 (value = 1). **Output File Description** This document (**Borenson_LD_Study_Output_File.pdf**) presents the statistical analysis results generated from the dataset. The analysis includes descriptive statistics, nonparametric tests (Mann-Whitney U Test and Kruskal-Wallis Test), and Friedman's Two-Way Analysis of Variance by Ranks, along with related pairwise comparisons and effect sizes. The document is organized into several sections, each detailing different statistical outputs: Descriptive Statistics (Pages 1-3) * Provides summary statistics for pretest, posttestM, and posttestWM variables. * Breakdown of descriptives by Classroom (1.00 to 8.00) and LD (0.00 and 1.00). * Includes: * N: Sample size for each group. * Minimum: Lowest observed value. * Maximum: Highest observed value. * Mean: Average score. * Std. Deviation: Measure of data dispersion. * Skewness: Measure of asymmetry of the probability distribution. * Kurtosis: Measure of the "tailedness" of the probability distribution. --- Nonparametric Tests: Mann-Whitney U Test (Pages 3-5, 27-30, 34-38, 42-44, 64-65) * This test is used to compare differences between two independent groups on a continuous or ordinal dependent variable. * Comparisons: * pretest, posttestM, posttestWM are compared across LD groups (0.00 vs. 1.00) for different Grade levels (6.00, 7.00, 8.00). * pretest, posttestM, posttestWM are compared across Classroom groups (e.g., 4.00 vs. 6.00, 4.00 vs. 5.00, 5.00 vs. 6.00) for Grade 7.00. * dif1 and dif2 are compared across LD groups (0.00 vs. 1.00). * Outputs include: * Ranks: Mean Rank and Sum of Ranks for each group. * Test Statistics: Mann-Whitney U, Wilcoxon W, Z-score, Asymptotic Significance (2-tailed), and sometimes Exact Significance. --- Nonparametric Tests: Kruskal-Wallis Test (Pages 5-18) * This test is used to compare differences between three or more independent groups on a continuous or ordinal dependent variable. * Comparisons: * pretest, posttestM, posttestWM are compared across Classroom categories for Grade 6.00 and 7.00. * Outputs include: * Hypothesis Test Summary: States the null hypothesis and the decision (Reject/Retain). * Test Statistics: Chi-Square, Degrees of Freedom (df), Asymptotic Significance. * Pairwise Comparisons: If the overall test is significant, this table provides comparisons between specific classroom pairs with adjusted significance values (Bonferroni correction). * Continuous Field Information/Histograms: Visual distribution of scores for pretest, posttestM, posttestWM by grade. * Categorical Field Information: Counts per classroom within a grade. --- Nonparametric Tests: Friedman Test (Pages 44-45, 47-55) * This test is used to compare three or more related (dependent) samples, typically within-subjects comparisons (e.g., pretest vs. posttest on the same individuals). * Comparisons: * pretest, posttestM, and posttestWM are compared within each Classroom (4.00, 5.00, 6.00). * Outputs include: * Ranks: Mean Rank for each variable within classrooms. * Test Statistics: Chi-Square, Degrees of Freedom (df), Asymptotic Significance. * Kendall's W: Coefficient of Concordance, indicating agreement among ranks. * Pairwise Comparisons: If the overall test is significant, this table provides comparisons between the three measures (pretest, posttestM, posttestWM) with adjusted significance values. --- T-Test and Effect Sizes (Pages 65-66) * Group Statistics: Provides means, standard deviations, and standard errors for dif1 and dif2 by the LD grouping variable. * Independent Samples Test: Conducts an independent samples t-test to compare dif1 and dif2 between the two LD groups. * Includes Levene's Test for Equality of Variances. * Provides t-statistic, degrees of freedom, significance (one-sided and two-sided), mean difference, and confidence intervals. * Independent Samples Effect Sizes: Calculates effect sizes (Cohen's d, Hedges' correction, Glass's delta) for the differences in dif1 and dif2 between the LD groups, along with their confidence intervals. **The Six Questions of Each Test** |   | X1 | X6 | X7 | | :-------- | :--------------------- | :--------------------- | :---------------------- | | Test Item | Benchmark Pre-test | Lesson 6 Post-test | Lesson 7 Post-test | | Item #1 | 2*x* = 8 | 2*x* = 10 | 2*x* = 6 | | Item #2 | *x* + 3 = 8 | *x* + 3 = 8 | *x* + 3 = 10 | | Item #3 | 2*x* + 1 = 13 | 2*x* + 2 = 12 | 2*x* + 1 = 7 | | Item #4 | 3*x* = *x* + 12 | 3*x* = *x* + 4 | 3*x* = *x* + 2 | | Item #5 | 4*x* + 3 = 3*x* + 6 | 4*x* + 3 = 3*x* + 9 | 4*x* + 3 = 3*x* + 7 | | Item #6 | 2(2*x* + 1) = 2*x* + 6 | 2(2*x* + 1) = 2*x* + 8 | 2(2*x* + 1) = 2*x* + 10 |