Learning environments of beginning algebra students : compulsory adolescent vs. voluntary adult classes

Abstract

The main purpose of this study was to investigate differences between adolescents and adults enrolled in beginning algebra courses in terms of their perceptions of preferred and actual learning environment and their attitudes toward mathematics. In addition, I investigated the validity of the learning environment and attitude questionnaires, as well as associations between the learning environment and attitudes among high-school and community-college students in Fresno County in California. A sample of 750 students from 38 classes in five high schools and two community colleges were involved. The learning environment was assessed with three scales (Teacher Support, Investigation, and Task Orientation) from the actual and preferred forms of the What Is Happening In this Class? (WIHIC), whereas students’ attitudes were assessed with two scales (Value of Mathematics and Self Confidence) from the Attitudes Toward Mathematics Inventory (ATMI).Principal axis factoring with varimax rotation and Kaiser normalization supported a strong facture structure for a 24-item three-scale version of the actual or preferred forms of the WIHIC and for a 25-item two-scale version of the ATMI. The total percentage of variance accounted for by the three WIHIC scales was nearly 60% for the preferred form and just over 60% for the actual form, and by the two ATMI scales was roughly 56%. The alpha reliability coefficient for every WIHIC and ATMI scale was at least 0.88, therefore demonstrating strong internal consistency for all scales.MANOVA and effect sizes were used to provide information about the statistical significance and magnitude of the differences between high-school and college students’ scores separately for each WIHIC and ATMI scale. For the WIHIC environment scales, between-group differences were statistically significant for actual Teacher Support (effect size of 0.24 standard deviations), actual Task Orientation (effect size of 0.70 standard deviations), and all preferred environment scales (effect sizes ranging from 0.36 to 0.78 standard deviations. For the ATMI, differences between groups were statistically significant for Value of Mathematics and associated with an effect size of 0.50 standard deviations. Differences between high-school students and community-college students were statistically nonsignificant for the ATMI scale of Self Confidence (with a small effect size of 0.18 standard deviations). Relative to high-school students, college students preferred more teacher support, involvement and focus on classroom tasks, perceived a greater level of teacher support and personal dedication to classroom activities, and reported higher ratings for the value in mathematics.Finally, the use of simple correlation and multiple regression analyses demonstrated positive associations between students’ attitudes toward mathematics and the learning environment. The simple correlation was statistically significant between each WIHIC scale (Teacher Support, Involvement and Task Orientation) and each ATMI scale (Value of Mathematics and Self Confidence) with the student as the unit of analysis, and between the ATMI scale of Value of Mathematics and the WIHIC scales of Teacher Support and Task Orientation and between Self Confidence and Involvement. The multiple regression analyses showed that the WIHIC scale of Task Orientation was a significant independent predictor of Value of Mathematics at both the individual and class level of analysis, and that Involvement and Task Orientation were significant independent predictors of Self Confidence when the student was used as the level of analysis. The direction of every significant correlation and regression coefficient was positive, suggesting that a greater emphasis on the three learning environment scales of Teacher Support, Involvement and Task Orientation was related to higher Value of Mathematics and Self Confidence scores.