The Influence of Instructional Aids on Mathematics Achievement

Abstract

Data from the Second International Mathematics Study were analyzed using dual scaling or correspondence analysis to identify dimensions on which 103 Ontario Grade 8 mathematics teachers varied in reported use of instructional aids. These dimensions were then related to teacher and student characteristics and student achievement in mathematics. Teachers reporting greater use of a variety of instructional aids in the teaching of geometry and of ratio, proportion, and percent also reported greater course coverage. Experienced teachers reported more use of instructional aids. Student achievement in geometry was related to teaching experience and occasional use of a variety of instructional aids. Student achievement in ratio, proportion, and percent was related to teaching experience but was associated with extensive rather than occasional use of aids. The effect of instructional aids did not remain after the influence of topic coverage was removed. The use of instructional aids in the teaching of measurement was unrelated to virtually all teacher and student characteristics as well as student achievement.

A Study Comparing Virtual Manipulatives with Other Instructional Treatments in Third- and Fourth-Grade Classrooms

“…The use of manipulatives (first physical manipulatives, now virtual manipulatives) has a long historical trajectory leading to their prevalence and use in mathematics classrooms today. The research has a 40-year history (Fuson & Briars, 1990;Moyer, 2001;Moyer & Jones, 2004;Parham, 1983;Prigge, 1978;Raphael & Wahlstrom, 1989;Sowell, 1989;Suydam, 1985;Suydam & Higgins, 1977;Thompson, 1992;Uribe-Florez & Wilkins, 2010). Studies of virtual manipulatives began over 25 years ago with the first computer-based manipulatives (Berlin & White, 1986;Clements & Battista, 1989;Clements & Sarama, 2007;Moreno & Mayer, 1999;Moyer-Packenham & Westenskow, 2012;Reimer & Moyer, 2005;Thompson, 1985).…”

‘Concrete’ Manipulatives, Concrete Ideas

“…Students who use manipulatives in their mathematics classes usually outperform those who do not (Driscoll, 1983;Greabell, 1978;Raphael & Wahlstrom, 1989;Sowell, 1989;Suydam, 1986), although the benefits may be slight (Anderson, 1957). This benefit holds across grade level, ability level, and topic, given that use of a manipulative 'makes sense' for that topic.…”

Teaching Aids Effectiveness in Learning Mathematics

“…This research aims to determine the effectiveness of TA in the primary schools especially in grade 7 to 9. The literature provides convincing evidence that TA in teaching Mathematics in the primary school is beneficial and has much significance (Ahmed et al, 2004;Musacchia, Sams, Skoe, & Kraus, 2007;Raphael & Wahlstrom, 1989;Sobel & Maletsky, 1988).…”