An Experiment in Teaching Ratio and Proportion

Abstract

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the corpus of ratio problems in a physical context. But in one class, here called "Partialexperiment", the learning environment was exclusively a paper-pencil one and the teacher followed his usual method in designing and conducting teaching sequences. In the other class, here called "Full-experiment", the teaching was based on a framework, emerging from our analysis of complexity of ratio problems, involving precise guidelines and a specific computer environment. Using a pre-test and a post-test, we observed clear progress in both classes compared to a sample of "standard" pupils. Our comparative pupil-oriented study indicates more complete improvement in the "full-experiment" class, i.e., a better acquisition of fractions and their use for solving usual proportionality problems. The average pupil's progress is greater in the "full experiment", with the pupils who were initially high-or low-level attainers benefiting the most from the "full-experiment".

Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

“…Furthermore, proportionality is closely associated with real-world applications and for understanding many problems in science, and technology (Karplus, Pulos, & Stage, 1983;Lo & Watanabe, 1997; Tourniare & Pulos, 1985). Thus, it is disconcerting that many SCHEMA-BASED INSTRUCTION 4 upper elementary and middle school students evidence difficulty in solving even simple proportion problems (Adjiage & Pluvinage, 2007).…”

“…Furthermore, proportionality is closely associated with real-world applications and for understanding many problems in science, and technology (Karplus, Pulos, & Stage, 1983;Lo & Watanabe, 1997; Tourniare & Pulos, 1985). Thus, it is disconcerting that many SCHEMA-BASED INSTRUCTION 4 upper elementary and middle school students evidence difficulty in solving even simple proportion problems (Adjiage & Pluvinage, 2007).Conventional efforts to improve the teaching and learning of proportions have had limited success, as evidenced by reports showing that college students and young adults continue to struggle with proportional reasoning (Ahl, Moore, & Dixon, 1992;Cai & Wang, 2006; Fujimura, 2001;Jitendra, Woodward, & Star, 2011;Lamon, 2007). Some scholars have proposed that students' difficulties with proportions may be related to the ways that this topic is treated in many mathematics texts (e.g., Lamon, 1999).…”

Mapping Free Educational Software Intended for the Development of Numerical and Algebraic Reasoning

“…It is important to use a variety of experiences involving proportional reasoning and to encourage students to make conjectures, create rules, and generalize learning (Adjiage & Pluvinage, 2007;Ontario Ministry of Education, 2012). In math education, some concepts are interconnected to aid in the construction of proportional thinking.…”

Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items

“…Many researchers claimed that proportion is a difficult concept for many students (Adjiage & Pluvinage, 2007;Alatorre & Figueras, 2005;De Bock, Van Dooren, Janssens, & Verschaffel, 2002;Litwiller & Bright, 2002;Watson, Beswick, & Brown, 2012). Researchers Behr, Harel, Post, & Lesh (1992) called for clarity in the definitions of rational numbers and fractions, claiming that in real-world problems, fractions and rational numbers have multiple "personalities".…”

“…Adjiage and Pluvinage (2007) reported on an experiment, which tested the framework for the acquisition of fractions and solving proportionality problems they had developed by analysing the complexity of ratio problems in the middle grades. They claimed that the concepts of fractions, ratios and proportionality are important in mathematics and that the teaching approach based on their framework and computer software, supporting trial and error methods, leads to gains in students' understanding of these concepts.…”