A Comparison of Two Approaches for Teaching Complex, Authentic Mathematics Problems to Adolescents in Remedial Math Classes

Abstract

Two groups of adolescents with learning difficulties in mathematics were compared on their ability to generate solutions to a contextualized problem after being taught problem-solving skills under two conditions, one involving standard word problems, the other involving a contextualized problem on videodisc. All problems focused on adding and subtracting fractions in relation to money and linear measurement. Both groups of students improved their performance on solving word problems, but students in the contextualized problem group did significantly better on the contextualized problem posttest and were able to use their skills in two transfer tasks that followed instruction.

Teaching Mathematical Problem Solving to Middle School Students in Math, Technology Education, and Special Education Classrooms

“…The content validity of the tests was supported by their use in previous studies (e.g., Bottge, 1999;Bottge & Hasselbring, 1993;Bottge et al, 2002) and by previous research showing that the test items reliably estimated mathematics achievement (Cohen, Bottge, & Wells, 2001). We calculated the interrater reliability of each measure on 20% of the test protocols from a randomly selected sample of pretests and posttests by dividing the number of agreements by the total number of agreements and disagreements and multiplying by 100 (Sulzer-Azaroff & Mayer, 1977).…”

“…Previous studies have shown that average-and low-achieving students who were taught with EAI solved sophisticated problems in mainstream and remedial math classrooms and were more successful in applying what they learned in technology education classrooms than students who were taught with TBI (Bottge, 1999;Bottge & Hasselbring, 1993;Bottge, Heinrichs, Chan, & Serlin, 2001). In a recent study conducted in inclusive classrooms, the same positive results were found for students without disabilities (Bottge, Heinrichs, Mehta, & Hung, 2002).…”

Cognitive Factors' Influence on Fraction Development in Students of Varying Ability Levels

“…Part of this is due to the logistical difficulty in finding large enough samples of students with math LD to analyze statistically. In fact several of the studies mentioned in the previous paragraphs included students with LD but did not disaggregate their findings from students who simply had MD (e.g., Bottge & Hasselbring, 1993;Kelly et al 1986;Moore & Carnine, 1989). Although the common use of MD in math research does provide some data about the performance of students who are most at risk, the practice cannot capture the differences that do exist between students who simply have MD and students who have LD (e.g., Mazzocco & Devlin, 2008).…”

“…Studies have found cue cards (Joseph & Hunter, 2001), mnemonic devices (Test & Ellis, 2005), and schema based instruction (Xin, Jitendra, & Deatline-Buchman, 2005) to be effective interventions for students with LD. Several other studies (Bottge, 1999;Bottge & Hasselbring, 1993;Bottge, Heinrichs, Mehta, & Hung, 2002;Bottge et al, 2010) have focused on using contextualized or anchored instruction to improve students' problem solving skills. Results of this line of research seem to show the most promise when the contextualized instruction is paired with extra instruction (e.g., Mastery Fractions videodisc program).…”

The effects of computer assisted instruction and structured curriculum on struggling mathematics students.

“…Researchers noted significant time must be allowed for the conceptual understanding to develop into strong computational performance (Bottge & Hasselbring, 1993;Woodward, Baxter, & Robinson, 1999). In fact, in their review of research connecting teaching practices to student learning, Hiebert and Grouws (2007) found that teaching promoting conceptual development also leads to increased procedural fluency.…”