Brian A. Bottge

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

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.

Effects of Contextualized Math Instruction on Problem Solving of Average and Below-Average Achieving Students

The purpose of the study was to investigate the effect of contextualized math instruction on the problem-solving performance of 17 middle school students in one remedial class and 49 middle school average-achieving students in two prealgebra classes. The study employed experimental and quasi-experimental designs to compare the impact of word problem instruction and contextualized problem instruction on computation skills and problem-solving performance. Results showed that students in the contextualized problem remedial and prealgebra groups outperformed students in the word problem groups on a contextualized and a transfer problem. In an extended transfer activity, students in the remedial class applied what they had learned in order to plan and build two skateboard ramps. Results support the use of contextualized problems to enhance the problem-solving skills of students in general and remedial classes.

Weighing the Benefits of Anchored Math Instruction for Students with Disabilities in General Education Classes

The purpose of this study was to examine the effectiveness of enhanced anchor instruction and traditional problem instruction in improving the problem-solving performance of 42 seventh-grade students with and without disabilities in general education classrooms. Qualitative research strategies embedded in a quasi-experimental, nonequivalent control-group design permitted investigators to describe and compare the problem-solving performances of individual students with disabilities in general education settings. Previous research has suggested that students with disabilities can solve math problems that are meaningful and motivating in remedial settings; however, few studies have examined whether those improvements can be achieved in general education classrooms. Results of this study indicated that the students without disabilities profited from contextualized instruction, but benefits for the students with disabilities were equivocal. Explanations for these findings are offered, and implications for instruction are described.

Shrinking Achievement Differences With Anchored Math Problems Challenges and Possibilities

Multiple measures administered in repeated waves within a nonequivalent dependent variables quasi-experimental design were used to test the effects of a reform-oriented instructional method called Enhanced Anchored Instruction (EAI) on the math achievement of 128 middle school students, including students with learning disabilities (LD). EAI problems are presented in multimedia and hands-on formats, a potential benefit for students with low skills in both reading and math. Overall, students of all ability levels benefited from EAI with effect sizes (η2) ranging from .53 to .59. Results revealed that although students with LD scored lower on pretests, their learning trajectories matched those of students without LD. A maintenance test administered several weeks after instruction showed that students with LD retained what they had learned. Implications for instruction and suggestions for future research are provided.

Reconceptualizing Mathematics Problem Solving for Low-Achieving Students

Over the past century, learning theorists have advised researchers and practitioners on ways to improve student math performance. Available evidence suggests that these messages are mostly undelivered or unaccepted, or both, especially as they pertain to students who are unsuccessful in school. One of the reasons for the disconnection may be confusion about how learning theory can help identify suitable ways of delivering mathematics instruction to special populations. Based on a review of the literature in general education and special education, this article proposes a key model for teaching math to at-risk students. Implications of the model for research and instruction are explored.

Effects of Video-Based and Applied Problems on the Procedural Math Skills of Average- and Low-Achieving Adolescents

The purpose of this study was to investigate the effects of video-based, anchored instruction and applied problems on the ability of 11 low-achieving (LA) and 26 average-achieving (AA) students to solve computation and word problems. A repeated-measures design with staggered baselines was used to compare the performance of two groups of LA students and one group of AA students across three instructional conditions: (a) baseline instruction, (b) anchored instruction, and (c) instruction with applied problems. The performance of all three groups was higher during anchored instruction than during the baseline condition, but no differences were found between instruction with applied problems and the baseline condition. Qualitative analyses revealed that some LA students made fewer errors on computation and word problems during the anchored condition, whereas other students continued to make the same procedural mistakes. The findings suggest that some LA students can improve their procedural math skills as they work on solving engaging problems but other students need more explicit instruction to improve their computation skills and basic math understanding.

Situating Math Instruction in Rich Problem-Solving Contexts: Effects on Adolescents with Challenging Behaviors.

This mixed-methods study assessed the effects of enhanced anchored instruction (EAI) on the math achievement of 17 adolescents who attended an alternative high school for at-risk students with challenging behaviors. EAI is a method specially designed for developing the math skills of low-achieving adolescents that uses multimedia-based and hands-on math problems to support learning in generative learning environments. Results indicated that students scored higher on both curriculum-aligned problem-solving tests (ES = 0.75 and 0.78), but they showed no improvement on a fraction computation test or on standardized measures. Descriptive data from classroom observations and poststudy interviews suggest instructional and learning factors that may account for the findings.

Impact of Enhanced Anchored Instruction in Inclusive Math Classrooms

The Common Core State Standards for Mathematics will place more pressure on special education and math teachers to raise the skill levels of all students, especially those with disabilities in math (MD). The purpose of this study was to assess the effects of enhanced anchored instruction (EAI) on students with and without MD in co-taught general education classrooms. Results showed that students in the EAI condition improved their performance on math skills contained in several of the standards. Effect sizes were especially large for students with MD when the special education teacher more actively participated in the instructional activities with the math teacher. Classroom observations provided examples of how teachers can work together to benefit students in inclusive math settings.

Effects of Blended Instructional Models on Math Performance

A pretest-posttest cluster-randomized trial involving 31 middle schools and 335 students with disabilities tested the effects of combining explicit and anchored instruction on fraction computation and problem solving. Results of standardized and researcher-developed tests showed that students who were taught with the blended units outscored students in Business As Usual classes. Students made the largest gains in computing with fractions and on problems related to ratios, proportions, and geometry. The findings suggest important implications for the way curriculum is designed for middle school students with disabilities who exhibit low performance in math.

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

Abstract This study compared two approaches for teaching sixth-grade middle school students to solve math problems in math, technology education, and special education classrooms. A total of 17 students with disabilities and 76 students without disabilities were taught using either enhanced anchored instruction (EAI) or text-based instruction coupled with applied problems (TBI). Results showed that both EAI and TBI students benefited from instruction in their math class, but EAI students were able to maintain and transfer what they learned in the technology education classroom several weeks later. The performance level of students with disabilities was low in both groups, but additional small-group instruction in special education settings helped several students with disabilities achieve at levels commensurate with their peers without disabilities.