The Effects of Instruction in Solving Mathematical Word Problems for Students with Learning Problems: A Meta-Analysis
Title
The Effects of Instruction in Solving Mathematical Word Problems for Students with Learning Problems: A Meta-Analysis
Author
Xin, Y.P., & Jitendra, A.K.
Source
Journal of Special Education
Year Published
1999
Background
Difficulties in math are greater for students with mild disabilities such as learning disabilities*, mild mental retardation*, emotional disabilities*; or at risk* for mathematic failure. Previous research has reported that students with learning disabilities tend to have mathematical performance below their grade level, that students with mental retardation score significantly lower than age-equivalent students with learning disabilities on four mathematic domains (basic concepts, listening, vocabulary, problem solving, and fractions); and that word-problem solving is difficult for students with disabilities who evidence problems in reading, computation or both (Cawley and Miller, 1989; Parmar, Cawley & Miller, 1994; Dunlap, 1982). It appears that students with mild disabilities follow the pattern of poor problem solving performance of general education students. According to the National Center for Education Statistics (1991, 1992) US students have ranked lower than students in other countries in many mathematical areas. Word-problem solving presents challenges for students of all abilities and age levels. This meta-analysis collected intervention studies on solving word problems and examined the relationship between students’ characteristics and intervention outcomes.
Research Questions
- What is the general effectiveness of word-problem-solving interventions (e.g. representation, strategy training, computer aided instruction (CAI)*?
- Is intervention effectiveness related to important student characteristics (i.e., grade/age, IQ level, or classification label)?
- Are treatment outcomes related to instructional features, such as (a) setting, (b) length of treatment, (c) instructional arrangement, (d) implementation of instruction, (e) word-problem task; (f) student-directed intervention?
- Is there a relationship between methodological features (publication bias, group assignment, and effect size)?
- What is the effectiveness of word-problem-solving instruction in fostering skill maintenance and generalization? Are skill maintenance and generalization functions of instructional features?
Findings
Word-problem solving instruction improved the performance of students with learning problems and promoted the maintenance and generalization of the skill.
- Findings Regarding the General Effectiveness of Word-Problem-Solving Interventions:
(a) Computer-assisted instruction yielded the largest effect sizes.
(b) Representation technique was seen to be the next most effective approach in facilitating word-problem performance.
(c) Strategy training was found to be moderately effective for increasing student’s problem–solving skills.
- Intervention Effectiveness and Student Characteristics
(a) Grade/age did not interfere with the effect size of the intervention.
(b) IQ had a mediating influence on the effect size. Students who had IQ scores below 85 scored higher than students with IQ scores above 85.
(c) Students labeled with LD seemed to benefit less from intervention than students with mixed disabilities or those at risk.
- Treatment Outcomes/ Instructional Features
(a) Long-term interventions are more effective than short-term interventions.
(b) Short-term interventions (no more than seven sessions), were seen to be more effective than the intermediate-term interventions (more than 7 sessions, but not more than 1 month).
(c) Individual instruction is more effective than group instruction.
(d) Interventions involving simple one step problems yielded larger effect sizes than multi-step word problems or mixed problem types.
- Relationship Between Methodological Features
(a) Publication bias and group assignment did moderate the effect size.
- Effectiveness of Word-Problem-Solving Instruction in Fostering Skill Maintenance and Generalization
(a) In general, word-problem solving instruction seemed to positively affect skill maintenance (d* = 0.78) and generalization (d = 0.84). Students may benefit from specific word-problem solving instruction for skill maintenance and generalization.
(b) Results of both group and single subject studies indicate that maintenance and generalization were influenced by treatment length.
(c) A high level of student directed intervention was seen to result in greater levels of maintenance and generalization.
Conclusion/Recommendations
- The effects of varied instructional approaches on student learning are encouraging.
- Students with learning problems should have the opportunity to apply the learned skills in new situations and contexts.
- The effectiveness of word-problem solving approaches could be diminished if students do not have a solid background or prerequisite skill knowledge.
- Teaching and assessing for generalization of word-problem solving is important.
For future research, it is important that studies:
- Provide detailed information of study characteristics, clearly define population, and provide detailed descriptions of the intervention and comparison conditions.
- Address how acceptable interventions are to teachers and students, and should continue to assess skill maintenance on an ongoing basis.
- Assess students understandings of concepts and skills needed to solve word problems.