Title | The Effects of Instruction in Solving Mathematical Word Problems for Students with Learning Problems: A Meta-Analysis
Authors | Xin, Y.P., & Jitendra, A.K.
Source | Journal of Special Education, 32(4), 207-225.
Year Published | 1999
Provides a synthesis of word-problem-solving intervention research with samples of students with learning problems. The effectiveness of word-problem-solving instruction in 25 outcome studies was examined across student characteristics (e.g., grade, IQ); instructional features (e.g., intervention approach, treatment length); methodological features; skill maintenance; and generalization components.
The overall mean (average) weighted effect size* and percentage of nonoverlapping data* for word-problem-solving instruction were positive across the group-design (GD) studies and single-subject* studies. In addition, positive effects for skill maintenance and generalization were found for GD and single-S studies. Computer-assisted instruction* was found to be most effective for GD studies. Effects for representation techniques and strategy training were found to be significantly higher than the “other” approach for both GD and single-S studies. Long-term intervention effects were significantly higher than short- or intermediate-term interventions for GD studies, whereas both long-term and intermediate treatments were seen to be more effective than short-term treatments for single-S studies. Other significant effects found for GD studies are reported. (PsycINFO Database Record (c) 2004 APA, all rights reserved)
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;
- 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
- 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), U.S. 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.
- 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?
- Number of Studies Included | 25
- Number of Subjects | 644
- Years Spanned | 1980-1996
Students with mild learning disabilities, mild mental retardation, and emotional disabilities; students who received remedial math instruction; and/or students at risk for math failure.
Age/Grade of Subjects
In group design studies, student age ranged from 8 to 65 (mean* = 14.7). In single-subject design studies, student age ranged from 8 to 18 (mean = 13).
Difficulty solving mathematical word problems; learning disabilities
Word-problem solving interventions employing one or more of the following 4 techniques:
- Representation techniques: This approach refers to the interpretation or representation of ideas or information that are given in a word problem. These techniques may include the use of diagrams or symbols, manipulatives, linguistic training, and the use of schemas.
- Strategy training: This approach refers to any explicit problem-solving procedures that lead to the solution of the problem. These techniques may involve teaching students to paraphrase, visualize, make hypothesis and estimate the answer; as well as teaching students how to solve a problem using self-instruction, self-questioning, and self-regulation procedures.
- Computer aided instruction (CAI): This technique uses tutorial or interactive video programs.
- Other: These techniques that may include attention only, the use of calculators and other type of task instruction not included in the above categories.
Some interventions took place inside the classroom, and others took children outside the special education or remedial education classroom for the purpose of participating in the intervention. Teachers and researchers implemented the instruction, and interventions took place individually and in groups.
Duration of Intervention
- Group-design studies ranged in length from 2 days to 4 months, and each session ranged from 30 to 50 minutes.
- Single-subject design studies ranged in length from 5 days to 4 months and each session ranged from 20 to 55 minutes.
Word-problem solving instruction improved the performance of students with learning problems and promoted the maintenance and generalization of the skill. Additional findings are detailed below.
Findings Regarding the General Effectiveness of Word-Problem-Solving Interventions:
- Computer-assisted instruction yielded the largest effect sizes.
- Representation technique was seen to be the next most effective approach in facilitating word-problem performance.
- Strategy training was found to be moderately effective for increasing student’s problem–solving skills.
Intervention Effectiveness and Student Characteristics:
- Grade/age did not interfere with the effect size of the intervention.
- 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.
- Students labeled with LD seemed to benefit less from intervention than students with mixed disabilities or those at risk.
Treatment Outcomes/ Instructional Features:
- Long-term interventions are more effective than short-term interventions.
- 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).
- Individual instruction is more effective than group instruction.
- Interventions involving simple one step problems yielded larger effect sizes than multi-step word problems or mixed problem types.
Relationship Between Methodological Features:
- Publication bias and group assignment did moderate the effect size.
Effectiveness of Word-Problem-Solving Instruction in Fostering Skill Maintenance and Generalization:
- 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.
- Results of both group and single subject studies indicate that maintenance and generalization were influenced by treatment length.
- A high level of student directed intervention was seen to result in greater levels of maintenance and generalization.
Combined Effects Size
The overall mean effect size* in the group design studies was large (d = 0.89), while the treatment effect for single subject studies was 89%.
- 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.
* Terms Defined
Computer Assisted Instruction | Instructional use of a computer to present material, practice skills, monitor student learning, and assess individual learner needs and progress.
Effect Size (ES or d) | A statistical calculation, often represented as ES or d, that measures the impact of an intervention. An effect size below d = 0.20 suggests that a treatment did not have a significant effect. An effect size of d = 0.20 is considered small or low; an effect size of d = 0.50 is considered moderate; an effect size of d = 0.80 or above is large.
Mean (a.k.a. Average) | A measure of central tendency, calculated by dividing the sum total of a set of numbers by the number of figures in the set (i.e. of the set 5, 6, 8, 10, the average is 7.25-derived by: 5+6+8+10=29, 29 divided by 4= 7.25).
Meta-Analysis | A widely-used research method in which (1) a systematic and reproducible search strategy is used to find as many studies as possible that address a given topic; (2) clear criterion are presented for inclusion/exclusion of individual studies into a larger analysis; and (3) results of included studies are statistically combined to determine an overall effect (effect size) of one variable on another.
Single-Subject Design | Research design that uses only a single participant or single unit of observation (e.g., a single family or a single organization) for measuring interventions.
Weighted-Mean | A method of calculating a mean score where greater or less significance is placed on some scores based on a predetermined sliding scale as opposed to combining all scores equally. Example: Often a weighted mean is calculated in meta-analytical research where findings across a number of individual studies are combined. The results of a study with fewer subjects would receive less weight than a study basing results on a larger number of subjects.