Mathematical Word Problem Solving Research Articles

Effects of Linguistic Complexity and Math Difficulty on Word Problem Solving by English Learners

Prior research suggests that linguistic complexity may impede mathematics word problem solving by English Learners, but results have been inconsistent. The present study employed an experimental design to investigate the effects of linguistic complexity and mathematics difficulty on word problem solving by middle school English Learners.   Results were consistent with predictions from Cognitive Load Theory: Performance was poorer for word problems written in more complex language compared to the same problems in easier text, and the weakest performance was observed for problems that were both linguistically and mathematically challenging. A Confirmatory Factor Analysis suggested a model including a latent factor, hypothesized to be working memory, provided a good fit to the data.   Additionally, linguistic complexity had a significant influence on students’ perceptions of the mathematical difficulty of the problems.   The results are consistent with recent suggestions that English Learners’ lower performance in math reflects the additional cognitive demands associated with text comprehension.

Instructing Low‐Achievers in Mathematical Word Problem Solving

We describe the effects of an intervention designed to develop the mathematical word problem solving of low‐achievers. The eight students participating in the intervention were selected from 429 10‐year‐olds on the basis of their difficulties in word problem solving. In the intervention, we combined intensive, systematic, and explicit teacher scaffolding in the cognitive, metacognitive, and motivational activities involved in skillful problem solving with carefully designed word problems embedded in a computer‐supported adventure game. The results from the pre‐test, post‐test, and follow‐up test indicate significant effects for the intervention students’ word problem solving compared to the two control groups. A single‐subject study describes the results also at the individual level.

A working memory model applied to mathematical word problem solving

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.

Impact of authenticity on sense making in word problem solving

The study presented in this paper seeks to investigate the impact of authenticity on the students’ disposition to make necessary real world considerations in their word problem solving. The aim is also to gather information about the extent to which different reasons for the students’ behaviors are responsible for not providing solutions that are consistent with the ‘real’ situations described in the word problems. The study includes both written solutions to word problems and interview data from 161 5th graders. The results show an impact of authenticity on both the presence of ‘real life’ considerations in the solution process and on the proportion of written solutions that were really affected by these considerations. The students’ frequent use of superficial solution strategies and their beliefs about mathematical word problem solving were found to be the main reasons for providing solutions that are inconsistent with the situations described in the word problems.

An Evaluation of Curriculum-Based Measurement of Mathematics Word Problem—Solving Measures for Monitoring Third-Grade Students' Mathematics Competence

The purpose of this study was to examine the tenability of a curriculum-based mathematical word problem-solving (WPS) measure as a progress-monitoring tool to index students' rate of growth or slope of achievement over time. Participants consisted of 58 third-grade students, who were assessed repeatedly over 16 school weeks. Students were measured once every 2 weeks on WPS and once each week on mathematics computation. Results provided corroborating data across the two measures and support the adequacy of the WPS measure for monitoring student progress. Findings of slope data are also discussed in terms of mathematical grade-level status (low-performing, LO; average-performing, AV).

Unraveling the culture of the mathematics classroom: A video-based study in sixth grade

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying these mathematical textbooks impact the current teaching of mathematics. Two problem-solving lessons were videotaped in 10 sixth-grade classrooms and a coding scheme was developed to analyze these lessons with regard to three aspects of the classroom culture that are assumed to enhance students’ mathematical beliefs and problem-solving competencies: (1) the classroom norms that are established, (2) the instructional techniques and classroom organization forms, and (3) the set of tasks students are confronted with. Two instruments were administered to measure students’ beliefs about learning mathematical word problem solving, and to assess their problem-solving processes and skills. The results indicate that some reform-based aspects seemed to be easier to implement (e.g., a strong focus on heuristic skills, embedding tasks in a realistic context) than others (e.g., the use of group work, an explicit negotiation of appropriate social norms).

The contribution of working memory to children's mathematical word problem solving

AbstractThe study explored the contribution of working memory to mathematical word problem solving in children. A total of 69 children in grades 2, 3 and 4 were given measures of mathematical problem solving, reading, arithmetical calculation, fluid IQ and working memory. Multiple regression analyses showed that three measures associated with the central executive and one measure associated with the phonological loop contributed unique variance to mathematical problem solving when the influence of reading, age and IQ were controlled for in the analysis. In addition, the animal dual‐task, verbal fluency and digit span task continued to contribute unique variance when the effects of arithmetical calculation in addition to reading, fluid IQ, and age were controlled for. These findings demonstrate that the phonological loop and a number of central executive functions (shifting, co‐ordination of concurrent processing and storage of information, accessing information from long‐term memory) contribute to mathematical problem solving in children. Copyright © 2006 John Wiley & Sons, Ltd.

An Exploratory Validation of Curriculum-Based Mathematical Word Problem-Solving Tasks as Indicators of Mathematics Proficiency for Third Graders

This study evaluated the validity of curriculum-based word problem-solving measures as indicators of proficiency in mathematics with a sample of 77 children in third grade. In the winter and spring of third grade, children completed a battery of general achievement tests in mathematics in addition to curriculum-based problem-solving and computation assessments. Specifically, the study investigated the reliability and concurrent and predictive validity of the word problem-solving measures through correlation and regression analysis. Results supported the adequacy of the word problem-solving measures as useful indicators of mathematics proficiency for third graders.

Mathematics word problem solving for deaf students: a survey of practices in grades 6-12.

One hundred and thirty-three mathematics teachers of deaf students from grades 6-12 responded to a survey on mathematics word problem-solving practices. Half the respondents were teachers from center schools and the other half from mainstream programs. The latter group represented both integrated and self-contained classes. The findings clearly show that regardless of instructional setting, deaf students are not being sufficiently engaged in cognitively challenging word problem situations. Overall, teachers were found to focus more on practice exercises than on true problem-solving situations. They also emphasize problem features, possibly related to concerns about language and reading skills of their students, rather than analytical and thinking strategies. Consistent with these emphases, teachers gave more instructional attention to concrete visualizing strategies than to analytical strategies. Based on the results of this study, it appears that in two of the three types of educational settings, the majority of instructors teaching mathematics and word problem solving to deaf students lack adequate preparation and certification in mathematics to teach these skills. The responses of the certified mathematics teachers support the notion that preparation and certification in mathematics makes a difference in the kinds of word problem-solving challenges provided to deaf students.

Effects of Mathematical Word Problem Solving by Students At Risk or With Mild Disabilities

The differential effects of 2 instructional strategies, an explicit schema-based strategy and a traditional basal strategy, on the acquisition, maintenance, and generalization of mathematical word problem solving were examined. Thirty-four elementary-aged students with mild disabilities or at risk for mathematics failure were randomly assigned to each of the 2 treatment conditions (schema and traditional). Results indicated that both groups' performance increased from the pretest to the posttest. All students were able to maintain their use of word problem-solving skills and generalized the strategy effects to novel word problems. However, the differences between groups on the posttest, delayed posttest, and generalization test were statistically significant, favoring the schema group. In addition, scores on the immediate posttest (77% correct) and delayed posttest (81% correct) for the schema group approached those of a normative sample of 3rd graders (M = 82% correct).

Mathematical Word-Problem-Solving Instruction for Students with Mild Disabilities and Students at Risk for Math Failure

This article reviews published research on mathematical word-problem-solving instruction involving students with mild disabilities and students at risk for math failure. The purpose of the review was to summarize 14 word-problem-solving intervention studies with regards to participants, procedures, and findings and provide implications for future research and classroom practice in teaching word-problem solving. Interventions gleaned from the review entailed representational techniques (e.g., diagramming), strategy-training procedures (e.g., cognitive and metacognitive), task variations (sequencing and word-problem context), and computer-assisted instruction. With the exception of one study, all studies reported positive effects of interventions on students' mathematical word-problem solving.

Interrelationships of Seven Mathematical Abilities across Languages

This study investigated the reliability of seven tests of mathematical abilities and their interrelationships among Spanish-speaking and English-speaking pre-algebra Hispanic students. Mathematical abilities were assessed by tests of divergent thinking, general reasoning, field-dependence, mathematics achievement, reading of mathematicalprose, syllogistic reasoning, and mathematical word problem solving. The results of the study indicated that all of these tests are reliable measures for Spanish-speaking students but that only four were reliable for the English-speaking subjects. None of the intercorrelation coefficients reached significance for the English-speaking pupils, but three intercorrelation indices were significant at the .01 level for the Spanish-speaking students. The implications of these findings for educational policy and mathematics education research are discussed.