Mathematical Word Problem Solving Research Articles

Towards Effective Learning: Understanding the Connections of Vocabulary, Reasoning, and Mathematical Word Problem-Solving in Islamic Elementary Education

Towards Effective Learning: Understanding the Connections of Vocabulary, Reasoning, and Mathematical Word Problem-Solving in Islamic Elementary Education

Task Characteristics Associated with Mathematical Word Problem-Solving Performance Among Elementary School-Aged Children: A Systematic Review and Meta-Analysis

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students’ performance is important. The objective of this systematic review and meta-analysis was to evaluate the effects of linguistic and numerical task characteristics associated with mathematical word problem-solving performance among elementary school-aged children (Grades 1 to 6). The systematic review was based on five electronic databases and citation searching. Reporting was conducted following The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA). The findings (K = 69) showed that five of the six investigated linguistic task characteristics (i.e., the position of the unknown, schematic structure, irrelevant information, realistic considerations, and lexical consistency) and one of the two numerical task characteristics (i.e., number of operations) were related (g = 0.39 to 4.26) with elementary school-aged children’s mathematical word problem-solving. However, the findings did not provide support for a general association between a familiar situational narrative or the required operation with mathematical word problem-solving. The findings highlight that elementary school-aged children especially struggle with mathematical word problems requiring realistic considerations or multiple mathematical operations, containing lexical inconsistency, and problems in which the position of the unknown is the first value. This further understanding of elementary schoolers’ word problem-solving performance may guide the design of appropriate and progressive instruction and assessment tools and steer research into the interactions within task characteristics and with individual characteristics.

Toward self-regulated learning: effects of different types of data-driven feedback on pupils' mathematics word problem-solving performance.

Mathematical word problems refer to word problems where the information that is presented needs to be integrated, typically into a mathematical formula, to arrive at a solution to the problem. When solving mathematics word problems, elementary school students often have difficulties improving their performance due to a lack of self-regulated learning (SRL). However, SRL can be developed by adopting an appropriate teaching approach which offers quantitative feedback or learning prompts. With the sophistication of interactive and data-driven feedback technology, it is possible to provide timely and personalized strategies for promoting students' SRL. In this study, an interactive e-book editing platform was used to design self-regulation-level-based feedback(SRLF) and task-level-based feedback(TLF) teaching models, which were respectively conducted in two similar fifth-grade classes for the mathematics word problem solving lessons. Using ANCOVA and repeated ANOVA, this study found that (1) the SRLF had a remarkably greater impact on elementary school students' mathematics word problem-solving performance than the TLF, with a partial η 2-value of .107; (2) In the short period of time, there was no significant difference between the two kinds of feedback on the learners' SRL. The TLF was slightly superior to the SRLF, especially in terms of total self-regulated learning scores and cognitive strategies; (3) The TLF had a significant interaction effect on self-regulated learning and cognitive strategies, respectively with a partial η 2-value of .059 and .056.

Effectiveness of Schema-Based Instruction Strategy in Improving Mathematical Word Problem Solving and Working Memory of Students with Learning Disabilities in The Sultanate of Oman

This study aimed to examine the effectiveness of a schema-based instruction strategy in improving mathematics word problem solving and working memory performance of third grade students with learning disabilities in schools in Oman. Students received a diagnosis of specific learning disability (SLD) based on the aptitude discrepancy model in which an achievement test and an aptitude test (Raven’s Coloured Successive Matrices) were used to determine the existence of a discrepancy. Students were then divided into two matched groups, a control group and an experimental group; each group included (20) students. Study instruments included a mathematics word problem solving test, a working memory test, and the schema-based intervention program. Results of the study showed that participants in the experimental group differed from controls in word problem solving and working memory performance following exposure to the intervention program. More specifically, performance of experimental group participants in the word problem solving varied across the pre, during the implementation, and post intervention phases in favor of the post intervention phases and in favor of the type of Assembly problems. Implications of using schema-based instruction strategy with students with SLD are discussed in the light of the study findings.

The effects of functional moves in teacher questioning on students’ contextualization of mathematical word problem solving

AbstractPosing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that the implementation of task clarification (TC) moves effectively enhanced contextualization only when students possessed a relatively strong sense of agency while solving word problems. Furthermore, when students’ attentional focus was not appropriately redirected by the functional moves, including procedural understanding (PU), making connections (MC), the rationale behind a strategy (RA), and an alternative strategy (AS), their understanding of the contextual features and construction of mathematical relationships in word problem solving could not be refined. Implications for field experience design and future research on the quality of teacher questioning in mathematics teacher education programs are discussed.

ExEqGen : An external symbolic solver for mathematical word problem solving

ExEqGen : An external symbolic solver for mathematical word problem solving

Teaching Mathematics Word Problem Solving to Students With Autism Spectrum Disorder

The National Council of Teachers of Mathematics (NCTM) emphasizes the teaching of “Big Ideas” in mathematics. This study focuses on the part–part–whole (PPW) relationship as a crucial aspect of word problem solving involving addition and subtraction. The research evaluates the effects of conceptual model-based problem-solving (COMPS) with the concrete-representational-abstract (CRA) sequence on teaching addition and subtraction word problem solving to students with autism spectrum disorder (ASD). Using a multiple-probe design across the participants, the study evaluates the impact of the intervention on students’ performance across three types of word problems: join-in, take-away, and combine. Results demonstrated significant improvements in students’ problem-solving abilities on criterion tests. In addition, students successfully generalized their skills to solve problems with new contexts. The findings of this study provide implications for future research and educational practice.

Determining the Effect of Bar Model Technique on Students’ Mathematical Word Problem Solving Skills

The study aims at probing the effect of Bar Model Technique on the word problem solving skills of primary level students in the subject of mathematics. Following were the objectives (i) to determine the effect of Bar Model Technique on student’s mathematical word problem solving skills; (ii) to compare the academic achievements of male students and female students by using Bar Model Technique. It was experimental study and pretest-posttest equivalent group design was used as a tool for data collection in this study. Sample of the study was 40 students (Male & Female) of Government Primary School District Nowshera, Khyber Pakhtunkhwa. The sample students were divided in two group control and experimental on the base of pretest score by using paired random technique. Data were analyzed by mean, SD and t- test.

Retrieval practice may not benefit mathematical word-problem solving.

The retrieval practice effect refers to the fact that one or even multiple retrievals of memory content during the same period are more effective than repeated studying to promote future memory retention. It is effective for numerous declarative knowledge learning materials. However, studies have demonstrated that retrieval practice does not benefit problem-solving skill learning. This study used worked examples from math word problem tasks as learning materials, considering the retrieval difficulty as the main factor. Experiment 1 explored the effect of retrieval practice on acquiring problem-solving skills under different initial testing difficulties. Experiment 2 manipulated the difficulty of materials as a variable to ascertain the effect of retrieval practice on problem-solving skills under different material difficulty levels. Experiment 3 introduced feedback variables to facilitate the generation of the retrieval practice effect and examined the effects of various difficulty feedback levels on problem-solving skills learning. Results showed that, compared with restudying examples (SSSS), the example-problem pairs (STST) did not promote delayed test performance. As for the retrieval practice effect, as no differences or advantages were found in the repeated study group on the immediate test, the retrieval practice group generally outperformed the repeated study group on the delayed test. However, across the three experiments, we found no evidence of retrieval practice affecting results during an enhanced delayed test. Therefore, there may be no retrieval practice effect on acquiring problem-solving skills from worked examples.

특별한 관심 영역을 활용한 전략 교수가 자폐 범주성 장애 학생의 수학 문장제 과제 수행률 및 정확도에 미치는 영향

This study examined the effects of an instructional strategy using areas of special interest to students with Autism Spectrum Disorders (ASD) on their performance rate and accuracy in mathematical word problem-solving. The study used a multiple probe design for three students with ASD under three experimental conditions: baseline, intervention, and maintenance. First, the computation level of the word problem was selected by interviewing special education teachers and parents. Next, each participant’s special interest area was determined. Then, the interest areas were used to modify students’ word problems. Finally, the students were taught the instruction strategy’s four steps. The results indicated that the intervention increased each participant’s mathematical word problem-solving performance rate and accuracy. Furthermore, these effects persisted after the intervention. Several implications of the study are discussed

Do students' errors still occur in mathematical word problem-solving?: A newman error analysis

Mathematical word problems can be utilized to improve students' mathematic problem-solving skills. However, students' error still occurs in mathematical word problem-solving. This research aimed to trace and reveal students' errors in problem-solving using the Newman Error Analysis stages. This research is descriptive qualitative research. The research subjects were moderate-ability students of State Madrasah Tsanawiyah (MTs) in Jambi. Mathematical word problem worksheets and interview templates were used as instruments in this research. Students with the moderate ability category were given worksheets on algebraic and the Pythagorean Theorem operation. The students were also interviewed to get more information about the errors they experienced. This research found that the students' errors during word problem-solving had implications for the incorrect answer. Students' errors occurred at the comprehension, transformation, process skill, and encoding stages of the Newman Error Analysis stages. Indeed, the Newman Error Analysis stage is a cycle that means errors at the first stage are more likely to cause errors in the next stages and lead to an incorrect answer. Furthermore, error at the comprehension stage is the most crucial error in mathematical problem-solving.

Brain imaging provides insights about the interaction between instruction and diagram use for mathematical word problem solving

Diagram use is generally considered an effective strategy in solving mathematical word problems, and many teachers demonstrate the use of this strategy when they are teaching. Despite such demonstrations, however, the majority of students evidence poor, ineffective use of diagrams in problem solving. This may be due to a lack of task-appropriate instruction, but to date, there is inadequate evidence to support this idea. Therefore, the present study aimed to better understand the development of diagram use competence following the provision of task-appropriate instruction, focusing on both behavioral and neurophysiological evidence (i.e., brain activity, using functional near-infrared spectroscopy or fNIRS). Sixteen participants (mean age 15.7 years) were asked to solve mathematical word problems for which the use of tables (which is one kind of diagram) was deemed effective. Data collection progressed in three phases: (1) Pre-test without the demand for diagram use, (2) Pre-test with demand to use a table, and (3) Post-test (after participants received instruction on table use for problem solving). Although table use increased in Phase 2, it was only in Phase 3 that such use led to increases in correct answers. In Phase 3, fNIRS measurements also indicated an increase in blood flow to the frontal area (DLPFC and VLPFC) of the brain usually associated with working memory activity. These results demonstrate important neurophysiological changes resulting from task-appropriate instruction that promotes effective strategy use and improves learning performance.

Problem-appropriate diagram instruction for improving mathematical word problem solving.

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, the effects of problem-appropriate diagram use instruction were investigated with an adaptation of the multiple baseline design method. The instruction for using line diagrams, tables, and graphs was provided to 67 junior high school students in a staggered manner and the effects on problem solving of three different types of problems was examined. The results showed that use of problem-appropriate diagrams increased and persisted over time. More importantly, the instruction led to increases in problem solving performance and to decreases in perceived cognitive load. These findings support the argument that effective diagram use depends on the acquisition not only of declarative knowledge, but also sufficient procedural and conditional knowledge.

A Meta-Analysis of Mathematics Word-Problem Solving Interventions for Elementary Students Who Evidence Mathematics Difficulties

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size ( g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propose recommendations for future research and classroom practice.

Sketchnote and Working Memory to Improve Mathematical Word Problem Solving among Children with Dyscalculia

Sketchnote and Working Memory to Improve Mathematical Word Problem Solving among Children with Dyscalculia

How effective is metacognitive instruction at improving the word problem-solving of children who are low-achievers in maths?

Metacognitive knowledge and skills are powerful predictors of academic outcomes (Wang et al., 1990) but are often lacking in children who are low-achievers in maths (Miller & Mercer, 1997). Metacognitive instruction seeks to address this deficit (Veenman, 2015). Interventions address strategy knowledge (plan-monitor-evaluate), task knowledge (when and why to apply strategies), and person knowledge (strengths, weaknesses, and motivation), and provide opportunity to practise (Flavell, 1979; Livingston, 1996; Pintrich, 2002). This review sought to evaluate the effect of metacognition interventions on mathematical word problem-solving. A systematic literature search was conducted, identifying seven studies for review. A meta-analysis showed a large combined effect size (g = 1.39) when comparing intervention to comparison participants. This, in combination with sufficient methodological quality among the reviewed studies, suggests metacognitive instruction can be recommended as evidence-based practice (Gersten et al., 2005). Recommendations for educational psychology practice, limitations of the review, and recommendations for future research are discussed.

Using Reciprocal Teaching for Improving Students’ Skills in Mathematical Word Problem Solving - A Project of Participatory Action Research

<p style="text-align:justify">This study aims to present the potential of Participatory Action Research (PAR) to bring together the experiences of teachers and researchers with the intention of improving teaching practices and students’ learning outcomes. Participants in the study were 7 teachers, their 160 fifths grade students, and researchers (authors). Teachers and researchers participated as partners in all collaborative activities during the period of 12 weeks. All teachers assisted by the researcher (first author) who serves as a teacher at the same school, were involved in implementing the reciprocal teaching method (RTM) in math classes. They examined each step of the implementation of this method in order to investigate whether it has an impact on student achievement in solving mathematical word problems. Teachers observed the work of students in their classes, whereas in the joint meetings they discussed occasional ambiguities as well as issues that were most challenging for them and their students. The results showed that there was a significant improvement of the students’ results in the post-test of the mathematical word problems. The analysis of teachers' reflections highlights the benefits of collaboration within the PAR project, both for students and teachers. The study suggests that the PAR model can be used effectively within school settings as a research model, and as a pedagogical practice.</p>

Different complex word problems require different combinations of cognitive skills

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.

The Effect of an Augmented Input Intervention on Subtraction Word-Problem Solving for Children with Intellectual Disabilities: A Preliminary Study

ABSTRACT Children with intellectual disabilities experience well-documented challenges in the development of problem-solving, particularly related to mathematical word-problem solving. Such challenges are related to both linguistic and conceptual skills. While interventions to assist children in developing conceptual skills are well reported, linguistic interventions within the mathematical field are limited. This study aimed to determine the effect of an augmented-input intervention, on subtraction word-problem solving for children with intellectual disabilities. A multiple baseline across behaviours design was used and replicated across the seven participants. Intervention was provided in three tiers (one week each) for change, combine, and compare subtraction word-problems. Intervention was withdrawn for a four week period and followed by a maintenance phase. Results suggested that for older participants with higher receptive language and numerical operation scores, the augmented-input intervention provided significant gains across all three types of word-problems. Overall, four of the seven participants showed improvement in subtraction word-problem solving. Augmented input may provide language supports for subtraction word-problem solving for some children with mild intellectual disability.

Working memory growth predicts mathematical problem-solving growth among emergent bilingual children

An area of mathematics found to be difficult for emergent bilingual children whose first language (L1) is Spanish in the United States is solving mathematical word problems. The purpose of this study was to determine the relationship between growth in the executive component of working memory (WM) and growth in mathematical word-problem solving in children whose L1 is Spanish. Elementary school children (Grades 1, 2, and 3) were administered a battery of mathematical, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, and WM) in both Spanish (L1) and English (second language [L2]) in Year 1 and again 1 year later. Multilevel growth modeling showed that growth in WM significantly predicted growth in L1 and L2 mathematical word-problem solving. Furthermore, the contributions of WM to mathematical word-problem-solving growth in both L1 and L2 were independent of language skills in vocabulary, reading, estimation, naming speed, inhibition, STM, and calculation. Overall, the results suggest that the mental activities that underlie WM play a significant role in predictions of L1 and L2 mathematical word-problem-solving accuracy.