Word Problem Solving Research Articles

Considerations for Intensifying Word-Problem Interventions for Students With MD: A Qualitative Umbrella Review of Relevant Meta-Analyses.

Word problem-solving (WPS) poses a significant challenge for many students, particularly those with mathematics difficulties (MD), hindering their overall mathematical development. To improve WPS proficiency, providing individualized and intensive interventions is critical. This umbrella review examined 11 medium- to high-quality meta-analyses to identify intervention and participant characteristics, informed by the Taxonomy of Intervention Intensity (TII) framework, that consistently moderate WPS outcomes for students with MD. Our analysis identified four characteristics with consistent moderating effects: intervention model, number of treatment sessions, group size, and academic risk area. This result suggests that these variables are potential considerations when customizing and intensifying WPS interventions to maximize their effectiveness for students with MD. We discuss the implications of these findings for practice and research and acknowledge the limitations of our review.

A Scoping Review of Mathematics Interventions: Moderation Analyses of Initial Mathematics Skills

This scoping review describes mathematics intervention studies that include initial skill moderation analyses. Sixteen studies were included that focused on students with or at risk for mathematics difficulties (MD). The results revealed that mathematics intervention studies with initial skill moderation analyses focused on students in kindergarten through Grade 6 (no studies that met inclusion criteria were located for Grades 7–12). Studies focused more on whole number concepts and fractions than other areas of intervention (e.g., computation, word problem solving). Further, the studies were mostly conducted by two research teams, which potentially limits the generalizability of the findings. Overall, the review serves as a call to action for researchers to address important gaps in initial skill moderation analyses within mathematics intervention studies.

A special contribution from spatial ability to math word problem solving: Evidence from structural equation modelling and network analysis

There is a growing body of research into the factors contributing to math word problem solving. However, these studies usually use limited number of potential predictors (precluding assessing of their contribution in comparison with other factors or “g” general intelligence) and some predictors (such as analogical and hypothetical reasoning) are largely omitted. Thus, the aim of the current study was to explore contributions of different types of reasoning to math word problem solving and whether these contributions have added value compared with each other and general cognitive ability. Chinese schoolchildren in Grades 3 (N = 199; Mage = 102.4 months), 4 (N = 162; Mage = 114.6), 5 (N = 174; Mage = 126.1) and 6 (N = 180; Mage = 138.6) completed 8 tasks tapping into spatial, mechanical, verbal, mathematic, hypothetical and analogical reasoning. Our data showed that when 6 general cognitive factors load onto General cognitive ability factor in a Structural Equation Model (SEM), only spatial visualization has additional contribution to Word problem solving factor. Gaussian Graphical models (GGMs) showed that 2 verbal tasks and spatial visualization showed stable (present in at least 3 out of 4 grades) contributions to both word problem solving tasks. Analogical reasoning showed contribution to Process of word problem solving only. To sum up, both SEM and GGMs converged on the importance of spatial ability for mathematical word problems solving. Our results call for verbal and spatial ability to be routinely assessed and targeted by educational interventions within maths curriculum.

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

The associations between mathematical skills, cognitive performance, and language background in elementary school children. a two-year follow-up study

ABSTRACT Early mathematical skills contribute to later school performance and socio-economic status. Working memory is related to mathematical skills, but spatial and language skills have independent effects on separate areas of mathematical skills such as solving word problems or arithmetic skills. In this study, 9- to 10-year-old children's (N = 57) cognitive and mathematical skills were assessed three times over 2 years. Spatial reasoning was associated with performance in solving word problems and working memory with performance in the arithmetic test. Regarding word problems, girls outperformed boys. Also, the second-language learners performed similarly to the native speakers in the beginning and in the end of the third grade, but worse in the end of the fourth grade. The results suggest that the students’ inadequate mastery of the school language may lead to underachievement in mathematics, implying that further efforts should be invested in supporting their language learning.

Analisis Hambatan Belajar Siswa dalam Menyelesaikan Soal Cerita Konsep Perkalian Bilangan Cacah

Effective education in this context involves preparing students to explore and apply mathematical knowledge in various situations, providing a strong foundation for the development of intelligence and thinking skills. This research focuses on the challenges faced by 4th-grade students at SDN 4 Sukajaya in solving word problems related to multiplication of whole numbers. The object of this study is the students' difficulty in understanding the concept of multiplication, while the subjects are 10 students who experience difficulties and a class teacher. The research method used is qualitative with a descriptive approach, aiming to provide a detailed account of the problems faced by students. The study found learning obstacles among 4th-grade students at SDN 4 Sukajaya in solving word problems involving the concept of multiplication of whole numbers. These obstacles include: 1) difficulty in understanding the problems, 2) difficulty in identifying mathematical concepts, and 3) difficulty in calculations. The contributing factors are: 1) internal factors, such as motivation, intelligence, behavior, attitude, and students' physical condition (e.g., fatigue), and 2) external factors, such as facilities, teacher quality, and curriculum. Efforts to address these obstacles include: regular problem-solving practice, the use of varied and enjoyable teaching methods and media to boost motivation, and cooperation between teachers and students in monitoring learning progress

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.

Schematic Presentations on the Achievement of Grade 6 Pupils in Solving Word Problems in Math

Schematic Presentations on the Achievement of Grade 6 Pupils in Solving Word Problems in Math

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.

Difficulties in mathematical language and representation among elementary school students when solving word problems

Difficulties in mathematical language and representation were the dominant difficulties in solving word problems for students in elementary school. The research aims to analyze students' mathematical language and representation difficulties when solving word problems. The research subjects were 114 fifth-grade elementary school students selected using a purposive sampling technique with different mathematical abilities. The research was conducted at an elementary school in Sumbawa District, West Nusa Tenggara, Indonesia. Data collection techniques included tests, questionnaires, and interviews. The research results show that students' difficulties in mathematical language were dominant indicators of sentences. Students had difficulties in mathematical representation indicators, which were dominant in symbols. The factors that cause difficulty for high, middle, and lower ability students are unaccustomed to solving word problems and using problem-solving procedures, difficulty with concepts, difficulty with reasoning, difficulty understanding what is known and what is being asked, not being careful in reading the problem, and difficulty with long sentences. Student word problem-solving is in the low category.

Template-Based Contrastive Distillation Pretraining for Math Word Problem Solving.

Since math word problem (MWP) solving aims to transform natural language problem description into executable solution equations, an MWP solver needs to not only comprehend the real-world narrative described in the problem text but also identify the relationships among the quantifiers and variables implied in the problem and maps them into a reasonable solution equation logic. Recently, although deep learning models have made great progress in MWPs, they ignore the grounding equation logic implied by the problem text. Besides, as we all know, pretrained language models (PLM) have a wealth of knowledge and high-quality semantic representations, which may help solve MWPs, but they have not been explored in the MWP-solving task. To harvest the equation logic and real-world knowledge, we propose a template-based contrastive distillation pretraining (TCDP) approach based on a PLM-based encoder to incorporate mathematical logic knowledge by multiview contrastive learning while retaining rich real-world knowledge and high-quality semantic representation via knowledge distillation. We named the pretrained PLM-based encoder by our approach as MathEncoder. Specifically, the mathematical logic is first summarized by clustering the symbolic solution templates among MWPs and then injected into the deployed PLM-based encoder by conducting supervised contrastive learning based on the symbolic solution templates, which can represent the underlying solving logic in the problems. Meanwhile, the rich knowledge and high-quality semantic representation are retained by distilling them from a well-trained PLM-based teacher encoder into our MathEncoder. To validate the effectiveness of our pretrained MathEncoder, we construct a new solver named MathSolver by replacing the GRU-based encoder with our pretrained MathEncoder in GTS, which is a state-of-the-art MWP solver. The experimental results demonstrate that our method can carry a solver's understanding ability of MWPs to a new stage by outperforming existing state-of-the-art methods on two widely adopted benchmarks Math23K and CM17K. Code will be available at https://github.com/QinJinghui/tcdp.

WAYS OF SOLVING MATHS TEXTUAL PROBLEMS IN ELEMENTARY CLASSESS OF PUBLIC SCHOOLS

The article presents a study of theoretical material on the methodology of solving word problems, theories and steps put forward by methodologists on word problems, as well as research among students during mathematics classes and the results of an online survey among teachers. We have represented the experimental-teaching work done among the students analyzing only the results obtained at the end of the research. We have presented our analysis based on the results of an empirical online survey conducted among teachers. In the article, at the end of the experimental-research work, conclusions are presented, from which the recommendations are derived. They refer to making it easier to solve the text problems in the textbooks, as well as to include in the textbooks such problems that have not yet been encountered or rarely encountered in elementary school mathematics textbooks. According to that, the scientific novelty lies in the fact that, based on a number of video-methodological studies carried out in this field, we have generalized and presented in a new way the uniqueness of solving text problems among younger schoolchildren within the framework of a single study.

Enhancing the Word Problem-Solving Skills Through Strengthening Reading Comprehension Skills of Grade 11 Learners: An Action Research Study

Context and Rationale: Word problem-solving in mathematics is a crucial skill for Grade 11 students, as it integrates mathematical concepts with reading comprehension. Many students struggle with word problems, not due to a lack of mathematical ability, but because of difficulties in understanding the problem's text. Research indicates that reading comprehension directly influences the ability to solve word problems effectively (Smith & Jones, 2023). This action research aimed to explore the impact of targeted reading comprehension interventions on improving the word problem-solving skills of Grade 11 students.

The development of math skills from grades 1 to 12: Novel findings using person-oriented approach.

The development of math skills is widely studied, but there is a lack of longitudinal studies investigating person-oriented developmental patterns of math skills. The present study aims to describe profiles of students with various calculation and word-problem solving skills from Grades 1 to 9, as well as the developmental trajectories of these profiles, how profiles are related to students' further educational pathways, and whether having a specific skill profile in Grade 9 is related to the results of math and language exams at the end of Grade 12. The sample included 1,023 Estonian students who completed calculation and word-problem solving tests in Grades 1, 3, 6, and 9 (ages 6-16 years old). Educational pathway information and results of the math and language exam in Grade 12 were retrieved from the Estonian Education Information System's registry. Socioeconomic status was determined via parental education level. Overall, results indicated that math skills were positively interrelated between the school years. However, person-oriented approach demonstrated that less than half of students tended to stay in a similar profile from Grades 1 to 9. This suggests that, in terms of math skills, most students have diverse developmental trajectories from elementary school through the end of middle school. Profiles were also related to further educational pathways and high school exam results. This study complements previous variable-oriented research to provide unique and valuable information regarding the development of math skills. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A Systematic Review of Mathematics Vocabulary Interventions for Students With or At-Risk for Mathematics Difficulty

This systematic review synthesizes the effects of mathematics vocabulary interventions on the mathematics outcomes of students with mathematics difficulty (MD) in Grades K through 12. We evaluated methodological rigor using three indicators: research design, implementation fidelity, and instruction in the counterfactual. Six peer-reviewed studies and three unpublished dissertations between 1990 and 2022 met inclusion criteria. Results showed mathematics vocabulary interventions improved students’ vocabulary knowledge, particularly when instruction was explicit with multiple opportunities to practice. Findings were less conclusive on whether improved mathematics vocabulary knowledge led to improved performance on related mathematics content. Results suggest mathematics vocabulary intervention is beneficial for higher-level mathematics reasoning, such as word-problem solving. The seven group design studies received an M rating of at least acceptable for methodological rigor, and one of two single-case studies met What Works Clearinghouse design standards without reservations. We highlight promising instructional practices implemented across studies that resulted in improved vocabulary outcomes.

The impact of various teaching methods on the knowledge of students of different genders: The case of mathematics word problems abstract

Despite significant progress in recent years, there is still evidence of gender differences and underrepresentation of women in leadership positions in mathematics. To promote equal opportunities for all students, it is essential to comprehend gender differences in math learning at school and identify potential barriers to educational equality. In this regard, our study examined the gender differences in solving word problems, and whether they relate to the solution strategy the students were taught.The study involved 100 10th-grade students divided into two groups and taught different solving approaches. One group was taught an algebraic approach using linear equations, while the other group was taught a combined approach, which incorporates the algebraic solution with a functional-graphic solution using a graph of a linear function.The research findings reveal gender differences in various aspects: Girls who learned the algebraic approach had better attainments than boys; Boys who learned the combined approach opted to solve problems with functions and graphs, whereas girls in the same group preferred an algebraic solution; Boys who learned the combined approach achieved significantly higher than boys who learned the algebraic approach.This study illuminates the importance of teaching word problems using diverse solution strategies because different populations of students respond differently to different strategies.

Analysis of Student Errors in Solving Word Problems using Polya Steps

This research was motivated by the many difficulties experienced by students in the mathematics learning process which had an impact on the occurrence of errors in working on mathematics story problems. These errors need to be known so that it is easier to find solutions so that these errors can be minimized. This research aims to determine the types and causes of errors made by students in solving mathematics story problems on single interest and compound interest materials using Polya's steps. This research method is qualitative with descriptive research type. The research subjects consisted of 2 students from 13 class XI TKP SMKN 1 Pariaman students, with the criteria being 1 student each from the medium group and 1 student from the low group. Data collection techniques include tests and interviews. The results of the research show that the percentage of errors made by students in solving mathematics story problems on single interest and compound interest material using Polya steps is: in question number 1, the biggest error made in the step of understanding the problem was 23.08%. Question number 2, the biggest error made during the rechecking step was 15.38%. In question number 3, the biggest mistake made in the step of understanding the problem was 19.23%. The factors that cause students to make mistakes include, not being used to writing information on questions using their own words, not writing down what they know and what is asked in the question correctly, not focusing when working on questions, not being careful in carrying out the calculation process, not being used to checking again, and rushing through the settlement process.

The mathematical word problem-solving performance gap between children with and without math difficulties: does working memory mediate and/or moderate treatment effects?

ABSTRACT This study determined the extent to which working memory (WM) played a moderating and/or mediating role in word-problem-solving (WPS) instructional outcomes between children with and without math difficulties (MD). A randomized pretest-posttest control group study investigated the effects of 8-week strategy instruction in one of four treatment conditions on WPS accuracy of third graders with MD (N = 136) when compared to children with (N = 28) and without MD (N = 43). Comparisons were made of three strategy conditions that included overt cues (e.g. underlining key sentences, filling in diagrams), another treatment condition that removed the overt cues (material-only), and two control conditions (children with and without MD). Four important findings emerged. First, posttest WM significantly predicted posttest WPS, computation, and schema accuracy independent of pretest and treatment conditions. Second, posttest WM mediated posttest WPS treatment outcomes when the control conditions included children without MD. Third, strategy conditions that included overt cues (e.g. crossing out irrelevant sentences) decreased WM demands compared to the Materials-Only condition (without overt cues) for children with MD. Finally, incremental attention allocation training within treatment conditions improved posttest WM in children with MD but not posttest WPS. Results indicated that WPS differences between children with and without MD across treatment conditions were mediated by posttest WM performance.

The effects of self-questioning on additive word problem solving

This study underscores the critical role of mental representation and advanced reading comprehension in solving mathematical word problems. Proficient problem solvers create nuanced mental models of problem situations, while less successful ones rely on simpler translations. Advanced reading comprehension aids in navigating the complexity of word problems, including element sequencing and semantic relations. The purpose of this study was to assess the impact of a self-questioning strategy on four elementary students’ comprehension of additive problems. These students were trained to ask questions that helped uncover semantic relations in problems. Results showed significant improvement in their ability to interpret these relations and apply the self-questioning method to comprehend two-step additive problems.

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.