Word Problem Solving Research Articles

Teaching Word Problem Solving to Students With Autism and Intellectual Disability

Word problem solving is the premise for students to generalize their problem solving skills to real world problems. This includes students with autism spectrum disorder (ASD) and intellectual disability (ID). Modified Schema-based Instruction (MSBI) is one strategy that research has shown is effective for teaching students with ASD/ID to acquire and generalize problem solving skills. The key word strategy is an ineffective strategy for teaching students to problem solve, especially since problems in everyday life do not contain key words. This article provided a practitioner friendly 7-step strategy for implementing MSBI with learners who have ASD/ID

Metacognitive and Non-Metacognitive Processes in Arithmetic Performance: Can There Be More than One Meta-Level?

The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens’ model of metacognition. According to the Nelson–Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more than two levels, cognitive processes from at least one level can be described as both meta- and object-level processes. The question arises whether it is possible that the very same cognitive processes are both controlled and controlling. The feasibility of owning the same cognitive processes—which are considered the same from an external point of view of assessment—as both meta- and object-level processes within the same individual opens the possibility of investigating the transition from meta-level to object-level. Modeling cognitive development by means of a series of such transitions calls forth an understanding of possible developmental phases in a given domain of learning. The developmental phases of arithmetic performance are described as a series of transitions from arithmetical facts to strategies of arithmetic word problem solving. For school learning and instruction, the role of metacognitive scaffolding as a powerful educational approach is emphasized.

Intelligent tutoring systems for word problem solving in COVID-19 days: could they have been (part of) the solution?

The COVID-19 pandemic led to the lockdown of schools in many countries, forcing teachers and students to carry out educational activities remotely. In the case of mathematics, developing remote instruction based on both synchronous and asynchronous technological solutions has proven to be an extremely complex challenge. Specifically, this was the case in topics such as word problem solving, as this domain requires intensive supervision and feedback from the teacher. In this piece of research, we present an evaluation of how technology is employed in the teaching of mathematics, with particular relevance to learning during the pandemic. For that purpose, we conducted a systematic review, revealing the almost complete absence of experiments in which the use of technology is not mediated by the teacher. These results reflect a pessimistic vision within the field of mathematics education about the possibilities of learning when the student uses technology autonomously. Bringing good outcomes out of a bad situation, the pandemic crisis may represent a turning point from which to start directing the research gaze towards technological environments such as those mediated by artificial intelligence. As an example, we provide a study illustrating to what extent intelligent tutoring systems can be cost-effective compared to one-to-one human tutoring and mathematic learning-oriented solutions for intensive supervision in the teaching of word problem solving, especially appropriate for remote settings. Despite the potential of these technologies, the experience also showed that student socioeconomic level was a determining factor in the participation rate with an intelligent tutoring system, regardless of whether or not the administration guaranteed students' access to technological resources during the COVID-19 situation.

Brain‐Anatomy Differences in the Commission of Reversal Errors during Algebraic Word Problem Solving

AbstractAn important line of research related to the resolution of word problems is the study of the cognitive processes involved when subjects translate problems into the language of algebra. One of the most common errors in problem‐solving is the reversal error (RE), which occurs when students reverse the relationship between two variables when translating equations from comparison word problems. The aim of this neuroeducational study is to investigate the brain anatomy differences between two groups, one group that commits RE and a second group that does not. Magnetic resonance images of 37 normal and healthy participants between the ages of 18–25 years were acquired. Differences in gray matter were assessed using voxel‐based morphometry analysis. Our results show that the RE group has a larger volume in the putamen, suggesting that these subjects have to make a greater effort to solve problems.

Evaluating the Effects of Adding Explicit Vocabulary Instruction to a Word-Problem Schema Intervention

Schema instruction improves word-problem solving for students with mathematics difficulty (MD; e.g., Powell et al., 2015 ); however, prior research suggests that students need word-problem-specific language comprehension in addition to schema knowledge to build word-problem models ( Fuchs et al., 2015 , 2018 ). Students have general word knowledge (e.g., more, less) but require word-problem-specific word knowledge to solve word problems successfully (e.g., more than, less than; Kintsch & Greeno, 1985 ). Prior word-problem schema interventions have not provided explicit instruction in word-problem vocabulary to support students’ development of word-problem models. We aimed to determine if word-problem vocabulary instruction combined with schema instruction provided an advantage to word-problem solving for third-grade students with MD. We randomly assigned 75 third graders with MD to three conditions: Word-problem intervention with explicit vocabulary instruction (WP + V), word-problem intervention without explicit vocabulary instruction (WP-only), and business-as-usual intervention (BAU). Students in the treatment conditions received 22, 50-min lessons provided virtually in small groups. On a word-problem vocabulary measure, students in the WP + V condition significantly outperformed students in the WP-only (ES = 0.43) and BAU (ES = 0.83) conditions. On a word-problem measure, students in the WP + V condition outperformed students in the WP-only (ES = 0.08) and BAU conditions (ES = 0.43), although these were not statistically significant. These findings provide preliminary support for the benefits of incorporating explicit vocabulary instruction in a word-problem schema intervention; future research is needed to fully understand the effect of vocabulary instruction on word-problem outcomes.

The role of language in word-problem solving: a meta-analysis

The relationship between language proficiency and word-problem solving has been extensively studied in the last three decades with one main finding: language proficiency is directly proportional to word-problem solving scores. Researchers have focused on language accommodations to standardized tests to level the playing field for nonnative speakers. Interestingly, several meta-analyses on language accommodation have noted that there are no significant effects on scores. At the same time, most research has reported significance and not effect sizes, which does not allow to establish comparisons between studies. Therefore, the purpose of this meta-analyses was to study the effect size of studies conducted in the US and the rest of the world to provide a new population effect size and identify possible moderator variables that have not been considered before. The main findings were that the differences in scores between native speakers and nonnative speakers (g=.360) were less pronounced than previously reported (g=.604). The participants’ age and the language of instruction and testing moderated a small percentage of the effect size, which leads to the need to include specific information about the participants to provide a clearer picture of this relationship and eventually provide language accommodations that have significant effects on scores.

Improving Numeracy Skills in First Graders with Low Performance in Early Numeracy: A Randomized Controlled Trial

Children with low performance in early numeracy are at risk of facing learning difficulties in mathematics, but few trials have examined how this can be ameliorated. A total of 120 first-grade children ( Mage= 6.4 years) were randomly assigned to an intervention or a control condition. The 14-week intervention targeted early numeracy skills and was delivered in small groups three times a week. Immediately after the initial 8-week intervention phase, moderate and positive effects were found on early numeracy ( d = 0.19), word problem solving ( d = 0.41), and approximate number sense ( d = 0.35). However, only the effects on word problems were significant, and all effects disappeared after the children undertook a second 6-week intervention phase. Overall, results indicate that (a) early numeracy skills are malleable in low-performing children, but (b) frequent and long-term interventions are needed for the positive effects to last.

MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers

While Math Word Problem (MWP) solving has emerged as a popular field of study and made great progress in recent years, most existing methods are benchmarked solely on one or two datasets and implemented with different configurations. In this paper, we introduce the first open-source library for solving MWPs called MWPToolkit, which provides a unified, comprehensive, and extensible framework for the research purpose. Specifically, we deploy 17 deep learning-based MWP solvers and 6 MWP datasets in our toolkit. These MWP solvers are advanced models for MWP solving, covering the categories of Seq2seq, Seq2Tree, Graph2Tree, and Pre-trained Language Models. And these MWP datasets are popular datasets that are commonly used as benchmarks in existing work. Our toolkit is featured with highly modularized and reusable components, which can help researchers quickly get started and develop their own models. We have released the code and documentation of MWPToolkit in https://github.com/LYH-YF/MWPToolkit.

A Meta-Analysis of Mathematical Interventions for Increasing the Word Problem Solving Performance of Upper Elementary and Secondary Students with Mathematics Difficulties

This meta-analysis synthesized the findings of experimental and quasi-experimental studies to determine the efficacy of math interventions for enhancing the word problem-solving accuracy of students with mathematics difficulties in Grades 4 to 12. Further, we identified intervention and design characteristics that moderate the effectiveness of interventions. We appraised study quality using Council for Exceptional Children (CEC's) evidence standards. We also used random-effects meta-regression models with robust variance estimation (RVE) to compute the overall weighted treatment effect and investigate the moderating impact of 15 variables. Results from 36 intervention studies published between 1989 and 2020 reveal a relatively large and positive mean effect size (g = 0.71; SE = 0.11, 95% CI [0.49, 0.92]) across 88 outcomes, suggesting the examined interventions were effective. The moderator analyses' findings showed the treatment efficacy varied as a function of five intervention characteristics, including intervention model, interventionist, grade level, math topic, and intervention duration. None of the design features we examined led to significant moderator effects. We discuss findings and limitations and provide directions for future research and practice.

What’s the Difference? Contributions of Lexical Ambiguity, Reading Comprehension, and Executive Functions to Math Word Problem Solving in Linguistically Diverse 3rd to 5th Graders

ABSTRACT Purpose Math word problem solving, a form of reading comprehension, is complicated by mathematical lexical ambiguity (e.g., the word difference can mean dissimilarity in everyday discourse but the answer in a subtraction problem in math). This study examined the role of mathematical lexical ambiguity in math word problem solving. Method Lexically ambiguous math word knowledge, reading comprehension, vocabulary breadth, executive function (EF) skills, and math word problem solving were assessed in 521 3rd- to 5th-grade emergent bilingual (EB) and English monolingual (EM) students. Results Students knew fewer math than common meanings of lexically ambiguous math words, and EBs knew fewer meanings than EMs. Multi-group path analysis indicated reading comprehension and lexically ambiguous math word knowledge contributed directly to math word problem solving and partially mediated the influence of EFs on math word problem solving. Conclusion Consistent with the language function hypothesis, language skills supported math word problem solving directly and mediated the influence of EF skills on math word problem performance for both EBs and EMs alike. Our findings move the field forward by revealing a specific mechanism by which EF skills contribute to a particular aspect of content area reading comprehension.

Attitude of class nine and ten students towards solving mathematical word problems

The study was conducted to understand the attitude towards solving mathematical word problems of 483 class nine and ten students. The quantitative method was used with purposive sampling, including all the students. Survey questionnaires with a five-point Likert scale were validated through pilot testing with 20 students and obtained a Cronbach’s alpha of 0.88. Views of students on attitude towards solving word problems, motivation of students, and implication of language in solving word problems were collected. MS Excel’s data analysis tool was used to analyze data using percentages, frequencies, descriptive analysis, and correlation. Paired t-test for the sample mean was used to see the significance of gender difference. The findings revealed a high positive attitude towards solving word problems. Students were motivated to solving word problems, the teacher is rated as the source of motivation. There was a high positive correlation between language and their love for solving mathematical word problems. There was no significant gender difference observed in attitude and motivation but gender difference was significant in the importance of language in solving word problems. Male students had a stronger belief than a female that language plays a vital role in one’s efficacy in solving mathematical word problems. Recommendations are suggested to the subject teachers to enable them to develop better instructions based on reflection.

Solving mathematical word problems using dynamic assessment for scaffolding construction

<span>Students need the ability to solve word problems can connect mathematics with the context of everyday life. However, students experience many difficulties and need assistance in the form of scaffolding can to solve word problems well. Dynamic assessment is an alternative approach to constructing the form of scaffolding that student need to solve mathematical word problems. This study aimed to analyze the students' difficulties in solving word problems and the required form of scaffolding through dynamic assessment. The subjects of this study consisted of 177 students spread across 10 public junior high schools in Jeneponto Regency, South Sulawesi Province, Indonesia. There was a four-word problem tested and analyzed using dynamic assessment. Student solutions were grouped based on the type and form of scaffolding needed: level 5 (no solution), level 4 (without analysis/unrepresentative), level 3 (computational error), level 2 (incomplete procedure), level 1 (lack of thoroughness in the final stage). The form of scaffolding is constructed to help students solve mathematical word problems step by step at each level. The use of scaffolding accompanied by instructions helps students develop word problem-solving skills. Dynamic assessment can be considered to be integrated with the mathematics learning process that supports scaffolding construction to solve students' word problems.</span>

Higher-order thinking word problem-solving errors made by low-performing pupils: Comparative case study across school types in Malaysia.

The achievement gaps existed among the three types of Malaysian elementary schools with different instruction mediums. Thus, this study sought to compare the types of errors made by the low-performing students from different school types in solving word problems involving higher-order thinking skills by conducting a multiple case study. The study involved 18 low-performing students from a National Primary School (NPS), National-Type Chinese Primary School (NTCPS), and National-Type Tamil Primary School (NTTPS) in Malaysia. The students’ errors in solving eight word problems were identified qualitatively through conducting four sessions of diagnostic interviews, followed by the Newman’s Error Analysis. Then, a cross-case analysis was conducted. The findings indicated that the participants of the three school types made reading, comprehension, transformation, process skills and encoding errors. However, the NPS and NTTPS low-performing students made more process skills errors and encoding errors, as compared to the NTCPS low-performing students. The findings imply the need to enhance the procedural fluency of NPS and NTTPS low-performing students for reducing the achievement gaps among the school types.

Emergent math difficulties among English learners: can the odds be reduced?

ABSTRACT Solving word problems in mathematics presents difficulties for many English learners (ELs), including those who use Spanish as a home language. In the early stage of learning to solve mathematics word problems, some children, including ELs, experience difficulties. By English status, EL refers to those children whose home language was Spanish while in the process of developing English at school. Math difficulties (MD) refers to those children with low normative mathematical problem-solving scores in both English and Spanish. The purpose of this study was to determine those measures that increase the odds of identifying EL children with emergent MD. Elementary school children (grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, working memory [WM]) in both Spanish (L1) and English (L2) in Year 1 and again one year later. Multilevel growth modeling compared MD children identified one year later who manifested MD to children who were average math achievers or poor math achievers across the two testing waves (year 1 and year 2). The results indicated that significant growth parameters (i.e., measures of estimation, WM) increased the odds of identifying emergent MD relative to children with Persistent math deficits and average achievers. The results were discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the odds of identifying later math difficulties.

CONNECTING THE MASTERY LEVEL IN TRANSLATING VERBAL STATEMENTS TO MATHEMATICAL SYMBOLS WITH VOCABULARY ENHANCEMENT

Translation from words to symbols is undeniably one of the solution processes in solving word problems that can be considered critical (Bardillion, Jr. 2004) cited by Dela Cruz, et.al (2014). Failure to translate the verbal statement to mathematical symbols can lead to incorrect solution. This study aimed at giving remedy to the least mastered competency in translating verbal phrases to mathematical symbols and improving the academic performance of the Grade 7 students at Tabuk City National High School, Tabuk City Division, School Year 2017-2018 using the Strategic Intervention Material developed by Ms. Apple Jean G. Yecyec (n.d.). This study focused on the fifteen (15) identified students having a score of 1-5 on a given formative test. A teacher-made pretest and posttest was utilized. The participants had a ?Very Low? performance on the pre-test at 24.65% level of mastery with regards to translating verbal phrases to mathematical symbols. Results showed there was a significant difference between the pretest and posttest of the participants. It implies that the strategic intervention material by Yecyec on translating verbal phrase to mathematical symbols is effective in improving the mastery level on the least learning competency. Thus, the Strategic Intervention Material (SIM) by Yecyec on translating verbal phrases to mathematical symbols is strongly recommended for dissemination and utilization.

Instruction in Proportion Word Problems for Secondary Students With Learning Disabilities in Mathematics

Increasing the performance of secondary students with learning disabilities (LD) in mathematics on word problem-solving tasks involving ratios and proportions is challenging for secondary math teachers. Teachers must use evidence-based practices to enhance secondary students’ problem-solving proficiency and math achievement. Schema-based instruction (SBI) is a powerful evidence-based practice to improve students’ understanding and approach to solving word problems involving ratios and proportions. This article describes the protocol for implementing SBI with examples specific to ratios and proportions. Also discussed are the ways teachers can provide additional assistance to students with more intensive instructional needs when implementing SBI.

Relationship between Teacher Trainee’s Proficiency in Solving Standard Linear Equations (SLE) and Their Proficiency in Posing Word Problems Involving Standard Linear Equations

The major aim of teaching Mathematics at every level of education is to help students solve problems. Mathematics teachers, therefore, need to possess these requisite skills to impact these problem-solving techniques in the students they teach. Hence, this paper employed a case study to investigate the strength of the relationship between teacher trainees' Problem Solving and their Problem Posing skills, using a simultaneous linear equation. It involved forty-five teacher trainees from College of Education. Three research questions were used and an achievement task was used to collect data. The data was analyzed along some thematic dimensions, in percentages. A Pearson Product Moment correlation matrix was used to determine the relationship between teacher trainees' proficiency in Problem Solving and Problem Posing. The result revealed a significant positive relationship r=0.34 between Problem Solving and Problem Posing ability of trainees. There also exist gender differences in this relationship, with females performing better than males. This shows that when the two concepts are integrated into teaching Mathematics, it could promote students' proficiency in solving word problems. Teaching mathematics through Problem Solving should be reinforced and the introduction of Problem Posing into the mathematics curriculum at the College of Education be considered.

Examining middle grades students’ solutions to word problems that can be modeled by systems of equations using the number sequences lens

This qualitative research study investigates the ways middle-grades students’ numerical reasoning relates to their solutions to word problems that can be modeled by systems of linear equations. 18 students in grades 6 through 9 participated in task-based semi-structured clinical interviews. Students’ numerical reasoning was assessed using the framework, number sequences, and their problem-solving was observed on two word problems that could be modeled using systems of linear equations. Results show that students’ stages of numerical reasoning were more closely related to their problem-solving strategies than their mathematics instruction. Additionally, students with less sophisticated numerical reasoning commonly used pre-algebraic strategies, whereas students with more sophisticated numerical reasoning more commonly utilized algebraic reasoning strategies. This study contributes a breadth of pre-algebraic strategies that students used to solve word problems that can be modeled by systems of linear equations in relation to their numerical reasoning. Theoretical and instructional implications are also discussed.

The role of mathematical language skills in arithmetic fluency and word-problem solving for first- and second-language learners.

The role of mathematical language skills in arithmetic fluency and word-problem solving for first- and second-language learners.

WORKING WITH MATHEMATICAL PROBLEMS: AN ANALYSIS OF STUDENTS MISCONCEPTIONS AND ITS IMPACT ON MATHEMATICS LEARNING

The great misconception about mathematics is the notion that mathematics is about formulas, solving word problems, and doing computations. Hence, it is the impetus for this study to explore why so many students havedifficulty learning mathematics. To achieve this goal, this study focuses on why so many students keep making the same errors over a long period of time. Generally, among the errors committed by the students in solving word problems, it was found out that students usually made encoding errors. These errors were the result of carelessness, rushing through a problem or misreading a problem. These students correctly work out the solution, but cannot express this solution in an acceptable written form.Moreover, this study stresses that one of the foremost problems encountered by the students was their inability to understand the language used in mathematics, which is English. For some students, mathematical disability was a result of problems with the language of mathematics. Students had difficulty in understanding mathematical terminologies which normally were not used outside the mathematics lesson. Furthermore, lack of comprehension of the students in algebraic expressions concepts and operations leads to an error in translating mathematical phrase into mathematical symbol. This was due to insufficient understanding of mathematical expressions and poor skills in mathematical translation. The conclusions drawn from this investigation strongly justify the needs for mathematics teachers to give more emphasis on students learning in mathematical concepts. They must also need to be empowered in order to help the learners to be conversant in the mathematical language. The study has demonstrated that mathematical language plays a vital role in learners comprehension of word problems, hence the language that is used in mathematical word problems needs to be taken into cognizance.