Arithmetic Word Problem Solving Research Articles

The Effect of Visual Reasoning on Arithmetic Word Problem Solving

First-grade students often encounter challenges in understanding and solving arithmetic word problems due to their limited reading comprehension abilities. Despite these difficulties, students may employ arbitrary strategies, such as combining numbers based on specific keywords, even if they lack a full understanding of the problems. Research suggests that effective mathematical reasoning involves the use of visual mental representations during the problem-solving process. To address this, some studies have explored methods to enhance students’ comprehension of word problems. Building on this, the current study explores the impact of first-grade pupils creating visual representations of problem situations on their comprehension and the number of correct solutions. In a typical math class, 45 first graders received a paper-and-pencil task, and, in a visual context, they solved similar problems after reading and illustrating the situation. The findings reveal that while most participants correctly represented the problem situations through drawing, about half struggled to determine the numeric solutions. Nevertheless, the visual context led to an increase in the number of correct problem solutions compared to the normal context, suggesting the potential benefits of incorporating visual representations in enhancing comprehension and problem-solving skills.

Morphological awareness in arithmetic word-problem solving among Chinese early adolescents

The current study explored a specific reading subskill, morphological awareness, in arithmetic word-problem solving among Chinese early adolescent students (N = 668, mean age = 11.3 years). Participants completed measures of Chinese morphological awareness, receptive vocabulary as well as arithmetic word-problem solving. Drawing upon multivariate analyses (hierarchical multiple regression and path analysis), the study showed that morphological awareness facets collectively contributed to arithmetic word-problem solving above and beyond age and receptive vocabulary. More specifically, recognition and discrimination of compound words were uniquely associated with word-problem-solving skills. The current study highlights the uniqueness of Chinese morphological awareness in structural linguistic input, and the facilitative effect of morphological awareness on arithmetic problem-solving.

Arithmetic Word Problem-Solving and Math Anxiety: The Role of Perceived Difficulty and Gender

ABSTRACT A crucial component of mathematics curriculum in primary education is represented by the ability to solve arithmetic word problems. Previous studies investigated predominantly the cognitive factors underlying this skill, neglecting the role of emotional (e.g. math anxiety – MA) and metacognitive aspects (e.g. perceived difficulty). Some findings suggested that emotional factors could influence perceived task difficulty which would, in turn, impair students’ performance. However, the relation between MA, perceived difficulty, and math problem-solving has not been explored yet. Moreover, although many studies reported gender differences in MA levels, findings involving primary school children are contrasting. Thus, this study aimed to evaluate the role of MA and perceived task difficulty on arithmetic word problem-solving proficiency in a sample of Italian primary school students, and to investigate gender differences in those variables. Results showed that MA had a direct and indirect effect through perceived difficulty on problem-solving performance. Furthermore, findings confirmed that girls exhibited higher MA levels, however no gender difference was observed in problem-solving accuracy nor in perceived difficulty. The study underlines the need to consider emotional factors when investigating children’s difficulties in math problem-solving and highlight the importance of MA interventions, especially for girls, already in primary education.

Structural and metabolic brain correlates of arithmetic word-problem solving in Huntington's disease.

Individuals with pre-manifest and early symptomatic Huntington's disease (HD) have shown deficits in solving arithmetic word-problems. However, the neural correlates of these deficits in HD are poorly understood. We explored the structural (gray-matter volume; GMV) and metabolic (18F-FDG PET; SUVr) brain correlates of arithmetic performance using the recently developed HD-word problem arithmetic task (HD-WPA) in seventeen preHD and sixteen HD individuals. Symptomatic participants showed significantly lower scores in the HD-WPA than preHD participants. Lower performance in the HD-WPA was associated with reduced GMV in subcortical, medial frontal, and several posterior-cortical clusters in HD participants. No significant GMV loss was found in preHD participants. 18F-FDG data revealed a widespread pattern of hypometabolism in association with lower arithmetic performance in all participants. In preHD participants, this pattern was restricted to the ventrolateral and orbital prefrontal cortex, the insula, and the precentral gyrus. In HD participants, the pattern extended to several parietal-temporal regions. Word-problem solving arithmetic deficits in HD is subserved by a pattern of asynchronous metabolic and structural compromise across the cerebral cortex as a function of disease stage. In preHD individuals, arithmetic deficits were associated with prefrontal alterations, whereas in symptomatic HD patients, more severe arithmetic deficits are associated with the compromise of several frontal-subcortical and temporo-parietal regions. Our results support the hypothesis that cognitive deficits in HD are not exclusively dominated by frontal-striatal dysfunctions but also involve fronto-temporal and parieto-occipital damage.

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

A subtraction game to scaffold primary students’ word problem solving skills

Solving arithmetic word problems has been a challenge for primary students due to difficulties in understanding the problem structure and relating the quantities in the problem to each other. This paper reports on an action research study to enhance students’ subtraction word problem-solving skills. The authors observed that their students had difficulties in representing the situations in word problems and solving the problems correctly. They designed, implemented, and analyzed an intervention to scaffold their students’ subtraction word problem-solving skills. As part of the intervention, a digital subtraction game was developed and used with second and third-grade students. The game involves three different representations: a discrete visual model, a bar model, and a number sentence. The students played the game and solved additional problems to strengthen their skills for representing and solving subtraction word problems. Twenty-four 2nd grade students in China and two 3rd grade students in Turkey participated in the study. Data sources included a pre-test, a post-test, student worksheets, and teachers’ filed notes. Data analysis showed an increase in students’ subtraction word problem-solving performance. They also effectively used a variety of representations to represent problem situations. The design and implementation processes of the intervention are discussed in the paper. We share suggestions for future implementation.

Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks

The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international assessments. In the current study, we delved into this question and compared the frequency and characteristics of arithmetic word problems (AWPs) contained in primary school math textbooks in two countries with different levels of performance in international assessments—Singapore and Spain. In our analyses, we focused on (1) the quantity of arithmetic word problems, (2) the variety of problems in terms of their additive or multiplicative structures and semantic-mathematical substructures, and (3) the quantity and nature of illustrations that were presented together with arithmetic word problems. Although a larger proportion of AWP activities was found in Singaporean textbooks, the results showed a similar variety of AWPs in both Singaporean and Spanish math textbooks. Furthermore, in both countries, math textbooks emphasized the structures classified as (additive) combine 1 and (multiplication) simple rate in AWPs. Notably, the Singaporean textbook contained a larger percentage of illustrations that reflected the semantic-mathematical structures of the problems and helped students learn how to solve AWPs (e.g., bar models). The findings are discussed in light of theories that posit that textbooks constitute a fundamental part of the teaching–learning process in the classroom.

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.

Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification

Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification

Arithmetic Word-Problem Solving as Cognitive Marker of Progression in Pre-Manifest and Manifest Huntington's Disease.

Arithmetic word-problem solving depends on the interaction of several cognitive processes that may be affected early in the disease in gene-mutation carriers for Huntington's disease (HD). Our goal was to examine the pattern of performance of arithmetic tasks in premanifest and manifest HD, and to examine correlations between arithmetic task performance and other neuropsychological tasks. We collected data from a multicenter cohort of 165 HD gene-mutation carriers. The sample consisted of 31 premanifest participants: 16 far-from (>12 years estimated time to diagnosis; preHD-A) and 15 close-to (≤12 years estimated time to diagnosis; preHD-B), 134 symptomatic patients (early-mild HD), and 37 healthy controls (HC). We compared performance between groups and explored the associations between arithmetic word-problem solving and neuropsychological and clinical variables. Total arithmetic word-problem solving scores were lower in preHD-B patients than in preHD-A (p < 0.05) patients and HC (p < 0.01). Early-mild HD patients had lower scores than preHD patients (p < 0.001) and HC (p < 0.001). Compared to HC, preHD and early-mild HD participants made more errors as trial complexity increased. Moreover, arithmetic word-problem solving scores were significantly associated with measures of global cognition (p < 0.001), frontal-executive functions (p < 0.001), attention (p < 0.001) visual working memory (p < 0.001), mental rotation (p < 0.001), and confrontation naming (p < 0.05). Arithmetic word-problem solving is affected early in the course of HD and is related to deficient processes in frontal-executive and mentalizing-related processes.

The Demands of Simple and Complex Arithmetic Word Problems on Language and Cognitive Resources.

Solving arithmetic word problems requires constructing a situation model based on the problem text and translating that into a mathematical model. As such, word problem solving makes demands on students’ language comprehension and their domain-general cognitive resources. These demands may decrease when students get more experienced and use strategies that do not require fully understanding the situation presented in the problem. The current study aims to address this hypothesis. Students (N=444) from third to sixth grade solved a paper-and-pencil task with 48 mathematics problems, comprising symbolic arithmetic problems and standard word problems, as well as more complex word problems that involve two arithmetic steps or include irrelevant numerical information. Their performance was analyzed with multilevel logistic regression analyses. Results showed that within each grade, performance on the different problem types did not differ, suggesting that already in third-grade students seem helped nor hindered by presenting arithmetic problems in a story, even if that story contains irrelevant numerical information. Non-verbal reasoning was more important in standard word problems than in arithmetic problems in symbolic format in one-step arithmetic, and reading comprehension was more important in solving two-step arithmetic word problems than in one-step arithmetic word problems.

Analyzing Difficulties in Arithmetic Word Problem Solving: An Epistemological Case Study in Primary School

This paper focuses on difficulties that primary school students have in facing mathematical word problems. In particular, we are interested in exploring how they develop in the transition from grade 2 to grade 5. The research basis of the hypothesis is that some difficulties detected in grade 5 are already predictable in grade 2. Starting from the data collected in grade 5 by the National Standardized Assessment, we carry out a quantitative analysis looking for word problems in which students experience difficulties. Subsequently, we conduct a backward analysis of the grade 2 test of the same cohort of students in order to identify a set of word problems linked with those selected in grade 5 test. The analysis shows the presence of many common difficulties in the two grades. We design and carry out specific educational activities concerning word problem-solving in grade 2. These activities produce positive changes in the experimental class compared to the control class. This could suggest that a previous intervention in grade 2 could allow overcoming future difficulties in word problem text comprehension in grade 5.

Contributions of Reading Comprehension Subskills to Arithmetic Word-Problem Solving among Chinese Primary School Students

ABSTRACT Learning to solve arithmetic word problems is an essential part of the primary school mathematics curriculum. The success of word-problem solving was previously found to relate to reading comprehension ability of children. However, the relationships between specific reading comprehension component skills and word-problem solving remain largely unknown. The current study examined the role of four comprehension subskills – morphological, syntactic, inference making, and comprehension monitoring – in children’s performance on word-problem solving. A total of 129 primary four, Chinese-speaking, children participated in this study. Participants were assessed with tasks of comprehension subskills and arithmetic word problems, as well as two control measures (word reading and nonverbal Intelligence). All four comprehension subskills were found to have unique and significant predictions on children’s equation formation performance. Furthermore, we proposed a model which described the relationships between the comprehension subskills and arithmetic word problems. The appropriateness of the hypothesized relationships was confirmed by path and mediation analyses. The present study not only provides evidences on the specific comprehension subskills that contribute to word-problem solving, but also provides practical implications for mathematics educators, and research insights for future word-problem studies.

Arithmetic Word Problems Revisited: Cognitive Processes and Academic Performance in Secondary School

Solving arithmetic word problems is a complex task that requires individuals to activate their working memory resources, as well as the correct performance of the underlying executive processes involved in order to inhibit semantic biases or superficial responses caused by the problem’s statement. This paper describes a study carried out with 135 students of Secondary Obligatory Education, each of whom solved 5 verbal arithmetic problems: 2 consistent problems, whose mathematical operation (add/subtract) and the verbal statement of the problem coincide, and 3 inconsistent problems, whose required operation is the inverse of the one suggested by the verbal term(s). Measures of reading comprehension, visual–spatial reasoning and deductive reasoning were also obtained. The results show the relationship between arithmetic problems and cognitive measures, as well as the ability of these problems to predict academic performance. Regression analyses confirmed that arithmetic word problems were the only measure with significant power of association with academic achievement in both History/Geography (β = 0.25) and Mathematics (β = 0.23).

Solving arithmetic word problems by scoring equations with recursive neural networks

Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to arithmetic word problems. In this work, we explore novel approaches to score such candidate solution equations using tree-structured recursive neural network (Tree-RNN) configurations. The advantage of this Tree-RNN approach over using more established sequential representations, is that it can naturally capture the structure of the equations. Our proposed method consists of transforming the mathematical expression of the equation into an expression tree. Further, we encode this tree into a Tree-RNN by using different Tree-LSTM architectures. Experimental results show that our proposed method (i) improves overall performance with more than 3% accuracy points compared to previous state-of-the-art, and with over 15% points on a subset of problems that require more complex reasoning, and (ii) outperforms sequential LSTMs by 4% accuracy points on such more complex problems.

Learning to be an opportunistic word problem solver: going beyond informal solving strategies

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students’ solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a pedagogical design for arithmetic word problem solving, which is part of a first-grade arithmetic intervention (ACE). The curriculum was designed to promote adaptive expertise among students through semantic analysis and recoding, which would lead students to favor the more adequate solving strategy when several options are available. We describe the ways in which students were taught to engage in a semantic analysis of the problem, and the representational tools used to favor this conceptual change. Within the word problem solving curriculum, informal and formal solving strategies corresponding to the different formats of the same arithmetic operation, were comparatively studied. The performance and strategies used by students were assessed, revealing a greater use of formal arithmetic strategies among ACE classes. Our findings illustrate a promising path for going past informal strategies on arithmetic word problem solving.

Language-related longitudinal predictors of arithmetic word problem solving: A structural equation modeling approach

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10–9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children’s later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed.

Learning Mathematics in Metacognitively Oriented ICT-Based Learning Environments: A Systematic Review of the Literature

This article encompasses a systematic review of the research on ICT-based learning environments for metacognitively oriented K-12 mathematics education. This review begins with a brief overview of the research on metacognition and mathematics education and on ICT and mathematics education. Based on a systematic screening of the databases Web of Science and ERIC wherein three elements—ICT-based learning environments, metacognitive pedagogies, and mathematics—are combined, 22 articles/studies were retrieved, situated at various educational levels (kindergarten, elementary school, and secondary school). This review revealed a variety of studies, particularly intervention studies, situated in elementary and secondary schools. Most studies involved drill-and-practice software, intelligent tutoring systems, serious games, multimedia environments, and computer-supported collaborative learning environments, with metacognitive pedagogies either integrated into the ICT software itself or provided externally by the teacher, mainly for arithmetic or algebraic word problem-solving but also related to other mathematical topics. All studies reported positive effects on mathematical and/or metacognitive learning outcomes. This review ends with a discussion of issues for further theoretical reflection and empirical research.

When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems.

Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical problems involving these entities? We argue that such daily-life knowledge interferes with arithmetic word problem solving, to the extent that experts can be led to failure in problems involving trivial mathematical notions. We created problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 - 2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple arithmetic problems evoking knowledge that was either congruent or incongruent with the problems' solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the problems "unsolvable" increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to arithmetic word problems, even among experts who have supposedly mastered abstract, context-independent reasoning.

Solving Arithmetic Word Problems by Object Oriented Modeling and Query-Based Information Processing

The paper presents an Object Oriented Analysis and Design (OOAD) approach to modeling, reasoning and a database query based approach to processing and solving addition-subtraction (Add-Sub) type arithmetic Mathematical Word Problems (MWP) of elementary school level. The system identifies and extracts the key entities in a word problem like owners, items and their attributes and quantities, verbs, from all the input sentences, using a rule based Information Extraction (IE) approach based on Semantic Role Labeling (SRL) technique. These information are then stored in predefined templates which are further modeled to represent an MWP in the object-oriented paradigm and processed using query based approach to generate the answer. These kind of applications are based on Natural Language Processing (NLP), Natural Language Understanding (NLU) and Artificial Intelligence (AI), and can be used as intelligent dynamic mathematical tutoring tools as part of E-Learning systems, Learning Management Systems, on-line education, etc. The proposed object oriented mathematical word problem solver can solve arithmetic MWPs involving only addition-subtraction operations and it has produced an accuracy of 94.35% on a subset of the AI2 arithmetic questions dataset.