Algebra Word Problems Research Articles

Investigating pre-tertiary students’ mistakes in solving algebraic word problems: Insights from Asutifi North District, Ghana

Algebra word problems inculcate in learners the skills and ability to think critically and look for answers to problems in society and the world. Using an explanatory sequential mixed design, the study investigated the errors made by pre-tertiary students in algebraic word problems in a selected school in the Asutifi North District of the Ahafo Region of Ghana. Whereas the Newman Error Analysis Model was used to find the types of errors students make when translating and solving algebraic word problems, protocols from topics relating to the study were carefully selected and used as interview guides alongside inspiration from the Newman Error Analysis Model. Quota and simple random sampling techniques were used to select ninety-eight (98) respondents. The Algebraic Word Problem Achievement Test (AWPAT) was given to the ninety-eight students who had studied several topics on word problems, followed by a structured interview to elicit more information from the respondents. The scores gained from the marked test items illustrated that students made more transformation errors, which happened indirectly from a lack of understanding of the concept. A careful analysis of the written responses of the five (5) students interviewed also revealed that, lack of comprehension directly translated into students’ inability to transform algebraic word problems into mathematics equations. In the same vein, the study showed that the main cause of students’ failure to translate and solve algebraic word problems was students’ lack of understanding of the concept of “word problem” among others. The study recommends that students be motivated by encouragement and praise to arouse their interest in translating and solving algebraic word problems.

Students' ‘Looking Back’ in Solving Algebraic Word Problems

Solving mathematics problems is a complex cognitive process that involves a series of steps. These steps typically include understanding the problem, devising a plan, carrying out the plan, and looking back (checking the solution). While each of these steps is crucial, the ‘looking back’ step has not received much attention in mathematics education research. This study investigated Grade 10 mathematics students’ looking back in solving algebraic word problems in Namibia. The study followed a qualitative approach. The sample of the study was 351 Grade 10 students from ten secondary schools in the Ohangwena Region in Namibia. Data was collected using the Algebra Word problem-solving Achievement Test and Interview. The results show that, in general, the students did not look back on their solutions to the algebraic word problem. While some students indicated that looking back necessitates the consolidation of their work, others said looking back on their solutions could be time-wasting and confusing. These findings point to the need for mathematics teachers in Namibia to incorporate and model the looking-back step of mathematical problem-solving in their mathematics teaching.

Rasch model assessment of algebraic word problem among year 8 Malaysian students

<p>Word problems continue to be a challenge for students today. All students must meet the prerequisites for problem solving and reasoning skills, which are important components of the critical thinking component of 21st century skills. This study is being conducted to assess students’ strategies for solving word problems with numbers, consecutives, and ages. The Rasch model is used to analyze the item difficulty level of word problems and students’ strategies for solving ten-word problems at various levels of item difficulty in a similar trait. Then, Pearson correlation analysis is used to investigate the item difficulty level in relation to linguistic, algebraic, and arithmetic factors of word problems before evaluating students’ performance on solving these word problems using various strategies. Rasch model found these algebraic word-problem questions are slightly harder for year 8 Malaysian students in relative to an international standard. Meanwhile, the item difficulty of word problems is driven by linguistic and algebra factors where students can score accurately if the word problems contained explicit information. However, the students encountered difficulties while losing their solution strategy when the questions contained implicit data that demanded critical thinking ability.</p>

Evaluating the Impact of the WEI4S Instructional Approach on Middle School Students’ Algebraic Problem-Solving Skills

This study investigates the effectiveness of an instructional approach called “Worked-out Examples Involving 4 Stages” (WEI4S) for enhancing middle school students’ algebraic problem-solving skills and reducing CL. Based on cognitive load theory (CLT), WEI4S combines four stages (analyse, explain, investigate, and apply) to facilitate deep comprehension. This study involved 36 novice seventh-grade students identified as having challenges solving algebraic word problems. Participants were randomly assigned to different groups, including the experimental group that received the WEI4S intervention and a control group that participated in problem-solving activities. Pre- and post-tests, as well as a transfer test, were administered to measure algebra performance and CL, and students’ opinions about the intervention were collected. The findings revealed that students exposed to WEI4S showed significant improvements in algebra performance, decreased intrinsic CL, and no negative changes in terms of extrinsic and germane load compared to the control group. Overall, the WEI4S approach offers a promising avenue for effective mathematics instruction by providing a structured framework that encourages active engagement and problem-solving skills.

Effects of Case-based Strategy on Academic Achievement in Mathematics Algebraic Word Problems among Junior Secondary School Students in Ibadan Metropolis, Oyo State, Nigeria

This study investigated the Effect of Case-based Strategy on Academic Achievement in Mathematics Word Problems among Junior Secondary School Students in Ibadan Metropolis, Oyo State, Nigeria. The research focused on evaluating learning outcomes, knowledge retention, and overall students’ performance when exposed to this teaching approach based on constructivism and behaviorism theories of learning. The study employed a quasi-experimental research design. The population of the study consisted of all 20244 Junior Secondary School students in Oyo State, while two intact classes of 68 JSS2 students participated in the study. Two lesson plans and a validated Mathematics Achievement Test (MAT) were used as instruments for data collection. The MAT was tested for reliability having a value of 0.85 and the data generated was statistically analyzed using frequency counts, percentages, standard deviation and Analysis of Co-variance (ANCOVA) at a significance level of 0.05. The findings revealed that the effect of case-based strategy on students’ academic achievement was significant (F(1,65) = 72.771, p< 0.05) and was found to be more effective in enhancing students’ academic achievement in algebraic word problems. It was recommended that educators should incorporate case-based strategies in teaching Mathematics Algebraic word problem at the Junior Secondary School for effective outcome.

Students’ mathematics and real life contexts in solving algebraic word problems

Background: Algebra involves rules of operations, signs of operations, equations, and algebraic structures. Previous studies have indicated that students often struggle with mathematics in both academic and real-life contexts.Aim: The main objective of this study was to explore how students handle word problems in both mathematics and real-life contexts.Method: The study utilized a cross-sectional design to examine these issues in the developing world, specifically targeting junior high school students in Ghana. A total of 200 students, comprising 91 males and 109 females from various public Junior High Schools, were randomly sampled. The research categorized problems into mathematics context and real-life context, with analysis further divided into 'attempt statuses' (either 'attempted' or 'not attempted') and 'performance statuses' (either 'correct' or 'wrong'). Follow-up interviews, each lasting 15 minutes, were conducted with three groups of both male and female students.Results: The results from the independent samples t-test revealed that the mean score for male students (M =15.37, SD =3.435) was not significantly different from that of female students (M = 15.35, SD = 3.619). It was observed that male students attempted all word problems, while some problems were not attempted by female students.Conclusion: The study concluded that there is no statistically significant difference in the ability of male and female students to solve algebraic word problems. The lack of attempts by female students on some items suggests a potential lack of understanding in context problems. It is recommended that teachers employ multiple representations, technology tools, and metacognitive strategies to help bridge these gaps.

NCS 수리능력 영역의 대수 문장제 해결 과정에서 나타난 오류 분석에 관한 연구

Objectives The purpose of this study is to analyze errors that arise during the problem-solving process of alge-braic word problems in the mathematical reasoning domain of NCS(National Competency Standards) for speci-alized high school students and to explore instructional strategies to address these errors.
 Methods A test consisting of six items was administered to 70 students attending specialized high schools lo-cated in medium city. After conducting the test using the questionnaire, the response sheets were analyzed by error type. Additionally, in-depth interviews were conducted with five participants, and the content of these inter-views was recorded, transcribed, and analyzed.
 Results Many students in specialized high schools experienced difficulties in solving algebraic word problems in the NCS mathematical competency domain. The types of errors observed during the problem-solving process in-cluded errors in skipping solution steps, difficulties arising from mathematical language, errors in problem com-prehension, and errors stemming from inadequate mastery of prerequisite skills, facts, and concepts.
 Conclusions To address significant errors in solving algebraic word problems, it is crucial to focus on algebraic translation, fundamental computational skills, acquiring prerequisite knowledge, and systematic problem-solving writing. Instruction should be centered around vocational foundational abilities, particularly emphasizing algebraic word problems within the context of vocational math competency assessment. Moreover, it is necessary to in-corporate algebraic word problems into the mathematical application domain of specialized high school vocational foundational assessments and develop and implement an education curriculum tailored to the specialized voca-tional context, preparing students for the NCS mathematical ability assessment.

Analysis of Students Mathematical Reasoning Ability in Solving Algebra Word Problems in terms of Learning Styles

This study aims to describe students' mathematical reasoning abilities in solving algebra word problems in terms of learning styles. This type of research is descriptive qualitative research. The research subjects were class VII A students of SMPN 1 Pasrepan for the 2022/2023 academic year. The subjects in this study were 2 students with a visual learning style, 2 students with an auditory learning style, and 2 students with a kinesthetic learning style. Data collection techniques in this study were learning style questionnaires, mathematical reasoning ability tests, and interviews. Triangulation in this study uses triangulation techniques. The results of this study indicate that subjects with a visual learning style have high mathematical reasoning abilities with a percentage of 78.75%, subjects with an auditory learning style have high mathematical reasoning abilities with a percentage of 93.75%, and subjects with a kinesthetic learning style have reasoning abilities moderate mathematics with a percentage of 60%.

ANALYSIS OF SENIOR HIGH SCHOOL STUDENT’S ERRORS IN SOLVING WORD PROBLEMS USING NEWMAN’S ERROR ANALYSIS (NEA) PROCEDURE

The study was intended to analyze Senior High School students’ errors in solving algebra word problem using Newman’s Error Analysis (NEA). The study employed descriptive qualitative design. 70 S.H.S 1 students were randomly sampled from the three Senior High Schools within the Nkoranza North District. Teacher-made word problem diagnostic test was conducted and Newman’s Error Analysis (NEA)checklist used to analyze students’ errors in the test. Various descriptive statistics such as Bar graph, pie chart and frequency distribution were used to described the errors committed. The study found that, out of the 623 total errors committed by the 70 students in the 10-item test, 45.4% wasoncomprehension errors, 34.4% was transformation errors, 13% was process skills errors, 5% was encoding errors and the least being reading errors which is 2.2%. It is recommended that mathematics teachers thoroughly teach the meaning of words used in crafting word problem items and also tailor their strategies towards the changing of word problemsinto mathematical models and equation.The finding of this study would equip mathematics teachers within the study settingwitha scientific based information on the kind of errors students make in solving word problems. This information would then be used as foundation in coming out with strategies to mitigate or curtail the errors students commit in solving word problem

Grade 10 Namibian learners' problem-solving skills in algebraic word problems

Grade 10 Namibian learners' problem-solving skills in algebraic word problems

Twinned Teachers’ Mathematical Discourse Using Problem-Solving

Discussing and debating mathematical ideas through integrating natural and mathematical language is vital for conceptual understanding and ultimately for learner performance. In schools with low performance, it is likely that teaching mathematics follows an approach largely involving rote learning. In rural Limpopo where schools are isolated, professional development takes the form of twinning, where a well-functioning school twins with a school in need. In this study two teachers twinned to teach algebraic word problems to Grade 11 to improve learner performance through a problem-solving approach. A central aspect of the study was attention to discourse informed by the commognitive framework, where both natural language (learners home language and the language of instruction) and language of mathematics spoken by the teachers and encouraged in the learners, was the focus. This quasi-experimental design was implemented to examine the effect of the twinned teachers discourse in a class where English, the language of instruction, was a second language. In the study a pre-test and post-test were administered to the experimental group of 34 learners, and to a comparison group of 40 learners. The study aimed at testing the hypothesis that the twinned mathematics teachers’ discourse using a problem-solving approach informed by the commognitive framework has a significant effect on learner performance in algebraic word problems. In summary, using the commognitive framework in implementing problem-solving approach with the twinned teachers’ mathematical discourse had significant effect in improving learner performance of algebraic word problems in the target group.

Algebra word problem difficulties: A case study in Tema Education Metropolis in Ghana

Modern mathematics education used a different approach when dealing with word problems in algebra because of how people perceive mathematics. The teacher can aid students in honing their problem-solving abilities to assist them build mathematical concepts that can be applied in real-world situations. This research is a case study involving junior high school (JHS) pupils in Ghana’s Tema Metropolis. For the study, data collection and analysis used a qualitative methodology. Using a purposive sample technique, data from 12 participants–six JHS mathematics teachers and six students–were gathered. Data were gathered through observation, interviews, and document analysis. The primary finding is that JHS pupils at Tema Education Metropolis are unable to present their own issues as proof of conceptual knowledge of algebra word problems.

Solving Algebraic Word Problems Using General Heuristics Instruction

Solving word problems is a large part of algebra coursework and statewide testing. However, solving secondary mathematics word problems is difficult for most students and extremely challenging for students with specific learning disabilities (SLD). In recent meta-analyses, two problem solving strategies emerged as effective for secondary students with SLD: Schema-Based Instruction (SBI) and General Heuristics Instruction (GHI). While SBI has been highlighted in recent works, GHI deserves further explanation. In this article, we provide details of GHI and highlight its flexibility and utility using different algebra examples.

Boys' advantage in solving algebra word problems is mediated by spatial abilities and mathematics anxiety.

Adolescents' (n = 342, 169 boys) general algebra and algebra word problems performance were assessed in 9th grade as were intelligence, academic achievement, working memory, and spatial abilities in prior grades. The adolescents reported on their academic attitudes and anxiety and their teachers reported on their in-class attentive behavior in 7th to 9th grade. There were no sex differences on the general algebra measure or for mathematics achievement, but boys had an advantage on the algebra word problems measure (d = .51) and for spatial abilities (ds = .29 to .58). Boys had higher mathematics self-efficacy (d = .24 to .33), lower mathematics anxiety (ds = -.31 to -.53) and were less attentive in classrooms (ds = -.28 to -.37). A series of structural equation models revealed the sex difference for algebra word problems was mediated by spatial abilities and mathematics anxiety, controlling myriad confounds. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Some Correct Strategies Are Better Than Others: Individual Differences in Strategy Evaluations Are Related to Strategy Adoption.

Why do people shift their strategies for solving problems? Past work has focused on the roles of contextual and individual factors in explaining whether people adopt new strategies when they are exposed to them. In this study, we examined a factor not considered in prior work: people's evaluations of the strategies themselves. We presented undergraduate participants from a moderately selective university (N = 252; 64.8% women, 65.6% White, 67.6% who had taken calculus) with two strategies for solving algebraic word problems and asked them to rate these strategies and their own strategy on a variety of dimensions. Participants' ratings loaded onto two factors, which we label quality and difficulty. Participants' initial evaluations of the quality of the strategies were associated with whether they used the strategies at posttest, and this effect held even when controlling for individual and contextual factors. However, people's evaluations of the difficulty of the strategies were not consistently associated with their later adoption of those strategies. We also examined individual and contextual predictors of strategy ratings and strategy adoption. Participants' need for cognition and their spatial visualization ability were associated with their strategy evaluations, and the framing of the story problems was associated with their strategy adoption. The findings highlight that strategy adoption depends on multiple interacting factors, and that to understand strategy change, it is critical to examine how people evaluate strategies.

The underlying neural bases of the reversal error while solving algebraic word problems

Problem solving is a core element in mathematical learning. The reversal error in problem solving occurs when students are able to recognize the information in the statement of comparison word problems, but they reverse the relationship between two variables when building the equations. Functional magnetic resonance images were acquired to identify for the first time the neural bases associated with the reversal error. The neuronal bases linked to this error have been used as inputs in 13 classifiers to discriminate between reversal error and non-reversal error groups. We found brain activation in bilateral fronto-parietal areas in the participants who committed reversal errors, and only left fronto-parietal activation in those who did not, suggesting that the reversal error group needed a greater cognitive demand. Instead, the non-reversal error group seems to show that they have developed solid algebraic knowledge. Additionally, the results showed brain activation in the right middle temporal gyrus when comparing the reversal error vs non-reversal error groups. This activation would be associated with the semantic processing which is required to understand the statement and build the equation. Finally, the classifier results show that the brain areas activated could be considered good biomarkers to help us identify competent solvers.

Asking the right questions to solve algebraic word problems

Word algebra problems are among challenging AI tasks as they combine natural language understanding with a formal equation system. Traditional approaches to the problem work with equation templates and frame the task as a template selection and number assignment to the selected template. The recent deep learning-based solutions exploit contextual language models like BERT and encode the natural language text to decode the corresponding equation system. The proposed approach is similar to the template-based methods as it works with a template and fills in the number slots. Nevertheless, it has contextual understanding because it adopts a question generation and answering pipeline to create tuples of numbers, to finally perform the number assignment task by custom sets of rules. The inspiring idea is that by asking the right questions and answering them using a state-of-the-art language model-based system, one can learn the correct values for the number slots in an equation system. The empirical results show that the proposed approach outperforms the other methods significantly on the word algebra benchmark dataset alg514 and performs the second best on the AI2 corpus for arithmetic word problems. It also has superior performance on the challenging SVAMP dataset. Though it is a rule-based system, simple rule sets and relatively slight differences between rules for different templates indicate that it is highly probable to develop a system that can learn the patterns for the collection of all possible templates, and produce the correct equations for an example instance.

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.

The role of the Singapore bar model in reducing students’ errors on algebra word problems

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students’ errors on algebra word problems. To accomplish this purpose, we first assessed students’ errors on a written test involving algebra problems and identified ten students based on the errors they demonstrated. These students were then offered instruction on how to use the bar model method. Following the instruction, we did clinical interviews and observed that the Singapore bar model method helped students understand the problem and transform words into mathematical expressions. Hence, the bar model served as an assistive tool for the remediation of students’ errors in algebra word problems by facilitating students’ comprehension and transformation.

Neural Sequence-to-grid Module for Learning Symbolic Rules

Logical reasoning tasks over symbols, such as learning arithmetic operations and computer program evaluations, have become challenges to deep learning. In particular, even state-of-the-art neural networks fail to achieve \textit{out-of-distribution} (OOD) generalization of symbolic reasoning tasks, whereas humans can easily extend learned symbolic rules. To resolve this difficulty, we propose a neural sequence-to-grid (seq2grid) module, an input preprocessor that automatically segments and aligns an input sequence into a grid. As our module outputs a grid via a novel differentiable mapping, any neural network structure taking a grid input, such as ResNet or TextCNN, can be jointly trained with our module in an end-to-end fashion. Extensive experiments show that neural networks having our module as an input preprocessor achieve OOD generalization on various arithmetic and algorithmic problems including number sequence prediction problems, algebraic word problems, and computer program evaluation problems while other state-of-the-art sequence transduction models cannot. Moreover, we verify that our module enhances TextCNN to solve the bAbI QA tasks without external memory.