Word Problem Solving Research Articles

Teaching Students With Mild Intellectual Disability to Solve Word Problems Using Schema-Based Instruction

This study, which used a multiple baseline across participants’ design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem solving performance of three students with mild intellectual disability, two of whom had an autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent on change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed.

Words Problem Based Creation for Thematic Mathematical Stories: A Collaborative Action Research

This research aims to improve the classroom practices of rural primary teachers in developing mathematics word problem through collaborative action research. The cooperation between fourth grade teachers and researchers from university focused on examining the results of the implementation of the two activities within the action plans, ‘Creating word problems communicatively based by teachers’ and ‘Solving word problems easily by students’. From the analysis of qualitative data (interviews with students, observation and journal entries) and quantitative (tests and questionnaires) seen a significant improvement of the results of teacher in word problem creating and students in word problem solving. Developing word problem based on thematic mathematical stories enabled students to guide in using storytelling as a tool for understanding word problems

Words Problem Based Creation for Thematic Mathematical Stories: A Collaborative Action Research

This research aims to improve the classroom practices of rural primary teachers in developing mathematics word problem through collaborative action research. The cooperation between fourth grade teachers and researchers from university focused on examining the results of the implementation of the two activities within the action plans, ‘Creating word problems communicatively based by teachers’ and ‘Solving word problems easily by students’. From the analysis of qualitative data (interviews with students, observation and journal entries) and quantitative (tests and questionnaires) seen a significant improvement of the results of teacher in word problem creating and students in word problem solving. Developing word problem based on thematic mathematical stories enabled students to guide in using storytelling as a tool for understanding word problems

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.

Analysis of Students’ Errors in Solving Social Arithmetic Word Problems in terms of the Learning Styles

Some abilities are needed to solve word problems, one of which is the ability to understand sentences and symbols in the problem. One factor that affects the ability of each student is learning style. Learning style is a person's tendency to receive and process information to the maximum, learning styles can be grouped into three, namely visual, auditory, and kinesthetic learning styles. The purpose of this study is to analyze and describe the forms of errors made by students in solving social arithmetic word problems in terms of the learning styles. Data collection procedures in this study are giving learning style questionnaire, written test, and interview. The research subjects are two VII grade students at SMP Negeri 1 Malang from each learning styles. The results of the analysis of this research are that students with visual learning style error occurs at the step of devising a plan, carriying out the plan, and looking back. While students with auditory and kinesthetic learning style error occurs at the understanding the problem, devising a plan, carriying out the plan, and looking back. The error forms occur in all learning styles.

The Roles of Initial Mathematics, Reading, and Cognitive Skills in Subsequent Mathematics Performance: A Meta-Analytic Structural Equation Modeling Approach

In the present meta-analysis, we systematically investigated the relative contributions of students’ initial mathematics, reading, and cognitive skills on subsequent mathematics performance measured at least 3 months later. With one-stage meta-analytic structural equation modeling, we conducted analyses based on 580,437 students from 265 independent samples and 250 studies. Findings suggested fluency in both mathematics and reading, as well as working memory, yielded greater impacts on subsequent mathematics performance. Age emerged as a significant moderator in the model, such that the effects of comprehensive mathematics and working memory on subsequent mathematics increased with age, whereas attention and self-regulation’s impacts declined with age. Time lag between assessments also emerged as a significant moderator, such that the effects of word-problem solving and word recognition accuracy decreased as the time lag increased, whereas vocabulary, attention, and self-regulation’s effects increased as the time lag increased.

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.

Profile of Students’ Problem-Solving Skills Viewed from Polya's Four-Steps Approach and Elementary School Students

&lt;p style="text-align:justify"&gt;Problem-solving is considered one of the thinking skills that must be possessed in 21&lt;sup&gt;st&lt;/sup&gt;-century education because problem-solving skills are required to solve all problems that arise. The problem-solving stages that can be used are Polya's four steps, namely, understanding the problem, devising a plan, carrying out the plan, and looking back. Problem-solving skills are essential for solving word problems. Word problems based on arithmetic operations are divided into three types: one-step, two-step, and multistep. This qualitative research aimed to see problem-solving skills viewed from the type of word questions and elementary school students’ third, fourth, and fifth grades. A purposive sampling technique with 22 third-grade students, 28 fourth-grade students, and 21 fifth-grade students was used. The data were collected using documentation, testing, and interview methods. The findings of the study showed that fourth-grade students’ problem-solving skills are better than those of third-grade students, and the problem-solving skills of fifth-grade students are better than those of fourth-grade students. The percentage of Polya's steps always decreases because not all students master problem-solving. Based on the types of questions, the percentage of the one-step word problem is better than that of the two-step while the percentage of the two-step word problems is higher than that of the multistep.&lt;/p&gt;

Cooperative Learning as a Strategy in Solving Word Problems in Mathematics

Cooperative Learning as a Strategy in Solving Word Problems in Mathematics

ANALYSIS OF STUDENTS' ERRORS IN SOLVING WORD PROBLEMS ABOUT SOLID FIGURES IN FIFTH GRADE OF SDN TAMBAKREJO, PURWOREJO REGENCY, IN ACADEMIC YEAR OF 2020/2021.

&lt;p&gt;&lt;em&gt;The study aimed: (1) to analyze the types of students’ errors of fifth grade in solving math word problems about solid figures, (2) to describe the factors causing students' errors in solving math word problems about solid figures, (3) to describe solutions to overcome students’ errors in solving math word problems about solid figures in fifth grade of SD Negeri Tambakrejo. The research was a qualitative case study method. The subjects were 24 fifth grade students. Data collection techniques included observation, tests, interviews, and documents. Data analysis techniques were data reduction, data presentation, and verification. The results showed that: (1) the types and the percentage of students’ errors were: reading error = 5.3%, comprehension error = 20.7%, transformation error= 24%, process skill error= 11%, encoding error= 20.5%. (2) The factors causing students’ errors were internal factors and external factors. (3) The solutions to solve students’ errors were (a) the students were discipline to do word problems step-by-step, (b) the teachers emphasized the students in order to write steps in solving word problems completely, (c) the teachers emphasized the students about the basic concept in doing word problems, (d) the teachers applied effective and creative learning models.&lt;/em&gt;&lt;/p&gt;

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.

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

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

Does Word-Problem Performance Maintain? Follow-Up One Year After Implementation of a Word-Problem Intervention

We conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a pre-algebraic reasoning component (relational understanding of the equal sign as well as standard and nonstandard equation solving); the other included word-problem intervention without pre-algebraic reasoning. Students in both interventions significantly outperformed students in the BaU with large effect sizes (2.66 and 2.44), but there were no significant differences between the two intervention conditions. The purpose of the present analysis was to assess maintenance of effects 6–12 months after intervention with the students (n = 229), now in fourth grade. At follow-up, only students in the word-problem intervention with pre-algebraic reasoning significantly outperformed the BaU on a measure of word-problem solving. This finding suggests an advantage for the pre-algebraic reasoning component, yet the follow-up effect between intervention conditions was not significant. The ESs of 0.43 and 0.31 and persistence rates of 16% and 13% reveal substantial forgetting for both conditions, which suggests the dose of intervention may not be adequate for many students.

Tangram Proficiency Leading to Numeracy Skills Enhancement

This study focused on determining the ways in which numeracy skills are enhanced through tangram. An exploration on ways of solving patterns in tangram, power of imagination, enhancement of logical, analytical and critical thinking, and desirable characteristics being formed in playing tangram became part of this study. The community quarantine in the Philippines due to COVID-19 caused the design of this study to gather data through online tangram tournament. Seven learners accepted the seven-day challenge. They solved 55 tangram puzzles and answered 6 qualitative questions. After a week of tangram challenge, the following findings were established. In solving tangram puzzles, players can consider (1) looking into the details, (2) trial-and-error, or (3) planning. The best ways to solve tangram puzzles are (1) focusing on the whole portion, (2) focusing on the bigger portions, or (3) focusing on the smaller portions. Imagination plays an important role because (1) it makes things clear and the solution easier to obtain, (2) it put things into proper perspective, and (3) it reduces useless effort. Logical, analytical and critical thinking are enhanced because (1) proper flow of thought in the process of making decisions or conclusion is exercised, (b) deep thinking in considering different ways and solutions is given importance, and (c) correct reasoning based from facts or evidence is practiced. Numeracy skills are enhanced due to the following reasons: (1) Tangram can train the mind in dealing with abstracts and apply them in concrete things, (2) Tangram can assist in molding right attitude towards achieving goals and success, thereby improving skills like numeracy, (3) Tangram can aid learners in looking at the big picture without taking for granted the small details, and (4) Tangram can enhance skill in solving word problems. Desirable characteristics were discovered by-products of playing tangram.

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

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

The effect of Constructivism on Students’ Performance in Solving Mathematical Problems under Trigonometry

This paper is an action research which involves a sample of thirty five (35) second year students of Akontombra Senior High School comprising 24 males and 11 females. The study was aimed at using the constructivist approach to enhance students’ competence in solving word problems under trigonometry. Prior to the study, it was observed that the students were not able to understand and solve word problems under trigonometry. The constructivist approach of teaching and learning was employed as the intervention strategy and series of activities was carried out. The pre – test and post – test scores obtained by the students were analyzed quantitatively based on the research questions of the study. Comparatively, the results obtained from the pre – test and post – test showed a significant improvement on the students’ ability to solve word problems under trigonometry. It was then inferred from the results that the constructivist teaching and learning methodology employed during the intervention phases enhanced the academic achievements of the students. The constructivist approach to teaching encouraged students to participate in the process and environment of teaching and learning and to promote mathematics as a creative and meaningful activity that involves interpretation, effort and exploration.

Different complex word problems require different combinations of cognitive skills

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

Individual differences in the development of children’s arithmetic fluency from grades 2 to 3.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Senior High School Students’ Ability in Mathematical Word Problems

Nowadays, students have trouble solving word puzzles, even though they are trained to conduct another mathematical activity. The primary purpose of this study was to enhance the students’ ability to solve word problems. A questionnaire was used as a data-gathering tool, and the descriptive survey-correlational design was used. The data were treated using frequencies, ratios, weighted mean, and correlation analysis. The research sample consisted of 286 high school students from the University of La Salette, Incorporated in Santiago City. The majority of students are female, and took ABM as their strand. The findings of the study showed that choosing/writing an appropriate equation and performing it in a given problem affects most students’ ability to solve word problems. Moreover, the results showed that students were not sure of what they will feel when they encounter a complicated word problem. Furthermore, the study implies that their teachers did not allow them to use different strategies in solving word problems. Correlation analysis revealed that the different factors such as understanding word problems; attitudes of the students towards solving word problems; prior knowledge about the basic concept of math; and Teacher’s instructional techniques are highly and positively correlated to one another. The results imply that the teachers should be encouraged and be familiarized in using digital teaching methods and other significant emerging mathematics teaching and learning developments.

Schema-based Instruction an Effective Approach to Word Problem Solving in Students with Specific Learning Disorders: A Review Study

Schema-based Instruction an Effective Approach to Word Problem Solving in Students with Specific Learning Disorders: A Review Study