Mathematical Word Problem Solving Research Articles

The effects of functional moves in teacher questioning on students’ contextualization of mathematical word problem solving

AbstractPosing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that the implementation of task clarification (TC) moves effectively enhanced contextualization only when students possessed a relatively strong sense of agency while solving word problems. Furthermore, when students’ attentional focus was not appropriately redirected by the functional moves, including procedural understanding (PU), making connections (MC), the rationale behind a strategy (RA), and an alternative strategy (AS), their understanding of the contextual features and construction of mathematical relationships in word problem solving could not be refined. Implications for field experience design and future research on the quality of teacher questioning in mathematics teacher education programs are discussed.

Teaching Mathematics Word Problem Solving to Students With Autism Spectrum Disorder

The National Council of Teachers of Mathematics (NCTM) emphasizes the teaching of “Big Ideas” in mathematics. This study focuses on the part–part–whole (PPW) relationship as a crucial aspect of word problem solving involving addition and subtraction. The research evaluates the effects of conceptual model-based problem-solving (COMPS) with the concrete-representational-abstract (CRA) sequence on teaching addition and subtraction word problem solving to students with autism spectrum disorder (ASD). Using a multiple-probe design across the participants, the study evaluates the impact of the intervention on students’ performance across three types of word problems: join-in, take-away, and combine. Results demonstrated significant improvements in students’ problem-solving abilities on criterion tests. In addition, students successfully generalized their skills to solve problems with new contexts. The findings of this study provide implications for future research and educational practice.

Determining the Effect of Bar Model Technique on Students’ Mathematical Word Problem Solving Skills

The study aims at probing the effect of Bar Model Technique on the word problem solving skills of primary level students in the subject of mathematics. Following were the objectives (i) to determine the effect of Bar Model Technique on student’s mathematical word problem solving skills; (ii) to compare the academic achievements of male students and female students by using Bar Model Technique. It was experimental study and pretest-posttest equivalent group design was used as a tool for data collection in this study. Sample of the study was 40 students (Male & Female) of Government Primary School District Nowshera, Khyber Pakhtunkhwa. The sample students were divided in two group control and experimental on the base of pretest score by using paired random technique. Data were analyzed by mean, SD and t- test.

Retrieval practice may not benefit mathematical word-problem solving.

The retrieval practice effect refers to the fact that one or even multiple retrievals of memory content during the same period are more effective than repeated studying to promote future memory retention. It is effective for numerous declarative knowledge learning materials. However, studies have demonstrated that retrieval practice does not benefit problem-solving skill learning. This study used worked examples from math word problem tasks as learning materials, considering the retrieval difficulty as the main factor. Experiment 1 explored the effect of retrieval practice on acquiring problem-solving skills under different initial testing difficulties. Experiment 2 manipulated the difficulty of materials as a variable to ascertain the effect of retrieval practice on problem-solving skills under different material difficulty levels. Experiment 3 introduced feedback variables to facilitate the generation of the retrieval practice effect and examined the effects of various difficulty feedback levels on problem-solving skills learning. Results showed that, compared with restudying examples (SSSS), the example-problem pairs (STST) did not promote delayed test performance. As for the retrieval practice effect, as no differences or advantages were found in the repeated study group on the immediate test, the retrieval practice group generally outperformed the repeated study group on the delayed test. However, across the three experiments, we found no evidence of retrieval practice affecting results during an enhanced delayed test. Therefore, there may be no retrieval practice effect on acquiring problem-solving skills from worked examples.

특별한 관심 영역을 활용한 전략 교수가 자폐 범주성 장애 학생의 수학 문장제 과제 수행률 및 정확도에 미치는 영향

This study examined the effects of an instructional strategy using areas of special interest to students with Autism Spectrum Disorders (ASD) on their performance rate and accuracy in mathematical word problem-solving. The study used a multiple probe design for three students with ASD under three experimental conditions: baseline, intervention, and maintenance. First, the computation level of the word problem was selected by interviewing special education teachers and parents. Next, each participant’s special interest area was determined. Then, the interest areas were used to modify students’ word problems. Finally, the students were taught the instruction strategy’s four steps. The results indicated that the intervention increased each participant’s mathematical word problem-solving performance rate and accuracy. Furthermore, these effects persisted after the intervention. Several implications of the study are discussed

Do students' errors still occur in mathematical word problem-solving?: A newman error analysis

Mathematical word problems can be utilized to improve students' mathematic problem-solving skills. However, students' error still occurs in mathematical word problem-solving. This research aimed to trace and reveal students' errors in problem-solving using the Newman Error Analysis stages. This research is descriptive qualitative research. The research subjects were moderate-ability students of State Madrasah Tsanawiyah (MTs) in Jambi. Mathematical word problem worksheets and interview templates were used as instruments in this research. Students with the moderate ability category were given worksheets on algebraic and the Pythagorean Theorem operation. The students were also interviewed to get more information about the errors they experienced. This research found that the students' errors during word problem-solving had implications for the incorrect answer. Students' errors occurred at the comprehension, transformation, process skill, and encoding stages of the Newman Error Analysis stages. Indeed, the Newman Error Analysis stage is a cycle that means errors at the first stage are more likely to cause errors in the next stages and lead to an incorrect answer. Furthermore, error at the comprehension stage is the most crucial error in mathematical problem-solving.

Brain imaging provides insights about the interaction between instruction and diagram use for mathematical word problem solving

Diagram use is generally considered an effective strategy in solving mathematical word problems, and many teachers demonstrate the use of this strategy when they are teaching. Despite such demonstrations, however, the majority of students evidence poor, ineffective use of diagrams in problem solving. This may be due to a lack of task-appropriate instruction, but to date, there is inadequate evidence to support this idea. Therefore, the present study aimed to better understand the development of diagram use competence following the provision of task-appropriate instruction, focusing on both behavioral and neurophysiological evidence (i.e., brain activity, using functional near-infrared spectroscopy or fNIRS). Sixteen participants (mean age 15.7 years) were asked to solve mathematical word problems for which the use of tables (which is one kind of diagram) was deemed effective. Data collection progressed in three phases: (1) Pre-test without the demand for diagram use, (2) Pre-test with demand to use a table, and (3) Post-test (after participants received instruction on table use for problem solving). Although table use increased in Phase 2, it was only in Phase 3 that such use led to increases in correct answers. In Phase 3, fNIRS measurements also indicated an increase in blood flow to the frontal area (DLPFC and VLPFC) of the brain usually associated with working memory activity. These results demonstrate important neurophysiological changes resulting from task-appropriate instruction that promotes effective strategy use and improves learning performance.

Problem-appropriate diagram instruction for improving mathematical word problem solving.

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, the effects of problem-appropriate diagram use instruction were investigated with an adaptation of the multiple baseline design method. The instruction for using line diagrams, tables, and graphs was provided to 67 junior high school students in a staggered manner and the effects on problem solving of three different types of problems was examined. The results showed that use of problem-appropriate diagrams increased and persisted over time. More importantly, the instruction led to increases in problem solving performance and to decreases in perceived cognitive load. These findings support the argument that effective diagram use depends on the acquisition not only of declarative knowledge, but also sufficient procedural and conditional knowledge.

A Meta-Analysis of Mathematics Word-Problem Solving Interventions for Elementary Students Who Evidence Mathematics Difficulties

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size ( g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propose recommendations for future research and classroom practice.

Sketchnote and Working Memory to Improve Mathematical Word Problem Solving among Children with Dyscalculia

Sketchnote and Working Memory to Improve Mathematical Word Problem Solving among Children with Dyscalculia

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 & 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.

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

<p style="text-align:justify">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.</p>

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.

The Effect of an Augmented Input Intervention on Subtraction Word-Problem Solving for Children with Intellectual Disabilities: A Preliminary Study

ABSTRACT Children with intellectual disabilities experience well-documented challenges in the development of problem-solving, particularly related to mathematical word-problem solving. Such challenges are related to both linguistic and conceptual skills. While interventions to assist children in developing conceptual skills are well reported, linguistic interventions within the mathematical field are limited. This study aimed to determine the effect of an augmented-input intervention, on subtraction word-problem solving for children with intellectual disabilities. A multiple baseline across behaviours design was used and replicated across the seven participants. Intervention was provided in three tiers (one week each) for change, combine, and compare subtraction word-problems. Intervention was withdrawn for a four week period and followed by a maintenance phase. Results suggested that for older participants with higher receptive language and numerical operation scores, the augmented-input intervention provided significant gains across all three types of word-problems. Overall, four of the seven participants showed improvement in subtraction word-problem solving. Augmented input may provide language supports for subtraction word-problem solving for some children with mild intellectual disability.

Working memory growth predicts mathematical problem-solving growth among emergent bilingual children

An area of mathematics found to be difficult for emergent bilingual children whose first language (L1) is Spanish in the United States is solving mathematical word problems. The purpose of this study was to determine the relationship between growth in the executive component of working memory (WM) and growth in mathematical word-problem solving in children whose L1 is Spanish. Elementary school children (Grades 1, 2, and 3) were administered a battery of mathematical, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, and WM) in both Spanish (L1) and English (second language [L2]) in Year 1 and again 1 year later. Multilevel growth modeling showed that growth in WM significantly predicted growth in L1 and L2 mathematical word-problem solving. Furthermore, the contributions of WM to mathematical word-problem-solving growth in both L1 and L2 were independent of language skills in vocabulary, reading, estimation, naming speed, inhibition, STM, and calculation. Overall, the results suggest that the mental activities that underlie WM play a significant role in predictions of L1 and L2 mathematical word-problem-solving accuracy.

Pre-service Mathematics Teachers Created Animated Stories to Improve their Technological Pedagogical Content Knowledge

In an attempt to improve pre-service mathematics teachers’ Technological Pedagogical Content Knowledge (TPACK), pre-service teachers (N=52) were trained in creating technology-based mathematics teaching materials. Pre-service mathematics teachers learned visual programming to create computer-based animated stories in this study. They worked in pairs and created animated stories, which are intended to improve fourth grade students’ mathematics word problem solving. Six of these pre-service teachers were willingly participated in this study and observed students completing two animated stories in actual classroom environments. The purpose was to investigate the value of their work and provide advice with regard to improve their TPACK. The pre-service teachers (n=6) were interviewed within a qualitative research framework. This study reveals the pre-service teachers´ opinions and beliefs regarding various aspects of the projects, such as students´ interest, students´ performance, as well as the teachers´ professional, pedagogical and individual improvement. The pre-service teachers are convinced that teaching with the use of technology support students’ learning and that technology use in the classrooms is valuable. As a result, it can be confirmed that the process helped them improve their TPACK.

Cognition and mathematics education: Processing speed and word problem solving performance in children

Learning mathematics is a complex progressive process and a wide range of cognitive skills influences one’s success. The present work aims to study the relationship between processing speed and mathematical word problem solving performance in primary school children. The researchers evaluated the performance of 40 children with a mean age of 12.5 years in mathematics word problem solving and their processing speed. This work is theoretically underpinned in Atkinson and Shiffrin’s (1968) information processing model and used a quantitative approach. Correlation analysis showed that total processing speed is associated with learners’ performance in mathematics word problems. However, out of the two aspects of processing speed like perceptual speed and number facility, it is observed that number facility is significantly correlated with performance in solving word problems. The result of independent t-test indicated that gender does not have any effect on participants’ performance in processing speed and mathematics word problem solving. The researcher suggests that educators should design suitable problem-solving strategies with the integration of cognitive tasks to enhance learners’ mathematical knowledge.

Creation of possible fictional worlds as a process of validation in mathematical word problem-solving and mathematical modeling activities

Creation of possible fictional worlds as a process of validation in mathematical word problem-solving and mathematical modeling activities

Linguistic Influences on Junior High School Students’ Mathematics Word Problem Solving

Mastery of language of instruction is important for the successful teaching and learning of Mathematics since mathematical concepts are communicated through the use of language. The study sought to find Ghanaian Junior High School (JHS) 2 students’ performance in Mathematics word problems. It also investigated the linguistic difficulties students face when solving Mathematics word problems and how their English language proficiency affect their problem-solving procedures. A sequential mixed methods design was employed in the study. The target population was made up of all JHS 2 public school students in the Cape Coast Metropolis in the Central Region of Ghana. One hundred and eighty-seven JHS 2 students were selected from six public schools in the Cape Coast Metropolis through stratified random sampling procedures. Achievement test and interview guide were developed and used for the study. The data collected through the test were analysed using descriptive statistics, while that of the interview were analysed using percentages and presented as narrative description with some illustrative examples from what students said in the process of explaining their procedures. The results from the study showed that students had very weak ability in Mathematics word problem solving. Their performance declined as the difficulty level of the questions increased from primary to JHS. The authors recommended amongst others, the need for Mathematics teachers to pay extra attention to the teaching of word problem solving in Mathematics and in- service and pre-service providers to pay attention to Mathematics word problem in professional development programmes.

Implementing Schema- Based Instruction on the Mathematical Word Problem Solving in Specific Learning Disability with Impairment in Mathematics: A Systematic Review Study

چکیده هدف پژوهش حاضر معرفی ماهیت، ویژگی‌ها، و شواهد پژوهشی پیرامون موثر بودن آموزش حل مسئله کلامی مبتنی بر طرحواره در ارتباط با نارسایی‌های یادگیری ویژه است. در پژوهش حاضر از طریق پژوهش مروری نظامند و جستجوی کلیدواژه‌های تخصصی مرتبط با اختلال‌ یادگیری ویژه با آسیب ریاضی و آموزش حل مسئله کلامی مبتنی بر طرحواره در پایگاه‌های اطلاعاتی تخصصی ایران و جهان بین سال‌های 2017-1996 یافته‌ها و اطلاعات مورد نظر جهت دستیابی به هدف پژوهش مورد واکاوی قرار گرفت. از 36 پژوهش انجام شده، غالب پژوهش‌ها (25 پژوهش) بر روی آزمودنی‌های دارای اختلال ریاضی از سن 5 تا 12 و در پایه 1-6 انجام شده است. بیشتر پژوهش‌های انجام شده از نوع مطالعات آزمایشی می‌باشند( با فراوانی 25 پژوهش). کلاس آموزش فراگیر (با فراوانی 15 پژوهش)، مراکز استثنایی یا توانبخشی اختلال‌های یادگیری (با فراوانی 9 پژوهش)، کلاس مجزا (با فراوانی 8 پژوهش)، و مراکز فعالیت (با فراوانی 4 پژوهش) به ترتیب پرکاربردترین موقعیت‌های کارآموزی هستند که مورد استفاده قرار گرفته‌اند. در شیوه اجرای آموزش مبتنی بر طرحواره، ارائهآموزش در کل کلاس، و انفرادی از بیشترین فراوانی برخوردار است (با فراوانی 26 پژوهش). اثربخشی آموزش حل مسئله کلامی مبتنی بر طرحواره بر متغیرهای وابستهسیالی(دقت و صحت حل مساله ریاضی)،اکتساب و تعمیم به ترتیب در 36، 16 و 11 پژوهش مورد سنجش قرار گرفته است. نتایج این پژوهش‌ها حکایت از اثربخشی مثبت آموزش مبتنی بر طرحواره بر متغیرهای وابسته دارند.