Comprehension Of Word Problems 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.

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

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

EFFECTS OF STUDENTS’ COMPREHENSION SKILLS ON SOLVING MATHEMATICAL WORD PROBLEMS

Mathematical word problems are concepts taught at the end of every topic to allow students apply the content that was taught. This paper looks at the effect of students’ comprehension skills on solving mathematic word problems in Tindiret Sub County public secondary schools, Kenya. The target population was form three mathematics students and teachers. Stratified random sampling techniques were employed to select nine public secondary schools; one boys’ school, one girls’ school and eight mixed secondary schools. Questionnaires, achievement test items were used to collect data. The data collected was coded and analyzed using the SPSS. The study revealed that students had difficulties in (1) comprehending mathematical word problems. It was concluded that the poor comprehension of word problems led to student difficulties in solving word problems in mathematics. The paper recommends that the teachers should find ways of ways of improving comprehension skills of the students by having activities like debates and public speaking to improve language mastery and comprehension. Article visualizations:

ACALCULIA IN PATIENT WITH BROCA APHASIA AND MILD COGNITIVE IMPAIRMENT - A CASE STUDY

Acalculia is an acquired disorder of calculating which occures isolated or with association with aphasia and mild cognitive impairment. We described a case study of 37-year-old Ms. R. after hemorrhage and ischemia with Broca aphasia and acalculia in the article. Ms. R. was assessed by own diagnostic test for acalculia, by test for aphasia and cognitive functions. The aim of the study was to investigate the link between Ms R.´s acalculia, Broca aphasia nad mild cognitive impairment. Assessment revealed Broca aphasia, verbal apraxia, alexia, agraphia, poor attention, weak working memory and poor later recall of remembered words. Assessment of acalculia showed transcoding impairments, disorders of aritmetic fact retrieval and disorders of calculation procedures. Poor working memory and alexia influenced transcoding of numbers. Alexia is also manifested in comprehension of word problems. Counting backward and counting dots were complicated by poor concentration of attention and weak working memory. Symptoms of aphasia, acalculia and mild cognitive impairment affected each other.

ACALCULIA IN PATIENT WITH BROCA APHASIA AND MILD COGNITIVE IMPAIRMENT - A CASE STUDY

Acalculia is an acquired disorder of calculating which occures isolated or with association with aphasia and mild cognitive impairment. We described a case study of 37-year-old Ms. R. after hemorrhage and ischemia with Broca aphasia and acalculia in the article. Ms. R. was assessed by own diagnostic test for acalculia, by test for aphasia and cognitive functions. The aim of the study was to investigate the link between Ms R.´s acalculia, Broca aphasia nad mild cognitive impairment. Assessment revealed Broca aphasia, verbal apraxia, alexia, agraphia, poor attention, weak working memory and poor later recall of remembered words. Assessment of acalculia showed transcoding impairments, disorders of aritmetic fact retrieval and disorders of calculation procedures. Poor working memory and alexia influenced transcoding of numbers. Alexia is also manifested in comprehension of word problems. Counting backward and counting dots were complicated by poor concentration of attention and weak working memory. Symptoms of aphasia, acalculia and mild cognitive impairment affected each other.

It’s not a math lesson - we’re learning to draw! Teachers’ use of visual representations in instructing word problem solving in sixth grade of elementary school.

Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the problem structure and the relations between solution-relevant elements (so-called visual-schematic representations). Research shows that instructional effectiveness depends largely on teachers’ mathematical knowledge for teaching. Teachers’ knowledge of visual representations is therefore essential to instructing word problem comprehension in this way. As there is little to no literature investigating teachers’ practices in this area, the goal of the present study is to examine teachers’ use of visual representations to support non-routine word problem solving. Eight mainstream elementary school teachers implemented an innovative approach focused on the use of visual-schematic representations. After a short training, teachers were able to produce these representations during instruction. However, some teachers seemed unclear about what these representations comprise and what function they serve within the word problem solving context. Teachers seemed to base their use of representations on personal preferences rather than on an optimal fit with the word problem characteristics. These aspects need to be addressed in teacher training and professional development programs. This study makes an unique contribution to research in the important and problematic area of word problem solving in regular classrooms. The results of this study are relevant for educational researcher, teachers, and teacher educators who deal with difficulties in instructing mathematical word problems.

LIM-G: Learner-initiating instruction model based on cognitive knowledge for geometry word problem comprehension

Computer-assisted instruction systems have been broadly applied to help students solve math word problem. The majority of such systems, which are based on an instructor-initiating instruction strategy, provide pre-designed problems for the learners. When learners are asked to solve a word problem, the system will instruct the learners what to do. However, systems employing an instructor-initiating instruction strategy offer little help to advanced learners or to learners encountering problems that are not in the pre-designed database. Therefore, in this study, a learner-initiating instruction model (LIM-G) is proposed to help learners’ comprehension of geometry word problems. Geometry word problems are math word problems involving geometric concepts. Many researches indicate that learners encounter difficulties while comprehending math word problems. In this model, a learner can seek help with any geometry word problem he is interested in. Based on a learner-initiating instruction strategy, LIM-G first comprehends the problem and then gives the learner the telegraphic and diagrammatic representations of the problem, which are more intuitive to understand. For LIM-G, the comprehension mechanism plays a critical role in solving word problems. For this study, a system is built based on LIM-G. In this system, the cognitive knowledge needed for comprehending geometry word problem is constructed with an ontology-based tool called InfoMap. Using cognitive knowledge and frame-template structures, the system can extract the relevant concepts in geometry word problems for comprehension.

Guide Students to Better Comprehension of Word Problems

(1997). Guide Students to Better Comprehension of Word Problems. The Clearing House: A Journal of Educational Strategies, Issues and Ideas: Vol. 71, No. 1, pp. 26-32.

Cognitive Consequences of Participation in a “Fifth Dimension” after-School Computer Club

The Fifth Dimension is an after-school computer club aimed at improving the literacy of English- and Spanish-speaking elementary school children. Children who attended the club at least ten times during the 1994–95 school year (treatment group) showed larger pretest-to-posttest gains on tests of word problem comprehension than did non-participating children matched for grade, gender, school teacher, and language proficiency (comparison group). The same effect was noted for both Spanish and English versions of the test, and under a variety of matching techniques. The superiority of the treatment group was still present when the children were retested after the summer in the fall of the next year. These results provide support for the hypothesis that experience in using computer software in the Fifth Dimension computer club produces measurable, resilient, and sustained cognitive changes related to children's literacy.

Much Ado About Nothing: The Relation Among Computational Skill, Arithmetic Word Problem Comprehension, and Limited Attentional Resources

In this article, we examine the hypothesis that problem comprehension and computational processes interact during the solving of an arithmetic word problem. Two experiments tested subjects on a series of addition and subtraction word problems, the content of which varied on the basis of problem type and on the magnitude of the numbers involved (problem size). Performance data are presented and analyzed in terms of solution reaction times and error patterns. Results confirmed the main effects of problem size and problem type as factors determining reaction times but failed to show any significant interaction between the two factors. These results suggest that the cognitive processes involved in understanding an arithmetic word problem and in performing the required computations are best explained by a serial processing model. The absence of an interaction between problem comprehension and computational processes questions the notion that automatized retrieval facilitates problem solving and assertions sugg...

A simple learning environment improves mathematical reasoning

Abstract ANIMATE, an interactive computer animation-based tutor, has been developed as part of an on-going test of a theory of word problem comprehension. Tutor feedback is unobtrusive and interpretive: unexpected behavior in the equation-driven animation of a situation highlights equation errors which the student resolves through iterative debugging. The student has responsibility for learning, goal-setting and diagnosis. Experimental controls (n = 96) with Motion problems show that improvement cannot be solely attributed to practice, computer use, or use of the situation-based method. Concurrent think-aloud protocols of students (n = 7) solving Motion, Work and Investment problems over two days (in a pretest-posttest design) uncover specific changes which underlie these improvements. ANIMATE is an effective problem-solving aid, and there is transfer of learning. Problems with impossible situations were acknowledged by median-level subjects (posttest scores between 77% and 85%), but solved blindly by hig...

Generated meanings in the comprehension of word problems in mathematics

A “Generative-Predicational Model” is proposed and applied to the generation of meanings of simple mathematical word-problems. The model suggests that a fundamental property of cognition is a generative process that takes arguments and that produces results, such as events, answers and inferences. This fundamental property, called predication, generates a task-environment i.e., a problem and its corresponding problem-space i.e., its solution. More precisely, a task-environment is a predication consisting of a written mathematical problem and a writer's life experience. A problem-space is a predication consisting of a leamer's problem solving schema and of the meaning that the learmer generates for the text.

Understanding Word Problems

For several years now, I have been asked to share with junior and senior high school mathematics teachers in North Carolina ways to improve students' reading comprehension of word problems. My work with teachers and students has given me the opportunity to field-test several strategies for improving reading skills. One such strategy uses comprehension guides (Earle 1976; Herber 1978).

Sharing Teaching Ideas: Improving Students’ Comprehension of Word Problems

Sharing Teaching Ideas offers practical tips on the teaching of topics related to the secondary school curriculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the beginning and the experienced teacher. Please send an original and four copies of your ideas to the managing editor for review.