Teaching word problems : a practical approach

This article reports a study of the difficulties that primary school children experience whilst tackling school mathematical word-problems. A case study of four Year 5 children was conducted; this involved interviews which probed the children's views of their own difficulties and discussions with the children as they tackled word problems. The data were qualitatively analysed using a thematic analysis approach based on categories of difficulty identified from existing literature. Examples of transcripts and responses which show the children experiencing difficulties are included, as well as the children's opinions on their difficulties. My interpretation of these findings, including proposed subcategories of difficulty, is also given. The report concludes with suggestions of methods – subject to further research – that teachers may use to help children overcome their difficulties with school mathematical word problems.

Australian Primary Mathematics Classroom, 2005

math.nie.edu.sg

This is a workshop on word problems in primary mathematics. The workshop is based on a paper derived from an investigation into children' responses to standard and non-standard mathematics word problems before and after an intervention programme. Standard word problems can be solved by identifying the correct operation and performing the necessary computation. The story context does not affect the solution. In solving non-standard word problems the story context is important in obtaining a correct solution. Primary Three children in five Singapore schools participated in a year-long intervention where their teachers used several lessons that included non-standard problems. The children were asked to solve standard and non-standard word problems at the start and at the end of the school year. Among these word problems, there were those that were similar to, those that were similar in the mathematical structure to but different in the superficial features from, and those that were different in mathematical structure from the problems in the intervention programme. The responses from four intact classes were selected for analysis. It was found that the children were able to make sense of their computation results. However, in situations that went beyond computation, many children were not able to make sense. Intervention and use of concrete materials were found to encourage sense-making.

2016

This article repots a study of the difficulties that primary school children experience whilst tackling school mathematical word problems. A case study of fifteen second grade children who were part of a broader doctoral study was conducted; this involved interviews which probed the children’s views of their own difficulties and discussions with children as they tackled word problems. The data were qualitatively analyzed using a thematic analysis approach based on categories of difficulty identified from existing literature. Exemplars of transcripts and responses which show the children experiencing difficulties are included, as well as the children’s opinions on their difficulties. Our interpretation of these findings, including proposed subcategories of difficulty, is also given. The report concluded with suggestions of methods-subject to further researchthat teachers may use to help children overcome their difficulties with school mathematical word problems.

In this feasibility study the authors describe and evaluate a word problem solving instruction, based on the principles underlying instructional programs like Solve it! and schema-based instruction. This instruction is executed during a five-week intervention period in a group of four less successful second grade word problem solvers. The effectiveness of the word problem solving instruction is reported by means of students' performances on combine, change and compare problems before and after the intervention period, as well as by examining whether they executed the solution steps of the instruction correctly. This feasibility study provides important insights with regard to varying ways in which a word problem solving instruction can influence the solution strategies and performances of students who perform poorly on word problems. WORD PROBLEM SOLVING PROCESS Look at the following example of a word problem [Word problem example] " Mary has 9 marbles. She has 4 marbles more than John. How many marbles does John have? " Tim, a seven-year-old boy who is in the second grade of elementary school, has difficulties with solving word problems like the one that is given in the example above. While solving these word problems, Tim often uses an impulsive, superficial solution strategy. Significantly, he only focuses on selecting the presented numbers (9 and 4) and identifying the relational keywords (more than), which subsequently form the basis for his mathematical calculations. Tim's strategy often leads to an incorrect answer to the word problem. In this situation, Tim performed an addition operation where a subtraction operation was required, that is 9 + 4 = 13 instead of 9 – 4 = 5. The incorrect answer is not the result of a lack of calculation ability, but a result of a problem with deeply and correctly understanding the word problem text. Mathematical word problem solving plays a prominent role in the curriculum of contemporary approaches to teaching mathematics [1-4]. The solution of a word problem generally depends on two major phases: (1) problem comprehension, and (2) problem solution. The problem comprehension phase generally involves the identification and visual representation of the problem structure of the word problem. The identification and representation of the problem structure facilitates the correct understanding of the word problem text and helps distil the mathematical operation(s) that should be performed. In the problem solution phase, on the other hand, the mathematical operations to be used are identified and the planned computations are executed to solve the problem [5, 6]. Hence, errors in word problem solutions frequently occur in the problem comprehension phase rather than in the problem solution phase. These errors are often ascribed to students' insufficient reading comprehension skills [7] .

International Electronic Journal of Mathematics Education, 2013

This study investigated teachers' perspectives of difficulties students have solving mathematical word problems and causes of those difficulties. Classroom practices and strategies teachers used in their attempts to foster student problem solving success were also studied. Participants were 70 second-fifth grade teachers from 42 different schools in a south central region of the United States. Data included analyses of interview transcriptions of teachers' responses. Findings from teachers' responses showed students' abilities to read and understand the problem was the most frequently cited difficulty; standardized testing and text difficulties were the most cited causes of those difficulties. Examination of teachers' responses to practices and strategies used in the classroom revealed the most cited practice was working the problem independently and the most cited strategy taught to students was to identify key words. This study revealed the significant role reading plays in teachers' perspectives of students' difficulties solving mathematical word problems and provided insight into practices and strategies teachers reported using to teach word problems. With attention to teacher-reported causes of difficulties and importance of this ability for students, this study also showed the impact state mandated testing has on instruction of mathematical word problems.

Diversity Dimensions in Mathematics and Language Learning, 2021

2011

This paper describes the systematic approach used by a sample of 30 Primary 2 pupils from one primary school to solve two non-routine problems. The study focused on (a) the relationship between pupils' academic mathematics achievement and problem solving abilities, (b) the differences in problem solving abilities among the pupils for each problem item, and (c) the different heuristics they used to solve these two non-routine problems. This study found a very low correlation between achievement in academic mathematics and success in solving problems. From this we can deduce that even if a pupil performs well in academic mathematics, the pupil may not be proficient at solving non-routine problems.

International Journal of Scientific and Research Publications (IJSRP)

The study was conducted to determine the difficulties encountered in mathematical word problem solving in Butuan Central Elementary School. Descriptive type of research through survey questionnaire was used in the study. The researchers used quota sampling with a random selection in order to limit researcher's choice of sample. Each selection of Grade 6 class had the number of respondents that were randomly selected with the help of corresponding teachers. The researchers had 100 respondents as a sample size. The difficulties encountered by the pupils were categorized into children's attitude towards problem solving in Mathematics, teaching skills among teachers and instructional materials used by the teacher. Based on the data gathered, the overall mean for the children's attitude towards word problem solving is 3.44 showed that the children should develop a positive attitude in dealing word problem solving. The overall mean of the level of teaching skills among teachers was 2.41and it was found out that the teacher executed teaching skills in teaching word problem solving. For the instructional materials, it obtained the mean of 3.03 which showed that the most instructional materials used by the teachers were the textbooks, worksheets, chalk, and board. In answering word problem solving, the pupils got the correct answer when it was already given in the problem but most of them got the wrong answer when they had to translate word problem into mathematical symbol. Furthermore, it implied that the problem was not with the teaching skills and the instructional materials used, but with the attitude of the pupils towards mathematical word problem solving.

International Journal of Trends in Mathematics Education Research, 2023

Addition and subtraction have long been topics of study from early childhood development (ECD) through grade 2 of primary school (Carpenter et al., 2020). Research examined how learners in primary school work with single-digit numbers and sums of 20 or less. Research on cognitively guided instruction (CGI) (Carpenter et al., 2020), suggests that learners are able to solve more complex problems than teachers might expect. Learners in elementary grades were able to solve many different types of problems, including multiplication and division problems at early ages. Most primary school programmes make assumptions about addition and subtraction, especially word problems. For example, teachers assume that word problems are best introduced through physical or pictorial representations of putting together or breaking up sets of objects. Another common assumption is that word problems are difficult for learners of all ages, and that learners must master addition and subtraction operations before they can solve even simple word problems. These assumptions could impact on learners' approaches to word problems. In their study, Carpenter et al. (2020) indicate that both assumptions may be false. There is considerable research literature that demonstrates that school learners, especially in the primary school, solve addition and subtraction computation exercises by using several basic counting strategies (Hopkins et al., 2022). This finding identifies the strong relation between types of word problems and solution strategies. However, because a variety of semantically different word problems can be solved by addition or subtraction, the choice of solution strategy becomes more complex. Understanding solution strategies that learners use in solving word problems is at the heart of our understanding of how learners solve addition and subtraction word problems. Statement of the Problems A relatively recent review of South African studies on mathematics education has revealed a paucity of research issues at