The role of understanding in solving word problems

ZDM

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics concerning linguistic and numerical factors and their difficulty level were investigated. In contrast to our expectations, the results did not show a clear connection between WP difficulty level and their other characteristics regarding linguistic and numerical factors. In the second phase, text comprehension and arithmetic skills were used to classify participants into four groups: skilful in text comprehension but poor in arithmetic; poor in text comprehension but skilful in arithmetic; very poor in both skills; very skilful in both skills. The results indicated that WP-solving performance on both easy and difficult items was strongly rela...

Frontiers in psychology, 2016

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded tha...

Mathematics Education Trends and Research, 2016

This paper focuses on two approaches for facilitating the process of word problems solving. The first approach distinguishes different kinds of occurred errors and the second one recognizes various required and underlying knowledge. The first approach applies Kinfong and Holtan's framework of occurred errors and the second approach applies Mayer's theory (1992) of underlying knowledge for solving word problems. The main aim of this paper is to examine the relationship between different kinds of occurred errors and various required knowledge in solving Arithmetic word problems. The research methodology is a semi experimental method. The subjects include 89 eight grade students (male and female). The research tools are a descriptive math test regarding six word problems and a directed interview. The results indicate that in solving the arithmetic word problems, increasing students' errors result from lack of linguistic, semantic, structural and communicational knowledge. This study explored that the possible connection between the two approaches for facilitating solving word problems is very important. That is because clarity of this relationship may increase math teachers' insight about the nature of different kinds of occurred errors and the different aspects of knowledge necessary for solving 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] .

Azim Premji University, 2016

Word problems become a stumbling block for many children, including those who are adept at operational and procedural skills. Many children develop an approach to tackling word problems based on looking for cue words such as altogether, difference, sum and so on; but this has a very limited value. Too often, such children resort to guesswork while figuring out an operation. These children experience significantly greater math anxiety when they are confronted by word problems. Why is this? Primary reasons Here are some reasons which lie behind such math anxiety: 1. Lack of exposure to problem situations and problem contexts during the introductory and teaching phase. 2. Lacunae in the usage of concrete materials as an aid in the visualisation of the problem. 3. Insufficient training in representation of problems through drawings and other means of reconstruction. 4. Difficulty in following multiple statements and instructions at the same time. 5. Inadequate stress on vocabulary and weak linkages or connections between concepts and associated words. 6. Absence of discussion and conversation around the questions (whether in English or in the mother tongue). 7. Lack of recording of the solution by the children in their own words. Most teachers follow rigid ways of writing statements for word problems. Writing in the initial years must come from the child s own experience and understanding. It need not be structured according to any norms; on the contrary, it needs to be personal. All of these reasons point to poor teaching practices. In conjunction with this is the fact that many textbooks are not particularly child-friendly. By the time the child reaches class 4 or 5, he or she would have basic literacy skills. Yet very few children read the textual material for the following reasons: 1. The language used is not close to the child s experience. 2. The word problems are not based on real life and familiar situations. 3. They are not phrased in a sufficiently interesting way, and do not draw the child into the problem. 4. They are not accompanied by drawings (this is crucial for non-English-speaking learners). 5. They are often limited in variety and repetitive, and thus hold no challenge. Often the problems are not posed in a properly graded sequence.

Australian Primary Mathematics Classroom, 2005

2015

This paper focuses on two approaches for facilitating the process of word problems solving. The first approach distinguishes different kinds of occurred errors and the second one recognizes various required and underlying knowledge. The first approach applies Kinfong and Holtan's framework of occurred errors and the second approach applies Mayer’s theory (1992) of underlying knowledge for solving word problems. The main aim of this paper is to examine the relationship between different kinds of occurred errors and various required knowledge in solving Arithmetic word problems. The research methodology is a semi experimental method. The subjects include 89 eight grade students (male and female). The research tools are a descriptive math test regarding six word problems and a directed interview. The results indicate that in solving the arithmetic word problems, increasing students' errors result from lack of linguistic, semantic, structural and communicational knowledge. This ...

1993

This paper attempts to provide some insights on students' various approaches towards solving words problems in Mathematics. 15 students were randomly selected from SSIII students of Demonstration Secondary School, Azare Bauchi State. Three (3) visits were scheduled to the school for interview, questions administration on words problem and discussions, the findings revealed that the students lack necessary knowledge and skills to solve word problems. It is recommended that teachers should employ various heuristics when teaching words problem to enable the students develop necessary skills needed to solve words problems.

EURASIA Journal of Mathematics, Science and Technology Education, 2016

To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization, i.e., the activity to transform a problem into a symbolic mathematical problem, and to reorganize the mathematical system, was used to identify student difficulties on the topic of linear equations in one variable. The results show that formulating a mathematical model-evidenced by errors in formulating equations, schemas or diagrams-is the main difficulty. This highlights the importance of mathematization as a crucial process in the learning and teaching of algebra.