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Understanding the Factors Affecting Students’ Ability to Solve Math Word Problems
Abstract
Word problems are a question type commonly seen in math tests and exams. Since word problems are an integral part in teaching and learning of mathematics in schools, understanding what factors that would affect students’ ability to solve math word problems may help students understand where their weaknesses lie and help teachers adopt effective approaches to assess students’ ability of solving math word problems. Through the data collected from a timed online math quiz and an online questionnaire survey, the present study suggests that math word problems that are not presented in participants’ first language will be likely to cause disturbances to their process of solving the problems, but even when the questions are not presented in participants’ first language, the difference in the length nor the complexity of sentence structure of the questions would greatly affect their understanding of the context. Participants in general have the perception that their English reading comprehension ability is a critical factor that affects their performance of solving math word problems, but surprisingly, even though the participants could extract accurate information from the question context, they might not be able to apply the appropriate math model to solve the problems.
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In this research we aim to reproduce and extend the positive results about the effect of humor in solving mathematical word problems. We examined whether solving humorous word problems has some effect on either word problems demanding realistic consideration or word problems of the well-known routine type. Fifth- and sixth-grade students (N=1,153) solved different types of tasks including humorous, routine and “problematic” word problems, answered further questions concerning their attitude towards mathematics. Our results suggest that while sixth-graders outperformed their fifth-grade peers, the positive effect of humorous word problems proved to be even more relevant than the school grade. However, there has been some possible negative effect of humor when solving routine word problems. Furthermore, students expressed a positive attitude toward humorous word problems by selecting these as their favorite tasks compared to other types of word problems. The results obtained provide further evidence on the desirability and feasibility of introducing (more) humor in mathematics education.
ABSTRACT
Purpose: Math word problem solving, a form of reading comprehension, is complicated by mathematical lexical ambiguity (e.g., the word difference can mean dissimilarity in everyday discourse but the answer in a subtraction problem in math). This study examined the role of mathematical lexical ambiguity in math word problem solving.
Method: Lexically ambiguous math word knowledge, reading comprehension, vocabulary breadth, executive function (EF) skills, and math word problem solving were assessed in 521 3rd- to 5th-grade emergent bilingual (EB) and English monolingual (EM) students.
Results: Students knew fewer math than common meanings of lexically ambiguous math words, and EBs knew fewer meanings than EMs. Multi- group path analysis indicated reading comprehension and lexically ambiguous math word knowledge contributed directly to math word problem solving and partially mediated the influence of EFs on math word problem solving.
Conclusion: Consistent with the language function hypothesis, language skills supported math word problem solving directly and mediated the influence of EF skills on math word problem performance for both EBs and EMs alike. Our findings move the field forward by revealing a specific mechanism by which EF skills contribute to a particular aspect of content area reading comprehension.
To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.
The purpose of this study is to investigate to what extent the use of L2 in math tests influences bilingual education learners’ process of word problem solving in a mandatory secondary education school with Content and Language Integrated Learning (CLIL). The reading comprehension level of the students was analysed using a standards-based assessment and the questions used in Programme for International Student Assessment (PISA) tests. The word problems were selected according to the students’ level of reading-comprehension and mathematical competence. Leaners also had to answer a questionnaire, which was used to analyse if contextual factors were affecting mathematical performance in L2. To this end, the questionnaire included some questions related to the bilingual history of the students and their perception about solving word problems in English. Data were analysed through one-way or two-way ANOVA tests to find out which factors were relevant. Results show that solving word problems is not only affected by the use of L2, but that it also depends on the mathematical difficulty, irrespective of the students’ level of language proficiency. The findings, hence, imply that interaction between linguistic difficulty and mathematical complexity is at the centre of the issues affecting word problem solving.
Previous local research findings have found that students are generally weak in solving mathematics word problems especially in problems that required skills in choosing the various mathematical techniques they have learned in previous years. Too often, students see the knowledge taught by teachers as mathematical procedures and they failed to apply the importance of such knowledge to their daily lives. This research investigated two main areas, namely students' performance in solving mathematics word problems and the relationship between English competency and the ability to do mathematics. A total of 78 Year 9 students from four secondary schools participated in this study. The findings revealed that the time or period spent in school does not determine students' ability in mathematics but rather a strong foundation in basic mathematics is a factor that contributes to a better performance in the subject. Furthermore, the English competency does not influence students' performance in doing mathematics word problems significantly. It was proven that students does not require good English to do Mathematics word problems questions with less than 40 words (those categorised as 'Not Wordy' and 'Average Wordy' questions).
This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as good or poor readers. The results showed that performance on maths word problems was strongly related to performance in reading comprehension. Fluent technical reading abilities increased the aforementioned skills. However, even after controlling for the level of technical reading involved, performance in maths word problems was still related to reading comprehension, suggesting that both of these skills require overall reasoning abilities. There were no gender differences in maths word problem-solving performance, but the girls were better in technical reading and in reading comprehension. Parental levels of education positively predicted children's maths word problem-solving performance and reading comprehension skills.
Does using a bilingual's 1st or 2nd language have an effect on problem solving in semantically rich domains like school mathematics? The author conducted a study to determine whether Filipino-English bilingual students' understanding and solving of word problems in arithmetic differed when the problems were in the students' 1st and 2nd languages. Two groups participated-students whose 1st language was Filipino and students whose 1st language was English-and easy and difficult arithmetic problems were used. The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a 1st-language advantage; that is, the students were better able to understand and solve problems in their 1st language, whether the 1st language was English or Filipino. Moreover, the advantage was more marked with the easy problems. The theoretical and practical implications of the results are discussed.
In learning mathematics through English, one of the major challenges facing English as a Foreign Language (EFL) learners is understanding the language used to present word problems in mathematics texts. Without comprehending such language, learners are not able to carry out the targeted calculations no matter how familiar they are with the mathematical concepts behind. As many researchers have pointed out, distinctive combinations of certain vocabulary and grammatical structures are often found in the mathematical register. It is therefore important for teachers to discover, analyse and provide guidance on how learners can best tackle those linguistic challenges. This paper attempts to achieve this goal by first identifying and classifying, from word problem examples, the potential linguistic challenges at the word, phrase, clause and discourse levels. It then proceeds to suggest specific linguistic and multimodal strategies with good potential to help EFL learners overcome such challenges, with reference to the relevant literature and examples. It concludes by reiterating the importance of mathematics teachers' active engagement with the language used in word problems and suggesting possible collaboration between them and English language teachers in promoting EFL learners' awareness of the language of mathematics.