Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) calls for opportunities for students to use mathematics as a tool for the communication of ideas. In this project, students in any level of mathematics, working in a cooperative, active setting, can develop their understanding of mathematical concepts through the collaborative writing of word problems. In so doing, they see mathematics from the inside out, as creators rather than mimickers; they are “doers” of mathematics, reflecting on and clarifying their own thinking about mathematical ideas in specific situations. Additionally, projects of the type described here can give teachers valuable information on which they can base further instructional decisions regarding the development of students' ability to communicate effectively using the language of mathematics.

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A Comparison of Two Approaches for Teaching Complex, Authentic Mathematics Problems to Adolescents in Remedial Math Classes

Council review ◽

10.1177/001440299305900608 ◽

1993 ◽

Vol 59 (6) ◽

pp. 556-566 ◽

Cited By ~ 80

Author(s):

Brian A. Bottge ◽

Ted S. Hasselbring

Keyword(s):

Problem Solving ◽

Word Problems ◽

Learning Difficulties ◽

Linear Measurement ◽

The Other ◽

Remedial Math ◽

Problem Solving Skills ◽

Mathematics Problems ◽

Transfer Tasks ◽

Standard Word

Two groups of adolescents with learning difficulties in mathematics were compared on their ability to generate solutions to a contextualized problem after being taught problem-solving skills under two conditions, one involving standard word problems, the other involving a contextualized problem on videodisc. All problems focused on adding and subtracting fractions in relation to money and linear measurement. Both groups of students improved their performance on solving word problems, but students in the contextualized problem group did significantly better on the contextualized problem posttest and were able to use their skills in two transfer tasks that followed instruction.

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THE LINGUISTIC CHALLENGES OF MATHEMATICS WORD PROBLEMS: A RESEARCH AND LITERATURE REVIEW

Malaysian Journal of Learning and Instruction ◽

10.32890/mjli.2017.7798 ◽

2017 ◽

Author(s):

Namirah Fatmanissa ◽

Kusnandi Kusnandi

Keyword(s):

Word Problems ◽

Teaching And Learning ◽

Point Of View ◽

Linguistic Features ◽

Semiotic System ◽

Linguistic Feature ◽

Mathematics Word Problems ◽

Complex Syntax ◽

Mathematics Problems ◽

Linguistic Challenges

Purpose – Word problems are still considered challenging for students when compared to other type of mathematics problems. Many emerging findings regarding this issue highlight that the challenges are predominately caused by linguistic aspects. This article aims to present a review and synthesis of literatures regarding the linguistic challenges of mathematics word problems and recommend solutions to address these challenges. Methodology – Systematic search was done and 35 articles from inside and outside Indonesia were selected. The linguistic challenges and recommended solutions found were analyzed using the main features constructing mathematics language: multiple semiotic system, particular features of vocabulary and grammar, and complex syntax. Findings – The review shows various difficulties shown by students in each feature of mathematics language. The review also recommends the practice of mathematics teaching and learning in which language aspects are discussed and exercised both among students and between the students and the teacher in order to help students face their linguistics challenges. It is also imperative for teachers to understand the structure and linguistic features involved in constructing word problems. Significance – This review breaks down the difficulties of mathematics word problems from the perspective of linguistic features constructing them. The findings of this review offer teachers different point of view to deal with teaching word problems, which is by understanding word problem as an entity of language rather than only as an entity of mathematics. This review also provides some solutions to help teachers address the difficulty for each linguistic feature.

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Influence of Task Characteristics on Eye-Movement Patterns Related to Numerical and Textual Information in Arithmetic Word Problems

10.31234/osf.io/6mpcx ◽

2020 ◽

Author(s):

Gabriella Daroczy ◽

Christina Artemenko ◽

Detmar Meurers ◽

Magdalena Wolska ◽

Hans-Christoph Nuerk

Keyword(s):

Eye Movements ◽

Problem Solving ◽

Eye Movement ◽

Word Problem ◽

Word Problems ◽

Text Comprehension ◽

Movement Patterns ◽

Task Characteristics ◽

Arithmetic Task ◽

Word Problem Solving

Both linguistic and arithmetic task characteristics contribute to the difficulty of a word problem. However, the role of these characteristics and the exact cognitive processes underlying arithmetic word problems are often not clear, but they might be detectable by analysing eye-movement patterns. Not much is known about how eye-movements change under different linguistic and arithmetic task characteristics in regard to the whole problem as well as to specific parts of it (numerical and textual elements). This study examined the effects of linguistic and arithmetic task characteristics on the word problem-solving ability of children aged 10-13 years while their eye-movements were monitored. We manipulated the task characteristics independently of each other, using the mathematical factor operation (addition/subtraction) and the linguistic factors consistency (consistent/inconsistent) and nominalization (verbalized/nominalized). The results showed that eye-movements generally increase with increasing linguistic (i.e., nominalization) or arithmetic (i.e., operation) difficulty. However, specific parts of the text were differentially affected based on task characteristics: In general, increasing arithmetic difficulty shifts eye-movements towards numerical elements and increasing linguistic difficulty shifts eye-movements towards textual elements. However, the increase of difficulty in the arithmetic domain can also affect processing in the linguistic domain. For instance, as textual parts of the word problem were more frequently attended to when arithmetic difficulty increased but not vice versa. This indicates that in the process of word problem-solving, text comprehension and calculation are not sequential independent processes, but partially rely on the same processing components, such as working memory resources.

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Are students more interested in solving mathematics problems related to reality?

New Trends and Issues Proceedings on Humanities and Social Sciences ◽

10.18844/prosoc.v4i9.3037 ◽

2018 ◽

Vol 4 (9) ◽

pp. 10-16

Author(s):

Anggi Anggaraa

Keyword(s):

Mathematics Teacher ◽

Word Problems ◽

Mathematical Problem ◽

Point Of View ◽

Specific Interest ◽

Mathematics Problems ◽

Before And After ◽

Girl Students ◽

Modelling Problems

Eleven lower-achieving girl students (13/14 years old) were asked about their task-specific interest in solving mathematics problems that either related or did not relate to reality, both before and after solving problems. Six of the eleven students were interviewed about the reasons behind their interest in particular problems. Furthermore, an interview was also carried out with a mathematics teacher, to know the types of problems that students usually worked on and students’ interest in those problems from a teacher’s point of view. The analysis revealed that students possessed different interests concerning problems, which either related or not with reality. However, generally, they preferred to solve problems that had no connection to reality, because they were easily able to work on such problems without much confusion. Keywords: Students’ interest, modelling problems, dressed-up word problems, intra-mathematical problem.

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Connecting Research to Teaching: Linking Task Characteristics to the Development of Symbol Sense

Mathematics Teacher ◽

10.5951/mt.94.6.0494 ◽

2001 ◽

Vol 94 (6) ◽

pp. 494-499

Author(s):

Margaret Tatem Kinzel

Keyword(s):

Word Problems ◽

Task Characteristics ◽

Similar Statement ◽

Algebraic Notation ◽

Symbol Sense ◽

Calculus Student

“Let x equal the number of miles.” How many explanations of solutions to word problems begin with a similar statement? As teachers, we frequently encourage students to state what their variables represent when they begin to solve a problem. However, we frequently see students who get lost in the notation and seem to have little or no means for finding their way out—or worse, students may not realize that they are lost. Lisa, a calculus student working on the Alpha and Beta travel task shown in figure 1, confidently began work on the task, used algebraic notation to represent quantities within the task, and arrived at a solution. In addition, Lisa was very comfortable with her answer. Lisa's work, as discussed in the next paragraph, was not correct and actually reveals a problem in her interpretation of notational expressions. We use this example to lead into a discussion of symbol sense, our goals for students, and how tasks can be used to help meet those goals. Readers may wish to try the tasks shown in figures 1, 3, 5, 7, and 9 before reading further.

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The Demands of Simple and Complex Arithmetic Word Problems on Language and Cognitive Resources

Frontiers in Psychology ◽

10.3389/fpsyg.2021.727761 ◽

2021 ◽

Vol 12 ◽

Author(s):

Marian Hickendorff

Keyword(s):

Word Problems ◽

Situation Model ◽

Sixth Grade ◽

Cognitive Resources ◽

Numerical Information ◽

Complex Arithmetic ◽

Mathematics Problems ◽

One Step ◽

Grade Performance ◽

Standard Word

Solving arithmetic word problems requires constructing a situation model based on the problem text and translating that into a mathematical model. As such, word problem solving makes demands on students’ language comprehension and their domain-general cognitive resources. These demands may decrease when students get more experienced and use strategies that do not require fully understanding the situation presented in the problem. The current study aims to address this hypothesis. Students (N=444) from third to sixth grade solved a paper-and-pencil task with 48 mathematics problems, comprising symbolic arithmetic problems and standard word problems, as well as more complex word problems that involve two arithmetic steps or include irrelevant numerical information. Their performance was analyzed with multilevel logistic regression analyses. Results showed that within each grade, performance on the different problem types did not differ, suggesting that already in third-grade students seem helped nor hindered by presenting arithmetic problems in a story, even if that story contains irrelevant numerical information. Non-verbal reasoning was more important in standard word problems than in arithmetic problems in symbolic format in one-step arithmetic, and reading comprehension was more important in solving two-step arithmetic word problems than in one-step arithmetic word problems.

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