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

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.

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

1993 ◽  
Vol 59 (6) ◽  
pp. 556-566 ◽  
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.

Sharing Teaching Ideas: Collaborative Writing of Mathematics Problems

1990 ◽  
Vol 83 (7) ◽  
pp. 542-544
Author(s):  
Kitty Carton
Keyword(s):  
Word Problems ◽  
Collaborative Writing ◽  
Instructional Decisions ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Problems ◽  
Teaching Ideas ◽  
Inside Out ◽  
Development Of Students

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.

Role of Schemas in One-Step Word Problems

1999 ◽  
Vol 5 (3) ◽  
pp. 269-289 ◽  
Author(s):  
Constantinos Christou ◽  
George Philippou
Keyword(s):  
Word Problems ◽  
One Step

Semantic structures of one-step word problems involving multiplication or division

1995 ◽  
Vol 28 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Siegbert Smidt ◽  
Werner Weiser
Keyword(s):  
Word Problems ◽  
One Step

scholarly journals Profile of Students’ Problem-Solving Skills Viewed from Polya's Four-Steps Approach and Elementary School Students

2021 ◽  
Vol 10 (4) ◽  
pp. 1625-1638
Author(s):  
Riyadi*, Triana ◽  
Triana Jamilatus ◽  
Puput Nikmaturrohmah
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Fourth Grade ◽  
School Students ◽  
Problem Solving Skills ◽  
Fifth Grade Students ◽  
Third Grade Students ◽  
Fourth Grade Students ◽  
One Step ◽  
Better Than

<p style="text-align: justify;">Problem-solving is considered one of the thinking skills that must be possessed in 21<sup>st</sup>-century education because problem-solving skills are required to solve all problems that arise. The problem-solving stages that can be used are Polya's four steps, namely, understanding the problem, devising a plan, carrying out the plan, and looking back. Problem-solving skills are essential for solving word problems. Word problems based on arithmetic operations are divided into three types: one-step, two-step, and multistep. This qualitative research aimed to see problem-solving skills viewed from the type of word questions and elementary school students’ third, fourth, and fifth grades. A purposive sampling technique with 22 third-grade students, 28 fourth-grade students, and 21 fifth-grade students was used. The data were collected using documentation, testing, and interview methods. The findings of the study showed that fourth-grade students’ problem-solving skills are better than those of third-grade students, and the problem-solving skills of fifth-grade students are better than those of fourth-grade students. The percentage of Polya's steps always decreases because not all students master problem-solving. Based on the types of questions, the percentage of the one-step word problem is better than that of the two-step while the percentage of the two-step word problems is higher than that of the multistep.</p>

scholarly journals Aerobic Fitness Relates to Superior Exact and Approximate Arithmetic Processing in College-Aged Adults

2020 ◽  
Author(s):  
Amanda Lee McGowan ◽  
Madison C. Chandler ◽  
Matthew B. Pontifex
Keyword(s):  
Aerobic Fitness ◽  
Cardiovascular Health ◽  
Quantitative Information ◽  
Cognitive Resources ◽  
Behavioral Measures ◽  
Processing Efficiency ◽  
Arithmetic Task ◽  
Fitness Level ◽  
Exact Arithmetic ◽  
Complex Arithmetic

Compelling evidence supports the association between the attribute of aerobic fitness and achievement scores on standardized tests of mathematics, but the underlying reasons for this association remain unclear. The present investigation sought to clarify the nature of the relationship between aerobic fitness and arithmetic processing by examining the extent to which these fitness-related differences in mathematics are attributed to individual differences in more efficient processing (efficiency hypothesis) or enhanced allocation of cognitive resources (resources hypothesis) in a sample of 118 college-aged adults. Combining behavioral measures to examine speed and accuracy of processing with pupillary measures that indicate resource allocation, participants completed a complex arithmetic task prior to performing a maximal graded exercise test to assess their aerobic fitness level. The arithmetic task comprised problems with varying levels of difficulty, requiring participants to determine whether a sum of two numbers was greater than or less than 100, which could be solved using either approximate or exact calculation strategies. Higher aerobic fitness was associated with 1) shorter reaction time across all problems, 2) superior accuracy for difficult problems employing exact arithmetic, and 3) greater task-evoked pupillary reactivity for the difficult problems requiring approximate and exact arithmetic strategies. These results indicate that individuals higher in aerobic fitness have more cognitive resources available to solve difficult problems faster and more accurately. These data provide initial evidence to suggest that fitness-related differences in mathematics achievement may result from modulation of cognitive resources underlying superior execution of procedural strategies during arithmetic performance. Accordingly, higher cardiovascular health may be implicated in superior health literacy (e.g., interpreting blood sugar readings and other clinical data), thus affecting the motivation to take action and engage in health behaviors based on quantitative information.

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