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

Marian Hickendorff1

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Summary

Students can solve arithmetic word problems effectively, regardless of complexity or irrelevant details, even in third grade. Reading comprehension and non-verbal reasoning skills are key for more complex problems.

Keywords:
arithmeticcognitive abilitiesmathematicsnon-verbal reasoningreading comprehensionword problemsworking memory

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Mathematics Education

Background:

  • Solving arithmetic word problems involves creating situation and mathematical models.
  • This process demands language comprehension and domain-general cognitive resources.
  • Expertise and strategy use may reduce these cognitive demands.

Purpose of the Study:

  • To investigate if cognitive demands in word problem solving decrease with experience.
  • To examine the impact of problem presentation (symbolic vs. word problems) on performance.
  • To determine the role of irrelevant information and problem complexity.

Main Methods:

  • A paper-and-pencil task administered to 444 students (grades 3-6).
  • Included symbolic arithmetic, standard word problems, and complex word problems (two-step or with irrelevant information).
  • Performance analyzed using multilevel logistic regression.

Main Results:

  • No significant performance differences across problem types within each grade.
  • Students in third grade were not hindered by story context or irrelevant numerical information.
  • Non-verbal reasoning was crucial for one-step word problems over symbolic ones.
  • Reading comprehension was vital for two-step word problems compared to one-step problems.

Conclusions:

  • Early elementary students can handle arithmetic word problems with varying complexity and irrelevant details.
  • Cognitive demands related to language comprehension and reasoning are differentially important for different problem types.
  • Instructional approaches should consider the specific cognitive skills required for different arithmetic problem formats.