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Problem-appropriate diagram instruction for improving mathematical word problem solving.

Hiroaki Ayabe1,2, Emmanuel Manalo1, Erica de Vries3

  • 1Graduate School of Education, Kyoto University, Kyoto, Japan.

Frontiers in Psychology
|October 20, 2022
PubMed
Summary
This summary is machine-generated.

Instruction on using diagrams significantly improved mathematical word problem-solving skills in students. This approach enhanced performance and reduced cognitive load, demonstrating the importance of procedural and conditional knowledge in diagram use.

Keywords:
Japanese studentscognitive loadinstructional methodsmathematical word problem solvingmultiple baseline designrepresentational effectself-constructed diagramsvisual representation

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Area of Science:

  • Educational Psychology
  • Cognitive Science
  • Mathematics Education

Background:

  • Diagrams are valuable tools for solving mathematical word problems.
  • Students often struggle with unprompted diagram construction and effective usage.
  • Lack of procedural and conditional knowledge hinders effective diagram application.

Purpose of the Study:

  • To investigate the impact of problem-appropriate diagram use instruction on students' mathematical word problem-solving abilities.
  • To examine the effects of instruction on diagram usage, problem-solving performance, and cognitive load.
  • To determine if explicit instruction enhances students' ability to utilize diagrams effectively.

Main Methods:

  • An adapted multiple baseline design was employed.
  • Instruction on using line diagrams, tables, and graphs was delivered to 67 junior high school students.
  • Instruction was implemented in a staggered manner across participants.
  • The study examined the effects on solving three distinct types of mathematical word problems.

Main Results:

  • Student use of problem-appropriate diagrams increased and was sustained over time.
  • The diagram use instruction led to significant improvements in mathematical problem-solving performance.
  • Perceived cognitive load decreased following the instruction.
  • Acquisition of procedural and conditional knowledge was linked to effective diagram use.

Conclusions:

  • Explicit instruction in problem-appropriate diagram use is effective in enhancing mathematical word problem-solving.
  • Effective diagram use requires more than declarative knowledge; procedural and conditional knowledge are crucial.
  • Targeted instruction can improve students' strategic use of diagrams, leading to better academic outcomes and reduced mental effort.