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An alternative time for telling: when conceptual instruction prior to problem solving improves mathematical

Emily R Fyfe1, Marci S DeCaro, Bethany Rittle-Johnson

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Area of Science:

  • Cognitive Science
  • Educational Psychology
  • Mathematics Education

Background:

  • Learner knowledge construction is influenced by the sequencing of educational materials.
  • The timing of explicit instruction relative to problem-solving is a key area of research in learning theory.
  • Optimal sequencing for conceptual instruction in mathematics remains unclear.

Purpose of the Study:

  • To investigate the impact of conceptual instruction timing (before vs. after problem-solving) on mathematics learning.
  • To determine the optimal point for delivering conceptual instruction in relation to problem-solving activities.
  • To examine underlying learning processes to inform broader learning theories.

Main Methods:

  • A randomized experiment was conducted with 122 second- and third-grade children.
  • Participants received instruction on the concept of mathematical equivalence.
  • Instruction was delivered either before or after solving and explaining challenging equivalence problems with feedback.

Main Results:

  • Conceptual instruction preceding problem-solving led to superior procedural and conceptual knowledge of equation structures.
  • Early conceptual instruction improved problem-solving by enhancing the quality of explanations and attempted procedures.
  • The sequence of instruction significantly impacted learning outcomes.

Conclusions:

  • Sequencing conceptual instruction before problem-solving is more effective than the reverse order.
  • These findings contribute to a framework for understanding optimal instructional sequencing, including when to delay instruction.
  • The study highlights the benefits of "productive failure" when appropriately scaffolded with conceptual understanding.