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Area of Science:

  • Cognitive psychology
  • Educational psychology
  • Developmental psychology

Background:

  • Subtraction mastery is a key elementary math goal.
  • Subtraction research is limited, often assuming cognitive similarity to addition.
  • The borrow operation in subtraction is known to increase difficulty in adults.

Purpose of the Study:

  • To investigate the relationship between the borrow effect in subtraction and the carry effect in addition.
  • To examine the developmental trajectory of the borrow effect in children.
  • To evaluate the assumption that subtraction is cognitively similar to addition.

Main Methods:

  • A longitudinal study using a choice reaction paradigm.
  • Examined the borrow effect in subtraction and carry effect in addition.
  • Assessed children's performance across different grade levels.

Main Results:

  • In contrast to adults, both carry and borrow effects were categorical in elementary school children.
  • Children showed general improvement in two-digit subtraction from grades 3 to 4.
  • No specific developmental progress was observed in place-value computation related to borrowing.

Conclusions:

  • Subtraction and addition may not be as cognitively similar as assumed in children.
  • Children's improvement in subtraction is procedural rather than based on specific place-value understanding.
  • The categorical nature of borrow/carry effects in children highlights developmental differences in arithmetic processing.