Acquisition of children's addition strategies

A model of impasse-free, knowledge-level learning

Randolph M. Jones, Kurt VanLehn

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

When children learn to add, they count on their fingers, beginning with the simple Sum Strategy and gradually developing the more sophisticated and efficient Min strategy. The shift from Sum to Min provides an ideal domain for the study of naturally occurring discovery processes in cognitive skill acquisition. The Sum-to-Min transition poses a number of challenges for machine-learning systems that would model the phenomenon. First, in addition to the Sum and Min strategies, Siegler and Jenkins (1989) found that children exhibit two transitional strategies, but not a strategy proposed by an earlier model. Second, they found that children do not invent the Min strategy in response to impasses, or gaps in their knowledge. Rather, Min develops spontaneously and gradually replaces earlier strategies. Third, intricate structural differences between the Sum and Min strategies make it difficult, if not impossible, for standard, symbol-level machine-learning algorithms to model the transition. We present a computer model, called Gips, that meets these challenges. Gips combines a relatively simple algorithm for problem solving with a probabilistic learning algorithm that performs symbol-level and knowledge-level learning, both in the presence and absence of impasses. In addition, Gips makes psychologically plausible demands on local processing and memory. Most importantly, the system successfully models the shift from Sum to Min, as well as the two transitional strategies found by Siegler and Jenkins.

Original languageEnglish (US)
Pages (from-to)11-36
Number of pages26
JournalMachine Learning
Volume16
Issue number1-2
DOIs
StatePublished - Jul 1994
Externally publishedYes

Fingerprint

Learning systems
Learning algorithms
Data storage equipment
Processing

Keywords

  • cognitive simulation
  • impasse-free learning
  • induction
  • probabilistic learning
  • problem-solving strategies

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Artificial Intelligence

Cite this

Acquisition of children's addition strategies : A model of impasse-free, knowledge-level learning. / Jones, Randolph M.; VanLehn, Kurt.

In: Machine Learning, Vol. 16, No. 1-2, 07.1994, p. 11-36.

Research output: Contribution to journalArticle

@article{f193e3748662467f9c246acd0e409bf7,
title = "Acquisition of children's addition strategies: A model of impasse-free, knowledge-level learning",
abstract = "When children learn to add, they count on their fingers, beginning with the simple Sum Strategy and gradually developing the more sophisticated and efficient Min strategy. The shift from Sum to Min provides an ideal domain for the study of naturally occurring discovery processes in cognitive skill acquisition. The Sum-to-Min transition poses a number of challenges for machine-learning systems that would model the phenomenon. First, in addition to the Sum and Min strategies, Siegler and Jenkins (1989) found that children exhibit two transitional strategies, but not a strategy proposed by an earlier model. Second, they found that children do not invent the Min strategy in response to impasses, or gaps in their knowledge. Rather, Min develops spontaneously and gradually replaces earlier strategies. Third, intricate structural differences between the Sum and Min strategies make it difficult, if not impossible, for standard, symbol-level machine-learning algorithms to model the transition. We present a computer model, called Gips, that meets these challenges. Gips combines a relatively simple algorithm for problem solving with a probabilistic learning algorithm that performs symbol-level and knowledge-level learning, both in the presence and absence of impasses. In addition, Gips makes psychologically plausible demands on local processing and memory. Most importantly, the system successfully models the shift from Sum to Min, as well as the two transitional strategies found by Siegler and Jenkins.",
keywords = "cognitive simulation, impasse-free learning, induction, probabilistic learning, problem-solving strategies",
author = "Jones, {Randolph M.} and Kurt VanLehn",
year = "1994",
month = "7",
doi = "10.1007/BF00993172",
language = "English (US)",
volume = "16",
pages = "11--36",
journal = "Machine Learning",
issn = "0885-6125",
publisher = "Springer Netherlands",
number = "1-2",

}

TY - JOUR

T1 - Acquisition of children's addition strategies

T2 - A model of impasse-free, knowledge-level learning

AU - Jones, Randolph M.

AU - VanLehn, Kurt

PY - 1994/7

Y1 - 1994/7

N2 - When children learn to add, they count on their fingers, beginning with the simple Sum Strategy and gradually developing the more sophisticated and efficient Min strategy. The shift from Sum to Min provides an ideal domain for the study of naturally occurring discovery processes in cognitive skill acquisition. The Sum-to-Min transition poses a number of challenges for machine-learning systems that would model the phenomenon. First, in addition to the Sum and Min strategies, Siegler and Jenkins (1989) found that children exhibit two transitional strategies, but not a strategy proposed by an earlier model. Second, they found that children do not invent the Min strategy in response to impasses, or gaps in their knowledge. Rather, Min develops spontaneously and gradually replaces earlier strategies. Third, intricate structural differences between the Sum and Min strategies make it difficult, if not impossible, for standard, symbol-level machine-learning algorithms to model the transition. We present a computer model, called Gips, that meets these challenges. Gips combines a relatively simple algorithm for problem solving with a probabilistic learning algorithm that performs symbol-level and knowledge-level learning, both in the presence and absence of impasses. In addition, Gips makes psychologically plausible demands on local processing and memory. Most importantly, the system successfully models the shift from Sum to Min, as well as the two transitional strategies found by Siegler and Jenkins.

AB - When children learn to add, they count on their fingers, beginning with the simple Sum Strategy and gradually developing the more sophisticated and efficient Min strategy. The shift from Sum to Min provides an ideal domain for the study of naturally occurring discovery processes in cognitive skill acquisition. The Sum-to-Min transition poses a number of challenges for machine-learning systems that would model the phenomenon. First, in addition to the Sum and Min strategies, Siegler and Jenkins (1989) found that children exhibit two transitional strategies, but not a strategy proposed by an earlier model. Second, they found that children do not invent the Min strategy in response to impasses, or gaps in their knowledge. Rather, Min develops spontaneously and gradually replaces earlier strategies. Third, intricate structural differences between the Sum and Min strategies make it difficult, if not impossible, for standard, symbol-level machine-learning algorithms to model the transition. We present a computer model, called Gips, that meets these challenges. Gips combines a relatively simple algorithm for problem solving with a probabilistic learning algorithm that performs symbol-level and knowledge-level learning, both in the presence and absence of impasses. In addition, Gips makes psychologically plausible demands on local processing and memory. Most importantly, the system successfully models the shift from Sum to Min, as well as the two transitional strategies found by Siegler and Jenkins.

KW - cognitive simulation

KW - impasse-free learning

KW - induction

KW - probabilistic learning

KW - problem-solving strategies

UR - http://www.scopus.com/inward/record.url?scp=0028464785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028464785&partnerID=8YFLogxK

U2 - 10.1007/BF00993172

DO - 10.1007/BF00993172

M3 - Article

VL - 16

SP - 11

EP - 36

JO - Machine Learning

JF - Machine Learning

SN - 0885-6125

IS - 1-2

ER -