### Abstract

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design.

Original language | English |
---|---|

Pages (from-to) | 1036-1079 |

Number of pages | 44 |

Journal | Cognitive Science |

Volume | 40 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2016 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Experimental and Cognitive Psychology
- Cognitive Neuroscience
- Artificial Intelligence

### Cite this

*Cognitive Science*,

*40*(5), 1036-1079. https://doi.org/10.1111/cogs.12275

}

*Cognitive Science*, vol. 40, no. 5, pp. 1036-1079. https://doi.org/10.1111/cogs.12275

**Learning Problem-Solving Rules as Search Through a Hypothesis Space.** / Lee, Hee Seung; Betts, Shawn; Anderson, John R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Learning Problem-Solving Rules as Search Through a Hypothesis Space

AU - Lee, Hee Seung

AU - Betts, Shawn

AU - Anderson, John R.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design.

AB - Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design.

UR - http://www.scopus.com/inward/record.url?scp=85028271636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028271636&partnerID=8YFLogxK

U2 - 10.1111/cogs.12275

DO - 10.1111/cogs.12275

M3 - Article

C2 - 26292648

AN - SCOPUS:85028271636

VL - 40

SP - 1036

EP - 1079

JO - Cognitive Science

JF - Cognitive Science

SN - 0364-0213

IS - 5

ER -