The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra

@article{Sweller1985TheUO,
  title={The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra},
  author={John Sweller and Graham Cooper},
  journal={Cognition and Instruction},
  year={1985},
  volume={2},
  pages={59-89}
}
The knowledge required to solve algebra manipulation problems and procedures designed to hasten knowledge acquisition were studied in a series of five experiments. It was hypothesized that, as occurs in other domains, algebra problem-solving skill requires a large number of schemas and that schema acquisition is retarded by conventional problem-solving search techniques. Experiment 1, using Year 9, Year 11, and university mathematics students, found that the more experienced students had a… 
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References

SHOWING 1-10 OF 13 REFERENCES
Expertise in Problem Solving.
TLDR
An examination of the shift from consideration of general, domain-independent skills and procedures, in both cognitive psychology and artificial intelligence, to the study of the knowledge base shows the importance of differences in the knowledge bases of experts and novices to their problem solving success.
Control mechanisms in problem solving
TLDR
It is suggested that altering a problem solver’s major source of information from a goal to feedback or vice versa will have important implications for the course of problem solving and what is learned during the solution process.
Some Examples of Cognitive Task Analysis with Instructional Implications
  • J. Greeno
  • Education
    Aptitude, Learning, and Instruction
  • 1979
TLDR
Analysis of knowledge structures used to understand and solve problems in high school geometry and in primary-grade arithmetic word problems raises questions about relationships between students' learning of computational procedures and their understanding of general types of quantitative relationships.
Categorization and Representation of Physics Problems by Experts and Novices
TLDR
Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably different problem categories, and completion of the representations depends on the knowledge associated with the categories.
Expert and Novice Performance in Solving Physics Problems
Although a sizable body of knowledge is prerequisite to expert skill, that knowledge must be indexed by large numbers of patterns that, on recognition, guide the expert in a fraction of a second to
Models of Competence in Solving Physics Problems
TLDR
A set of two computer-implemented models that solve physics problems in ways characteristic of more and less competent human solvers are described, providing a good account of the order in which principles are applied by humansolvers working problems in kinematics and dynamics.
Effects of Goal Specificity on Means-Ends Analysis and Learning.
はじめに ▶ 変換問題(transformation problem) 初期状態 ゴール状態 オペレータのセット ▶ 主要なメカニズム means-ends analysis • ゴール状態と続く状態の差を分析 • 最も差を減らせるオペレータを選択する ▶ 解決がゴールから遠ざかることを必要とする問題の場合 補助的なメカニズム • サブゴール • 計画 ▶
Consequences of history-cued and means–end strategies in problem solving.
There are two broad processes that people can use when attempting to solve a problem. The first of these is a means-ends strategy in which attempts are made to reduce differences between a given
...
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