Learning Mathematics From Examples and by Doing

Zhu, Xiaobing; Simon, Herbert A.

doi:10.1207/s1532690xci0403_1

Cited by 280 publications

(173 citation statements)

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“…Mandl and Ballstaedt (1982) also found that a high level of elaboration impaired learning. It may be that an active and strategic approach to learning, as it is supposed to be induced by a teaching expectancy, is more effective with other forms of learning, for example, learning by doing or learning from worked-out examples (Zhu & Simon, 1987). In the present study, students had to learn from worked-out examples.…”

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confidence: 81%

Learning for later teaching: An exploration of mediational links between teaching expectancy and learning results

Renkl

1995

Learning and Instruction

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It was investigated to what extent the expectancy of a teaching demand influences learning results. In addition, possible mediator effects were explored. Thirty-six subjects (students of education) learned from worked-out examples in the domain of probability calculus under two different conditions: The experimental group expected to be required to explain similar worked-out examples to a third person, whereas the control group merely anticipated to be tested on similar problems. The results showed that the teaching expectancy decreased the superficiality of studying the worked-out examples, lowered intrinsic motivation, and increased, to some extent, anxiety during learning. The learning results were negatively influenced by anxiety during learning and were positively associated with the time allocated to construct a sound problem representation. However, no assumed mediator effect proved to be of real significance. In addition, the learning gains were not affected by the teaching expectancy.

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confidence: 81%

Learning for later teaching: An exploration of mediational links between teaching expectancy and learning results

Renkl

1995

Learning and Instruction

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“…Although algebra textbooks and classes include lots of verbal instruction, much of the process of learning appears to occur while students are studying examples and practicing on problems (cf. Matsuda et al, 2008;Zhu & Simon, 1987), and neither examples nor problems contain verbal descriptions of the to-be-learned patterns or rules. Many of the pattern, rule, or schema induction processes that carry out this learning are implicit (see Evans, Chapter 8), that is, are not mediated by (nor involve the subvocalization of ) the verbal rules read in the text or heard in class.…”

Section: Learning To Ink By Learning Languages To Ink Withmentioning

confidence: 99%

Learning to Think: Cognitive Mechanisms of Knowledge Transfer

Koedinger

Roll

2012

The Oxford Handbook of Thinking and Reasoning

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Learning to think is about transfer. The scope of transfer is essentially a knowledge representation question. Experiences during learning can lead to alternative latent representations of the acquired knowledge, not all of which are equally useful. Productive learning facilitates a general representation that yields accurate behavior in a large variety of new situations, thus enabling transfer. This chapter explores two hypotheses. First, learning to think happens in pieces and these pieces, or knowledge components, are the basis of a mechanistic explanation of transfer. This hypothesis yields an instructional engineering prescription: that scientific methods of cognitive task analysis can be used to discover these knowledge components, and the resulting cognitive models can be used to redesign instruction so as to foster better transfer. The second hypothesis is that symbolic languages act as agents of transfer by focusing learning on abstract knowledge components that can enhance thinking across a wide variety of situations. The language of algebra is a prime example and we use it to illustrate (1) that cognitive task analysis can reveal knowledge components hidden to educators; (2) that such components may be acquired, like first language grammar rules, implicitly through practice; (3) that these components may be "big ideas" not in their complexity but in terms of their usefulness as they produce transfer across contexts; and (4) that domain-specific knowledge analysis is critical to effective application of domain-general instructional strategies.

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“…Learning from worked-out examples is an important source of learning (VanLehn, 1986(VanLehn, , 1996, and it is a learning mode preferred by novices (e.g., Anderson, Farell, 8z Sauers, 1984;LeFevre & Dixon, 1986;Pirolli & Anderson, 1985;Reeker & Pirolli, 1995). Furthermore, research has shown that learning from worked-out examples is typically very effective (e.g., Sweller & Cooper, 1985;Tarmizi & Sweller, 1988;Ward & Sweller, 1990;Zhu & Simon, 1987). However, in order to successfully learn from these types of examples, the learner has to actively explain the solution steps to himself or herself because not all the information about the rationale of the solution steps, that is necessary for understanding the solution procedure, is included in the examples (cf.…”

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confidence: 99%