Learning Mathematics From Examples and by Doing
Open accessAbstract
This article demonstrates the feasibility and effectiveness of teaching several mathematical skills by presenting students with carefully chosen sequences of worked-out examples and problems - without lectures or other direct instruction. Thinking-aloud protocols of 20 students learning factorization by this method are analyzed to determine the kinds and depth of understanding students attained. Students did not simply memorize procedures but were able to recognize when the procedures were applicable and to apply them. Most students were also able to use their understanding of the concept of factorization to help learn the procedures and to check their results. The method of learning from examples has now been tested successfully with a class covering the entire 3-year curriculum in algebra and geometry in a Chinese middle school.
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Zhu and Simon (1987) demonstrated the feasibility and effectiveness of teaching Chinese middle school students' mathematical skills through selected sequences of worked examples.
“Zhu and Simon (1987) demonstrated the feasibility and effectiveness of teaching Chinese middle school students' mathematical skills through selected sequences of worked examples.”
From Worked Example Mid-Semester Intervention in College Algebra (2022) · cites this paper as Zhu and Simon (1987)
Zhu and Simon (1987) found that students retained the material at a very high level and experimental groups retained material at a slightly higher percentage than the control group taught by traditional lecture.
“When the students were retested after a year or two had passed, Zhu and Simon (1987) found that students retained the material at a very high level and the experimental groups retained material at a slightly higher percentage than the control group that was taught by traditional lecture.”
From Worked Example Mid-Semester Intervention in College Algebra (2022) · cites this paper as Zhu and Simon (1987)
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“As with the goal-free effect , a wealth of studies lend support to the effectiveness of worked examples in terms of improving memorisation (Carroll, 1994; Cooper & Sweller, 1987; Paas & Van Merriënboer, 1994; Sweller & Cooper, 1985; Trafton & Reiser, 1993; Zhu & Simon, 1987).”
Worked Example Mid-Semester Intervention in College Algebra
Miller, D., & Schraeder, M. (2022) · Journal of Research in Mathematics Education · doi:10.17583/redimat.9645
- Authors
- Zhu, X., & Simon, H. A.
- Affiliations
- Chinese Academy of Sciences (CN)
- Carnegie Mellon University (US)
- Venue
- Cognition and Instruction
- Publisher
- Informa UK Limited
- Published
- 1987-09
- Volume
- 4
- Issue
- 3
- Pages
- 137-166
- ISSN
- 0737-0008 (ISSN-L)
- 1532-690X
- OpenAlex
- W2028487549
- Cited by
- 357
- References
- 0
- Citations by year
- 2026: 4 · 2025: 13 · 2024: 6 · 2023: 10 · 2022: 6 · 2021: 6 · 2020: 11 · 2019: 6 · 2018: 12 · 2017: 8 · 2016: 6 · 2015: 22 · 2014: 17 · 2013: 14 · 2012: 19
- FWCI
- 7.55
- Type
- journal article
- Language
- en
- Open access
- green
- ir.psych.ac.cn
- Licence
- cc-by-nc-sa
- Locations
- Cognition and Instruction (publishedVersion)
- KiltHub Repository (submittedVersion)
- Institutional Repository of Institute of Psychology, Chinese Academy of Sciences (Institute of Psychology, Chinese Academy of Sciences) (submittedVersion, cc-by-nc-sa)
- Funders
- Office of Naval Research
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Visual and Cognitive Learning Processes
- Keywords
- learning from examples, worked examples, mathematics learning, factorization, algebra instruction, problem solving, think-aloud, conceptual understanding, junior high school mathematics
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