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ERIC Number: EJ1054508
Record Type: Journal
Publication Date: 2013-Aug
Pages: 17
Abstractor: As Provided
Reference Count: 58
ISBN: N/A
ISSN: ISSN-0022-0663
Integrating Formal and Grounded Representations in Combinatorics Learning
Braithwaite, David W.; Goldstone, Robert L.
Journal of Educational Psychology, v105 n3 p666-682 Aug 2013
The terms "concreteness fading" and "progressive formalization" have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empirical reasons to believe that such an approach may improve learning outcomes relative to instruction employing only grounded or only formal representations (Freudenthal, 1991; Goldstone & Son, 2005; McNeil & Fyfe, 2012; but see Kaminski, Sloutsky, & Heckler, 2008). Two experiments tested the effectiveness of this approach to instruction in the mathematical domain of combinatorics, using outcome listing and numerical calculation as examples of grounded and formal representations, respectively. The study employed a pretest-training, posttest design. Transfer performance, that is, participants' improvement from pretest to posttest, was used to assess the effectiveness of instruction received during training. In Experiment 1, transfer performance was compared for 4 types of instruction, which differed only in the types of representation they employed: pure listing (i.e., listing only), pure formalism (i.e., numerical calculation only), list fading (i.e., listing followed by numerical calculation), and formalism-first (i.e., listing introduced after numerical calculation). List fading instruction led to transfer performance on par with pure formalism instruction and higher than formalism-first and pure listing instruction. In Experiment 2, an enhanced version of list fading training was again compared to pure formalism. However, no difference in transfer performance due to training was found. The results suggest that combining grounded and formal representations can be an effective approach to combinatorics instruction but is not necessarily preferable to using formal representations alone. If both grounded and formal representations are employed, the former should precede rather than follow the latter in the instructional sequence.
American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation
Authoring Institution: N/A
Identifiers - Location: Indiana
Grant or Contract Numbers: 0910218