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Tell Me Why! Content Knowledge Predicts Process-Orientation of Math Researchers' and Math Teachers' Explanations

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Title: Tell Me Why! Content Knowledge Predicts Process-Orientation of Math Researchers' and Math Teachers' Explanations
Language: English
Authors: Lachner, Andreas, Nückles, Matthias
Source: Instructional Science: An International Journal of the Learning Sciences. Jun 2016 44(3):221-242.
Availability: Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Peer Reviewed: Y
Page Count: 22
Publication Date: 2016
Document Type: Journal Articles
Reports - Research
Descriptors: Pedagogical Content Knowledge, Predictor Variables, Educational Quality, Instructional Effectiveness, Mathematics Instruction, Mathematics Teachers, Educational Researchers, Expertise, Mathematics, Professional Personnel, Comparative Analysis, Teaching Methods, Scaffolding (Teaching Technique), Learning Processes
DOI: 10.1007/s11251-015-9365-6
ISSN: 0020-4277
Abstract: In two studies, we investigated the impact of instructors' different knowledge bases on the quality of their instructional explanations. In Study 1, we asked 20 mathematics teachers (with high pedagogical content knowledge, but lower content knowledge) and 15 mathematicians (with lower pedagogical content knowledge, but high content knowledge) to provide an explanation about an extremum problem for students. We found that the explanations by teachers and mathematicians mainly differed in their process-orientation. Whereas the teachers mainly presented the solution steps for the problem (product-orientation), the mathematicians also provided information to clarify why a certain step in the solution was required (process-orientation). In Study 2, we investigated the effectiveness of these differing explanations. Eighty students either received a process-oriented mathematician's explanation, a product-oriented mathematics teacher's explanation, or no explanation for learning. We found that students who learned with a process-oriented explanation outperformed students who learned with a product-oriented explanation on an application test. Students who only had the problem but no explanation for learning showed the lowest learning gains. Apparently, deep content knowledge helped instructors generate explanations with high process-orientation, a textual feature that served as a valuable scaffold for students' understanding of mathematical procedures.
Abstractor: As Provided
Number of References: 28
Entry Date: 2016
Accession Number: EJ1104177
Database: ERIC
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  Data: In two studies, we investigated the impact of instructors' different knowledge bases on the quality of their instructional explanations. In Study 1, we asked 20 mathematics teachers (with high pedagogical content knowledge, but lower content knowledge) and 15 mathematicians (with lower pedagogical content knowledge, but high content knowledge) to provide an explanation about an extremum problem for students. We found that the explanations by teachers and mathematicians mainly differed in their process-orientation. Whereas the teachers mainly presented the solution steps for the problem (product-orientation), the mathematicians also provided information to clarify why a certain step in the solution was required (process-orientation). In Study 2, we investigated the effectiveness of these differing explanations. Eighty students either received a process-oriented mathematician's explanation, a product-oriented mathematics teacher's explanation, or no explanation for learning. We found that students who learned with a process-oriented explanation outperformed students who learned with a product-oriented explanation on an application test. Students who only had the problem but no explanation for learning showed the lowest learning gains. Apparently, deep content knowledge helped instructors generate explanations with high process-orientation, a textual feature that served as a valuable scaffold for students' understanding of mathematical procedures.
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