Student,teacher, and instructional characteristics related to students' gains in flexibility |
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| Institution: | 1. Harvard University, USA;2. Temple University, USA;3. Vanderbilt University, USA;4. University of Louisville, USA;1. Research Department of Clinical, Educational and Health Psychology, University College London, London, United Kingdom;2. Norwegian Business School, Oslo University College London, United Kingdom;1. Department of Developmental & Educational Psychology, Leiden University, the Netherlands;2. Department of Clinical Psychology, University of Osnabrück, Germany;1. Department of Psychology, Philipps University Marburg, Gutenbergstr. 18, 35032 Marburg, Germany;2. Department of Psychology, TU Dortmund, Emil-Figge-Str. 50, 44227 Dortmund, Germany;3. Department of Psychology, Heidelberg University, Hauptstrasse 47-51, 69117 Heidelberg, Germany;1. Department of Psychological, Humanistic and Territorial Sciences, University of Chieti-Pescara, Chieti, 66100, Italy;2. Department of Clinical Psychology, University of Rome “La Sapienza”, Roma, 00185, Italy;3. Department of Educational Psychology, Baylor University, Waco TX, 76798, USA;1. School of Education and Human Development, University of Virginia, United States of America;2. Department of Psychology, University of California, Los Angeles, United States of America |
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| Abstract: | Flexibility in problem solving has been widely recognized as an important skill for students' mastery of mathematics. Here we utilize the Opportunity-Propensity framework to investigate student characteristics, teacher characteristics, and teacher instructional practices that may be associated with students' gains in flexibility in algebra. Teacher and student data were collected from 8th and 9th grade Algebra I teachers in Massachusetts as part of a larger study on the impact of a researcher-developed year-long supplementary curriculum that focused on improving students' flexibility. We explore student demographics, teacher background characteristics and teacher instructional practices as predictors of student gains in flexibility. We further investigate instructional practices associated with flexibility gains through an analysis of teacher questioning in the classroom for teachers whose students achieved the greatest gains in flexibility and those whose students achieved the least gains. Our results indicate that prior knowledge is a reliable predictor of flexibility gains and that gender is an important student background characteristic associated with the development of flexibility. In addition, although high and low gain teachers did not differ in their implementation fidelity, high flexibility gain teachers asked more open-ended questions that prompted students to verbalize the main ideas of the lesson. |
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