Discussion as a mechanism for learning has been emphasized in both curriculum standards and psychological theories. However, US students get few opportunities to explain their mathematical thinking during classroom instruction. This project is aimed at answering three related questions about the role of discussion in elementary student learning.
1) Are there fewer student explanations in the US than in higher achieving East Asian locales? What predicts the prevalence of student explanations and do those predictors vary across countries? A machine-learning system was developed and validated for identifying explanations using transcripts of 232 mathematics classes in Japan, Hong Kong, and United States. Results suggest that Japan and Hong Kong lessons feature more student explanations than US lessons do. In all countries, lessons with a higher proportion of student talk showed more explanation; in Hong Kong and Japan (but not in the US), teachers’ requests for procedures and reasoning, as well as their language modeling of contradicting opinions predicted increased student explanations. One reason for this difference may be that teachers in the East Asian settings were more stringent in what they accepted as an adequate explanation.
2) Do US students differ from their Chinese peers in the quality of their mathematical explanations? Chinese and US elementary students were interviewed about mathematical equivalence. Results indicated US students underperformed their Chinese peers in the accuracy and mathematical richness of students’ explanations.
3) Do students process peer explanations differently than those of adults? US elementary students watched matched mathematical explanations from children vs. adults. The ones who watched peer-produced explanations were more likely to recognize the insufficiency of explanations and provide elaborated reasoning. Moreover, difference in processing moderated the learning gain from pre- to post-tests of their understanding of mathematical equivalence.
Overall, the current study showed that although US students are providing and hearing both fewer and lower quality explanations, they may still benefit from hearing peers’ less fluent or flawed explanations. Teachers play a crucial role in directing student explanations, but this role goes beyond the questions they ask to the way in which they socialize students about what is an acceptable explanation.
PhD
Education & Psychology
University of Michigan, Horace H. Rackham School of Graduate Studies
http://deepblue.lib.umich.edu/bitstream/2027.42/108964/1/xypan_1.pdf