Productive Failure in Learning Math

Cognitive Science - Tập 38 Số 5 - Trang 1008-1022 - 2014
Manu Kapur1
1National Institute of Education, Nanyang Technological University

Tóm tắt

AbstractWhen learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized‐controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem‐solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student‐generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem‐solving attempts or those of others before receiving instruction as alternatives for better math learning.

Từ khóa


Tài liệu tham khảo

10.1016/j.cognition.2010.10.001

Bransford J. D., 2000, How people learn: Brain, mind, experience and school

10.1016/j.jecp.2012.06.009

10.1016/j.learninstruc.2011.11.001

10.1207/s1532690xci0301_3

Hiebert J., 2007, Second handbook of research on mathematics teaching and learning, 371

10.1207/S15326985EP3801_4

10.1007/s11251-009-9093-x

10.1007/s11251-012-9209-6

10.1080/10508406.2011.591717

10.1080/10508406.2013.819000

10.1007/s11251-012-9235-4

10.1207/s15326985ep4102_1

10.1111/j.0956-7976.2004.00737.x

10.1037/0022-0663.84.4.429

10.1037/a0014224

Roll I., 2011, Proceedings of the 33rd Annual Conference of the Cognitive Science Society, 2824

10.1111/j.1467-9280.1992.tb00029.x

10.1037/a0025140

10.1207/s1532690xci2202_1

diSessa A. A., 1991, Inventing graphing: Meta‐representational expertise in children, Journal of Mathematical Behavior, 10, 117

10.1111/1467-8721.ep10769817

10.1017/CBO9780511489709.002

10.1207/s1532690xci0804_5

10.1080/13803610802481265

Thông tin
Thông tin xuất bản

Cognitive Science

Tập 38 Số 5

1008-1022

Thông tin tác giả