Seminar - Productive failure in mathematical problem solving
18 November 2010
Can failure be a uniquely effective learning tool? Join Manu Kapur from the National Institute of Education in Singapore, as he presents evidence of how "productive failure" can lead to some surprising outcomes, specifically, in the area of mathematical problem solving.
Productive Failure in Mathematical Problem Solving - "I will start by discussing the theoretical basis for designing for productive failure in mathematics problem solving. I will then describe how we can design tasks and activity structures that afford students opportunities to generate and explore a diversity of representations and methods for solving complex problems that target mathematical concepts they have yet to learn. Even though students expectedly fail at producing the canonical representations and solution methods, this seeming failure can be germane for learning, provided an appropriate form of instructional structure subsequently follows.
By evidencing findings from a series of classroom-based experiments, I will describe how designing for productive failure requires engaging students in a learning design that embodies four core, interdependent mechanisms: a) activation and differentiation of prior knowledge in relation to the targeted concepts, b) attention to critical conceptual features of the targeted concepts, c) explanation and elaboration of these features, and d) organization and assembly of the critical conceptual features into the targeted concepts. I will end my talk by deriving broader implications for mathematics education and learning designs."
Manu Kapur is an Assistant Professor in the Curriculum, Teaching and Learning (CTL) Academic Group and a researcher at the Learning Sciences Lab (LSL) at the National Institute of Education (NIE) of Singapore.
He received his doctorate in instructional technology and media from Teachers College, Columbia University in New York where he also completed a Master of Science in Applied Statistics. He also has a Master of Education from the NIE and a Bachelor of Mechanical Engineering (Honours) from the National University of Singapore. His research takes a complexity-grounded perspective to study the ontology of individual and collective cognition.
He conceptualized the notion of Productive Failure and used it to explore the hidden efficacies in the seemingly failed effort of small groups solving ill-structured problems collaboratively in an online environment. His current research extends this line of work across the modalities of classroom settings in Singapore.
Location: Room number 418, Education Building A35