An approach to design of mathematical task sequences: Conceptual learning as abstraction

Martin Simon, Professor Mathematics Education, NYU Steinhardt, describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from approaches in which learning to solve the problem posed is the intended learning.

Martin Simon’s current research focuses on understanding the process by which students develop mathematical concepts through their mathematical activity, and how such learning can be fostered. Simon has also done extensive research on the development of mathematics teachers as they learn to teach mathematics with a conceptual focus. Simon has served as a professor of mathematics education at Penn State University and director of the Summer Math for Teachers program at Mount Holyoke College. He has served as principal investigator on five National Science Foundation projects, and was awarded the Distinguished Research Award by the Association of Teacher Educators in 2000, and a Career Achievement Award by the Penn State University College of Education in 2001. He earned his doctorate in mathematics education from the University of Massachusetts at Amherst in 1986.

Simon’s current project, Measurement Approach to Rational Numbers (MARN), continues his research on how students learn mathematical concepts, while developing and researching an approach to teaching fractions and ratios building on measurement concepts.

 

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