Reference Work Entry

Encyclopedia of Mathematics Education

pp 272-275


Hypothetical Learning Trajectories in Mathematics Education

  • Martin SimonAffiliated withSteinhardt School of Culture, Education, and Human Development, New York University Email author 


Learning Teaching Constructivism Teacher thinking Learning progressions


Hypothetical learning trajectory is a theoretical model for the design of mathematics instruction. It consists of three components, a learning goal, a set of learning tasks, and a hypothesized learning process. The construct can be applied to instructional units of various lengths (e.g., one lesson, a series of lessons, the learning of a concept over an extended period of time).

Explanation of the Construct

Simon (1995) postulated the construct hypothetical learning trajectory. Simon’s goal in this heavily cited article was to provide an empirically based model of pedagogical thinking based on constructivist ideas. (Pedagogical refers to all contributions to an instructional intervention including those made by the curriculum developers, the materials developers, and the teacher.) The construct has provided a theoretical frame for researchers, teachers, and curriculum developers as they plan instruction for conceptual learning.

Simon (1995. P. 136) explained the compon ...

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