Hypothetical Learning Trajectories in Mathematics Education
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.
KeywordsLearning Teaching Constructivism Teacher thinking Learning progressions
- CCSSO/NGA (2010) Common core state standards for mathematics. Council of Chief State School Officers and the National Governors Association Center for Best Practices, Washington, DC. http://corestandards.org
- Clements DH (2002) Linking research and curriculum development. In: English LD (ed) Handbook of international research in mathematics education. Erlbaum, Mahwah, pp 599–630Google Scholar
- Clements DH, Sarama J (2004b) Hypothetical learning trajectories (special issue). Math Think Learn 6(2). Erlbaum, MahwahGoogle Scholar
- Daro P, Mosher FA, Corcoran T (2011) Learning trajectories in mathematics: a foundation for standards, curriculum, assessment and instruction. CPRE research report # RR-68Google Scholar
- Tzur R, Lambert MA (2011) Intermediate participatory stages as zone of proximal development correlate in constructing counting-on: a plausible conceptual source for children’s transitory “regress” to counting-all. J Res Math Educ 42:418–450Google Scholar