Hypothetical Learning Trajectories in Mathematics Education
 Martin Simon
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Definition
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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 Clements DH, Sarama J (2004b) Hypothetical learning trajectories (special issue). Math Think Learn 6(2). Erlbaum, Mahwah
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 McGatha M, Cobb P, McClain K (2002) An analysis of students’ initial statistical understandings: developing a conjectured learning trajectory. J Math Behav 16:339–355 CrossRef
 Simon MA (1995) Reconstructing mathematics pedagogy from a constructivist perspective. J Res Math Educ 26:114–145 CrossRef
 Simon M, Tzur R (2004) Explicating the role of mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory. Math Think Learn 6:91–104 CrossRef
 Simon M, Tzur R, Heinz K, Kinzel M (2004) Explicating a mechanism for conceptual learning: elaborating the construct of reflective abstraction. J Res Math Educ 35:305–329 CrossRef
 Simon MA, Saldanha L, McClintock E, Karagoz Akar G, Watanabe T, Ozgur Zembat I (2010) A developing approach to studying students’ learning through their mathematical activity. Cognit Instr 28:70–112 CrossRef
 Tzur R (2007) Fine grain assessment of students’ mathematical understanding: participatory and anticipatory stages in learning a new mathematical conception. Educ Stud Math 66(3):273–291 CrossRef
 Tzur R, Lambert MA (2011) Intermediate participatory stages as zone of proximal development correlate in constructing countingon: a plausible conceptual source for children’s transitory “regress” to countingall. J Res Math Educ 42:418–450
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 Title
 Hypothetical Learning Trajectories in Mathematics Education
 Reference Work Title
 Encyclopedia of Mathematics Education
 Pages
 pp 272275
 Copyright
 2014
 DOI
 10.1007/9789400749788_72
 Print ISBN
 9789400749771
 Online ISBN
 9789400749788
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media Dordrecht
 Additional Links
 Topics
 Keywords

 Learning
 Teaching
 Constructivism
 Teacher thinking
 Learning progressions
 eBook Packages
 Editors

 Stephen Lerman ^{(501)}
 Editor Affiliations

 501. Department of Education, Centre for Mathematics Education, London South Bank University
 Authors

 Martin Simon ^{(88)}
 Author Affiliations

 88. Steinhardt School of Culture, Education, and Human Development, New York University, 239 Green St. 420, New York, NY, 10003, USA
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