TY - JOUR
T1 - An empirically-based trajectory for fostering abstraction of equivalent-fraction concepts
T2 - A study of the Learning Through Activity research program
AU - Kara, Melike
AU - Simon, Martin A.
AU - Placa, Nicora
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/12
Y1 - 2018/12
N2 - Promoting deep understanding of equivalent-fractions has proved problematic. Using a one-on-one teaching experiment, we investigated the development of an increasingly sophisticated, sequentially organized set of abstractions for equivalent fractions. The article describes the initial hypothetical learning trajectory (HLT) which built on the concept of recursive partitioning (anticipation of the results of taking a unit fraction of a unit fraction), analysis of the empirical study, conclusions, and the resulting revised HLT (based on the conclusions). Whereas recursive partitioning proved to provide a strong conceptual foundation, the analysis revealed a need for more effective ways of promoting reversibility of concepts. The revised HLT reflects an approach to promoting reversibility derived from the empirical and theoretical work of the researchers.
AB - Promoting deep understanding of equivalent-fractions has proved problematic. Using a one-on-one teaching experiment, we investigated the development of an increasingly sophisticated, sequentially organized set of abstractions for equivalent fractions. The article describes the initial hypothetical learning trajectory (HLT) which built on the concept of recursive partitioning (anticipation of the results of taking a unit fraction of a unit fraction), analysis of the empirical study, conclusions, and the resulting revised HLT (based on the conclusions). Whereas recursive partitioning proved to provide a strong conceptual foundation, the analysis revealed a need for more effective ways of promoting reversibility of concepts. The revised HLT reflects an approach to promoting reversibility derived from the empirical and theoretical work of the researchers.
KW - Equivalent fractions
KW - Guided reinvention
KW - Hypothetical learning trajectories
KW - Reflective abstraction
KW - Reversibility
KW - Task design
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U2 - 10.1016/j.jmathb.2018.03.008
DO - 10.1016/j.jmathb.2018.03.008
M3 - Article
AN - SCOPUS:85048497155
SN - 0732-3123
VL - 52
SP - 134
EP - 150
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
ER -