TY - JOUR

T1 - Looking back to the roots of partially correct constructs

T2 - The case of the area model in probability

AU - Ron, Gila

AU - Dreyfus, Tommy

AU - Hershkowitz, Rina

N1 - Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We use the notion Partially Correct Constructs (PaCCs) for students’ constructs that partially match the mathematical principles underlying the learning context. A frequent expression of partial construction of mathematical principles is that a student's words or actions provide an inaccurate or misleading picture of the student's knowledge. In this study, we analyze the learning process of a grade 8 student, who learns a topic in elementary probability. The student successfully accomplishes a sequence of several tasks without apparent difficulty. When working on a further task, which seems to require nothing beyond his proven competencies, he encounters difficulties. Using the epistemic actions of the RBC model for abstraction in context as tracers, we analyze his knowledge constructing processes while working on the previous tasks, and identify some of his constructs as PaCCs that are concealed in these processes and explain his later difficulties. In addition, our research points to the complexity of the knowledge structures students are expected to deal with in their attempts to learn an elementary mathematical topic with understanding.

AB - We use the notion Partially Correct Constructs (PaCCs) for students’ constructs that partially match the mathematical principles underlying the learning context. A frequent expression of partial construction of mathematical principles is that a student's words or actions provide an inaccurate or misleading picture of the student's knowledge. In this study, we analyze the learning process of a grade 8 student, who learns a topic in elementary probability. The student successfully accomplishes a sequence of several tasks without apparent difficulty. When working on a further task, which seems to require nothing beyond his proven competencies, he encounters difficulties. Using the epistemic actions of the RBC model for abstraction in context as tracers, we analyze his knowledge constructing processes while working on the previous tasks, and identify some of his constructs as PaCCs that are concealed in these processes and explain his later difficulties. In addition, our research points to the complexity of the knowledge structures students are expected to deal with in their attempts to learn an elementary mathematical topic with understanding.

KW - Abstraction in context

KW - Area model

KW - Knowledge construction

KW - Partially correct constructs

KW - Probability

UR - http://www.scopus.com/inward/record.url?scp=84995750543&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2016.10.004

DO - 10.1016/j.jmathb.2016.10.004

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AN - SCOPUS:84995750543

SN - 0732-3123

VL - 45

SP - 15

EP - 34

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

ER -