Published In
ZDM
Document Type
Post-Print
Publication Date
4-1-2019
Subjects
systems, Place value (Mathematics), Arabic numeration
Abstract
Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to understanding and teaching number and place value. The research aims of this paper are (1) to present a local instructional theory (LIT), designed to familiarize PTs with these features through comparison with historical number systems and (2) to present the effects of using the LIT in the PT classroom. A theory of learning (variation theory) is paired with a framework related to motivation (intellectual need) to illustrate the mutually supporting roles they may play in mathematical learning and task design. The LIT, a supporting task sequence, and the rationale for task design are shared. This theoretical contribution is then paired with evidence of PTs’ changing growth in their conceptions of whole number before and after courses leveraging this task sequence.
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DOI
10.1007/s11858-018-0984-7
Persistent Identifier
https://archives.pdx.edu/ds/psu/28756
Citation Details
Thanheiser, E., & Melhuish, K. (2019). Leveraging Variation of Historical Number Systems to Build Understanding of the Base-Ten Place-Value System. ZDM: The International Journal on Mathematics Education, 51(1), 39–55.
Description
© FIZ Karlsruhe 2018