The development of year 3 students' place-value understanding : representations and concepts

Price, Peter Stanley (2001) The development of year 3 students' place-value understanding : representations and concepts. PhD thesis, Queensland University of Technology.


Understanding base-ten numbers is one of the most important mathematics topics taught in the primary school, and yet also one of the most difficult to teach and to learn. Research shows that many children have inaccurate or faulty number conceptions, and use rote-learned procedures with little regard for quantities represented by mathematical symbols. Base-ten blocks are widely used to teach place-value concepts, but children often do not perceive the links between numbers, symbols, and models. Software has also been suggested as a means of improving children's development of these links but there is little research on its efficacy.

Sixteen Queensland Year 3 students worked cooperatively with the researcher for 10 daily sessions, in 4 groups of 4 students of either high or low mathematical achievement level, on tasks introducing the hundreds place. Two groups used physical base-ten blocks and two used place-value software incorporating electronic base-ten blocks. Individual interviews assessed participants' place-value understanding before and after teaching sessions. Data sources were videotapes of interviews and teaching sessions, field notes, workbooks, and software audit trails, analysed using a grounded theory method.

There was little difference evident in learning by students using either physical or electronic blocks. Many errors related to the "face-value" construct, counting and handling errors, and a lack of knowledge of base-ten rules were evident. Several students trusted the counting of blocks to reveal number relationships. The study failed to confirm several reported schemes describing children's conceptual structures for multidigit numbers. Many participants demonstrated a preference for grouping or counting approaches, but not stable mental models characterising their thinking about numbers generally. The independent-place construct is proposed to explain evidence in both the study and the literature that shows students making single-dimensional associations between a place, a set of number words, and a digit, rather than taking account of groups of 10. Feedback received in the two conditions differed greatly. Electronic feedback was more positive and accurate than feedback from blocks, and reduced the need for human-based feedback. Primary teachers are urged to monitor students' use of base-ten blocks closely, and to challenge faulty number conceptions by asking appropriate questions.

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ID Code: 15783
Item Type: QUT Thesis (PhD)
Supervisor: English, Lyndall & Atweh, William
Keywords: Place value, base-ten blocks, Year 3, mathematical understanding, place-value software, representations of number, conceptions of number, electronic base-ten blocks, conceptual structures for multidigit numbers, feedback, misconceptions of number, independent-place construct, face-value construct, mathematics teaching with technology, number models, Payne-Rathmell model for teaching number topics
Department: Faculty of Education
Institution: Queensland University of Technology
Copyright Owner: Copyright Peter Stanley Price
Deposited On: 03 Dec 2008 03:49
Last Modified: 21 Jun 2017 14:40

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