# Improving Preservice Teacher Understandings of Arithmetic: The Division Theorem

Grant program: Teaching and Learning Development Grant (TLDG)

Grant recipient: Stephen Campbell, Faculty of Education

Project team: TBD

Timeframe: December 2018 to September 2019

Funding: \$6000

Course addressed: EDUC 475 – Designs for Learning: Elementary Mathematics

Description: There is a plethora of literature in mathematics education research indicating that preservice teacher understandings of elementary arithmetic is woefully lacking. Indeed, their understandings are essentially limited to rote procedures and simplistic applications. The result is that elementary arithmetic is typically learned by preservice teachers and subsequently taught to young children as a collection of isolated topics. Most notably, topics such as division with remainder, fractions, and decimals are taught, and learned, as though there were no procedural or conceptual relationships between them.

I have identified two foundational areas largely ignored in contemporary curriculum documents in elementary mathematics education that can be investigated as core competencies in preservice teacher education to help mitigate these discrepancies: The division theorem and base representation.

I would like to investigate the implementation of educational software to enable preservice teachers in the Faculty of Education’s Professional Development Program (PDP) to improve their procedural and conceptual understandings of relationships between isolated aspects of the elementary school mathematics curriculum, not only between whole number division with remainder and rational number division, but also between elementary whole number theory concepts involving factors, multiples, and divisors, as well as fractional and decimal representations of rational numbers.

In sum, the aim is to determine whether this approach can contribute to improving preservice teacher understandings of elementary mathematics, and potentially their subsequent teaching to young children.

• What demographic and math anxiety differences exist between the experimental and control groups participating in this study?
• What preferential differences exist with regard to symbolic and graphic learning modalities within the experimental group?
• What differences can be detected in the procedural and conceptual understanding of concepts related to whole number and rational number division between the experimental and control groups?

Knowledge sharing: Findings from the study will be shared and discussed in the Faculty of Education with other faculty members, graduate students, and sessionals involved in teaching Educ 475, possibly in a Faculty Forum venue or some facsimile.

In addition, findings will be submitted for presentation at the Annual British Columbia Association of Math Teachers (BCAMT) Conference, as well as submission of the project final report for publication in a suitable mathematics education journal.

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