Date

2015-11-05

Author

Strachota, Susanne
İşler Baykal, Işıl
Kang, Hannah

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For many students, algebra continues to be a gatekeeper to future academic and employment opportunities. As a result, it is now widely accepted that algebra should be treated as a grades K–12 strand of thinking. In response, our project aims to examine the effectiveness of a longitudinal early algebra intervention on grade 3-5 students’ algebra learning and algebra-readiness for middle school. The study described here compares understandings of the Commutative Property of Addition demonstrated by students who participated in an early algebra intervention in grades 3 and 4 to those of students who experienced more traditional elementary grades instruction. Arithmetic properties provide students an opportunity to look at arithmetic expressions “in terms of their form rather than their value when computed,” and can serve as a route into algebra (Kaput, 2008, p. 12). Based on the results of our study, we argue that traditional arithmetic approaches to properties do not provide sufficient opportunities for students to engage in the important algebraic thinking practices of generalizing, representing generalizations, justifying generalizations, and reasoning with generalizations (Kaput, 2008). Participants included approximately 100 intervention students and 60 comparison students from two elementary schools in the same district in the Northeast. Written assessments administered at the beginning of grade 3, end of grade 3, and end of grade 4, were coded based on correctness as well as strategy use. On the grade 3 pre-test, there were no significant differences between the performances of intervention and comparison students. At the grade 3 and grade 4 post-tests, there were no significant differences between the proportions of students who invoked the Commutative Property of Addition when justifying the correctness of a specific numerical example (23 + 15 = 15 + 23). However, when students were asked to represent and justify this generalization, the groups’ results differed significantly. Students who participated in the intervention were more successful representing the property using variables (e.g., a + b = b + a) and justifying why the property holds true for all numbers. Our findings suggest that arithmetic properties can serve as useful contexts to engage students in developing, representing, and justifying generalizations. The inclusion of field properties in early grade mathematics instruction may provide teachers with the opportunity to use them as a springboard for engaging students in algebraic reasoning. The development of teachers’ “algebra eyes and ears” and the use of supplemental “algebrafied” instructional materials are critical to teachers’ ability to encourage such algebraic activity amongst elementary students (Blanton & Kaput, 2003).

Subject Keywords

Algebra and algebraic thinking, Elementary school education, Teacher education-inservice

URI

http://www.pmena.org/pmenaproceedings/PMENA%2037%202015%20Proceedings.pdf
https://hdl.handle.net/11511/85597

Collections

Department of Secondary Science and Mathematics Education, Conference / Seminar