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This study consisted of Grades 1 and 2 (ages 6-8) classroom teaching experiments (CTE) with a lesson sequence focused on graphical representations of algebraic relationships. We interviewed students before, during, and after the CTE. Here we report on the progression of one Grade 2 (age 7) student’s thinking across the CTE. Prior to the CTE, the student had not previously interacted with representations of algebraic relationships. By the end of the CTE, the student was able to generalize about the functional relationships using graphs. This study illustrates how a learning trajectory modeling students’ understandings of function graphs can be used to characterize one children’s learning and provides evidence that young students are able to reason with function graphs.
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Kindergarteners’ Understandings and Representations of the Additive Inverse
This study involved a 7-lesson generalized arithmetic classroom teaching experiment (CTE) with kindergarten students. We interviewed four students individually before and after the seven weeks to explore their understandings and representations of arithmetic properties. Here, we report on students' responses to questions on the additive inverse property. Using Skemp’s framework of relational and instrumental understandings (2006), our analysis revealed that most of the interviewed kindergarteners could understand the additive inverse relationally by the end of the CTE. Our interviews revealed that tables and number lines enabled students to articulate more sophisticated understandings of the additive inverse.
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- Award ID(s):
- 2201095
- PAR ID:
- 10534113
- Editor(s):
- Lindgren, R; Asino, T I; Kyza, E A; Looi, C K; Keifert, D T; Suárez, E
- Publisher / Repository:
- International Society of the Learning Sciences.
- Date Published:
- Journal Name:
- Inženernotehničeskoe obespečenie APK
- ISSN:
- 1819-0138
- ISBN:
- 979-8-9906980-0-0
- Page Range / eLocation ID:
- 1199-1202
- Format(s):
- Medium: X
- Location:
- Buffalo, NY, USA
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Proceeding:
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