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ERIC Number: EJ774913
Record Type: Journal
Publication Date: 2007-Nov
Pages: 19
Abstractor: Author
Reference Count: N/A
ISSN: ISSN-0013-1954
Fine Grain Assessment of Students' Mathematical Understanding: Participatory and Anticipatory Stages in Learning a New Mathematical Conception
Tzur, Ron
Educational Studies in Mathematics, v66 n3 p273-291 Nov 2007
This study addressed a twofold problem--the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students' mathematical understandings. As a context for the study served the difficult-to-grasp concept of "inverse" order relationship among unit fractions, that is, the larger the number of parts the smaller the size of each part (e.g., 1/7 greater than 1/10 although 10 greater than 7). I conducted this study as a whole-class teaching experiment in a third grade classroom at a public school in Israel. The qualitative analysis of tasks presented to students and students' responses to those tasks, as well as a quantitative measurement of percents of student responses to assessment questions, indicated that the distinction between a participatory and an anticipatory stage is sound and useful in guiding the teacher's selection of tasks to assess/teach students' mathematical thinking. In particular, this analysis demonstrates that in a classroom where the vast majority of students "appear" to understand a new concept, a substantial portion of the class--those who formed the new conception only at the participatory stage--may be at risk of being left behind. This study also highlights a new way of organizing assessment to minimize such unfortunate situations, including three levels of assessment rigor a teacher can use in regular classroom settings.
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Grade 3
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Israel