Teachers' Perspectives on "Authentic Mathematics" and the Two-Column Proof Form

We investigate experienced high school geometry teachers' perspectives on "authentic mathematics" and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to ass...

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Bibliographic Details
Published in:Educational studies in mathematics 2009-04, Vol.70 (3), p.275-293
Main Authors: Weiss, Michael, Herbst, Patricio, Chen, Chialing
Format: Article
Language:English
Subjects:
Art teachers
Education
Focus Groups
Geometry
High school students
Interrater Reliability
Mathematical Logic
Mathematics
Mathematics curricula
Mathematics Education
Mathematics teachers
Microteaching
Reasoning
Secondary School Teachers
Teacher Attitudes
Teachers
Validity
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Summary:We investigate experienced high school geometry teachers' perspectives on "authentic mathematics" and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it, provided he return to complete the argument later. Prompted by this episode, the teachers in our focus groups revealed two apparently contradictory dispositions regarding the use of the two-column proof form in the classroom. For some, the two-column form is understood to prohibit a move like that shown in the video. But for others, the form is seen as a resource enabling such a move. These contradictory responses are warranted in competing but complementary notions, grounded on the corpus of teacher responses, that teachers hold about the nature of authentic mathematical activity when proving.
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-008-9144-2