This study examined teacher pedagogical content knowledge changes through a
Middle School Mathematics Program professional development workshop, development
of noticing use of student representations, and teacher changes in hypothetical learning
trajectories due to noticed aspects of student representation corresponding to the
hypothetical learning trajectory model.
Using constant comparatives and repertory grid analysis, data was collected in
two phases. Phase one, the teacher pre-test, occurred at the beginning of the summer of
the 2003 professional development workshop. Phase two, the teacher post-test, occurred
at the end of the workshop. Twenty-four teachers supplied data on pre- and post-tests
during phases one and two. Eleven teachers were from Texas and 13 from Delaware. Six
Texas and eight Delaware teachers worked with the algebraic expression concepts. Five
Texas and five Delaware teachers worked with the equivalent fraction concepts. Four
mathematics education researchers from Texas, three from Delaware, and two from the American Association for the Advancement of Science participated in facilitating the
professional development.
The results show that teacher pedagogical content knowledge changes with the
help of a professional development partnership. The differences in knowledge can be
measured with a hierarchal cluster analysis of the repertory grid by analyzing
relationships between constructs and elements. Teacher hypothetical learning trajectories
change depending on student representations of what they do and do not know about
concepts.
The study encourages teachers to use knowledge of students’ representation
about a concept to determine what to teach next and how the concept should be taught.
Teachers should use different types of representations including formal, imagistic, and
action representations in teaching mathematical ideas. This will promote student
development in all process standards including reasoning and proof, communication,
problem solving, and connection.
The findings suggest that teacher pedagogical content knowledge can be
redefined during professional development partnerships. Furthermore, teachers’
knowledge of representation is varied and emphasis on the imagistic representation
should be explored further. Finally, professional development models that facilitate how
to extract what a student does and does not know based on representation, can be the
basis for defining hypothetical learning trajectories.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-3153 |
| Date | 15 May 2009 |
| Creators | Woodard, Leslie Dorise |
| Contributors | Kulm, Gerald |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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