Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form

Middle grades geometry and Measurement: Examining change in knowledge needed for teaching through a practice-based teacher education experience

Steele, Michael David (2006) Middle grades geometry and Measurement: Examining change in knowledge needed for teaching through a practice-based teacher education experience. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

Primary Text

Download (4MB) | Preview


Geometry and measurement represent topics of great significance in mathematics; however, efforts to teach this content in the middle grades have been formulaic, with students memorizing formulas and definitions without conceptual understanding. Moreover, students and teachers demonstrate gaps and misconceptions in their knowledge of geometry and measurement, particularly with respect to relationships between measurable quantities of geometric figures and proof. This study investigated changes in knowledge needed for teaching geometry and measurement through engagement in a practice-based course for preservice and practicing teachers. Pre- and post-course measures showed significant teacher growth along all three aspects of knowledge needed for teaching. Teachers grew in their ability to attack non-routine problems relating dimension, perimeter, and area and dimension, surface area, and volume; and in their use of multiple solution methods, multiple representations, and production of mathematically sophisticated solutions. Teachers also grew in content knowledge for teaching, becoming more representationally fluent and increasingly able to modify tasks to target key geometry ideas and about the affordances of different formulas for area and volume, and in knowledge of proof, including identification of the key aspects of the definition of proof, the role of proof in the classroom, and creation of proofs and proof-like arguments.Teachers grew in knowledge of mathematics for student learning as conceptualized by the five practices for productive use of student thinking: anticipating student solutions to a mathematical task, the use of high-level questions to assess and advance student thinking, selecting and sequencing student work to share, and connecting that work in ways that targeted the big mathematical ideas. Teachers also grew in their identification of routines, an example of practices that support teaching. Qualitative analysis of the course tied these results to opportunities to learn in the course.The results suggest that teachers can grow in their knowledge of content and pedagogy through practice-based teacher education experiences. The results suggest a value for focusing methods courses on particular slices of mathematical content. The design principles articulated in the analysis predicted teacher learning, and generalize to the design of teacher education experiences that enhance knowledge needed for teaching mathematics.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Steele, Michael Davidmds11@pitt.eduMDS11
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSchwan Smith, Margaretpegs@pitt.eduPEGS
Committee MemberAnsell, Ellenansell@pitt.eduANSELL
Committee MemberLeinhardt, Gaeagaea@pitt.eduGAEA
Committee MemberGreeno, James Gjimgrno@pitt.eduJIMGRNO
Date: 26 April 2006
Date Type: Completion
Defense Date: 5 April 2006
Approval Date: 26 April 2006
Submission Date: 20 April 2006
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: School of Education > Instruction and Learning
Degree: EdD - Doctor of Education
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: geometry; inservice teachers; mathematical knowledge for teaching; mathematics education; measurement; middle school; practice-based; preservice teachers; professional development; routines; teacher change; teacher education
Other ID:, etd-04202006-120111
Date Deposited: 10 Nov 2011 19:39
Last Modified: 15 Nov 2016 13:41


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item