2023 Theses Doctoral
The Effects of Professional Development on Teaching for Conceptual Understanding in Algebra I: An Action Research Study
This action research study examined the effects of professional development on teaching for conceptual understanding in Algebra I. “Conceptual knowledge refers to knowledge of the underlying structure of mathematics - the relationships and interconnections of ideas that explain and give meaning to mathematical procedures” (Eisenhart et al., 1993). Conceptual knowledge is “explicit or implicit understanding of the principles that govern a domain and of the interrelations between pieces of knowledge in a domain” (Rittle-Johnson & Wagner, 1999).
The study took place in a large metropolitan school district. The participants for the study were two Algebra I instructors with varying pedagogical experiences. Participant #1 is a novice teacher with seven months of classroom experience at the start of this study. The participant holds an undergraduate degree in mathematics and a professional mathematics teaching license. Participant #2 is a tenured teacher with five years of classroom experience at the start of this study. The participant does not hold an undergraduate degree in mathematics and is licensed in special education, not mathematics.
The study was formulated in response to the growing difficulty in recruiting qualified mathematics teachers, and the increasing number of mathematics teachers with limited studies in mathematics. Concept-based instruction techniques were presented to participants through a series of six professional development workshops, the first three of which followed classroom observations, and the second three after a second round of observations. The study was qualitative in nature and the collected data were used to develop responses to two research questions. After classroom observations, a concept-based instruction checklist and scoring criteria was used to note evidence of concept-based instruction, as well as any changes to instructional strategies following professional development workshops. Student artifacts were also examined to note evidence of conceptual understanding. Study participants engaged in a semi-structured interview where they were asked to describe changes, if any, to their instructional practices as a result of participating in professional development on teaching for conceptual understanding.
The research findings suggested that effective professional development positively affects pedagogical practices in mathematics. After participating in a series of professional development workshops, the researcher observed shifts in participant pedagogical practices that included emphasis on using appropriate math language and encouraging explanations and justifications through questioning as tools for fostering conceptual understanding. Responses to semi-structured interviews suggest that teachers most value professional development that leads to positive impacts on student performance. An analysis of student artifacts demonstrated growth in student written responses and problem-solving approaches. Participant #1 stated: “Participating in this research has allowed me to wonder about the misconceptions and problems within my classroom; I am able to go over student coursework and come up with a solution to better help students with common errors.”
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More About This Work
- Academic Units
- Mathematics, Science, and Technology
- Thesis Advisors
- Karp, Alexander P.
- Smith, J. Philip
- Ed.D., Teachers College, Columbia University
- Published Here
- May 24, 2023