Experienced colleagues’ observation feedback on mathematics instructional practices of first-time calculus teachers
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Having experienced colleagues observe new mathematics instructors’ teaching and provide feedback is an integral part of professional development for new teachers. This descriptive multiple-case study investigated the nature and influence of experienced colleagues’ feedback with the following questions: (a) What mathematical areas or mathematics instructional practices do experienced colleagues notice and address in their feedback to new instructors, and (b) In what ways do new instructors describe how they plan to modify their mathematics instructional practices based on experienced colleagues’ feedback? Categories of mathematics instructional practices were identified using the Mathematical Knowledge for Teaching (MKT) and Mathematical Understanding for Secondary Teaching (MUST) frameworks. Four new instructor/experienced colleague mentor pairs (eight participants) from the mathematics department at an undergraduate military institution were the subjects of this cross-case synthesis. During one semester, each pair completed one or two observation cycles consisting of a pre-observation meeting, classroom observation, and feedback session. I witnessed each portion of the cycle and separately interviewed each member after the feedback session. I analyzed meeting and interview data and journal writings. Findings suggest the primary feedback focus was on the new teachers’ knowledge of content and students (KCS) and teaching (KCT). Teachers’ reflection on the mathematics of practice and instructional actions primarily focused on mathematical representations and meaning, accessing and understanding the mathematical thinking of learners, assessing the mathematical knowledge of learners, and developing learners’ mathematical reasoning skills. This research suggests how to foster meaningful feedback and potentially establish a sustainable and effective form of professional development for mathematics teachers.
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