The relationship between teacher practices and mathematical goals in a non-traditional university mathematics course

This is a study of university mathematics teacher practices, such as, teachers' planning, minute-to-minute classroom decisions, construction and scoring of assessments, and evaluation of and comments on students' work (Speer, Smith, & Horvath, 2010). Prior to 2010 teacher practices were largely unexamined at the university level, although there were a number of examples at the K-12 level (Speer et al., 2010).;The two courses studied in this dissertation were an undergraduate transition-to-proof course and an unusual beginning graduate course on proof construction. Both courses were co-taught by two mathematics professors, Drs. P and Q, who share a rich background in mathematics and mathematics education. Each class was video recorded and extensive field notes were taken. During both courses the teaching/research team held regular debrief and planning sessions that were video recorded.;During previous iterations of the graduate course, the professors had observed a number of difficulties students encountered while writing proofs. Both courses in this study were designed to encourage students to do certain actions that the professors had found helpful and discourage other actions the professors found detrimental when proving mathematical theorems. The two courses were taught using almost the same notes written by the professors. The courses were non-traditional in the sense that they were focused on the process of proving mathematical theorems and not on specific mathematical content and were based entirely on the work of the students.;Although the enactment of the teacher practices differed between the two courses in this study, the teacher practices were of the same nature. I identified five classifications of teacher practices that occurred during the debrief/planning sessions and five classifications of teacher practices that occurred during class. The relationship between the teacher practices observed in the two courses in this study and the mathematical goals set by the teaching/research team is discussed. The professors' teacher practices were intended to support the mathematical goals related to enacting or not enacting the specific actions that the professors identified as helpful or detrimental to proving mathematical theorems. The professors' teaching practices were aligned with the professors' mathematical goals for the students.