Highlighting Content and Pedagogy in the Arizona Teacher Institute Master's Degree Program

Authors: Erin Turner, Rebecca McGraw

In our presentation we highlight key activities from three of the four content courses (i.e., Number, Algebra, and Geometry), and discuss how these activities not only deepen teachers' mathematical understanding but also how they provide opportunities to explore important issues related to mathematics pedagogy. Data from our evaluation team (i.e., classroom observations (RTOP), content knowledge assessments) is used to support the effectiveness of these content courses. For example, the following is data from the administration of the content knowledge measure with the first cohort of ATI participants. Since cohort II participants are only in their first year of the program, comparable data is not yet available.

Preliminary analysis of this data suggests that geometry continues to be the strongest area for the teacher candidates. Skill within the area of  number concepts area has increased, as has algebra.

Data from RTOP assessments support the impact of the ATI on participants. The results of the RTOP assessment for Cohort I teachers are as follows. The table shows the change from 2006-07 to 2007-08. (Since Cohort II teachers are only in their first year of the program, comparable RTOP data is not yet available.)

This data reflects that most participants made positive change or remained stable across the year. Seven participants demonstrated gains in the areas of Lesson Design and Implementation which reflects more preparation and explanation of daily lessons. Eight of the participants demonstrated gains in content which reflects the understanding of math concepts used in the teaching process. Seven of the participants reflected positive change in the area of Classroom Culture which provides an observational measure of students interacting around curriculum. Overall, participants averaged an increased change of 30 points.

Although not a direct measure of change in content knowledge, candidate survey data is also helpful as a tool for examining knowledge and growth of ATI participants. With respect to Cohort I, the area with the greatest increase is in the candidate's agreement that they demonstrate teacher leadership at their site.  Other areas of increase are in the use of problem solving, use of student exploration, confidence in teaching mathematics content, valuing problem solving and knowledge about mathematics content.  The area with a decrease is in the use of direct instruction which is not what is being taught in the program. The difference in scores from 2007 to 2008 ranged from -0.1 to 1.0. Overall for Cohorts I and II, on the self-report instrument, the area with the lowest average score was in the area of demonstrating teacher leadership with an average score of 6.6 out of 10 possible points.  When looking at answers as to why participants wanted to enter the ATI program, it is apparent that there is an interest in learning how to be a teacher leader at their site.  Other areas that were below an average of 8 points include providing opportunities for student reflection (7.6), utilizing student exploration (7.1), helping students to make connections to real life experiences (7.3), using differentiated instruction (7.2), knowledge of mathematics content (7.3), and use of direct instruction (7.7). The area with the highest average score is in listening to what students have to say and treating them with respect (8.8).  The other areas with scores with an average of more than 8 were feeling confident about teaching mathematics (8.4), using a variety of methods to help students learn mathematics (8.2) and the use of problem solving strategies with students. The overall average for all participants and all answers was 7.7.  It is interesting to note that although candidates had an average score of only 7.3 on feeling very knowledgeable about mathematics content, there was an average score of 8.4 in the confidence in teaching mathematics.