Researchers at the University of Delaware (UD) propose a model for teacher development focused on analyzing teaching in terms of student learning to support teachers’ continual improvement over time (Hiebert et al., 2007). This model aims to prepare preservice teachers (PSTs) to continue learning from their practice once they begin teaching by developing four analysis of teaching skills: (a) planning instruction linked to specific learning goals, (b) gathering and evaluating evidence of student learning relative to the learning goals, (c) hypothesizing connections between the content taught and student learning, and (d) revising instructional plans based on the evidence collected. This process is then repeated over time in an effort to systematically improve teaching by collaboratively refining learning goals (Jansen, Bartell, & Berk 2009) and documenting effective hypotheses about instructional activities that support PSTs’ learning (Berk & Hiebert, 2009). In an effort to empirically test this model, faculty and graduate students at UD have applied the model to their own teaching within the university’s elementary mathematics teacher preparation program since 2002.

Research to date demonstrates that the model can not only improve mathematics curricula over time, but can support PSTs’ learning of particular mathematical content (Berk & Hiebert, 2009). However, whether and how this model improves instruction within the teacher education program over time, as evidenced in PST learning, remains largely untested. Berk and Hiebert (2009) document that PSTs’ ability to write subtraction and division of fractions story problems improved for one cohort of PSTs participating in this particular model. Building on their work, we examined PSTs’ learning of particular mathematics content across four cohorts.

Since 2002, all PSTs have completed a Baseline Assessment at the beginning of each of the four courses in the mathematics education component of the teacher education program (three content courses, one methods course). The Baseline Assessment consists of 22 items designed to reflect the mathematical knowledge elementary school mathematics teachers would draw on when teaching. While some items have undergone revision, 13 items have remained consistent. We grouped these 13 items into four topic areas: division of fractions, subtraction of fractions, place value, and percentages. Within each topic area, items include straightforward computational items as well as more conceptually-oriented items. These might also be considered items that assess PSTs’ common content knowledge and specialized content knowledge (see descriptions of mathematical knowledge for teaching: Ball & Bass, 2000; Ball et al. 2008).

Data was analyzed from four cohorts of PSTs between 2002 and 2010 for the Baseline Assessment administered at the beginning of both the first and fourth courses in the program. At the beginning of the fourth course, PSTs have successfully completed all three content courses.  Moreover, sufficient time has passed (8-12 months) to suggest that the knowledge PSTs demonstrate is knowledge they have and will continue to retain. Only those PSTs who completed all four mathematics education courses are included in our analysis (n = 68, n = 168, n = 132, and n = 131 for Cohorts 1-4 respectively).

Data analysis began with teams of two to three researchers coding individual PST’s Baseline Assessments. Coders were each assigned a set of 5-8 Baseline Assessment items and accompanying codes written to account for the correctness of PSTs’ responses and PSTs’ strategy use. Using 10 Baseline Assessments as the measure, an inter-rater reliability of 85% or higher was established within each team. Henceforth, items were coded by the individual coding team members. Next, to analyze PSTs’ performance over time across cohorts, we calculated the percentage of PSTs that provided correct responses for each item. We conducted Chi-Square tests of significance between each successive cohort to ascertain whether there were significant differences between cohorts in PSTs’ mathematical knowledge for teaching and to assure there were no differences between cohorts on the initial Baseline Assessments. Evidence of continuous improvement over time was defined as significant improvement between at least two of the four cohorts (e.g., between Cohort 1 and Cohort 2 and again between Cohort 3 and Cohort 4).

In the areas of division and subtraction of fractions, most PSTs in each cohort came into the program already demonstrating common content knowledge (solving number sentences requiring division and subtraction of fractions), and they maintained this knowledge even though the development of procedural fluency was not a goal of the program’s mathematics courses. Additionally, we see improvement in PSTs’ common content knowledge of percentages and place value. While the improvement of PSTs’ common content knowledge alone would be suggestive that the model is, indeed, producing results, there is the possibility that teacher educators are improving only in the ability to facilitate PSTs’ rote memorization of skills. The more compelling result is the improvement of PSTs’ specialized content knowledge across multiple topic areas. PSTs showed continuous improvement across cohorts in their ability to write division and subtraction of fractions story problems, and in their ability to evaluate student responses on decimal-number items.  Moreover, PSTs maintained their incoming ability to correctly identify common student errors on problems involving percent increases. Given that PSTs were assessed at least 8 months after course instruction, it seems the PSTs are both developing and retaining mathematical knowledge for teaching. This continued improvement in PSTs’ learning occurs even with at least seven different instructors teaching PSTs in any given cohort, suggesting such improvement is not due to the improved practices of particular instructors, but rather to the model itself. The process of collecting and evaluating relevant and revealing evidence regarding PSTs’ learning of particular learning goals, generating and testing hypotheses about instructional activities that support such learning, and making revisions to instruction that can be shared over time serves to improve the instruction of both new and experienced course instructors.

To increase student learning, instruction must improve over time. Rather than continually “reinventing the wheel,” teacher educators can analyze their teaching with respect to student learning in a way that generates a knowledge base for current and future instructors. The results of this study suggest that such a model can continuously improve PSTs’ mathematics learning.

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport, CT: Ablex.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

Berk, D. & Hiebert, J. (2009). Improving the mathematics preparation of elementary teachers, one lesson at a time. Teachers and Teaching, 15(3), 337-356.

Hiebert, J., Morris, A. K., Berk, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58, 47-61.

Jansen, A., Bartell, T., & Berk, D. (2009). The role of learning goals in building a knowledge base for elementary mathematics teacher education. Elementary School Journal, 109(5), 525–536.