International Portal of Teacher Education

Source: Teachers College Record, Volume 118, No. 5, May 2016.
(Reviewed by the Portal Team)

In this article, the authors explore the level, variation, and change in teacher knowledge and instruction in the first two years of teaching, the relationship between Mathematical Knowledge for Teaching (MKT) and more distal measures such as certification.

Methods
The participants were 45 middle school math teachers in their first two years of teaching in 11 districts of varying size and urban status in two southeastern and two mid-Atlantic states.
This is a longitudinal (two-year) study of natural variation, which includes descriptive, correlational, individual growth curve, and regression analyses.
Based on multiple administrations of survey data, MKT assessments, and classroom observations using the Instructional Quality Assessment (IQA), teacher educators developed measures of (a) the rigor of lesson activities and classroom discussion, (b) the quality of classroom discussion, (c) the relative emphasis on procedural versus higher-order cognitive demands, (d) the proportion of time spent on basic versus advanced math topics, and (e) the number of topics covered, or instructional breadth.

Level, Variation , and Changes in Knowledge and Instructional Quality
The authors found that many beginning math teachers had neither a degree in math nor substantial coursework in math. These results suggest that despite recent attempts to upgrade the subject-area expertise of middle school teachers, there is still room for significant improvement for states and districts to do a better job of ensuring that math teachers have a firm grounding in subject-matter knowledge.

They also found that beginning teachers in this study generally had low levels of knowledge (as measured by the MKT), a balanced approach to cognitive demands, low levels of discussion quality, and substantial across-teacher variation in topic coverage.
Furthermore, this study provides empirical evidence documenting that in their first two years of teaching, middle school math teachers improved in their math knowledge and improved on some but not all measures of instructional quality. Specifically, on average teachers showed small but significant growth on the MKT in the first two years of teaching and significantly decreased their coverage of basic topics and increased their instructional breadth (number of topics covered).
Findings from the study suggest that pre-service preparation and in-service mentoring would do well to provide opportunities for teachers to practice and receive feedback on the use of particular instructional strategies, in combination with building knowledge for teaching mathematics.

The Links Between Knowledge and Instruction
The authors found no direct relationships between MKT and instructional quality, although our findings suggest possible relationships. The authors found no direct relationships between teachers who scored higher on the MKT and task rigor, the use of higher cognitive demands, or less time on basic topics.

Using Distal Knowledge Measures to Predict Instruction
The authors found little evidence that MKT is a better predictor of instructional quality than distal measures, but they did find suggestive evidence that MKT may help to explain their predictive power.
They also found suggestive evidence that taking more advanced math courses predicts desirable teaching practices.
A possibly novel finding is that the number of weeks of student teaching in math was consistently related to more rigorous instruction and less emphasis on basic topics. The authors found that having 17 weeks or more of student teaching, even with no formal mathematics training, was related to less use of basic instruction.
Thus, the authors emphasize that increasing the length and quality of preservice teacher apprenticeships could be a fruitful avenue to improving teacher preparation programs.
The authors conclude that these results have implications for shaping teacher preparation programs, teacher in-service professional development, and certification policies.