Carolyn R. Kilday and Mable B. Kinzie have written an article called An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood. This article was published online in Early Childhood Education Journal on Friday. A starting point for this article (both authors work at the University of Virginia, in the U.S.) is that "the National Mathematics Advisory Panel (2008) has recently called for more research to determine the skills and practices underlying teacher effectiveness, and on methods for developing this capacity". The article gives an interesting overview of some of the major instruments for evaluating and measuring teaching quality in the U.S. Here is the abstract of the article:
The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics education, so too does the focus on teaching quality. This paper reviews nine instruments designed to measure mathematics teaching quality—their theoretical bases, foci, and psychometrics—and examines their appropriateness for administration in early childhood settings. Three of the nine measures are identified as having highly desirable characteristics, with one of them specifically designed for early childhood administration. The measures, our review process, and our recommendations for practice are presented. As school divisions and teacher educators examine teaching quality, they will be better able to support their teachers’ practice, and better able to reap the benefits in improved child outcomes.