Growth in Teachers' Mathematics Content Knowledge for Teaching
We identified the Learning Mathematics for Teaching (LMT) instruments as the most appropriate for obtaining measures of participants' mathematical content knowledge for teaching. The LMT measures situate mathematical tasks in the context of teachers' day-to-day work. For example, typical items might ask the teacher to examine student work and determine its mathematical correctness or generalizability. The LMT measures have been validated in the sense that there is a positive effect size (comparable to SES) of teachers' LMT scores on the student achievement in their classrooms.
A total of four forms of the instrument were used: two forms (A and B) for teachers at K-5 elementary grade levels and two forms (A and B) for teachers at middle/secondary 6-12 grade levels. One of these forms was administered to the teachers at the beginning of the first summer institute. The other form was administered at the conclusion of the first summer institute. The first form was administered again at the conclusion of the second summer institute and the second form was administered again at the conclusion of the third summer institute. For example, approximately half of the elementary school teacher participants were administered these measures in the following sequence:
| pre-summer 1 | post-summer 1 | post-summer 2 | post-summer 3 |
| elem form A | elem form B | elem form A | elem form B |
The other half of the elementary school teacher participants were administered these forms in a B-A-B-A sequence. Similarly, half of the middle/secondary school teacher participants were administered the middle/secondary forms in the A-B-A-B pre-post-post-post sequence and the other half were administered the forms in the B-A-B-A sequence. The LMT forms used had been previously administered to similar populations and we used the LMT scales for determining IRT scores for participants. The three summer institutes took place in 2005, 2006, and 2007, so we have completed the data analysis across all administrations of these content knowledge measures.
