Math TNE Work for 2006-2007

The 2006-2007 work within Mathematics in TNE is concerned with the math department content courses for future multiple subject teachers—namely Math 210, 310 & 310L. Our goal is to improve our candidates’ success in boosting achievement scores for their pupils. We should mention that there is other work involving collaboration with Elem Ed 472 (Math Methods) and the field experience that will be described elsewhere. In the past we have changed the form and structure and extended Math 391, the early field experience for secondary math teacher candidates.

TREATMENT:

  1. Teach conceptual understanding as well as procedural proficiency.
  2. Engage candidates in classroom tasks such as explanation and discourse.
  3. Present different representations—verbal, pictorial, physical manipulatives and symbolic/analytic expressions. In addition, our students (and their pupils) should be practiced in articulating the links between these representations and how these representations bolster understanding.
  4. Emphasize solving demanding problems that stretch students’ capabilities and force them to make deeper connections with concepts.

Each of these factors has been cited in international studies including the work of both Liping Ma and Stigler & Hiebert et al’s TIMSS studies.

RELIABILITY OF TREATMENT:

While it is difficult enough to find teachers who will all endorse a common goal and activities on how to achieve it, we have a core of several regular teachers who have attended several of our past workshops, study groups and public lectures who think along similar lines andsupport these common goals. In order to insure that we are actually, reliably doing what we intend and also to work together toward improvement, we have video taped several our classrooms and are viewing and analyzing our teaching. This includes the teaching of Basta, Gold, Mason (the current Teacher in Residence) and Zeitlin. In order to assess the extent to which we are adhering to our treatment goals we have started using part of a video coding rubric developed by Deborah Ball and her colleagues for validating her work on survey Mathematical Knowledge for teaching.

MEASURING SUCCESS:

While we can not directly measure the effect of our candidates on pupils in the short term we have found a measure, which is reliable, valid and correlated with boosting pupil achievement on a national achievement test (the Terra Nova).This is the test of MKT (Mathematical Knowledge for Teaching) aka CKTM (Content Knowledge for TeachingMathematics), developed by Deborah Ball & Heather Hill, see We have given pre and post tests since spring 05. We can report that our students’ gains have been stronger than those shown by a large group of in-service teachers who were used to calibrate the test during summer professional development in California. For the most part, in-service teachers’ scores are stronger, as you would expect, although our students seem to do as well or better in geometry. I speculate that the actual topics of geometry are used only obliquely in the classroom so recent study is an important factor.

SCALABILITY:

We have not lead the whole department to take up our ideas although the value of student explanation seems to be more accepted. The current chair and coordinators of math 210 & 310 are not administering the MKT instruments and are attempting to mandate a single choice of text which is good but not our first choice. There seems to be considerable support in the department for allowing faculty to teach courses as they deem appropriate, so that we expect to be able to continue our work with those teachers who are interested. With the recent turnover of the old coordinator of one of these courses we are exploring the development of a more rigorous evaluation of various approaches.

We have built up a data base of scores and the students that we have had in the past are now starting their field experiences. We are tracking the success of our students and are assessing their success at various points in the pathway through the math methods course, and student teaching and also are beginning to influence the evaluation process in the field experience—Hillary’s work on this will be described in much greater detail in another document. We expect to continue building the database in the next several years.

Joel Zeitlin & Hillary Hertzog

December 2006