Secondary Lenses on Learning:
Leadership for Mathematics Education
in Middle and High Schools - Survey
Making Sense of the Leadership Function Data
Our survey presented respondents with a list of 30 leadership functions and asked them to indicate the degree of responsibility they had for each. Each item was represented by a five-point Likert-like scale, in which 0 was labeled as “no responsibility” and 4 was labeled as “sole responsibility”. If respondents had no responsibility for a leadership function they were asked to write in the position of the person who was responsible.
In this particular research project, schools and districts participated in the Lenses on Learning Secondary course, and thus this study, by sending teams of leaders who had responsibility for the school’s or district’s mathematics program. These teams were to include any of the following: principals, assistant principals, math department heads, teachers, guidance counselors, special education teachers, and central office staff. The purpose of the course was to extend participants’ understanding of effective mathematics instruction, collect data and analyze the degree to which their schools and districts were providing adequate mathematics instruction for all students, and develop and recommend action plans in targeted areas. Therefore, respondents in this research were often configured in district or school teams that were meaningful with respect to policy-making for mathematics education.
With the data provided by this survey it is possible to analyze the LCK for mathematics held by a number of administrators, by position across the national sample; for example, all principals, all assistant principals, all math coaches, all guidance counselors, etc. It is also possible using the data provided by this survey to analyze the LCK for mathematics held by the teams of administrators from a school or district who reported having responsibility for particular leadership functions with respect to the mathematics program -- for example, choosing new curricula, hiring teachers, communicating with stakeholders, etc. Some of these functions are district-wide, others are largely school-based functions.
We provide below an example of how these data can be scored and displayed to produce an analysis of the collective LCK available to district teams responsible for particular leadership functions. A display of the data for analyzing the LCK available to a team can look like the following:
TABLE 1
Mathematics Knowledge for Teaching, Level of Comfort, Views about Math, and Classroom Reflection (Pedagogy) Score, for Madison District* by Position (N=10)
Position
z-score**
Reflection1. * Names of districts are pseudonyms.
** The permission to use the mathematics knowledge for teaching items that we received from the University of Michigan included the stipulation that we not report raw scores but standardize them. Z-scores take the average response to a given item by all participants and then determine how far a given participant’s response is from the mean. That result is then divided by the standard deviation to determine how many standard deviations above or below the mean a given participant’s response on that item is. For the results reported here we took the z-score of the number of problems each participant answered correctly.
To extend the example, by identifying which members of the Madison team reported responsibility for a particular leadership task one can characterize the LCK for mathematics available for performing that function. For example, the chart below shows the LCK for mathematics of the members of the Madison district team who reported having responsibility for developing a vision for the mathematics program.
TABLE 2
LCK of Leaders Developing a Vision for the Mathematics Program
Level of Responsibility, Mathematics Knowledge for Teaching, Level of Comfort, Views about Math, and Classroom Reflection (Pedagogy) Score, for Madison District by Position (N=9)
In Madison, reported responsibility for developing a vision for mathematics is quite widespread, with four team members, nearly half of the group, reporting substantial responsibility (3 or 4) and five reporting little responsibility (1 or 2).
It is striking to note how relatively limited is the math knowledge for teaching (as measured by our assessment) of virtually all of the decision-makers who reported substantial responsibility for this function (3 or 4), and how relatively progressive are their beliefs about how students learn mathematics and how it should be taught. All respondents who reported substantial responsibility (scoring 3 or 4) scored above the mean (3.5) on the Views of Math Likert measure of beliefs and all scored 3 or 4 on the Classroom Reflection, indicating that they at least could recognize features of standards-based methods of instruction, although only one with substantial responsibility was solidlyoriented toward student thinking in mathematics classrooms (scoring 4). (Two members of the Madison team who reported little responsibility also had scores of 4 on the open-response beliefs item.)
For an extended discussion of the scoring and analysis methodology that underlies this kind of role analysis and an analysis of our data with respect to the collective LCK available to a number of school and district teams reporting responsibility for leadership functions related to the mathematics program, see Nelson, B. S., Stimpson, V. A. & Jordan, W., (2008). Leadership Content Knowledge for Mathematics of Staff Engaged in Key School Leadership Functions. (Paper presented at the annual meeting of the University Council of Educational Administration, Washington, D.C. This paper will appear in the Proceedings of the conference.)