Secondary Lenses on Learning:
Leadership for Mathematics Education
in Middle and High Schools - Survey
Doing Mathematics Section
Our survey measured respondents’ ability to perform certain computations involving fractions and algebra, and their conceptual knowledge for the teaching of pre-algebra and algebra.
The computational items included 6 problems that required respondents to:
Express the product of two mixed numbers as a whole number or a mixed number. Express the quotient of a mixed number divided by a proper fraction as a whole number or mixed number. Determine the quotient of two decimal numbers as an exact decimal number. Evaluate the value of an expression that includes subtraction and multiplication using order of operations. Solve a quadratic equation that is easily factored. Determine that there is no solution for the given equation that includes an algebraic fraction. The conceptual items on the survey are not a measure of the kind of mathematics knowledge held by the general public or used in other occupations like accounting or engineering. Rather, the mathematics items on our survey are specifically designed to examine conceptual aspects of mathematics that it would be necessary to know if one were to be teaching children (Hill, Schilling, & Ball, 2003). We chose these items from the pilot of the middle school SII instrument on the assumption that, in order to observe mathematics classrooms in a discerning way, administrative leaders need to be able to understand what the teacher is doing, mathematically.
Below is a released item from the SII middle school instrument:
This problem involves identifying an expression that correctly represents a rectangle with particular dimensions, differentiating area from perimeter, and using the distributive law in flexible ways.
Teachers must not only recognize correct expressions for representing area but must also understand what students might be attending to when they write inappropriate responses. Such understanding allows teachers to challenge and extend students’ invalid or limited responses as a strategy for helping them develop robust understanding. Through problems like this one, our survey assesses mathematical knowledge particular to teaching rather than to other occupations or possibly present in the public at large. We believe that principals and other classroom observers need this kind of mathematics knowledge if they are to be able to evaluate whether the teachers whose classrooms they are observing are responding appropriately to the mathematical thinking of the students in their classes.
Survey Overview Assembling Your Own Mathematics Knowledge The Survey - section by section for Teaching Section Part 1 Background Information (pdf) Coding Schemes and Sample Responses Part 2 Teaching and Learning Mathematics (pdf) a. Coding Scheme for a Classroom Reflection Section A A Classroom Reflection (pdf) BELIEFS Scoring Scheme Sample Responses Section B Views About Math (pdf) b. Making Sense of the Leadership Function Data Part 3 Doing Mathematics (note that on the survey, itself, this is labeled Part 2, Section C)
