Measuring Middle School Teachers’ Mathematical Knowledge Of Teaching Rate And Proportionality


Shechtman, N., Roschelle, J., Haertel, G., Knudsen, J., & Vahey, P. (2006). Measuring middle school teachers’ mathematical knowledge of teaching rate and proportionality. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.


The overarching purpose of the Scaling Up SimCalc research program is to test at scale the following hypothesis: A wide variety of middle school teachers can use an innovative integration of technology and curriculum to create opportunities for their students to learn complex and conceptually difficult mathematics. Specifically, we are investigating if teachers from across the state of Texas can use a specially designed replacement unit and SimCalc software to help their students learn mathematics important to the Texas state frameworks, as well as content that goes beyond the state framework—the beginning pieces of the “mathematics of change,” leading to Calculus.

The specific components of our intervention provide access for teachers and students to important mathematics through SimCalc. The components include:

  • A replacement unit that addresses state standards and specialized “mathematics of change” content in an easy-to-use form for teachers.
  • SimCalc’s Java Math Worlds software that uses simulations of motion (and general accumulation) and dynamically linked representations.
  • A three-part training, including a summer and fall session, totaling six days.
  • Availability of software and curriculum trouble-shooting during the school year.
  • Teachers’ use of the materials for 2-3 weeks in their classroom, replacing the materials they would usually use to teach the same content.

We are testing our hypothesis using a randomized experimental design. Our primary outcome measure is student learning of mathematics. “Math knowledge for teaching” (MKT) is also a potentially important variable. We measure teacher MKT using a paper-and-pencil assessment administered before and after the summer workshop. We will use results from this assessment to determine: (a) what relevant mathematics, if any, teachers learn during the summer workshops, and (b) the extent to which teachers’ MKT is related to student outcomes.

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