New Data: GPS or Understanding?

In Geometry in Construction, we believe that what gets measured gets improved.  Throughout the past six years, our math program is analyzed by a third party research team of doctoral candidates from the two largest universities in Colorado.  During this time, we have experienced staff turnover, district and state budgetary crises, increased pressure to push a higher level of mathematical standards (Common Core), and local demand for more credits to graduate.  Despite these challenges, data analyses continue to show a trend where students from Geometry in Construction perform at a higher level than other Geometry students.  More information about data analysis is available at

The following section summarizes research conducted by Susan Thomas, a doctoral student from the University of Colorado at Boulder in Research Evaluative Methods.  The figure below illustrates these trends by averaging state test scores for the past three years (2010-2012).
Colorado State Test Scores Longitudinal Mean Average
GIC:  Geometry in Construction at Loveland High School

LHS:  Traditionally taught Geometry classroom at Loveland High School
MVHS: Mountain View High School Geometry, our district’s school of the arts and Project Lead the Way high school
TVHS:  Thompson Valley High School Geometry, our district’s AP high school
BHS:  Berthoud High School Geometry, our district’s math and science high school and Project Lead the Way high school
Important Note:  This is an average over 3 years, which provides a general idea of performance trends.
Method of Evaluation: Linear Regression modeling.
How Linear Regression Modeling Works: Using current data, the linear regression model will predict state standardized test (CSAP/TCAP) Geometry scores based on several variables, such as previous test scores, demographic student information, as well as enrollment in particular Geometry courses (e.g., Geometry in Construction and traditional Geometry classes).
Results: These variables explain 66.3% of the variance of state standardized test (CSAP/TCAP) Geometry scores.  Geometry in Construction at Loveland High School was a significant variable in the model, with a coefficient of 14, which means that on average, being enrolled in Geometry in Construction at Loveland High School added 14 points to a student’s state standardized test (CSAP/TCAP) Geometry score.
Why do we believe Geometry in Construction students outscore their peers?
On a recent trip we discovered an intriguing explanation to answer this very question.   Simply stated, students in Geometry in Construction have fewer opportunities to “GPS” their way through the program.
On our last consulting trip we used a GPS unit we affectionately refer to as Maggie (Magelan). These smart devices are great for getting people from point A to point B.  However, we found ourselves lost when Maggie malfunctioned mid-drive.  We had simply followed the step-by-step directions Maggie provided without paying attention to where we were headed.  We had done what thousands of people do daily and put all of our trust in the technology; this is very similar to how students use memorized formulas in many traditionally taught math classes. We could not back track or trouble shoot our route without some serious remediation; this is the very same thing that often happens when students attempt to solve unfamiliar math problems.  In this case, our solution was to find a gas station and do exactly what the majority of men hate to do while in unfamiliar territory: ask for directions.
As math teachers, we are often times guilty of “GPS-ing” our students.  We are really good at giving 5 steps to completing the square or 3 steps to solving the equation.   Many of us have had successful careers by doing this.  Have our students been as successful?  Do our students have a solid understanding of the mathematics?  Do they understand why they are doing “the steps”?  Can they apply it to real world situations?