Powerful Tool for Learning Geometry

In the spring and summer of 2006, SERP launched its first multi-district field site in collaboration with MSAN and its member districts. During the initial partnership meetings, superintendents set parameters to guide the work. On the basis of decades of experience, they put off limits:

• a supplemental approach (because these are always the first to be cut when budgets tighten)
• an intervention that targeted lower performing minoritized students alone (because this would exacerbate stereotype threat)
• a whole new curriculum (because too much time is lost in political battles to introduce the curriculum, and performance drops while a new curriculum is learned)

District math coordinators emphasized that asking teachers to substantially change the way they teach was not going to work. One argued that teachers needed a “back door” approach in order to see the benefit of a new practice without having their primary routines uphended.

Among the team of mathematics researchers recruited by SERP for the partnership work, Ken Koedinger (Carnegie Mellon University) saw a potential solution. Decades of laboratory research demonstrate that worked examples interleaved with problems to solve are an effective way to improve student learning compared to assignments that include only problems to solve. Over a six-year period, the SERP-MSAN partners worked to design, test, and redesign assignments that interleaved worked examples that targeted common misconceptions. After many waves of experimentation using rigorous research designs, AlgebraByExample emerged as a finished product with 42 assignments.

MSAN Partner School Districts: AlgebraByExample

• Ann Arbor Public Schools, MI (2011-2013)
• Arlington Public Schools, VA (2007-2010, 2012-2013)
• Chapel Hill-Carrboro City Public Schools, NC (2010-2012)
• Evanston Township High School, IL (2007-2010)
• Evanston/Skokie School District 65, IL (2007-2013)
• Green Bay Public Schools, WI (2010-2012)
• Madison Metropolitan School District, WI (2007-2013)
• Shaker Heights School District, OH (2007-2013)

Watch what MSAN Teachers Said About AlgebraByExample

Analysis of SERP's AlgebraByExample materials revealed that many misconceptions have their roots in earlier grades. Addressing elementary math misconceptions before middle school is doubly important because early student failure can decrease motivation, hindering students’ future success even further. Traditional practice activities do not address common misconceptions about the problems to solve, allowing misconceptions to linger long after elementary school. Addressing this early is even more important as standards for rigor rise. Better-prepared students will free teachers in higher-level math courses to focus on grade-level content, making it more likely that students will succeed in higher-level math. From 2015-2019, the SERP-Temple team received funding to develop and test MathByExample. In 2019, the MathByExample materials emerged as a finished product with 139 assignments aligned to 4th and 4th grade math standards. 

Watch Video about MathByExample

During the original partnership work to create AlgebraByExample, many partner algebra teachers also taught one or more classes of geometry. As they piloted the AlgebraByExample assignments in their algebra classrooms and saw first hand the insight that the worked-example approach provided on student thinking, they started asking about what similar assignments for geometry would look like. Once AlgebraByExample was released, the requests for Geometry assignments multiplied. But adapting the approach to Geometry content presented a new challenge, as much more of geometry is visual, spatial, and conceptual, rather than the general procedural nature of algebra or fractions learning.