As the Common Core State Standards are being rolled out nationwide, mathematical argumentation—the line of reasoning that shows or explains why a mathematical result is true—has become an important skill for math teachers and students alike. To teach argumentation skills to teachers and bridge the gap between professional development (PD) and classroom practice, SRI Education’s Center for Technology in Learning developed the Bridging Professional Development program. Funded by the National Science Foundation, the program has helped middle school math teachers learn improvisational techniques for teaching mathematics argumentation to their students.
We are now starting the next phase of the program, which will take place in the District of Columbia Public Schools (DCPS) as part of a district-wide initiative that focuses on argumentation. Over two years, researchers will focus on PD with teachers and staff across this major urban district. Teachers will co-design new online tools to enhance teachers’ learning and ability to weave mathematics argumentation into their curriculum.
The new tools will help teachers in the planning and enactment stages of teaching, both of which are essential for argumentation. Our prior research found that learning about and practicing improvisation can improve teachers’ skill in teaching argumentation. As disciplined improvisers, teachers need to be able to respond in the moment, especially in argumentation where students are thinking for themselves and coming up with novel ways of expressing ideas. This is a new demand on teachers: to not only react to what students are saying, but also to move students towards being generative in mathematics rather than merely being receivers of knowledge.
One area of focus in our workshops is visualization planning, where a teacher will describe aloud what a student might say about a mathematical subject, and then describe what she would say in response. While the teacher is talking through this argumentation process, another teacher will write down everything the first teacher is visualizing, and then turn it into a lesson. As part of the new project, we’ll design an online tool to support this process, enabling the teacher to do this independently. Using a computer or mobile phone or tablet, the teacher can describe her lesson just like she would to a partner, and the online tool will turn it into text, which will then be formatted into a lesson.
Teachers also need a bank of examples from which to draw when they’re developing this new practice. The online tools will include a searchable bank of mathematical arguments, specific to the middle school math topics that teachers will be focusing on in their curriculum.
Additionally, we plan to include a series of teaching games that are adapted from improv games. In each game, teachers are given the rules and character for role-playing, as well as the setting and problem. The teacher plays the game by improvising a scene and deciding what to do in the moment. Responding to these complexities is challenging. Of course, teaching in general can be challenging, but this is a different kind of work than giving a traditional lesson, with definitions first, examples second and practice problems third. Teaching for argumentation requires significant improvisation.
This expansion of the Bridging program with DCPS provides exciting opportunities for additional research, where we will measure how much argumentation the teachers used in their classrooms before the project, compared to the amount of argumentation at the end of the project and the change over time. And, with the advantages that new online tools will bring to teachers, we’ve strengthened the program and designed it for success.
While our current work with Bridging is mathematical, we believe the Bridging approach could work with other content areas where teachers are aiming for complex student outcomes and have to acquire challenging new practices. In particular, the challenge of learning to teach 21st century skills—with high cognitive, creative and communicative demands—could be addressed through Bridging.