Touchstone 10: Help students develop deep knowledge

Hattie et. al (2017) delineate three important types of knowledge in the mathematics classroom: Surface, Deep, and Transfer learning. Surface learning is the acquisition of rules and procedures that allow students to access new materials. While a student with only surface learning will not be a master of the content, surface learning is an important part of learning that must not be overlooked. However, learning and teaching at this level is much easier for most. Therefore, it is important to devote time to developing the ability to foster deep and transfer learning in students. Goodwin and Hubbell (2013) follow much of the same framework as in Visible Learning Mathematics. Students need to connect the current learning to their prior knowledge and require coaching to acquire coherence for the larger structures being learned. While there are many strategies for fostering such understanding, the two most effective I have found for the mathematics classroom is accountable talk and utilizing multiple representations. Hattie et al (2017) provide a broad description for the possibilities in the classroom. It begins with teachers pressing students to provide further context for all of their answers, ensuring that students provide evidence, and prompting students to challenge each other’s thinking. In short, expectations for discourse should be central to the expectations in a mathematics classroom and must be explicitly taught to students. However, accountable talk can be much more. Students, especially at lower grade levels, often lack proper syntactic structures and modes of academic conversation in addition to content specific vocabulary. In order to properly support student discourse, I have found that providing students with sentence frames and protocol for rigorous discourse ensures that students have both the content and format supports necessary for rich dialogue. The other effective strategy I have found for ensuring deeper understanding is the use of multiple representations. The authors in Visible Learning Mathematics have the following to say, “Deep learning is about making connections. In mathematics, one of the power forms of connection is noticing how different representations are related or similar”(Hattie et al 2017, p 169).  Mathematics task from simple arithmetic to the study of complicated polynomials, can benefit from encouraging students to create and analyze multiple representations of the concept at hand. Ensuring that students have rich thoughtful discussions and can connect a variety of mathematical representations, will go far in establishing deep learning in the classroom.  

References:

Goodwin, B., & Hubbell, E. (2013). The 12 touchstones of good teaching: A checklist for staying focused every day. Alexandria, VA: Association for Supervision & Curriculum Development.

Hattie, J., Fisher, D., Frey, N., Gojak, L. M., Moore, S. D., & Mellman, W. (2017). Visible learning for mathematics: What works best to optimize student learning, grades K-12. Thousand Oaks, CA: Corwin Mathematics.