Over the course of the last week and a half I’ve taken my old lesson plan over the Fundamental Theorem of Calculus and made several revisions to it as it was examined through different frameworks. The lesson plan was originally very traditional (direct instruction to start, modeling with guided instruction, independent practice, and follow up the next day). However, as I looked at it through different lenses I made several modifications to the original lesson plan that made a better use of technology, made the learning more accessible and engaging, and leveraged networks in an effective way. You can check out my original lesson plan and my revised lesson plan directly below it, here.
I want to first highlight some of the major revisions I implemented and my justification for them. I started with the beginning of the lesson. I wanted to start with some sort of inquiry style activity to get students familiar with the concepts on their own terms. I did this because often when students are faced with tasks lacking apparent meaning or logic, it will be “difficult for them (students) to learn with understanding at the start; they may need to take time to explore underlying concepts and to generate connections” (Bransford, Brown, Cocking, 1999, p. 58). You can check out the activity I developed and the Wolfram Alpha animation it’s centered around.
In addition to making a shift towards inquiry, I wanted to leverage technology in a more effective way. To do that I decided that each student would do the activity mentioned above, on a Google doc. This will allow me to easily follow along and provide feedback as they work through the activity. Frequent and timely feedback is incredibly important to the learning process (Bradsford et al, 1999, p. 59). During the proof stage of the lesson, I will have them participate in a backchannel via Google Docs, providing me with questions they still have and a summary of their understanding of the proof. I can then send this out to a few teachers in my network and get feedback on how to approach whatever student misconceptions still exist. I will still be using “low tech” methods in the collaborative whiteboarding, but will be having them share out their solutions with the class in a more structured way. I will be pushing them to verbally explain their thinking process as they worked through each problem. This gives students another means by which to express their understanding (beyond writing) which breaks down barriers to learning by allowing multiple means of expression (Rose and Gravel, 2011).
One of my last revisions was to create a more focused prompt for students focus on in there weekly blog reflection. My research on Gifted and Talented Learners suggested that it’s good for students to consider how they used inductive and deductive learning so I built that into the learning prompt (Sheffield, 1994, p. xvi). In addition to the blog post post they will also have to give constructive feedback on their blog posts to each other. They will look at a peer’s post through a critical lens which will help students further explore their own understanding of the concept.
Thoughts on the Revision Process
This process has allowed me to see assessment and evaluation differently. Some of the technology I’ve implemented will allow me to assess and provide feedback during and after the lesson in a much more effective way. In other lessons I want to build in a better continuous feedback loop to help students understand where they’re at in the learning process. I tried to do this before, but I think I have some techniques that will allow me to do a better job of it in the future.
More broadly speaking I’ve grown as a professional in this process. Now that I’ve studied the constructivist approach to learning, Universal Design for Learning, the TPACK framework, and network learning I will be able to better utilize these frameworks in my other lessons. I won’t do it in such a formal way, but as I revise in the future I will look through each one of these lenses to create effective lessons that integrate technology and reach more learners. These are powerful tools that I didn’t have prior to going through those revisions. I think being a quality educator means being able to evaluate lessons from different perspectives and I think I’m closer to that standard now.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.
Rose, D.H. & Gravel, J. (2011). Universal Design for Learning Guidelines (V.2.0).Wakefield, MA: CAST.org. Retrieved from http://www.udlcenter.org/aboutudl/udlguidelines
Sheffield, L. J. (1994). The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standards. Storrs, CT: The National Research on the Gifted and Talented.