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Audience: my intended audience is primarily other math teachers. While blogging is a general tool that I see being helpful to all teachers and the TPACK approach is, again, general to all teachers, using dynamic geometry software is specific to math teachers. That said, I hope that my piece is reflective enough that all teachers can benefit from thinking about my approach.
The Wicked Problem: Students both being capable of working problems and having a deep conceptual understanding of mathematics is difficult to achieve in any classroom.
The Solution: There is not a magic bullet; however, I believe the following approach will work with many content areas in mathematics. A dynamic geometry piece that allows students to explore a concept. This is supported by prompts and other questions that students are given before and during their exploration to help guide their thinking. In addition to being able to calculate answers, students will have to write in their blog about their understanding of the concept.
This allows me as the teacher to check their conceptual understanding, allows students to make a personal and deep connection with the mathematical concept and still allows for students being able to solve practice problems and story problems. Group work can be part of this solution. This approach allows for many different learning styles, is student centered given curriculum constraints and has tasks ranging the gamut of Blooms Taxonomy.
For further analysis of TPACK and how this approach integrates technology, content and pedagogy please read Blog Post B.
For a deeper look at the problem, thoughts about logistics and future plans, please read Blog Post A.
The approach outlined above requires more work than simply giving students the page numbers, a few minutes of notes and a problem set. However, the good news is that in addition to providing a much better educational experience for students, this approach can be implemented incrementally. If the blogging portion is overwhelming, this can be changed to pencil and paper essay. Not all content needs to be taught this way initially, and this would probably be a mistake in any case. However, this approach could initially be taken with one or two lessons a class where students struggle and this TPACK approach is most appropriate. Additional lessons and units can incorporate this method in following trimesters. This is extra work but does not need to be a crushing amount of work while supporting our students understanding of mathematics.