According to this article in order to be able to understand something you must be able to do some of the following: give examples, explain it in your own words, make connections, use it in different ways, see the opposite, see the consequences, and recognize it in multiple circumstances (Davis, 190). This applies in mathematics as well. However, "Understanding a concept is different from understanding a procedure" (Davis, 191). The way I comprehend what the author is trying to say is that when you complete a problem, understanding how to get to your answer is different from understanding the concept behind it. When we teach students how to solve a problem we use logical thinking to get them there. Students ask questions, complete exercises, explain, and demonstrate to show their understanding. We must help students understand a concept by using physical representation and then moving to more symbolic methods. The way I understand it, if we don't teach students the concepts behind problems at their level they will have understanding the significance of the procedure. They may be able to complete the procedure, but have no clue what it means.
"Thinking Through a Lesson: Successfully Implementing High-Level Tasks"
The TTLP method of lesson planning for higher level thinking tasks focuses heavily on organization and a lot of preparation in advance. It talks a lot about how you need to plan out exactly what you expect from your students, what you expect to get from them, and how you can help them get to their correct solution. Although their may be more than 1 path to the solution their if often 1 solution. It is important to not to heavily guide students through their thinking process. Instead have questions prepared for every situation you can think of in order to be best prepared on how to guide them. The less you leave up to chance the better prepared you will be. I think that one of the most important things to take from this article is that all students learn and think differently and it is important to embrace that and to put in the extra effort that it takes to make sure that each and every student is able to explore their thinking processes.
Smith, M.G., Bill, V., & Hughes, E.K.
Thinking through a lesson: Successfully implementing high-level tasks.
Designing and Enacting Rich Instructional Experiences (pgs. 11-18)
Nice job:) Thanks Jen!
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