"Thinking Through a lesson" and "A model for understanding"

                  For this blog, I am going to discuss two different articles. The first article is called "thinking through a lesson." I found this article very interesting. This is because the topic of this article is a process that teachers can use when planning a math lesson that involves higher or more complex thinking. It is a three part process. The three parts are selecting and setting up the mathematical task, supporting students' exploration of the task, and sharing and discussing the task. The article then goes into detail about each part, and explains what questions teachers should be asking their students at each part during the process. This article also gave an example of the type of problem that would be great to use this process with. Another part of this article was talking about how you should be looking at your students prior responses and responses to the other tasks you give them so you know how you can help your students succeed even more.
                 The second article was called "A model for understanding." The first item discussed was the definition of understanding. The article gave seven signs that you will exhibit if you truly understand something. They are you are able to state it in your own words, give examples, recognize it in various situations, make connections between that topic and other topics covered or discussed, use it in multiple ways, foresee some of its consequences, and be able to state its opposite.The author also discusses understanding as a process. This process involves organizing and integrating knowledge according to a set of criteria. Another idea discussed is the idea that understanding is also a continuum. This means that students only have partial understandings. The rest of the article goes into detail by explaining how to understand different concepts in math and gives examples to go off of when planning lessons or activities. You can implement both of these articles into my teaching career by taking these processes to heart when I am planning my activities for my students. For example, if I was going to plan a problem that dealt with colored candies in a bag, I would go through these processes. From reading these two articles, I know now that it is important to keep these processes in mind to make sure that I am pushing each of my students to challenge themselves so they can succeed at their fullest potential.