Journal Reflections

Thinking Through a Lesson: Successfully Implementing High-Level Tasks - 
       Many teachers don't successfully implement high-level math tasks. A high-level math task allows students to use reasoning skills with thinking skills. Tasks also have different ways of solving the problem so different students would solve the problem in their own way. Teachers can make sure to implement high-level math tasks by using TTLP (Thinking Through a Lesson Protocol). It is divided into three parts. Part one is choosing the mathematical task. Teachers plan the lesson in this part. This helps teachers never to loose sight of what they want to teach the students in math. Part two is supporting the students exploration of the task. Part three is sharing and discussing the task. The TTLP is intended to be used periodically. I think that is would be a useful and helpful strategy to have in my classroom. Like the article said it wouldn't be realistic to do it for every lesson every day. But it is important to use this strategy periodically. By then practicing this method periodically it will end up becoming into my everyday lessons because I will end up asking the TTLP questions. Teachers have described and I would probably agree with them that the TTLP is useful for planning, instructing, and reflecting. Three important aspects of teaching. The TTLP I think really allows teachers to think deeper into what and how they are teaching.

A Model For Understanding Mathematics - 
      What I found interesting, which I have never realized, is that mathematical understanding of a concept is different from understanding a procedure. Concepts are usually single terms such as equations or greater than. It is the most basic subject matter in math. The relationships between two concepts is called a generalization. On the other hand procedures are more in depth. Examples of procedures are constructing proofs, geometric constructions, synthetic division, and solving equations. The article then describes that teacher need to be making moves so that students understand mathematics. Teachers should move from physical to pictorial and then finally to symbolic representations. Students should then be able to take their symbolic representations and make physical and pictorial representations. I agree with this and I think I will implement this while I am teaching students. Making moves also helps teachers in making lessons plans, instructing and testing. So therefore it will be very useful to me when I am teaching an elementary classroom.