I was really intrigued by the readings this week since I was a student who struggled with math throughout school. The readings helped verify that struggling is not necessarily a bad thing, it can help you progress even further in the long run. If I had realized this in my earlier years of learning, I may have enjoyed my math experience more.
From doing the readings, I feel as though TTLP is imperative for lesson planning in order to promote understanding from students. By preparing for various outcomes ahead of time, it may be easier to push lessons back in a direction that can help students understand the learning goal. You cannot expect that continuously pushing ideas on a student will help them understand. Instead, it is our job as teachers to take what they already know to further push the students' understanding.
In DMI Ch. 3, many teachers struggled with place value and the questions their students had in terms of providing responses to the questions. By implementing TTLP, teachers could have used what they know of their students' knowledge to anticipate the students' thinking in order to push their understanding. Having questions to help draw out responses that could lead students in the direction of understanding are important for teachers to form ahead of time. Although some teachers did ask great questions, most stories were kind of open-ended so it was difficult to verify if the questions helped the students understand the concept of place values and counting. I observed a similar situation in the 5th grade classroom this week when Mrs. C. was thrown off by the lack of understanding in adding fractions with different denominators. She attempted to use clocks to show students how to complete the task, but many students were extremely confused. Since she realized most of the students were just getting frustrated, Mrs. C. decided it would be beneficial to stop the math lesson for the day and try to come up with a more meaningful way to teach the concept the next day. It was beneficial to cut the lesson short that day and plan something to help the students understand the next day; however, if Mrs. C. had implemented TTLP, she could have continued on with the lesson and used the students' questions to help drive the lesson to help them understand.
My favorite article was the The Value of Mistakes because it shows that students truly learn concepts by making mistakes. If we take this out of the math context, this becomes pretty obvious. Take a relationship for example. All of your friends and family can tell you that someone is not right for you but it takes multiple mistakes and learning how to work through these mistakes to finally make you see that what everyone else was telling you was right. This is parallel to what I have seen in math as a student and observing in the classroom. Regardless of how many times a teacher tries to repeat their method of completing a math problem, some students cannot completely come to terms with understanding if they don't see how and why that concept works. In the 5th grade classroom, the students have been working on reciprocal fractions and lowest terms. The teacher has a saying, "Whatever you do to the top, you do to the bottom." This saying is supposed to help the students remember how to create reciprocal fractions. Most of the students know how to do this but it seems as if they are not aware of why they are doing it and how it has any value to them. Although I know Mrs. C. does have good intentions by trying to find a way for students to remember how to create reciprocal fractions, the students are not able to form complete understanding of the concept because they have not had to struggle through understanding how to do this, which could help them understand why reciprocal fractions are important.
Although it may be difficult to implement TTLP everyday in extensive lesson plans, as one of the teachers said in the article, it's important to have three questions in mind when generating lessons everyday: 1. What are students' misconceptions? 2. How am I going to organize the work? 3. What are my questions? Since I know it will be impossible to create long lesson plans every day, I can at least incorporate these questions when I think about how I'd like to introduce concepts to my future students.
