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.
Tracy, I loved your connections with the readings! As I was reading, TTLP was sounding more and more like our math student interviews we have to do this week. It was so helpful to read how beneficial this activity is because we will be practicing it in class and seeing first hand how these results can alter a lesson plan.
ReplyDeleteAs students, still learning how to become a constructive teacher, some of these activities and concepts seem so easy to implement and we can see how beneficial they would be, however, like Tracy said it's not that easy to make sure you're using TTLP everyday for every lesson. I think as student teacher we don't see how hard the school day can be and how difficult it will be to implement all these constructive strategies and ideas. I love the three questions you listed from the article. This is awesome that you have them pointed out and listed because some information like this in readings people may miss and not see but can be so vital to understand and utilize.
In my placement I have seen something similar to Tracy but instead of the teacher realizing the students were confused, I realized and didn't have answers to questions. I become frazzled when other students were asking me how to complete a problem or just simply saying I don't get it. I felt embarrassed because as a student teacher I am still trying to learn what students misconceptions may be and how to answer them. I wish my teacher could have been walking around and hearing the questions because i don't think she knew how many misconceptions there were among the students. I think doing that student interview will be somewhat like TTLP and i can learn how to incorporate and understand students misconceptions!
I really got a kick out of reading you ladies' posts. I think that we all benefited a lot from the reading about TTLP, before we are all becoming more cognizant of effective teaching practices. I agree, it does sound a lot like the student interviews that we will be conducting. I have been making it a priority to keep the readings organized, because I plan on being able to go back and use them as resources as much as possible.
ReplyDeleteI think that the issue with teachers not fully recognizing when they, themselves, have conceptual gaps and misunderstandings is initiated during teacher preparation courses. Reason being, I have taken quite a bit of classes that focus on making sure the teachers maintain complete control of the classroom at all times, and I have taken classes that focus on methodology. I know that these are very important, but I think it is problematic when teachers are constantly being taught to maintain their superiority in the classroom and methods of teaching material, but not being taught how to answer questions. This week’s Monthly Math assignment made me think about how important it is for teachers to anticipate student responses, whether they are correct or incorrect. ¬
In Chapter 3 of DMI, I was also drawn to the teacher that was having difficulty explaining and teaching place value to her students. In my field placement, my teacher has the students in math centers everyday, and one of the centers is “Race to Two Flats”. In this game, the students use a spinner to draw a number and that number determines what they have to draw from the base 10 set. The winner is the first student to get to 200. The first couple of times I saw the students doing math centers, I was a bit worried that they would not be getting the appropriate math experience. However, judging by what we read, working with base 10 blocks can be difficult. So, now I feel like since they can do so well with trading and everything, then they really are learning something. Not only that, but they are getting a lot of practice.