Sometimes students can be confused by a lesson that is a continuation of a subject that they have already learned. They may not make a connection because it is not meaningful to them. I liked the quote from Smith, Bill, and Hughes that stated: “When this occurs, students must apply previously learned rules and procedures with no connection to meaning or understanding, and the opportunities for thinking and reasoning are lost.” From this quote, I understand it as that students will solve a problem step by step from what they learned by the teacher, but they do not actually understand what they are doing, and how to apply it to other problems. As future teachers, we need to find a way to connect the meaning and understanding.
I liked the example they used for fractions. They determined the number of red marbles, and then blue marbles, turning them into fractions. It helped them to show that they are taking a portion out of the whole. I believe the students will be able to add this and apply this to everyday life.
The ttlp is a strategy to use the students’ mathematical thinking critically. Connecting their understanding to critical thinking. It is divided into three sections, 1. Selecting and setting up a mathematical task. 2. Supporting students’ exploration of the task, and 3. Sharing and discussing the task. These three sections of the TTLP help to make the mathematical activities more meaningful so the students can apply it to anything they need, not just in a worksheet. Before giving your lesson, evaluate it. Ask yourself, what ways does the task I’m about to teach build on student’s previous knowledge, life experiences, and culture? What methods will the students be able to use outside of class… what errors may they make? … what misconceptions could they have? Asking yourself these questions before hand will help you to better prepare for this so you can be more accommodating when it does happen. When giving a lesson, you need to be flexible. Not every lesson will go how you had planned. It’s almost better if it doesn’t, because that means that the students have become more involved and engaged, and letting them take the lead is an important part of being a flexible teacher.
Part two of the ttlp is ensuring that your students are on task. How can you ensure they are, and continue guiding them. Plan ahead by making the activities meaningful and entertaining.
The last part of the ttlp is sharing and discussing the task. How will you assess their understandings and review the main events. Do their answers display that they made sense of the mathematical ideas you wanted them to learn, etc.
The ttlp to me is a task for teachers, with step by step ideas on how to make your lesson more effective, and keeping the students engaged. I wonder if my CT knows about this. Yesterday in her math lesson I noticed that the students were not engaged, and bored by her repetitive approaches. I wonder if I showed her this TTLP, if it would help her realize that maybe she needs to adjust her ways so that her students are more interested and therefore more engaged.
Lauren and Rose, when looking at the TTLP graph , does it appear that your CT teaches in this manner. Does she have the students’ interest as she teaches? Is it meaningful to them, or are the students bored?
I related a lot to this article, and saw myself in a lot of the things Smith, Bill, and Hughes were saying. I remember sitting in class and being able to do the steps the teacher had taught us to do, but not really knowing why I was doing them, or how it related to anything else. Even now I can do make equations but not know when to use the formula other then when the question tells me to. For example FOIL. If you tell me to FOIL I can do it with the given set of numbers, but I don’t know what FOILing will tell me, or why I am doing the steps. I wouldn’t be able to see a problem and know to FOIL if it didn’t ask me directly to do it. This clearly proves that Smith, Bill and Hughes were saying in the article is true, and really does happen to many students. As teachers we have to recognize this and review with students over and over again why we are solving problems in a specific way. I liked how they provided questions to ask yourself while doing the equations; I think this will really help. Gabe, I also wonder if I get my CT the TTLP if she would consider it and take it into consideration for her students.
ReplyDeleteGabe, I agree with many things you pointed out in the article. I believe the first sentence of the article has much truth to it, "mathematical tasks that give students the opportunity to use reasoning skills while thinking are the most difficult for teachers to implement well." I think one main reason for this is that teachers are so afraid of allowing sudents to think on their own in math and use different reasonings to come up with their answers. They think they might loose control of the lesson, but the reality is this will allow the students to make more connections to the math and thus be more likely to understand the material.
ReplyDelete"The lack of a specific solution path is an important component of what makes this task worthwhile. It also challenges teachers to understnad the wide range of methods that a student might use to solve a task and think about how the different methods are related, as well as how to connect students' diverse ways of thinking to important disciplinary ideas." I think this quote illustrates what Rose is saying to a "T." I say this because I too am able to follow many mathematical algorithms, yet do not know how to connect them to eachother, or even the meaning of many of them. This is the same case for me in physics and chemistry. We need to diverge from the traditional ways we've been teaching students how to think about and use formulas and algorithms so they are able to make more sense of them, and thus have an easier time remembering them and using them in different situations.
Lastly, I really thought the Weist article was interesting and extremely important, becuase the number of ELL students is at about ten percent of our K-12 classrooms, and will continue to grow... With that said, it is imperative we as teachers find better ways to teach this large percentage of our students. It is our responsiblity to teach these students as much or more and as adequately as our native English speakers. To do this, we must be able to tailor the content to all our students. "Content for diverse learners can not be watered down, or second rate. Rather, the goal is to devise curriculum and instruction techniques so that these students can think, solve problems, and reason." It makes me irrate when teachers allow their ELL students to slide by in class by giving them easier work, and/or alowing them to copy off of the otther students, just to make their job easier. Rose and Gabe, how do you think we can ensure the instruction for all our future students is outstanding and tailored to meet their individual needs?