TTLP

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?

More fractions....

"Fractions both underpin the development of proportional reasoning and are important for future mathematics study, including that of algebra and probability. However, it is clear that many teachers find fractions difficult to understand and teach and many students find them difficult to learn" (Clarke, Roche, and Mitchell p. 373). Rose and Gabe, correct me if I am wrong, but I think it is clear to all of us that fractions are a difficult concept to teach and learn. The thing we are not so familiar with, is how to use different tactics to teach fractions more effectively. I thought the article gave great tips on how to make fractions more readily understandable for students. I also really liked the student's homework example on page 374 when the task asked Darcy to draw or write about 3/4 in as many ways as you can. She was able to come up with nine different examples, which seems to be really great to me. Some of the tips I thought were most helpful were the following: "give a greater emphasis to meaning of fractions than on procedures for manipulating them, emphasize that fractions are numbers making extensive use of number lines in representing fractions and decimals, and lastly provide a variety of models to represent fractions" (Clarke, Roche, and Mitchell p. 375). Gabe and Rose, what things did you find most interesting out of these three articles?

Rational Numbers!

"One topic that is particularly difficult for students is fractions" (Bezuk and Bieck). I find this to be a very true statement in my own experience. Rose and Gabe do you agree? I really liked the three ideas these authors have on making fractions easier to learn for students. They are: "a. instruction should be meaning oriented rather than symbol oriented, b. instead of delivering knowledge in prepackaged form, instruction should encourage students to construct their own knowledge, and c. instruction should provide students with structured learning experiences to help them acquire essential conceptual and procedural knowledge" (Bezuk and Bieck). It is important to teach children that rational numbers are ratios. In order to teach rational numbers more effectively, I believe we as teachers need to rely less on the conventional abstract math symbols, and rely more on using concrete tools. For example, all the materials listed on page 124 in this article seem much more helpful than a simple fraction sign. Another thing I found interesting in this article is to use word names such as one half before using symbol names, which seems like common sense to me, but I did not think of this before. Rose and Gabe, what things did you find interesting in these articles? Have you seen any rational number instruction in your placement? I have not yet...

Week 6 Lesson Study

Lesson study helps teachers to form long term goals for student learning and development, plan, conduct and observe a research lesson an designed to bring these long term goals to life. The lesson studies help teachers to have opportunities to observe student learning, engagement and the behavior during the lesson. Balancing teaching the lesson while also assessing each student is a difficult task, but important. During the lesson study process, the teachers are given opportunities to reflect on the teaching process and also the student learning. teachers need to learn how to balance these two aspects of teaching in order to make their lesson beneficial and meaningful. Lesson study began in Japanese schools a very long time ago. It helped their teachers to make sense of the educational ideas within their practice, change their perspectives and help them adapt to teaching more accommodating to their students' learning skills, learn from children' perspective, and lastly, collaborate among other colleagues. My TE friends have definitely discussed staying in touch in the future to share our stories, ideas and help each other with lesson plans. It is definitely beneficial to help other teachers with issues or give ideas for their classroom, as well as receive them! I really appreciated this article, talking about lesson study, but it is also something that should be required for teachers. They should have to work with other teachers and brainstorm and bounce ideas off each other in order to have better lesson plans. Everyone knows two brains are better than one. Why wouldn't we practice this?! Lesson studying with other teachers and colleagues will benefit you because you will also learn new teaching forms, if not new, different. In order to create a lesson study group, you can make it informal, amongst teacher friends, but as long as you are discussing and learning and adapting new ideas for lesson plans, I think it will be beneficial for your students. It helps putting more thought into it, and the lessons will be more successful. I do not see any of this happen at my placement school. The teachers during lunch in the lounge talk and discuss students, and ways to help them, but I have never seen them critique eachothers' lesson plans. Rosa and Lauranda, do you notice this at your school?