Week 3 Post - Laura Hilfinger

Cohen Chapter 5 Page 7

“The mix in any single group does not have to represent the proportion of minority students or gender balance in your class. Mechanically insuring that each group has equal numbers of males and females or one or two students of color has the disadvantage of making the basis of your decision clear to the students. They will tend to focus on their fellow members as representatives of their race or gender and are much less likely to respond to them as individual persons.” I thought this method of dividing the class into groups seemed like a very unusual way for a teacher to think. Most of the time when my teacher or I divide up the children into partners or groups it is random (we draw sticks), however, sometimes we use ability level to divide the students. For example, after the DRA tests were complete, we divided the class into reading groups according to their reading level. Even though the students in the highest group are sometimes silly together because they are good friends, we left the groups according to their reading levels because in my teacher’s experience this has been the most successful method for her classrooms. For our math groups, we have the class divided randomly in their groups according to their names. We did not look at race or gender when dividing the groups, however we kept some students separated because of problems within the first few weeks. After a few weeks of math workshops we are going to re-divide the math groups according to skill level.

I agree with Cohen’s statement that it is not a good idea to divide groups based solely on gender or race, however in the first grade setting I do not think his reasoning behind the statement is accurate. In our class, the only time we have talked about race was when one boy stated “my skin is darker than your skin so I am going to use a darker crayon”. The other boy nodded in agreement, and both boys continued to color. I do not feel first graders would see each other as representative of an entire race or gender, however this may easily happen in older grades.

Week 3 post

“Groupwork requires careful planning in advance. An orientation session focuses the students on the major concepts underlying the activities and prepares them for the challenges of working together.” (Cohen, E., 70)

This quote was particularly interesting because it is so relevant in my classroom. This concept, for me, is a given based upon the years of student teaching and teaching education courses however, many teachers often need to be reminded of this when planning group assignments. I think that at times, we underestimate the amount of planning and thought that group assignments require. The size and people in a group need to be well thought out. Whether or not you are going to group students together who are similar in terms of their development of that subject or group together higher students with lower students. Some students work really well together while others do not. This group dynamic is something that requires a great deal of thought it order for the group to work effectively together to complete their task. Another option is to let the children choose their own groups. This choice comes with its own benefits and challenges. On one hand, many children may have an idea of who they work really well with and prefer to work with. On the other hand, you risk having children choose to work with people who have difficult times staying on task or getting the groupwork completed. The expectations of the groups also need to be clearly identified. This is one thing we really try and focus on in my first grade class. Without these clear expectations, chaos and confusion is a big possibility. The materials need to be prepared in advance and easily accessible to the group members. A teacher also needs to consider where these groups will be working within the classroom. Each group needs to have enough space where they are able to work without interfering with any other group. There is a great deal of pre-planning that needs to be done before you introduce groupwork into the class. Not to mention what you want the groups to accomplish throughout the group work. As a teacher, you need to make sure that the groupwork isn’t just a filler for the day. It needs to contain rich and meaningful information that the students will obtain.

Week 3 Post

“When students are able to connect ideas and concepts to procedures and representations, learning is especially robust. Thus, one of the things we want to talk about in mathematics class is how concepts and relationships among concepts connect to what students already know” (Cohen, 2009).
As I read through the chapters, this specific quote really stuck out to me. In elementary school, I really struggled with mathematics. It never made sense to me, and I never saw the way in which math concepts connect. To me, math was a set of different procedures and algorithms. Nothing actually made sense to me. I know that math was this way for me because nobody really took the time to see if I understood what was going on, let alone, pointed out for me the connective nature of mathematical concepts. For example, I never realized how fractions, percentages, or ratios were all interrelated. Thus, this quote really spoke to me, because, as a future educator, I want to make sure that I really show the connections between different mathematical concepts to my learners. I want to teach mathematics by springing off of learners’ prior knowledge. All learners are going to have prior knowledge on a concept and I believe that my lessons should be differentiated for the different levels of prior knowledge my learners have on a given mathematical concept. In order to work with all my learners’ different levels of prior knowledge, and show connections between concepts, I must provide my learners with higher level tasks that allow for multiple types of representations. Thus, the way my learners work out the problems and describe their reasoning for their answers, the more I will start to understand their mathematical understanding of different concepts and how various concepts connect to other concepts. For those learners who don’t understand as well, I will be able to see what prior knowledge they do hold by how they went about solving the problem or how they justify their reasoning compared to learners who understand the concept. Furthermore, having a higher level task will allow me to differentiate learning for my different learners because I will be able to request those learners who understand the concept to provide another representation. I hope if I am able to really build off of learners prior knowledge and to connect mathematical concepts, my learners will start to understand mathematics as a world of interrelated concepts and start to make sense of math more than I did.

Week 2 Post - Laura Hilfinger

In the first grade case study about teaching the class what a triangle is, I think that the student’s small group conversations and the whole class conversation were both helpful in the teacher’s understanding of student thinking. The small group discussions showed the teacher which students were having problems with the objective. I thought it was a really good idea for the teacher to ask each student in the group that was having the most problem for their individual opinions. I thought the fact that she was able to single out each student led her to understand even more that they all were having the same problem. The last student she talked to (Sim) responded with “I don’t think so. I don’t know” and then stated that maybe the turned equilateral triangle was really a triangle but he/she still did not know. She was able to hear that the students were not using any type of formal definition to categorize a triangle, and that they were just remembering triangles that had been taught or shown to them as a “triangle”. I think small group discussions are a great method because she could clearly see the group that needed the most individualized help, and she might be able to assume that the groups who categorized the triangles correctly had explained to the group members why each shape was a triangle.

This type of teaching led Mrs. S to her next activity which was having the students create many individual triangles so that they could discuss all of the types of triangles as a class, and not just equilateral triangles. Remembering what she had learned in small group discussions, she was able to show students differences between small triangles and big triangles, and have the students realize that all of the triangles they had created and put on the board were made up of three sides.

Blog post 1 (9-21)

In response to the question “Which of the talk moves seem the most natural for you to use or see yourself using the most? Why?”

Reading Chapin and Anderson’s book Classroom Discussions: Using Math Talk to Help Students Learn taught me a lot of the talk strategies or “moves” that I use on a daily basis. Until this reading, I thought this was just something informal or unplanned that teachers do. After reading this, I understand the intention and significance of the talking moves within classroom discussion.

In my first grade classroom, student involvement is a must in order to maintain the attention of the children. One strategy that my mentor teacher and I use to keep their attention is to frequently ask the children questions. This forces the students to pay attention because they never know what questions will be asked and when. It also allows the children to take part in active learning. Many children in first grade are not familiar with the correct terminology when it comes to math discussions. After we ask a question and listen carefully for their response, we often find that we need to re-ask the question or ask for clarification. Revoicing is a technique that is repeatedly utilized to clarify or reiterate what the child had said. This shows the student that we are really listening to what they are saying. It also demonstrates to the child that what they are saying is meaningful and that they are a valued member of our classroom community. Lastly, it clarifies thing for the other students. They may not have completely understood the question or answer that the student gave but will now comprehend the topic of conversation. This most likely will lead to an extension or expansion of information by that same student (talk move 4) or another child to chime in with their thoughts or opinions. I believe that revoicing is very significant to a successful classroom discussion. It is also extremely easy for a teacher to do which makes it possible to take place without difficulty.

Chapin and Anderson pg. 1-22

“Which of the talk moves seem the most natural for you to use or see yourself using the most? Why?”

After reading about the five different types of productive talk moves to use to help facilitate a mathematics based discussion, from Classroom Discussions: Using math talk to help students learn, by Chapin and Anderson, I started to realize how natural I already do a lot of the different talk moves. At first, when I read that there were specific ways to help initiate discussion, I was a little nervous that they would be these types of talk that would be foreign to me. Luckily, however, I saw revoicing, and I was ecstatic because I already revoice everything my learners tell me. Being a child development major, I was taught to always revoice, or paraphrase, what a child says. Not only does it help a learner to “clarify his or her own reasoning, and help other students follow,” but it helps students to extend on their thinking (Chapin, O’Connor, Anderson, 2009). In child development, we learned that so often paraphrasing will show a child that you are listening and finding value in what they are saying. When you revoice what they say, they often further extend on what they were talking about because you are paying attention and you are helping them to refocus their thinking. For example, if a child says, ‘I saw a friend this weekend,” and you respond, “So you got to play with one of your friends,” the child may then respond with, “Yea, we got to go swimming in his backyard.” Thus, when I saw revoicing as one of the steps to helping facilitate a math discussion, I was excited because I feel I could possibly already be effective in one of the types of talk. I think that it is crucial to have revoicing in a mathematics discussion, especially for the individual learner. The repeating, reasoning, and adding on to thoughts are great for the actual facilitation of a discussion among peers, but the revoicing is really important for the individual learner. Revoicing shows that you care and it provides learners time to build upon their thinking. Thus, I am really excited to start implementing revoicing in my math lessons.