Seminar 4 Blog Post: Reading Summaries

Chapin, S. H., O’Connor, C., and Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions. Chapter 9 – Planning Lessons

This chapter walks us through how to plan effective lessons. Such lesson plans include: identifying the mathematical goals, anticipating confusion, asking questions, and planning the implementation. It describes the importance of using discussion (and different talk formats) to teach mathematical concepts and being open to altering your lesson to respond to what students know or don’t know. To conclude the lesson, summarizing what occurred in the lesson is important in order to solidify students’ understanding.

Stein, M. K. (2001) Mathematical argumentation: Putting the umph into classroom discussion. Mathematics Teaching in the Middle School. 7(2), 110‐112.

This article describes a real life example of classroom discussion used in a middle school mathematics class. Providing a more open-ended problem allowed individual students to determine the solution method that worked best for them. Then, the teacher facilitated a whole-class discussion in which the correct solution and a common incorrect solution were both presented. It was up to the students to present their arguments, defend their methods, and then decide which is correct. Overall, the teacher used classroom discussion to let students inquire about math.

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 289‐295.

This article discussed a classroom in which the teacher is not the sole source of knowledge. Students can teach each other and learn from one another as well. It focused on the importance of using classroom discussion and student-led mathematical conversation as a tool to promote higher-level thinking in our students.

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 410‐414

This article talks about ways to promote deeper-level thinking among our students (we must find a happy medium between rote memorization and fun exploration). Again, students were given a problem that allowed the possibility of several open-ended solution methods. After working in groups to solve the problem, each came up with a different strategy and could present and justify it to the class. Then, students could “practice articulating their thinking” by discussing and exploring correct and incorrect solutions (p. 413).

Article Summaries

Chapin, O’Connor, Anderson. (2009). Chapter 9: Planning Lessons – The chapter about lesson plans really lays out the lesson plan that Chapin, O’Connor, and Anderson feel is most effective. The lesson plan that they use has five components, these components are, identifying the mathematical goals, anticipating confusion, asking questions, managing classroom talk, and planning the implementation. This lesson plan focus’ highly on using talk to learn mathematical and how important it is to think about the mathematics prior to teaching the lesson. This in-turn will help keep the focus of the discussion on the students’ understanding and helps the talk move forward so the goals of the lesson are addressed.

Stein, M.K. (2001). Mathematical Argumentation: Putting the Umph into Classroom Discussion – Centering your classroom discussion on mathematical tasks does not have to become a routine, or how Stein puts it, “the IRE routine (teacher initiation, student reply, teacher evaluation)” (Stein, page 110). Instead, as the teacher you can step back and let the students do all the thinking and discussing. The teacher’s role then becomes to simply encourage risk taking and alignment with one position or the other in the debate, or to just be there to revoice and clarify student discussion.

Atkins, S. (1999). Listening to Students: The Power of Mathematical Conversations – This article focuses on the importance of the teacher taking a step back and allowing the students to do more of the talking as well as leading classroom discussions. When the teacher steps back and becomes a member rather than the leader, it opens up more relationship building between the students where they are being challenged and reconstructing each other’s ideas.

Kazemi, E (1998). Discourse that Promotes Conceptual Understanding – In Kazemi’s article, the point that is being made is what it means to “press” students to think conceptually about math. It is important that teachers help students build on their thinking so that their problem solving and conceptual understanding can increase. Kazemi also states in this article the importance of students make use of reasoning that justifies procedures rather than statements of the procedures themselves (Kazemi, page 410).

Seminar 4 Posting- Main Points of 4 Articles

Atkins, S. (1999, January). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 289‐295.

                   

This article focused mainly on the ways that you can foster children’s level of discussion in the classroom and how to guide learners in a mathematical community. The article discussed discussion by teachers asking the right types of question to push children’s thinking, as well as finding ways to position students in the classroom to talk to each other and to look at one another.

Stein, M. K. (2001) Mathematical argumentation: Putting the umph into classroom discussion. Mathematics Teaching in the Middle School. 7(2), 110‐112.

                   

This article focuses on ways to enhance your classroom discussions with mathematics and the roles that students play. This article talked about how students have to be responsible for their reasoning and standing up to defend their answer and correlate it to others. It is the teachers job to come up with a problem that enables students to answer the question in multiple ways and find reasoning differently as well.

Chapin, S. H., O’Connor, C., and Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions. Chapter 9 – Planning Lessons

                    This chapter focuses on the lesson plan format that is helpful to having discussions in class. Some main points include the things that need to be included in the lesson. These things being identifying the learning goal for the lesson, knowing what confusion might occur, asking the correct type of questions for students, outlining how you will implement the lesson as well as identify the type of moves you will use in the lesson ahead of time. It is also important to think about how you will react to questions and comments in the middle of the lesson. It is also important to go back and add notes to your lesson about things that worked and things that didn’t work.

Kazemi, E. (1998, March). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 410‐414

                    This article focused on classroom norms that need to be present within a classroom to have thorough discussion and understanding about mathematic topics. These norms are not just norms that you have for classroom management or typical rules. These norms include thinking about math reasoning rather than steps needed to solve a problem, using errors to further understanding a concept, comparing similarities and differences between strategies for problem solving and also accountability for students to think about an answer. Students had to prove their answers were correct and work together until a consensus was reached!

Seminar 3 Blog Posting

My quote:  “If status characteristics are allowed to operate unchecked, the interaction of the children will only reinforce the prejudices they entered school with.” (Cohen, page 37) I find this quote very interesting to me because it is important that stereotypes and prejudices are either discussed and are discounted or discounted by the way the classroom community works together. I think this is important because students do enter school with some sort of prejudice from where they live or what they hear from parents and others. Children are going to be getting their own sense about people and their environment and it is important that as teachers, we encourage an anti-bias curriculum and do not put certain children in a spot to become a stereotype by accident. I think teachers often do not think about what they are saying to children who are having a hard time and what that does to other children in the classroom. You are a mentor to children and when we put stereotypes on children or make children look like they are the class clown or the “smart” one of the group, children recognize these things.

               I think this will be important in my classroom because there are many children who are very different academically, socially, culturally among other differences. It is important to make sure when you are doing group work along with your everyday teaching that you be careful about the emphasis you put on certain students for the way you do things, especially when you start to pair people together in group work. I do not want students to start a hierarchy in the classroom and out of the classroom. That starts when teachers do not watch how they talk to students as well as preventing stereotypes and prejudices from occurring around them. A lot of observation should take place as well as establishing norms within the classroom.

Seminar 3 Blog Post

“Students generally have an idea of the relative competence of each of their classmates in important subjects like reading and math acquired from listening to their classmates perform, from hearing the teacher’s evaluation of that performance, and from finding out each others' marks and grades. They usually can, if asked, place each of their classmates in a rank order of competence in reading and math. This ranking forms an academic status order in the classroom” (Cohen, 28-29).

This quote really resonated with me for two different reasons. First, throughout my entire education (from elementary school through college) I can remember being able to put my peers in this academic status order. When my teachers placed students in groups, I can remember thinking “Oh no, I’m with him…that means I’m going to have to do everything.” Second, I found this quote to be so fascinating because I’ve already noticed students in my first grade classroom ranking each other in an academic status order. Specifically, we have books placed in leveled bins (red, green, orange, yellow) which vary in difficulty. The other day I heard one student who was picking books from the green bin tease a student picking books from the red bin, saying “Look how easy those are. Those are baby books!” So already, at 5 and 6 years old, students are beginning to compare and rank themselves academically among their peers. Overall, this academic status order is an unfortunate and real part of our classrooms. It especially comes into play when working in groups, as the perceived “expert” in the group will likely influence and dominate over the entire group (Cohen, 29). To combat this, I like the idea of assigning particular roles for each group member (i.e. recorder-responsible for writing, reporter- shares to class, etc.) to ensure that every student has the opportunity to participate! Overall, now that I am aware of the academic status order which is already developing in my classroom, I can talk with my mentor teacher about ways to address it and ultimately limit its impact.

Cohen Readings - Favorite Quote

Quote: “The multiple ability treatment requires you to convince the students that many different intellectual abilities are necessary for the group-work tasks” (Cohen, page 126).

Explanation: This quote was interesting to me first and foremost because I had never heard of the multiple ability treatment and I found it very fascinating. The multiple ability treatment consisted of explaining the different abilities necessary for a survival task of Lost on the Moon before groups began their discussions (page 123). This strategy was created so that individuals would be shown equal status behaviors as opposed to exhibiting a pattern of dominance by the high-ability students. Therefore this quote intrigued me to want to see this treatment be put into action. I feel that in our first grade classroom, if we made use of the multiple ability strategy the students would understand from the start how each individual student is equal and everyone has their own strengths and abilities. I also feel that at this age, this is a good way to introduce the students to treating everyone equal and not as superiors or inferiors, right from the start. This in-turn can help with self-esteem and confidence later in life.

Talk Moves - Question 1

While reading these chapters and the case study, I noticed a few things about talk moves. As I was reading, I realized that these talk moves can be used in more than one subject. You can use talk moves within literacy, math, social studies and science. To clarify understanding and look at what students are truly understanding is very important. The 5th talk move about waiting is one that stands out to me in more ways than one.  In many instances, teachers and others have a hard time being silent and truly waiting for students to form their ideas. In my own learning, when my teachers would become silent, I never wanted to talk because I never thought I was ready to give an answer. I also hated being called on because I did not have my answer formulated in my head. As a teacher now, I realize that giving students an opportunity to think about their answers are very important. There are many children especially in a younger classroom that raise their hand automatically without knowing what they are answering. By giving students more wait time, you are able to give students who do not automatically raise their a hands a chance to think about what you are asking them. This is also beneficial to students who may speak another language. Students who speak English as a second language, it is important to give wait time so they can translate what you are saying and then actually do the problem you are asking them to do. This will be a challenge for me in my own classroom as I start to teach not only math but other subjects where asking questions and encouraging conversation will be very beneficial.

Seminar 2 - Talk Moves

Prompt #4: Which of the talk moves seem the most natural for you to use or see yourself using the most? Why?

After reading through the five talk moves – revoicing, asking students to restate someone else’s reasoning, asking students to apply their own reasoning to someone else’s reasoning, prompting students for further participation, and using wait time – the talk move that seems the most natural for me to use or the talk move that I see myself using the most is, revoicing. One major reasoning for why I feel I would use this talk move the most is because I already make use of it daily. Having been in the child development program at Michigan State, we were taught how to use this talk move and I have utilized it ever since. However, after reading more about this talk move in Chapter 2, I am now exposed to its positive effects it can have when teaching my students. Revoicing can help students understand what their classmates are saying and it allows them to interact with each other in a way that will continue to involve the students in clarifying their own reasoning (Chapin, O’Connor, Anderson, pg. 12). When students have the ability to clarify their own reasoning, they become independent and aware of their own thinking processes which can help with problem solving and mathematical tasks.

Not only does revoicing help the students learn how to clarify their own reasoning, but it helps us teachers understand any misconceptions that our students may have. Once a misconception is made, as teachers we can immediately help them work through those misconceptions and find a way for them to understand and/or comprehend what is really being said or happening in the lesson/activity. Also stated in Chapter 2, revoicing is, “an effective move when you understand what a student has said but aren’t sure that the other students in the class understand” (pg. 13). When one student has an idea and others might not understand what that child had to say, it is nice to have the ability to revoice their idea so that the other student’s idea can become available to others. This then in-turn creates a classroom discussion, and provides more “thinking space” as Chapin, O’Connor, and Anderson stated. “It can help all students track what is going on mathematically” (pg. 13)!

Seminar 2 Blog Post

Prompt #3: Looking at your case study, how did student talk deepen the teacher’s understanding of his/her students’ thinking?

Case 2 describes a first grade teacher’s use of student talk to help her teach geometric shapes. Specifically, Mrs. Sigler’s first grade class is learning about what makes a shape a triangle. During the first day of her lesson she had students work in small groups to sort shapes into two categories—triangles and other. As she made her way around the room, stopping to work with individual groups, she noticed that most children were only placing equilateral triangles in the ‘triangle’ group and putting isosceles and scalene triangles with other shapes in the ‘other’ group. After talking with one group and asking children to defend their choices, it was clear that their understanding of triangles was limited. Most classified their shapes as triangles because “it just looks right.” From asking each student in the group to think out loud, Mrs. Sigler learned that they were relying on limited previous knowledge about triangles (i.e. seeing the shape on a poster in the classroom) and had little or no understanding of the actual properties of triangles. It’s important to note that the teacher asked each child to speak and elaborate on one another’s thinking in order to assess each student’s beliefs; she wasn’t correcting them or leading them to new understanding.

Through the student talk Mrs. Sigler facilitated, she gained a deeper understanding of her students’ thinking and could adjust the following day’s math lesson appropriately. In particular, she learned that she needed to focus on the generalization that all three-sided shapes are triangles. As a result, during the whole class lesson the following day, Mrs. Sigler spent a lot of time making sure her students understood this, as evidenced by her asking students (with different looking triangles) to share their shape and number of sides (always 3) with the class. This helped students make the connection with all triangles and three sides.