Reading Recap

Discourse that promotes conceptual understanding

This article really focuses on the social relationship students have with math. Students need to have an open environment, which promotes discussion and dissection of their math strategy. Students also should be able to compare strategies enhancing this idea of conceptual thinking and discussion. As for teachers, teachers need to allow students to explain their thinking and not interrupt their ideas but help them by asking them to restate or putting it into different wording for them.

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

Putting Umph into Discussion

The previous article talks about classroom discussion and critical thinking but this article focuses on what students actually talk about. Teachers need to find interesting problems that students will connect to and invest in, in order to promote classroom discussion. In order to find these tasks, teachers need to know and understand their students because not all tasks will promote discussion. Again this article focuses on more student lead activities than teacher lead activities where students are responsible for the discussion but the teacher is a resource to help.

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

Classroom Discussions: Chapter 6

This chapter was incredibly helpful as a reference for discussion based lesson plans. When planning these types of lessons teachers need to anticipate problems that my arise, plan what type of discussion students will be having weather small group or pairs, and come up with a higher level thinking question to generate conversation. There is a great deal more planning that needs to go into these types of lessons and teachers should prepare for this types of planning.

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

Listening to Students

This article was focused on the listening aspect of student lead discussion. It was shocking to find out that students engaged in a mathematic for over an hour. Often teachers cut off discussion and precede right into explanation but this example teacher allowed and encouraged this discussion. Once again this teacher also came up with intriguing activities and questions to ask her students but she ends the article by saying that this is an “evolutionary process” reassuring other teachers that this technique is a practice for the students as well as the teacher.

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

Summary of Readings:

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

When planning a lesson teachers need to keep in mind that not all students are going to be at the same level and this needs to be considered to make sure that all students are participating in the lesson and comprehending what is being taught. There are four main components for planning a lesson plan that the chapter talks about. These include identifying the math goals, anticipating questions, asking questions and planning the implementation. Each of these goals all work together to help a math lesson go smoothly in all directions. The chapter discuses what ways there are to form good questions that students are going to respond to and link to what they are learning in math, generating questions that will give students assessment type answers that they will have to think about. The chapter explains many examples that teachers have used and how students respond to help tie in each of the four components for planning a lesson and the benefit that the students and teacher will receive.

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

Some main points of this article include getting students to be interested in classroom discussions and the different ways that that is possible. The classroom needs to have a comfortable setting where all students feel comfortable to participate. The article suggests getting students to take sides on different instructional positions in math and having those discussed in the classroom. This gives students something to think about and participate in with their own thoughts and ideas. The article discusses different ways to make sure that all students are incorporated into the tasks and supplies that are needed to work with some tasks because having those supplies is vital to the outcome of the discussion. Walking around the room and making sure that students are working and participating correctly within the math instruction. Lastly it is important to get students involved and enthusiastic in explaining their thoughts and ideas to other students.

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

This article is very insightful and sheds light on the different ways that mathematical conversations can take place in a classroom during a math lesson. This article focus’s on student to student interaction during a math conversation verses a teacher to student interaction. A teacher demonstrates how a math conversation takes place within her classroom about cubes and the faces of cubes. She reflects on the way the two different conversations went and what the students were getting out of the conversations. Students were able to help answer each others questions about angles and cubes through conversation. The teacher was in the classroom but the students were doing most of the talking and learning on their own.

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

This article is about two teachers who demonstrate two different ways to perform sociomathematical norms in their classrooms. The teachers were explaining mathematical concepts within their classroom and both teachers had the same classroom norms but the outcome of the math discussions were completely different as well as the students interest in math. The classrooms were all different in the way that the students discussed math and how math was incorporated into their own thinking processes. Within the article there are four socimathematical norms that are listed within working in a classroom. These include, explanations of math, errors and exploring wrong answers, mathematical thinking and collaborative work. These four discourses are helpful in working with students and math and getting students to think about math in different ways.

Summaries of the Readings This Week

Classroom Discussions Chapter 9:
 This chapter focuses on what makes up a good lesson plan while providing numerous different examples as to how a lesson plan can look or include. Most of the information has already been taught to me like identifying the mathematical goals, anticipating confusion, have questions prepared for discussion, and planning the  implementation (Chapin, 2009). However, I believe that summarizing is something that I have never officially learned and is something that is taken for granted. Summarizing is a useful tool that allows for conclusions to be drawn and shared meaning among students can be developed (Chapin, 2009).

Stein Article:
This article focused on the discourse within that classroom. "Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom" (Stein, 2001). As I have discussed in previous post, discussion in mathematics has never been apart of my mathematical career. Everything has been lecture based with the numerical answer representing my understanding of the material. It is so important to get children to talk through math together to create a better understanding.

Atkins Article:
Similar to the Stein article regarding communication, Atkins focuses on power of bringing conversation into the classroom. The biggest item that stood out to me was the role of the teacher. Too often teachers are the leaders of the lesson but when discussions are brought into the classroom, the teacher can become a member of the mathematical community (Atkins, 1999).

Kazemi Article:
This was by far my favorite article. I believe that too often math is cut and dry. Throughout my experiences, there is no room for interpretation. However, it is so important to provide students with the flexibility to explore the mathematical world and to create their own arguments. Promoting students to create their own mathematical arguments will eventually foster a stronger classroom discourse (Kazemi, 2001). I loved that this article showed the importance of arguing for it helps students to come up with ideas of their own and to find passion within the material.

Group work- challenging our students and ourselves

“The Label of ‘problematic student’ should never be seen as permanent or as indicative of unchanging characteristics of the person. Similarly, avoid seeing some students as ‘natural leaders.’ With proper training and your insistence that people play their roles most students should be able to perform leadership functions” (Cohen 75).

This quote stood out to me for many reasons. But first off, I haven’t seen structured group work in the classroom yet but there has been group work, casually. No one has necessarily had jobs or “leader positions” because there has only been brainstorming or paired group activities. I do know that students will be in groups for guided reading but this is based off of their reading levels and I am wondering if there will be group activities for them to do as well. I am interested to see what happens throughout the year and I hope to include this form of regulated group work that includes both individual work as well as group responsibilities. I thought that was a key point in the article, as well. Students need to have individual responsibilities but then report to the group and participate in collaboration and I hope to plan for this in the classroom.

As for the quote, I thought that this is indicative to our teaching profession. Teachers, as hard as they may try not to, judge students based on their behavior, but often forget that students behavior differs based on the situation they are in at the time. Students who have a difficult time with group instruction may actually work better in groups and possess attributes teachers may overlook. This ideal is crucial to keep in mind. With this being said the article gave a great comparison and challenged to teachers to take this farther and avoid seeing certain students as leaders. Although students many be natural leaders other students need to be challenged in these positions as well and leaders must also learn to take a step back and allow others to lead them. In real world scenarios people need to be versatile in their roles and we need to prepare our students for all of these roles. Overall this article was very beneficial and I am hoping to incorporate all forms of group work in my teaching and planning as well as challenge my students for many roles in life.

Blog post 2- Cohen Article- Group Work

After reading this article I found many new insights on what group work entails and the different problems that may arise from having students work in groups. Out of the entire article-the most interesting thing that I thought of this article was the way that students were treating each other and acting when they were put into small groups. Reading about the student named Anna had to deal with seemed very upsetting to me and I feel that it is the teachers as well as the students responsibility to make the classroom seem like a community where everyone gets along and works together. Further down the article I came across a quote that I felt was very fitting for how I am feeling about group work upon reading the beginning of the article. “Small task groups tend to develop hierarchies where some members are more active and influential than others. This is a status ordering-an agreed-upon social ranking where everyone feels it is better to have a high rank within the status order than a low rank. Group members who have high rank are seen as more competent and as having done more to guide and lead the group” (The Dilemma of Group Work, page 27.) This blog is interesting to me because it explains why group work can go wrong when the classroom and students have little positive experience with working in small groups and developing hierarchies needs to be leveled down to developing more equal task work where all students feel comfortable contributing to the group. The group members that are scene as having a hiring rank and being more competent need to be leveled out and even give them a chance to ‘help’ the others, giving them more of a job type role verses just feeling like they are above the other students because they have more knowledge. This can be very troubling for the student (s) on the lower end of the hierarchy because they can feel like they are not good enough or the others in the group do not want their opinion so they shut down- which is never something that a student should be feeling or should happen while in school.
From this quote- in my classroom treating small group work in a status ordering rank is not what I want. This has helped me realize that I want my classroom to be a total community and for all students to feel comfortable when they have to break off into groups and work. I never want a student to feel like Anna or the two African-American students who were not given much chance to talk because they were the minority of the classroom. I want the total opposite of that and know that I will achieve it because I have been in Anna’s and the two African-American positions before and it was not fun and it made me not like working in groups and therefore my school work suffered. All around students need to be happy and willing to participate when given the chance.

Smith Difficulties

I chose to blog about the Smith article because I felt as though I was somewhat confused. Near the end of the task evaluations, a small disagreement begins about task A which involves students completing a dot pattern without providing any real directions. “The ensuing discussion highlighted the fact that no procedure or pathway was stated or implied for task A, yet the group had included the use of procedure as a hallmark of tasks that were classified as procedures without connections and procedures with connections” (Smith, pg. 347). The argument can be looked at more as higher-level tasks versus lower-level tasks. However, the group decided that this problem could be viewed as simply doing mathematics, which is considered an higher-level demand because it “requires students to explore and understand the nature of mathematical, concepts, processes, and relationships” and a variety of other reasons listed under the Levels of Demands section (Smith, pg. 348). This is confusing to me because no age group was ever listed. As a college graduate, this task is extremely easy and would definitely be classified as lower-level. I believe that this holds true to the higher grades in elementary. However, those in the younger grades would have to draw on their prior knowledge and really have to work to figure out on to solve this problem. Without any real directions or steps laid out for students, it becomes a higher-level task because they are simply not used to it. It is also higher-level for younger age groups because they cannot simply let their new pattern speak for their answer because they are then ask to put their thought into words. I believe explaining mathematical procedures  at any age is difficult because we are so used to letting different numbers, patterns, graphs, etc. speak for our thought process.

I believe that it is important for teachers to get together to brainstorm different mathematical activities because everyone has their own creative input. Leveling the different tasks using the Smith classifications can be extremely helpful. However, I believe that in my placement this type of classification can be very difficult because every concept is new to my students. They do not have much of a mathematical background besides counting and basic arithmetic. What do you girls think because I know that my thoughts are everywhere?  I think that reading this article a second time just confused me more!  

Case Study two- first grade

Case two: “This is a triangle because it just looks right.”

For this case study students were paired up into groups and had to categorize geometric shapes. They were working with triangles and one of the groups put all of the equilateral triangles into a pile with all of the obtuse and scalene triangles into an ‘other’ pile. The teacher came around and started engaging in discussion. From this discussion she learned, through student talk, that students thought triangles were only triangles if all of the sides are the same. They had a cookie cutter concept of triangles and couldn’t analyze that any shape with three straight sides and three corners was in fact a triangle. The teacher did not, however, correct them immediately but brought this up in another lesson with another activity.

For the second activity, she had students make triangles of all different sizes and then the talk was directed once again towards what makes up a triangle. After putting together different sized triangles using strips of paper and brads students were questioning the same idea: what makes up a triangle? She got students to the place where they have observed and encountered and now they were ready for explanation. Through talk she was able to discover students misconceptions and further develop their reasoning through their own thinking.

After reflecting on this I noticed that the teacher allowed students to sleep on a concept without correcting them immediately. As a teacher I often want to correct students right away, but by incorporating another activity and engaging students in another classroom discussion, students will understand the concept more fully as opposed to receiving a quick correction. This was an enlightening case study, which I will try and incorporate into my own teaching. I need to learn to give more wait time and allow students to sleep on their ideas.

Blog Post 1- Repeating

Blog Number one- This is the first blog for the semester. I am glad to have a blog to share with other’s in the class and hear their ideas as well.
Out of the five talk moves the one that I find the most interesting is ‘repeating.’ The reason that I find this most interesting is because I believe that a great way for students to learn is through their peers. I have always found that when a student is told an instruction by a teacher and they have some confusion but ask a peer it can sometimes can make more sense coming from a peer because it is put into their “own words” and easier for them to understand. I also think that this talk move stood out to me the most because myself as a student would not always hear the direction or information that was being said the first time and I would need it to be repeated. When I would raise my hand to ask my teacher I sometimes got in trouble because they thought that I was not listening. That was not the case, I was listening I just needed to hear it more than once for it to really sink in. By a teacher asking another student to repeat it, it gives the students a chance (like me) who may need to hear something more than once an out, they will not have to ask themselves but they will still receive the information.
Challenges or obstacles that can occur from the talk move that I chose (repeating) is that after awhile students can start to take advantage of this and may not be listening at all because they know that it is going to get repeated by another student, this poses as a challenge. An obstacle that could occur as well is if a student that is called on to repeat is not listening, they will not know what to repeat. Lastly, a challenge that this poses as well is if a student does not understand the math concept that is being taught and therefore has no idea how to repeat or even understand what is being said because they cannot comprehend it as they are struggling. That I believe is one of the biggest challenges.

Just a little clarification!

I know that it seems a bit odd to have Mrs. Stire as a contributer but I created a blog for my teacher, so I had to change the name. After curriculum night and once my teacher understands everything, I should be changing it back but for now I am Mrs. Stire! :)

Hope everyone has a great weekend!

Revoicing

While reading Chapin, I felt like all of the talk moves stood out. Each talk move stemmed from another and promoted better instruction and learning for the students. However, I felt like talk move 1, revoicing, was the most important because it helps to maintain clear lines of communication between one's thoughts and his or her explanation. Revoicing is also important for those on the other end of the conversation because it helps to clarify any confusion in the talk. As Chapin states, "When students talk about mathematics, it's often very difficult to understand what they say" (Chapin, 2009). Too often, mathematic classrooms are lecture-based, not allowing for any student talk to occur.

In many classrooms, mathematics is demonstrated through steps or procedures rather than talk. For example as I traveled through grade school, one would demonstrate his or her understanding of an idea by showing his or her work on the chalkboard. Many times, the student's demonstration contained little or no talk. It was evident through the student's work if he or she properly completed the problem. Math class was practically silent besides the teacher lecturing for so many years. On a rare occasion, the teacher would ask for someone to explain his or her ideas. This was always extremely difficult because math students are trained to explain their ideas through numbers or symbols, never through talk. Teaching kids the importance of talk at a young age will help to eliminate the uncomfortable feeling of explaining mathematic ideas through talk.

Revoicing is extremely important because it helps students to clarify their thoughts so they are clearly understood. As Chapin and myself explain, talking about mathematical ideas is difficult. Revoicing helps to track one's ideas and provides the best possible explanation. Through my prior experiences, I have seen how useful revoicing can be and through Chapin's examples, I can see how easily it can be applied.