Communication Article - "You Had to Be There!"

"You Had to Be There" is an article discussing the use of a demonstration classroom to teach other teachers about effective mathematics education. This article gives us an insight into the classroom of Duane Heide, a mathematics teacher in Canada. Mr. Heide answers questions about what attracted him to becoming a teacher. The article continues as Mr. Heide describes a typical situation a visiting teacher might see in the demonstration classroom. Heide explains in the article how he opens and closes the lesson in a way that allows students to works with each other and discuss how to address and solve the mathematical problem they have been given. After the class is dismissed, Heide holds a debriefing session for the visiting teachers in the classroom to ask questions and discuss what they just observed. The article is concluded with Heide answering questions about the experience of being the teacher in a demonstration classroom and how the students react to effective teaching of mathematics.

I thought that this article was very interesting to read. I had never heard of a demonstration classroom. As I read the article, I was intrigued by the amount of information that a teacher can learn from visiting a demonstration classroom. I thought this article was beneficial because it taught me that communicating with fellow teachers can enable a positive learning environment in the mathematics classroom. I liked when the article discussed the use of discussion among students during the lesson. This was beneficial to read about because it taught me that through communication with others in the classroom, students are able to better understand mathematical concepts. Discussion among students allows them to organize their thoughts and ask questions for clarification.

This article would be beneficial for classroom teachers. Through this article, teachers are reminded that lifelong learning is important to student's success in the classroom. Teachers can learn from this article that collaboration with other teachers can help improve their teaching skills. The article includes a list of questions that a teacher can ask themselves and discuss with other teachers to improve their teaching. These questions are very beneficial and useful to teachers. Reflective teaching by asking these questions can improve classroom practice. This article would be beneficial to first time teachers to help them begin feeling comfortable teaching mathematics.

Kotsopoulos, D. and Heide, D. (2009). You had to be there! Teaching Children Mathematics 15 (7), 410-415.

Communication Process Standard

The communication process standard is vital to the learning and understanding mathematics. As students ask questions and justify their reasoning behind the solution they found, they are communicating. Students must be able to communicate what they are thinking to others. In order to do this successfully, the student spends time organizing their thoughts and reflecting on what they have done.

The organization of the student's thinking helps them communicate clearly to others. It is important that students are encouraged to communicate their mathematical thinking to others in a clear way. Often, we find that students are intimidated by math, so the constant encouragement to communicate mathematical thinking will help students improve their skills. Teachers should encourage appropriate communication of mathematics as students become older. Students must also learn to communicate in written form.

Communication among peers about mathematics is very important. Discussion among students allows for them to see other perspectives and methods they can use to solve mathematical problems. Discussion of different solutions teaches students to become critical thinkers about mathematics. Students are able to form these critical thinking skills through analysis and evaluation of other students strategies.

Lessons on Variables - Lesson in Grade Four

The fourth grade videos are about a lesson covering variables. The students will be building a "variable machine." Prior to this lesson, the students did not have a good understanding of variables. The teacher taught the concept of variables through the use of the variable machine that each student made. The variable machine was made up of two strips of paper, one with the alphabet on it, and the other strip with the numbers 0-25 on it. The students took the two strips of paper and placed them next to each other to create a ring. The two strips of paper placed next to each other matched a number with a letter. The letter acted as a variable. The students worked together in groups and determined the value of the names of all members of their group using the variable machine. The students had to work together to figure out how they could increase the value of their names using the machine.

• Reflective Task 1: Describe how the teacher’s questioning, and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment. During the lesson, the teacher would ask the students many questions about what they had found. The way the teacher would ask the questions enabled the students to explain what they had found and how they had found it. The questions that were asked did not allow the students to fail. She would use answers that were not correct to teach the students the correct answer. The teacher created a more relaxed and friendly environment with the students in the classroom so when they were answering the questions they would feel comfortable, and not intimidated. I believe that the questioning contributed to a positive classroom environment. It allowed the students to feel confident in the work they had done, as well as allowing them to talk through the difficult parts of the work as a group to fully understand every part of what was being done.
• Lesson Analysis 1: Identify several strategies the teacher used to orchestrate and promote student discourse in this lesson. As the students are working in groups, the teacher is walking around to each group and asking them questions. She asked the question "what are you finding out?" After the student answered that question she said "you need to think about when you put one on 25 what that does to others." She says these things so that the students in the group would begin thinking of different ways to achieve a higher value. She also mentioned other ideas that might enable them to form a higher value. The students would then begin discussing what would make the value the highest. They would begin forming connections between the proximity of the letters and the value of the numbers. The teacher also promotes discussion in the lesson by continually asking the students what each other them are finding and having them explain how they found that result.
• Lesson Analysis 2: Describe what the teacher does to support learning while students are working in groups. As the students are working in groups the teacher is walking around and listening to the discussion each group is having. As she walks around, she stops at each table. She does many things while speaking with the groups. She asks them how they are achieving each answer. When the teacher asks that question it is supporting what the student learns because it makes them explain how they found the answer. When they have to explain how they found the answer it gives them a better understanding of the concept they are learning. The teacher also is watching what each group is doing to ensure the activity is being conducted properly. This supports learning because it is keeping the activity consistent. The students are supposed to discuss different ways to raise the value of their names without adding any letters to them. When the teacher clarifies what is being done, the students will be able to understand the concept better.

I found that watching these video clips were very reassuring to me. I have always felt intimidated

about teaching mathematics, especially those topics that can be confusing to students. When I

watched the experienced teacher in the videos teach the students about variables I felt more calm

about teaching mathematics. While watching the teacher in the videos, I noticed many of the

principles that were discussed in class being used. I liked being able to see the principles being

used effectively. I really liked the activity used in the lesson, and I liked being able to hear the

teachers justification of how certain things were done.

Teaching Principle

Important points of teaching pronciple:

1. A teacher must fully understand the mathematics they are teaching and be fully committed to applying the mathematics to experiences that will allow students to learn mathematics. Students learn best through different experiences the teacher provides.

2. The teacher must adapt the classroom to the proper environment needed for teaching math. Organization of the lesson is key to its success.

3. Improvement is important when teaching. A teacher must stay committed to learning and improving their lessons and teaching strategies. Continual learning is important because teachers need to increase their knowledge of mathematics and pedagogy.

What Values Do You Teach When You Teach Mathematics? - Alan J. Bishop

The article "What Values Do You Teach When You Teach Mathematics?" looks into the values that students are learning through mathematics. How a teacher allows their students answer a question can teach students certain values. The way the teacher responds to a student after they answer a question also teaches students about values. The article examines the connection between mathematics and culture, focusing specifically on values that are portrayed when teaching math and how we teach it.

Teaching values is not like teaching fractions. There is no right answer when teaching values. "The choices that you make depend on your values, which in turn influence your students' values. Understanding more about values is, in my view, essential to improving mathematics teaching" (Bishop, 2001). The article examines the different sociocultural values that are taught through mathematics. The different values that are taught through mathematics are rationalism, objectism, control, progress, openness, and mystery. The article gives different ways to explore the idea of values in mathematics teaching. There are different ways to examine lessons to see the values in each.

I thought this article was very interesting. The concept that values are being taught in a math lesson shed a new light on the subject area that I had never considered before. I liked that the article gave background information about values. I also liked the end of the article when the author listed different ways you can examine lessons to see the values being taught. I also liked that the article listed many questions that a teacher can ask themselves about a lesson to see how a value is taught by the way they respond to a certain situation.

Bishop, A. (2001). What values do you teach when you teach mathematics?. Teaching Children Mathematics, 7(6), 346-349. Retrieved January 22, 2010, from http://www.nctm.org/eresources/view_media.asp?article_id=766