Article- Aiming for Understanding: Lessons learned about writing mathematics

The article states how hard it is for teachers across the country to get students communicating about math whether it been infront of people or on paper. Teachers need to get students to feel comfortable with writing about math they cannot just give them a piece of paper and a pencil and expect them to do it correctly. The author says that students need to be provided with support like graphic organizers, demonstrations, and modeling, tips for improving written work, and specific lesson on ways to more effectively write or describe ideas (O'Connell, 2005).

Cooperative learning was a main part of the study that the teachers from the college level and elementary level noticed when working together. The student's benefitted because it allowed them to come up with more ideas from talking to another person. Being with a partner was a non-threatening environment because they did not have to share with the whole class if they did not want to. Problem solving activities were also another concept that was written about in this article. The students were writing out how they were solving the problems and it helped the teacher a lot because then she could follow the students logic step by step. The author stated that problem solving used to be an assessment tool but now they were using it as an instructional tool (O'Connell, 2005).

There were many good and bad examples of the communication process in this article. It helped for me to see where these elementary teachers were making mistakes and why they were getting so frustrated when their students could not explain the answers. This article was very interesting because it had a lot of different concepts that explained how students could using writing when doing mathematics. There were examples of what the teachers did in their classrooms and how they fixed the problems that they were having with their students communicating their answers through writing. Over all, I really liked this article because it showed me not only good techniques when trying to get students to communicate about math, but also the bad techniques that some teachers are using.

O’Connell, S. R., Beamon, C., Beyea, J. M., Denvir, S. S., Dowdall, L. A., Friedland, N. G. and

Ward, J. D. (2005). Aiming for understanding: Lessons learned about writing

mathematics. Teaching Children Mathematics 12 (4), 192-199.

Process Standard- Communication

Communication is an important part of math, which is why it is one of the process standards. The four points that my group came up with from reading the article were

-Organizing thoughts in order to explain them to others

-Communicating clear and developed thoughts to others

-Reflecting on other people's methods for solving problems

-Expressing concepts correctly

Being able to communicate about math is important because it helps the students to really understand the concept that they are learning by organizing their thoughts. In the video analysis we watched how the teacher used discussion to talk about math. This was a different way to do math rather than having them just do problems out of the book. The teacher and the students were communicating about what they were doing. They were also reflecting on what they were doing and trying to figure out new ways to come up with different words that were worth more points. Communication is such a vital tool for any subject and I think students would like math more, if there was more communication involved. If the students can correctly articulate about math concepts that means they really understood what they have learned. In the standard it said that if students are challenged to think and reason about math and communicate about it, then it will be easier to understand when they have to write it out on paper. Listening to other people talk about math helps students to make connections in there head. I found this process standard to be very interesting because I never knew that teachers should be discussing math. When I was in school I was used to only doing problems out of a book and on the board. By watching the videos and reading this I realized that there are many ways that students and teachers can communicate about math.

Video Analysis #1

The fourth grade video addresses teaching variables to the students. Variables are something new that they have not learned yet and the teacher is trying to get them to understand what variables are. The teacher gives the students a task to create a variable machine. The machine is made up of two strips of paper.

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.

The teacher is asking questions to the students to try and get them on the right track and to see how much of the information they are understanding. I think it definitely contributes to the class because the students are trying to answer her questions. It seems like the students wanted to know more information about what they are learning. I think the teacher asking the questions is a positive way to help the students when they are learning new information.

2- What techniques does the teacher use to determine whether students have learned the material you are teaching?

The teacher in the video just walks around and looks at what her students are doing and why they decided to do that. She is making sure that each table is doing the right thing and observing where the students are at. She wanted the students to make the realization that if they change a letter to another number that it will also be chaning the variable.

3- Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.

The task in this lesson was for the students to create a variable machine where they could create a word that was worth the highest amount of points or the lowest amount of points. The were also using addition and subtraction when they were figuring out how much the word was worth.

Over all, I felt that this video was helpful to me as a future teacher. I will have to be able to use the different approaches that this teacher did like observations and questioning. The students seemed very responsive to this lesson and I think that was a valuable lesson because they had to make connections between the letters and the numbers. I thought this was an interesting way to teach a math lesson and will have to use it when I'm teaching math in the future.

"Provoking Intellectual Need" By Kien H. Lim

This article talked about how students need an intellectual need or internal drive to solve problems. It gives teachers ideas on how to create an internal drive for students when teaching mathematical ideas or concepts. Lim makes it clear that teachers might just teach the information that is going to be on the standardized tests. He states in his article “Although tasks should engage students and align with assessments, they should also cause students to grapple with the mathematics that we want them to learn” (Lim, 2009). I agree with Lim I think that teachers need to make their lessons engaging but at the same time they have to still meet the states standards.

The next part of the article is about the need for prime factorization and least common multiple. There were helpful visuals in the article that helped explain to the reader how to make these concepts interesting when teaching them. It shows the order that the students should go in when completing the problems so that the students could connect what they just did in the first problem to the next problem.

According to Lim “The purpose of an intellectual-need-provoking task is to allow students to use their existing knowledge to, solve a problem, feel challenged because of the limitation of their existing knowledge, and experience the need for the target knowledge to solve the problem” (Lim 2009). I think that this is a vital part to teaching students mathematics. Teachers need to be aware of their student’s prior knowledge so that they are not overwhelming them and that their students are not falling behind. I think that students give up easily when doing math problems, which is why teachers need to have engaging ideas. If teachers do this then their student’s will not be discouraged but excited to learn.

Lim, K. H. (2009). Provoking intellectual need. Mathematics teaching in the middle school

15(2), 92-99.

The Learning Principle

The learning principle explained how students need to learn mathematics through understanding. Today many students are not learning mathematics because they don’t understand it; they are just memorizing the facts and numbers. Students who understand mathematics are able to use it in other subjects and can apply it in different places by the connections that they have made from prior knowledge and new knowledge.

The article also talks about using math in every day life. Children are interested in math concepts when they are younger. They like patterns and shapes and even learn these concepts before they have entered school. Teachers need to take hands on experiences and make math exciting for children to learn and understand. The article states that social interaction can be used to promote the recognition of connections among ideas and the reorganization of knowledge (NCTM, 2004). I agree with this article because I do not think that making kids memorize facts necessarily means that they understand them. I feel that this goes along with what we talked about in class. How teachers still use timed-tests even though research has proved that they are not effective.