As advertised, here is a post about Conversations from Algebra 1 and Research and Teaching.

There are several reasons this post has come a little later than anticipated. One of them is that I had a job change, some would even call it a career change, shortly after my last post. I am now working as an Instructional Designer for a company in Salt Lake City, Utah. Maybe someday I will post about why this change occurred, but not today.

CONVERSATIONS FROM ALGEBRA 1

During the two quarters I spent teaching this school year I worked with my Algebra 1 students on some problem sets obtained from the Philips Exeter Academy, a private school in New Jersey. The problem sets are designed to engage students in problem solving, not simply computing answers using methods shown by the teacher at the start of the class period. I was not sure how the students (or parents) would respond to this strategic shift. I did feel that it would be possible to get the students engaged and interested, and expected that I would have to encourage and prod to get some of them to work. All in all things turned out well.

Let me explain a little about the daily classroom procedures we followed. I would pass out a set of problems at the beginning of class and students would work on them. Problem sets varied in length from 7 to 12 problems. Almost all of the problems were what are generally referred to as 'story problems' among students and teachers. Students would work in groups or by themselves, whichever they preferred (some were initially opposed to talking to other humans, so they chose to work alone, though once they saw that everyone was struggling with the problems they quickly joined their peers). As the students worked on the problems I would stop by each group and ask more questions, get them to share their thoughts and ideas, and help foster discussion amongst themselves. I would then leave them alone to figure out a solution to the problem. Every fifteen or twenty minutes I would have students go to the board and share what they were thinking about a particular problem that was stumping the class. If the class had successfully solved a problem, I would ask several students to go to the board and show their solution. I would usually have two or three different students present solutions, and each would be unique. We would then talk as a class about why the presenters did the things they did. If a student made a comment that was inappropriate I would tell them that it was an inappropriate comment for the setting we were in. They quickly learned how to ask questions and challenge each other in a respectful manner. Students rarely got through more than five problems during our class time (89 minute class periods every other day).

One day we got into a discussion about positive numbers, negative numbers, and the number zero. The discussion may have been about opposites, it may have been about positive and negative numbers, I don't remember exactly what, but the students began asking each other questions and explaining why they felt zero was positive or negative or not a number at all. It was amazing to hear them carrying on a respectful, mathematics based conversation.

Several of the students in the class were students that did not get along well with other teachers. I taught in a high school, and many of the students were not academic over-achievers. They had learned to respect each other and to share their thoughts. I guess I was so impressed because it gave me a glimpse of what I think a mathematics classroom should be: a place where students are engaging with each other and with mathematics.

RESEARCH AND TEACHING

I think the teaching community has a long way to go before we can be called professionals. This is a strong statement, but I think it is an accurate one. I have heard recently the comments of professional athletes regarding their preparation for games. They talk about watching film, about studying other teams' players and plays. They use the latest research on training and health to keep their bodies in top physical condition. They are dedicated to improving themselves, and the better they get the more entertained the crowds that watch them, and ultimately pay them, are.

What about in teaching? Do we ever watch film of ourselves? Do we ever watch film of others teaching the lessons we teach? Do we know if the lessons we teach are effectively teaching the topics we think they are teaching? Do we know how the students see us, and more importantly, how they see the math?

There are some good things happening in math education. There are teachers and leaders who are working to create a quality environment so that their students can learn mathematics. But there is room for improvement.

I once sat in a meeting with those considered to be the leaders among math teachers in the school district where I taught. We were discussing ways to improve math instruction. An idea was presented that was in line with recent research on math education, and one of the veteran teachers in the group, remember this is a group of the leaders in the math teaching community of one of the largest school districts in the state of Utah, said something along the lines of "New teachers have too many other things to worry about." What other things was she talking about? Things like taking roll. Things like learning how to keep a classroom full of students busy so they didn't cause trouble. These are important things to learn as a teacher, but why not learn how to do them by becoming better at helping the students interact with the mathematics? Why not make mathematics education our primary concern, and figure out ways to use the mathematics to accomplish the things that we have to worry about as teachers?

It seems to me that there is not enough focus on, or knowledge of, recent research in mathematics education among secondary math teachers. Math teachers should be recording themselves teach, and then watching those recordings to see how students reacted to what was done. We should take what we learn from these videos and apply it in our teaching. We should have time to do these things, but currently we don't. Teachers, and those who ultimately make the decisions on spending for education, should be working on ways to make time.

CANS OF WORMS

I have probably opened several cans of worms above, more than I could eat in one sitting. I think many are aware of the current problems in education. I also believe that we should all do our part to come up with solutions and to solve these problems. I will write more on one proposed solution in days to come.

## Sunday, May 18, 2008

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