February 5, 2009

Thursday’s class began with a reading from the book The Number Devil by Hans Magnus Enzensberger. This children’s chapter book follows 12 dreams of a little boy who hates math. He meets a number devil in his dreams that goes on and introduces him to the wonders of math! Up until this semester I never knew that there were books which made math interesting and exciting for students, however since starting this class I’ve come to realize there are a lot of good books that teach children about the values of math. These books are quite useful and I plan on collecting and using them in my own class one day.

The second part of class had us working on a math problem. Each table were given sand and asked to count the number of grains. At first we all kind of looked at one another and had the expression of how in the world do we go about doing this! After discussing it for a bit we decided to take one cube of sand and split it into 4 pieces, we then went on to group estimate one of the quarters. That enabled us to get an estimate of one of the quarters and we then multiplied it by four. This gave us the amount of sand in one cube, we were then able to go on to fill the cubes in with sand and multiply them by the number of grains in the one cube. Another idea we came up with was using a sensitive scale to get the weight of one grain of sand, after which we could weigh the pile we were given and divide it with the weight of the one grain, therefore giving us an idea of how many grains of sand were in the pile. We began to realize that we would never really find the true answer to the question.

I’ve come to the realization over the last couple of classes that math can be very open-ended. There are many ways of going about solving math problems that don’t necessarily take a couple of seconds to complete. Throughout my own school experience we were always given a time limit when working on math problems, we were never given the opportunity to explore and look at them in different ways. We all had to complete them the same way in the same amount of time, the teacher did not take into consideration the type of learners we were. I have also learned that working in groups for math is a real eye opening. Everyone brought different ideas and opinions to the table and we were able to see how others look at going about solving a problem, we had to communicate and respect one another’s opinion!

February 3, 2009

Unfortunately I was sick for today’s class but after talking to some of my fellow students and reading some blogs I learned that the days focus was on the problem that was posed at the end of class on January 29th… “If a 2cm cube was dipped in paint, how many 1cm faces would have paint on them?” Even though I was unable to hear everyone’s answer, just from the time we spent on it on Thursday I could see that each of us at my table took the problem to mean something else. While I went about counting each side to get 24, some at my table questioned if the cube was submerged all the way into the paint or not, therefore the answer could have been 4 or 12. Just from this I was able to see that many people interpret questions differently and that open-ended questions have many possibilities!

January 29, 2009

On Thursday’s class we had an opportunity to go through the textbooks that are being used in schools. My table decided to look at the Grade 1 teacher’s text, workbook and curriculum guide. I can’t remember my books from that long ago but I enjoyed the ones they are using today. They use bright colors and illustrations to draw the attention of children and the activities seem interesting and fun. I especially enjoyed the teacher’s text. It gives great ideas on how to integrate math into other subjects like music and science, and it also contains worksheets and ideas for assessment like rubrics and checklists. We also had a chance to use manipulatives. It was nice to see some of the things students use in the classroom and I’m excited to learn more about the effects of them on the class. At the end we were given a problem to do amongst our table. It was interesting because we each went about it in different ways and came up with different answers, all of which could be right!

January 27, 2009

In today’s class we had the opportunity to discuss with our fellow classmates our experiences during our observation days that had taken place on January 26th. I enjoyed this because for the most part we really only discuss with people we talk to how our day went; it was nice to hear other peoples experiences. I also enjoyed hearing about the math lessons. Since starting our observation days I have only witnessed a couple of math lessons but it has become clear to me that math has changed quite a bit since I went to school. For the most part when I went to school we never did group work in math, however throughout a couple of my observation days I have witnessed two classes who did and they seem to work quite well.

I have also realized there are many new ways and techniques on how to teach a math lesson. In class we have discussed things like 10-frames, Mad Minutes and group work; things I had not heard of until my observation days and class. I hope to learn more about my classmates’ observation days and the new techniques that are being taught in the schools.

We also discussed how many math problems could be interpreted in different ways. There isn’t necessarily one right answer and that became apparent when we were asked the question “The answer is 5, what could the question be?” We were all coming up with different ideas on what the question could be. It made things very clear on how kids might feel when they are told an answer is wrong even though it could very well be right!

What is Mathematics?

Honestly this question confuses me to no end. You would think as someone who was working on a math major at one point in her life I would know the definition of what math is? But I’ll admit, I do not. When I think of math I think numbers and symbols used together to solve an equation. I think of protractors, rulers, graph paper and calculators to show how I proved an answer. But I cannot think of a correct definition. I do remember being given definitions for geometry, calculus, algebra, even statistics, but not math! When I think back on past teachers and professors I assume they must have given me a definition but too much time has past since then to be sure.

After reading chapter 2, I would definitely say my math education falls into what Vandewalle and Folk describe as the Traditional View of Mathematics. When thinking about past experiences math lessons always began with an explanation and then the teacher showing the class how to go about solving the problem. The goal was getting the right answer and having the teacher correct them. I do not remember hands on activities (this however does not mean my teachers didn’t do it) and if we did do anything it involved the teacher assigning questions and occasionally being allowed to ask a friend for help if needed. This probably accounts for why I have no recollection of a definition for the term; I was too busy trying to solve the next question.

Personally, when I think of math I envision my class as active participants in their learning. I want them to understand math, not just be able to solve an equation but to be able to understand what it means to see/use it in the written format. I want them to work with one another and use manipulatives, and discuss how they got an answer. I want them to know that it is okay if they do not understand a method and that there are many ways to go about finding an answer. I do not believe having students sit at their desks, copying the teacher is the right way to teach children about math.

The interview with Mister Reuben Hersh was very eye opening and left me thinking about math in a different sense. I agree with Hersh when he says that math is social. It is true when he says everywhere we turn math is present and I admit sometimes I don’t even notice it. It’s been a part of history from the beginning of times and our culture very much depends on it. He puts it nicely and makes one think when he says math is “Internal to society and culture as a whole, external to the individual, who has to learn it from books and in school”.

He also goes on to describe a “good math teacher”. He says teachers should start with examples, and then they should ask the question and then give the answer. He mentions observation of the students is essential to a teacher for it tells if the students understand what is going on. He says students should be allowed to speak for it is what makes a math lecture. If more teachers did this maybe math class would be more productive!