March 17, 2009 - Activities

Today’s class was very interactive, visually appealing and hands-on! To begin we had the opportunity to try out our new fraction kits we had made last class. We were given problems and were able to make up some of our own. At first there was a bit of confusion but after discussing it as a group we were able to come to an understanding about fractions. Being able to see the fractions laid on the table represented by pieces of paper was very eye opening and helped me in understanding the concept so much more. As I mentioned in an earlier posting, I had great difficulty understanding fractions as a child however using this manipulative made the concept so much easier to comprehend.

For the next activity we were given a sheet of paper with one large triangle, which contained smaller triangles located inside of it, as well as objects/manipulative such as triangles, octagons, etc. The goal of this activity was to cover the triangle using the given objects and getting your partner to place the last piece on the game board, hence making you the winner. This was a very fun game with many different strategies one could use to win. I actually remember doing this when I was younger, even though I did not know there was a point to it at the time.

The last activity we looked at dealt with straws. Each group were given a bunch of straws and then taking turns we had the option to pick 1, 2, or 3 straws, with the goal of getting your partner to pick up the last one. Again strategies are a big aspect to winning this game.

Overall, the day’s class was very rewarding. Having the opportunity to explore the fraction kits and activities helped me realize once again that there are no right ways in going about approaching a problem. Children need to know this and these activities provide the perfect opportunity for them to observe it. By being introduced to these activities I was able to walk away with ideas for my own class and a better understanding of how different strategies work to solve problems.

March 12, 2009 – Fraction Kits

During Thursday’s class we had the opportunity to construct our own fraction kits. This was my first introduction to fraction kits, up to this point I had never seen or even heard of one. To start, each of us were given eight different colors of paper, along with a handout that we were to follow in order to construct the kits properly. Then we had to follow the instructions and begin cutting the paper into the appropriate sizes according to the patterns illustrated on the handout. While this may have been time consuming it was actually fun. We were able to relax and talk with one another, while at the same time observe how each of us constructed out kits. If we were stuck on one, you were able to ask the person next to you how they did it, it was just another way to show us how differently people go about solving problems and how there are many ways to go about completing an activity. For example, at my table alone one would have observed four of us constructing our kits in different ways; some used scissors, others tore the paper, and some folded differently, however in the end we all ended up with the same size paper.

As a child, I had great difficulty understanding the concept of fractions, and to be honest I still do today. However, having the chance to construct this manipulative gave me more of an understanding on how they work. Being able to visually see the equation helped me understand fractions so much more. I believe this would be a great device to use in the classroom, not only is it inexpensive but once the kits are completed the kids will be able to keep it for future reference. Fraction kits are definitely something I will use in my future class!

February 17, 2009 - Mathematics for the Moment, or the Millennium?

On Tuesday, February 17, 2009 we read and discussed the article Mathematics for the Moment, or the Millennium? This article was based on a study that took place in England where researchers tested two different methods of teaching mathematics to children. Throughout the article the writers discuss thoroughly the two forms of teaching they conducted and the results they received by using these forms in schools.

For the teaching methods, they used a textbook approach, where the focus of teaching was based on the use of textbooks; and a problem-based approach, where the focus was on more of an authentic learning style, hence making the problems more open ended.

Over the three-year study, it was discovered that children in the problem-based school received higher grades in math examination due to the fact that they had a better understanding of mathematics, instead of relying solely on one method for solving a problem they went about solving them in different ways.

Throughout my own school experience I remember most of my teachers using the textbook approach, with the textbook and seatwork being the basis of each math class. What approach would I use? While I saw nothing wrong with the textbook approach back then I have come to the realization that the problem-based approach is much more useful/easier in a math setting. Unlike me, my students will know that there are many different ways of solving problems and that they do not have to rely on just one method for an answer. The problem-based approach helps children relate to everyday life, they do not have to memorize certain solutions; instead they get to work hands on to help understand the problems they are to solve.

Overall this was a very interesting article. It helped me see that while both of these approaches have their good qualities, I would prefer the project-based approach when it comes to teaching math in my class one day. Even though my focus will be the project- based approach I will make it a priority to use the textbook approach as well because I feel children will gain insight by learning math in different contexts. It will give them an overall feel of the different ways of going about learning. If textbooks worked for me there must be some merit to their use in the classroom.

February 10, 2009

Today’s class once again began with a discussion concerning our observation days. Each week I learn something new and more and more I appreciate hearing the stories from my fellow classmates.

The first thing we dived into this week was a discussion about conceptual and procedural knowledge. We talked about how conceptual knowledge consists of rich relationships or webs of ideas and how procedural knowledge is knowledge of the rules and the procedures used to carry out routine mathematical tasks and of the symbolism used to represent mathematics. I believe my own experience of mathematics dealt primarily with procedural knowledge. I remember all too well memorizing how to do the step-by-step procedures of certain equations but not quite understanding what they meant. It’s good that we take both into consideration today when we teach children. However, I also worry that I will end up like my own teachers and fall into the method I had grown up knowing; hopefully that will not be the case since we are learning the proper concepts in this course.

We were also introduced to the text Thinking Mathematically by John Mason, Leone Burton and Kaye Stacey. This book lists four processes that students use to help them think critically about mathematics, they are: specialize, generalize, conjecture, and convincing and justifying. I think this would be a great book to read and hopefully I’ll have the opportunity in the future to do so. I believe it would be a great asset to the classroom.

There was also a discussion about the three phrases one goes through to do a math problem: entry, attack, and review. I felt like this was a perfect way to look at a problem, its helps children be organized and puts the problem into perspective when they are working on it! Children are able to start off thinking about what they know about the problem, then how they would plan to go about solving it and then having the chance to think about what they just did. I really enjoyed looking at math problems this way and see myself using this in my own future class one day.

Overall, today’s class was excellent, very informative, giving plenty of ideas and sources that can be used one day in our own classes.