Reflection on Team Teaching Activity

Overall, I believe our activity went smoothly. Students seemed to enjoyed it and understand the rules and importance of the lesson. We were able to include everything we had planned to do and I believe we did so in a timely fashion. There was no rushing or unclear instructions; everyone had enough time to play the game and we were able to ask questions and review at the end. I believe our activity had many strong points, although there were some things we can do for next time to improve it.


I believe using the topic of money worked to our advantage because even at young ages children know that money has value. They are able to relate to it because it is an everyday necessity plus it is something they see their parents using, hence they want to learn about money so they are more like their parents. I believe by making this lesson more like a game peaked students interest, not only were they learning how to make a dollar but they were doing so in a manner that didn’t make them feel like they were doing school work. Another aspect I thought worked well in our lesson was bringing in different types of money. Even though different currency is most related to the social studies curriculum I thought it made the math lesson more relatable to the students by doing this as an introduction. Also, it is a perfect way of integrating both subjects together.


Some aspects that didn’t work the way we wanted them to and that we would do differently next time around included the game board, the size, the cutout coins, and the number of people we had playing the game at once. After watching students interact with the game we realized that it may have been to our advantage to laminate the boards and pieces for they had curved, therefore they would have been flat and would not have moved so easily or fly around. As well, we could have made the boards a bit bigger so students were better able to see it (especially for those with vision problems). I would make it a priority to use real money or toy money to make the lesson more authentic for the students. While the cutouts are ok it does not give the same affect as working with real money. However, due to the size of the class and time restraint, that was unable to happen this time around. Finally, I believe for future teaching of this lesson I will make it a priority to cut back the number of players per game board and instead allow students to do this lesson in pairs, that way students can work together and there aren’t too many playing at once.

Team Teaching - Counting with Coins

Team Teaching Lesson Plan
By: Mallory M. & Jennifer S.

GCO: Students will demonstrate number sense and apply number-theory concepts.
SCO: By the end of grade two students will be expected to count in a variety of ways.

For our team teaching episode, we will be concentrating on having students investigate the different ways they can make a collection of coins totaling one dollar. Through the use of teacher modeling, student participation, and problem solving activities, we will assist students’ acquire concepts and skills in coin recognition, counting sets of coins, and distinguishing the values of those coins. Our main activity will require students to move their game pieces around a board, while collecting and counting coins. The objective of the game is to be the first player to collect enough coins to total one dollar.

This activity will require students to expand upon their knowledge of counting skills by developing new strategies to assist them in counting. By using coins, students will be able to determine multiple representations of making one dollar, develop coin recognition, understand the values of different coins, learn how to count sets of coins, and select appropriate coins to make a given amount. By using coins to develop their counting skills, students can transfer their knowledge of money they use in their everyday lives, to the concept of counting.

Before we begin the Race for a Dollar activity, students will participate in a demonstration by the teacher. Though the teacher will be conducting this demonstration, the students will be asked for their input to show their knowledge and understanding of the concept. When the students divide into their groups and begin the Race for a Dollar activity, the teacher will circulate and take anecdotal notes to determine areas that may need re-teaching. At the end of the activity, students will be asked to explain how they got their answers and how many possible answers exist.

This activity is directly connected to the curriculum because students will be expected to count in a variety of ways, for example, by 2’s, 3’s, 4’s, 5’s, 10’s, 25’s, 100’s, and from various starting points (ex: 25, 50, 75, 100). The NCTM describes five process standards that refer to the mathematical process which students should acquire and use mathematical knowledge. Through our activity, students will practice each one of these standards in some way. For example, students will be required to provide reasoning and show proof for their answers to the problem, which complies with the Reasoning and Proof standard of the NCTM goals. They will also organize and consolidate their mathematical thinking through communication while participating in the main activity.

To take into consideration the diversity in the classroom, we will have students from different countries or students who have visited different countries, bring in currency from these locations and display it in the math center. There will be a brief discussion explaining how different countries have their own currency and the economic value of that currency.

Resources:

Department of Education. (2000). Mathematics: Primary – A Curriculum Guide 2000.
Canada: Division of Program Development

Van de Walle, J., & Folk, S. (2008). Elementary and Middle School Mathematics:
Teaching Developmentally. 2nd Edition. New Jersey, USA: Pearson Canada Inc.

Wortzman, R. (1996). Quest 2000: Exploring Mathematics, Grade 2, Revised Edition.
Dons Mills, Ontario, Canada: Addison-Wesley.

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.

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!