Team Teaching

Team Roster:
Sarah Harnum
Kim Burrage
Susan Whitten (me)

Team Goal:
Teach future teachers about a grade 4 lesson plan centred around a theme of estimation.

Game plan:

• We got together to decide on a topic and formed some opinions on what we would like to see happen.
• We decided that instead of addressing the class as if they were pretending to be grade 4’s, we wanted to propose an idea to future teachers for their classrooms.
• We looked through multiple education oriented resources such as Teaching Children Mathematics and Mathematics Teaching in the Middle School searching for the “perfect” problem.
• We wanted a problem that was different from what we had seen in previous team teaching lessons and we knew the problem had to be student-centred and inquiry based. This meant that our problem had to pose a question or task to our students and have them use a personal choice of mathematical strategies in order to solve it.
• When looking through Teaching Children Mathematics I came across a problem called “Counting is for the Birds” which I really liked. It dealt with estimation (something that hadn’t been taught yet in our class), and it asked the students to use whichever strategies they wanted (student-centred) to answer a question (inquiry-based).
• We chose to give the class 4 minutes on this task as we wanted to keep the time-frame small so that students wouldn’t be able to count every bird.
• After they had come up with methods, we wanted to get students to come to front of the class and explain how they got their answer. This gave a chance for all students in the class to see various estimation strategies.
• At the end of the class we wanted to emphasize that this lesson could be altered for a range of grades (by changing the complexity level of the picture) and that the outcomes could be diverse as well. Younger students could gain number sense of “bigger” and “smaller” or older students could learn new methods of estimating accurately and efficiently.

Post game reflection:
After completing our lesson there were a few things I wish had gone a little differently:

• I feel that the lesson was too short. The students completed their estimations in a very short amount of time which then pushed us to continue with the conclusion of our lesson. If completing the lesson again I would ask the students more questions like: “Show me 3 different ways you could estimate the number of birds” or I could use a more complex picture that had various “distraction” details in it such as trees or airplanes.
• I also would have had the discussion session continue for longer. I would have liked to get the students to ask more questions regarding their peers’ solutions and I would have liked more students to share their solutions in general.
• Finally, I feel that our outcome was not emphasized as much as it could have been. This could have been different if we asked the students to classify the strategies by characteristics; such as “used number sense of more or less”, “used division and multiplication” or “used grouping”.

Overall I feel that the team teaching experience, both as a teacher and student in the classes was a thought provoking learning experience. On the student side, I was forced to use my mathematical knowledge and determination to solve problems which we diverse and entertaining. As a teacher in the class I had to think about the characteristics of my problem and my students in order to give them the best learning opportunity possible. It was a rewarding chance to see the potential of mathematics in the classroom and will push me to continue learning about inquiry-based, student-centred teaching in the future. 

Step right up to The Math Fair

For the Math Fair myself and my partner Kim Burrage  facilitated the Double Dozen problem. This mathematical problem uses a deck of cards (where the face cards and aces are removed) and asks the student to create a mathematical sentence that equals 24. The student can use any or all of the four cards dealt and they can use any or all of: Addition, Subtraction, Multiplication or Division to design their sentence. The mathematical problem was to use a limited set of numbers and any operation(s) to find a way to make the numbers equal 24.
I think this problem caused a few of my classmates to feel uncomfortable. I believe they felt this way because they were forced to think on-the-spot and probably felt rushed for not knowing how to solve it right away. A few tried one round but were reluctant to keep going which was also most likely related to feeling "stupid" for not knowing their times tables or how to create a satisfying solution.
I noticed that many of the students were saying "Oh no, I'm not good at mental math" when really they had hardly given it much effort. The same thing occurred with guessing or trying out an answer, if the student found they were wrong, they seemed embarrassed and mumbled a similar response. I think this might speak for the way we were brought up to think of math; "if you can't get an answer quickly, you're not very good at math" or thinking that you always have to be right.

Due to the fact that our problem was so simplistic, there was not a whole lot to actually do, other than explain the game. If I were to do this very task again (and I hope to!) I would be sure to give the students more reassurance. Even though I did say things like: "take your time" or "it's okay, sometimes it isn't very easy" I feel like I could have given more reassuring feedback to explain that it takes time to manipulate your thoughts and try your answers.

When circulating the fair I realized that everyone has a different way of thinking of things. Everyone's perspective on one problem will be different than my own. When I was at one table, for example, Vicky mentioned as I was completing a puzzle that I was going about it a completely different way than other people- it made me feel smart to think that I can still get to the same solution but just by thinking about it differently. It made me feel special..in a good way!

What I loved most was seeing and experiencing what it feels like to figure something out. That pinnacle of success is such a rewarding feeling. On multiple occasions I squealed loudly (sorry everyone!) in excitement that I had figured out a problem. It was also really great to see others finally figuring out problems- you could see the pride on everyone's faces. The most challenging part was definitely restraining myself from giving clues to the students that tried Double Dozen. It was hard when I could see a solution myself and I could tell that they were stuck in thinking about only one operation- at times I desperately wanted to say "hmm, maybe you should try..." but I'm so proud that I never! Sometimes the best way to help someone is to not help them at all...hey doesn't that sound like a proverb or something?

In every respect I loved the math fair. I really did! I think it's a great way to get students' brains processing and applying all the knowledge they've gathered throughout their mathematical lives. Every problem can be challenging and rewarding in a different way; I think all students of any age, ability or interest level would benefit from an event like this. It's a new way to make Mathematics exciting and engaging that I plan on implementing in my own classroom.


Great job everyone! :)

What, oh what, might Mathematics be?

That's a great question! One that requires thought and thought and more thought. As we discussed in class, our view of mathematics will be constantly evolving. Every experience we have that involves mathematics (or any subject for that matter) will effect our perspective. Each course, each school, each class, each principle, and each student will have an effect on the way we think- and thank goodness! Without encountering different view points and opinions, our minds would never grow.
So, specifically about math: a mere few weeks have passed since the beginning of this course and already I can see a shift in my thinking patterns. At first, when I thought about math, I thought about the math classes of my past which involved teacher introductions, teacher demonstrations, class practice and independent practise- which was being instructed to do worksheets with countless monotonous problems. Looking back, I remember that whichever students enjoyed math were the students that came up with the right answer. So, these patterns contributed to my perspective on mathematics- Math is a series of processes and formulated strategies that are known to work, students follow the lead of the teacher until they can do as the teacher has taught and reach the answer.
After reading the Van De Walle text and attending classes, I have changed some of these perspectives. Although it is difficult to shift my way of thinking, I realize that math is not all about getting the right answers.I have learned that it is important to encourage my students to try what they think will work and then evaluate, criticize and explain their answer in order to determine if the answer makes sense. I have also come to realize that there is more to teaching math than instructing strategies that work and giving practice work to students. Instead of teaching them how to do it, I can teach my students how to experiment with math and how to find out what they need to do. Most of all, I have come to realize that math is about making sense. Problems must be solved in a way that is logical and that can be explained, without this, the science of math is flawed.

Might mathematics be a humanity?
Well, I just called math a science (due to what I've learned from the Van de Walle text)... so can it be both?
I think that humans play a large role in mathematics and the way is it understood and taught. But is it a humanity like philosophy, art or literature? I can't decide! Philosophy, art and literature seem to be subjects revolving around human creation (of thought, or artwork and of writing) but is math created by humans or does it exist and is discovered by humans? Hmm, Ill have to put more thought into that one..definitely a question that will get your mind churning.

Creativ... oh really? Art class is over already?

A student is drawing a picture
Teacher: "What are you drawing?"
Student: "I'm drawing a picture of God"
Teacher: "But how are you doing that? No one knows what God looks like."
Student: "They will in a minute."
That is my favourite anecdote from the Ken Robinson talk on creativity. I think this was a perfect story to tell in order to convey that children are with born creative minds and that it is our job to foster every single one of those imaginations.

Creativity is sparked in children through opportunities of self-expression. I believe that when students are given ample time and encouragement to express their ideas, thoughts and feelings, their creativity levels will soar. When looking at school by way of dividing subject areas, I would say that Art, Gym and Music would be the most obvious subjects that support creative expression (while other subjects do offer possibilities for creativity, these are the first to come to mind).
I think that all too often students do not have the time they need in these subjects in order to express themselves. For example, in my experience I remember my teachers using art class as a reward or bribe; "Boys and girls, if you can't be good listeners today we won't have time for art class". In addition, as the title of this post suggests, these classes are often cut short due to time constraints and curriculum demands. By cutting down on creative outlets for students, we are relaying a message to our students that creativity is not worthwhile and is there "just for fun". Ken Robinson wants us to realize the exact opposite. Creativity is a huge part of education and plays a large role in our daily lives. Imagine how boring our lives would be without any creativity; there would be no art, no music, no dance, no literature, no architecture, no fashion... we would be yawning all day long!

Mathematics is not one of those obvious subjects I mentioned above that scream "creativity" but I do believe it is possible to introduce imaginative thinking into the math class. Mathematics involves solving problems by experimenting, rearranging, constructing, inventing and questioning- all of these verbs involve using the creative aspect of the brain on order to come up with a response. While teaching mathematics teachers can utilize their knowledge of students' creativity and emphasize that mathematics is about thinking in different, creative ways.

I agree with Ken Robinson, I think we need to change our message to students and teach them how build on their creativity and use it as a life skill. In our world there are too many problems that need solutions- and who else but creative thinkers are going to solve them? I believe that in every subject area there is space to build on creative thinking and imagination, so as a future teacher (*holds up right hand*) I vow to devote the creative encouragement and opportunities my students need and deserve!

Math Memories- My Math Autobiograpy

Reflecting on my experiences from primary/elementary school is usually a challenge for me. It is difficult to look back on my experiences as a young child and view them through a totally different perspective. As a student going through grades K-6, I was not totally aware of the purpose of learning certain things- for example, I knew we studied math because we had to, because it was something everyone did. Looking back on my experiences now (as a teacher-to-be) will help me realize the views, emotions and ideas about math education in the lives of primary/elementary students.

• Mathematics was everywhere, in each of my classrooms going through K-6. There were always posters that depicted math problems, solutions and math topics. The walls in the classroom would be plastered with math paraphernalia. Also, there were always carts and supplies that were used for math, such as those yellow cubes used for doing equations, that were visible in the room. Everywhere you look in a primary/elementary classroom, you see math physically portrayed, ready to be absorbed.

• My best memory surrounding math would have to be when I was chosen to take part in an enrichment course outside of class. Myself and a few other students would leave the classroom with another teacher to learn about and do "more advanced" math problems. I loved this because I felt that in order to be chosen, I had to be really smart. It definitely affected my confidence in math, urging me to learn more. 
My worst memory involves learning about Problem Solving. I remember starting an entire unit on solving word problems in grade 4 or 5 and hating every minute of it. I had a lot of trouble understanding these problems and therefore was often not successful in completing them.
As an adult, reflecting on these memories reiterates how important being successful in math is to young children. The memories that are the "best" are usually when a child is successful and the worst memories involve "failure". I would say this still holds true today- when I understand math, I love it but when I struggle- I dislike it.

 • I feel like I was "good" at math. For the most part I grasped the concepts and moved forward at the speed of the classroom. I would say that my marks on my tests and my ability to complete a problem suggested by my teacher in a short amount of time made me feel confident in math class. 

• The role of the teacher in math class was to: explain a topic, provide examples, give out practice problems and circulate around the class in order to help students. This was the basic structure of the math classes I remember. I think many teachers saw math as a challenge to teach due to the amount of material covered in each grade and the problems that often developed from students frustrations.

• Math assessment in primary/elementary were mainly in the form of tests. After a math topic had been taught, practised and studied, a math test would follow to gauge final understanding. Throughout the topic, we would have worksheets and oral math problems to complete.

• I remember having issues with math as soon as I went into Junior High. I remember in grade seven , I got the lowest mark I ever received - a 23% on a math test. All throughout Junior High I struggled with math; I had tutors and extra help from teachers but the material was not "clicking". Eventually, something must have "clicked" because after grade nine I started to excel in math and it was that way all through to grade twelve. I blame that period of total frustration and confusion on the cursed hormones...

• In university I took Math 1090 and Math 1000. I enjoyed calculus and understood it fairly well but I stopped after those courses in order to complete other required prerequisites for the Education Faculty. I did not choose to complete any math electives because I chose to focus on French as my concentration area.

I feel that my education experience in math has been fairly positive and encouraging. I  know that math is everywhere and is in everything we do. It would be impossible to get through a day without using some part of my math knowledge. I know that even though I may not be capable of understanding the world's most complicated mathematical problems, I am confident and comfortable with teaching my future students the mysteries of math.

Welcome to my Blog

Hello! I warmly welcome you to My Math Blog!

My name is Susan Whitten, I am a 21 year old Education student at Memorial University. I am taking Education 3940- Mathematics in Primary and Elementary Grades with Dr. Mary Stordy.
I am from St. John's and have lived here my whole life. I chose to pursue education due to my interest in and affection for children and the way they learn. I hope that through this course I will learn and expand on teaching methods, processes and strategies. 

This blog will contain responses to class discussion, math education topics and my experience as both a student and pre-service teacher.