My Greatest Learning

What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?

Without a doubt, my greatest learning this term has been that mathematics is no longer about drill-and-practice and is now about creativity,  using manipulatives, and going down several different avenues to find the answer (or multiple answers) to a problem.

I have to say that at the beginning of this course, I was truly expecting to be sitting in rows, learning our multiplication tables, and making up worksheets of math problems to add to our portfolios for our students to complete. Boy, was I wrong! Through this course, I learned a lot about using different methods of solving a problem. One of the biggest things I learned was about the different ways of representing numbers and equations. I feel that this really clicked for me when we cut up our fraction papers.  Coming up with different ways to represent numbers made me think; "Wow.. this would have really consolidated my learning as a kid."

I also now think that it is incredibly important as teachers not to tell our students if it is "right" or "wrong". Students should be encouraged to explore all avenues on the way to solving a problem. Just because you came up with one answer does not necessarily mean it is right or wrong... just like any problem that we face in life, there may be other solutions! I have already started employing this strategy in my work as an ABA therapist. Whenever the child that I work with asks me "Kristen.. what's that? " I have started asking "Well.. you tell me!" Sometimes they do not come up with an answer at all, but I can see the gears going that they are certainly thinking about it! 

The bottom line is that as teachers, we need to allow our students to think of mathematics as a different way of thinking. Why should it matter if you can recite your times tables in a split second? It is much more important that students know where the answer came from, and how they can look at the problem to see all of the different answers. 

To conclude, I would like to say thank you, Mary, for an excellent term! I have learned so much about this different way of thinking not only in Mathematics, but in teaching in general! I wish you all the best in the future. :) 

A look at the Newfoundland Curriculum

On Tuesday, we had the privilege of taking a look at the province's prescribed curriculum, as well as the textbooks and supporting documents. There are three main things that I noticed about these documents:

1. They are not very "fun" 

2. They are quite comprehensive

3. They are laid out in chronological order

First the bad news, then the good news: simply looking at the curriculum documents and supporting texts, it does not seem like the mathematics curriculum is being presented as a problem that needs to be solved, but rather as work that needs to be done. As we have all heard so many times by now, children learn best trough play. This same concept applies to mathematics! It is so important for students to have the opportunity to learn rough inquiry-based learning to really dive into mathematics. The kindergarten through grade two textbooks seemed to begin to grasp this concept, because of the great use of colour and the integration  of children's literature. This was really exciting to see, and with the right planning, a teacher could have a very successful classroom in which children are learning collaboratively!  Unfortunately, it seems as if the textbooks in grades three through six are not as engaging as in the primary level. There is a certain lack of colour, which is not as eye-catching and fun as the primary program. The books do, however, utilize a lot of different strategies for problem-solving, which in incredibly useful for struggling learners.

The good news is that the mathematics textbooks do fit very well with the mathematics curriculum. Because the companies that produce the books are in the business of making money, they do their very best to cater to the needs of the provinces to which their product will be marketed. By this I mean that before they create the book, they take a careful look at the Newfoundland curriculum as well as the curriculum in other provinces to ensure that they are making a product that will sell. This works out very well for the teachers in this province, as most, if not all of the curriculum material that they need to cover is right there in the textbook! Furthermore, each grade level comes with not only a student textbook (and in the case of k-3, a workbook too!) but a teacher resource guide, which shows teachers how they should teach the material.Contrary to what students may (or may not) think, just because we are teachers does not mean that we don't need to learn!  While the textbook is an excellent resource for teaching math, teachers still need to ensure that they use appropriate manipulatives as well as games and technology in order to truly teach the subject so that the students will learn.

Finally, the best part of the curriculum guide itself is that it is in chronological order. I think that this aspect is crucial for students and teachers alike. I love it when things are laid out in a perfect order, and the curriculum guide does just that. As I look at the curriculum guide for other subjects, I begin to feel overwhelmed by the number of the number of curriculum outcomes to be met. Having them laid out in order is simple, yet almost calming in the way that they feel a lot more achievable.

Overall, I think that implemented correctly and integrated with technology and games, the curriculum documents are a great support to the curriculum outcomes in teaching mathematics.

YouCubed

YouCubed is a not-for-profit organization that provides free math resources for students and teachers of K-12. YouCubed strives to make mathematics fun, interesting, and relevant to students in order to provide a deeper understanding of what they have learned. Youcubed describes itself as a "revolutionary way to teach math education", as they provide real-life math problems from corporations such as Google. Furthermore, they will provide tools with which parents will be able to assist their children in learning mathematics at home.

I think that this is an invaluable organization that can definitely make the difference in a students' courage and confidence in mathematics.  It takes basic mathematics concepts, such as addition or subtraction, and makes them fun and exciting for students! One game in particular that I thought was fun was tic-tac-toe sums and products. This takes a simple game (Which, let's face it, students are already playing in class anyway!) and turns it into a learning experience for students that may otherwise be struggling, or thinking about how "boring" their math class is!

YouCubed is not yet fully operational, but encourages students, parents and teachers to sign up to receive emails and updates about new resources and news about when the project will be fully operational. (They even have a skill-testing question when you sign up. Fun!)

What does mathematics mean, anyway?

What does mathematics mean? Where do we use mathematics? Why do we love mathematics? Why do we hate mathematics? 

I consider myself to be a "scientific" thinker. I am always coming up with lists in my head and trying to figure out how things work. I feel that I always need to find the answer to a problem before moving on to the next one.

My boyfriend, on the other hand, hates mathematics. I asked him why he hates mathematics and when that started, and he replied that Mr. Jones spoiled it for him in graded eight when he couldn't understand the material that Mr. Jones was teaching them. 

Brandon is really good at mental math, adding simple numbers, and figuring out the price of an item after sales tax. But at the same time, feels that he cannot apply for a job in accounting because he "sucks at math".

I think that everybody thinks mathematically, whether or not they care to admit it or not. Whether you are an artist, sculpture, writer, mathematician or scientist, everyday life is full of fractions, symmetry, shapes, geometry and counting. From the time children begin to speak, we are counting their fingers, the number of steps that they are taking, the number of blocks in the tower they build. 

As humans, we are built to think mathematically! Do you have a song in your head right now? You are counting the beats of the song rhythmically into measures. Did you do your makeup this morning? There was a certain fraction of your face upon which you applied your makeup. 
Did you cook supper this evening? You used fractions to measure each ingredient that you added. Mathematics is everywhere, in nature and in our everyday lives.

Stanford University states that mathematical thinking, despite what we learned primary through high school, is about thinking outside of the proverbial box: "Mathematical thinking is not the same as doing mathematics... School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. "

Does Education Kill Creativity?

With his quick wit and humorous presentation, Sir Ken Robinson does a TED talk about the lack of creativity in today's classroom.

In all of my years of schooling, particularly in my four-and-a-half years at MUN, I have never once stopped to think about the lack of creativity in the classroom. I have always taken for granted that you go to school, it's a place that is boring, and you get to do fun stuff in your extracurricular activities or when you get home in the evening (if you have time between all of your homework). In fact, being in the Faculty of Education is the first time since my grade twelve music class that I can remember being encouraged to be creative.

What does this prepare our students for?
Robinson talks about the reasoning behind the drill-and-practice method of instruction as a product of the industrial age. When he puts it that way, it seems as if we are putting students on an assembly line to crank out future graduates.

This does not prepare students to be real people. Real life is not black and white. I recently read an article about how students do not remember the tests that teachers gave, or the homework that they assigned at night, but how they care for their students. How did the teacher connect with the student? This is a concept that seems to be missing from "modern" education. 

"Creativity is as important in education as literacy, and we should treat it with the sane status."
 To me, what this means is that we should spend equal time allowing students to be creative as we do teaching them to read and write. If a child is in school for six hours a day, they should be free to be creative for at least one third of this time. For me personally, when I am being creative, I am doing much more than creating something. I am learning a new skill! For me (and I am sure many others), creativity builds confidence,  which allows me to become more successful in the non-creative aspects in my life. If creativity allows our students to become the learners that they need to be, why aren't we inspiring them to unleash their creativity?

What does this video mean to me?
This video inspires me to bring creativity into my classroom. Instead of having students write a test, perhaps they can write a song about what they have learned. When I was in high school, I re-wrote the lyrics to one of my favourite songs so that I could remember the theories of several different biologists. To this very day, I can sing the song, and remember the significance of each biologist. This same idea should be brought into our schools every day. I guess it all has to do with finding your students' "zone", and finding the best ways in which they learn individually. Encourage them to be creative in their learning, and they will have a deeper, and more meaningful learning experience.

Mathematical Autobiography

After talking to several of my classmates, family members, roommates and friends, it is clear to me that everybody has a different math experience in school. My father was a physics teacher, and I remember at a young age (pre-school) sitting at our dining room table and solving simple math equations (1+1=2) for fun! I had a good beginning to my mathematical career, as I had a supportive home environment. I think that this was key to my success in math from K-8, but the downfall of my math experience in high school.

Mathematics: K-6

To be entirely honest, there is very little that I remember about mathematics in grades K-6. I do not remember a whole lot about Kindergarten as a whole, although I do remember my teacher not allowing me to play with the toys even though I had all of my seat work finished! I think that in Kindergarten and Grade one, our math classroom mostly consisted of us completing worksheets or workbooks at our tables with our classmates. Some manipulatives were used in our classroom, such as three-dimensional blocks, and counting pieces that looked like small, clear circles.

Although technology was not as advanced as it is today, I remember technology being a big part of our math classroom. At least once per week, we would have a chance to play Math Blaster in the computer lab. There were several other math games that we were encouraged to play, as well. 

Memories Surrounding Math

My best memory of Math was in the second grade. It was the first time that I had a male teacher, Mr. Giles. One day, he got us all to bring in a pair of socks. I cannot remember the exact point of the lesson, but I remember being incredibly excited that we all had our socks, and we were putting them on a clothesline that he had strung across the classroom. 

In K-6, I was very engaged and excited about math. One day, in grade six, the gym teacher covered a class for our regular classroom teacher, and he taught us about algebra. I remember that I had heard about it on television and in books, but had never known what algebra was. It was something that clicked instantly for me, I felt really smart when I figured out the value of 'x' for the first time. 

The only bad memory I have about math is when we had to learn our times tables. As hard as I tried, I could not bring myself to memorize the 6,7 or 8 times tables. I remember sitting in the classroom during our quick multiplication tests and just writing down random numbers.

I think that my overall positive experience in mathematics has opened a lot of doors for me as an adult. Although I was not necessarily a strong math student in high school, I feel that my background is strong enough that if I was required to do  a higher-level math course, I would be able to do it with a lot of hard work.

Math Skills

In K-6, Math came easily for me, so it often a subject that I typically enjoyed, or felt bored with when we would have to go over the same concepts several times. The one thing I remember really disliking about math was that we would have to copy down the whole equation into our notebooks instead of just writing an answer. Looking back on it, this was a silly thing to dislike. My dislike for such a small issue indicates to me that Math was a positive experience, because other people that I have spoken to indicated much bigger issues that they faced in the K-6 math classroom.

Role of the Teacher

Last semester, we learned a lot about the teacher being the facilitator of learning instead of an instructor. That the teacher should ask questions and encourage inquiry-based learning. Although I think that this approach would have been effective in our classroom, it was not employed to my knowledge. All of my math teachers were great, and I think that they provided an encouraging environment. However, I feel that a lot of what we learned was straight from a text book, with very little hands-on instruction.

Assessment

 Assessment in math was typically in the form of a test or assignment. Although this is a very concrete way to test students' learning, it can be quite unfair to students that have difficulty writing tests, or take longer to learn certain materials. 

High School Math

In high school, math went downhill very quickly for me. Although I was still a strong math student in comparison to my peers, the looming date of graduation brought a lot of pressure on me to get a good grade in math so that I could 

a) get into any math course that I needed in University

b) get an entrance scholarship into Memorial University.

This was a lot of pressure for me, which was oddly the opposite of motivating. My parents insisted that I take advanced mathematics, because I was capable of doing the work. I did not mind it in grade 11, but I was not at all comfortable with Math 3207, an introduction to calculus in grade 12. While I did pretty well in 3205 (our required course to graduate), 3207 was completely optional, and as such, the homework piled up and up and up, and I failed every test, and every assignment. This was completely out-of-character for me, as I was an honours student in every other class. This course made me feel completely overwhelmed, which made me shut down entirely, and really ended math on a sour note at the end of high school. 

University Math

I enjoyed completing Math 1050 and 1051. I did not do any electives.

Mathematics in Real-Life

On a day-to-day basis, I do not incorporate mathematics in a major way. I use it as anybody else does; to split bills with my roommates, to calculate the price of an item on sale, or to add the weight or measurements of my food. Although I did have a bad experience in one of my high school math courses, I do feel that I am a scientific/mathematical thinker, so I probably do use math a lot more than I consciously think. 

Feelings about Mathematics

Today, I feel pretty positive about math. It is not something that scares me, as it does a lot of people I know. I think that it is a necessary component of being a functional and successful adult, and I think that it is important for teachers to provide an encouraging environment in which students can learn math so that they do not feel intimidated when learning math as they get older. 

Welcome!

Welcome to my Math Blog!
My name is Kristen and I am a fifth year student at Memorial University of Newfoundland. As an assignment in Education 3940, this blog is meant to allow me to reflect upon my experiences, memories, ideas, theories and challenges in math education. I look forward to learning more about math education!