This Hour Has 22 Minutes Presents: An Interesting Method of Calculating Probability

Canada did win the gold... does this make his reasoning sound?

A "Mathematial Revolution"

The organization YouCubed aims to revolutionize the way mathematics education is taught through free content and tips for teachers and parents.  My favourite part of this website was the focus on how we can change the way our students think and feel about mathematics.

Mathematical Empowerment > Mathematical Failure

The section that stood out for me the most was "Unlocking Children's Math Potential".  So many attitudes about math that I recognize in myself and my past classmates were highlighted.  Some of the concepts that really resonated with me are:

 1. Mathematics as a "gift"

•   It is so easy to believe that some have the natural ability to be successful in math while others do not and will not ever achieve what the "gifted" students do.  I experienced this in grades 5-8 when I attended a school for "gifted" students.  I could not calculate many of the same problems as fast as my peers, and for the longest time I believed that because I didn't have the gift of math that I was probably selected for that program accidentally.

2. Fixed vs. Growth mindset

• Mindset is the students' idea about their own abilities and potentials.  Many students with a "fixed" mindset believe that their abilities are static, and that if they are unsuccessful in a task the first time it isn't "meant to be" because they don't have the ability to complete it.  Students who persist and learn from their mistakes have a "growth" mindset.  Something that surprised me was that even high achievers (according to the article it is mainly high-achieving girls) have a fixed mindset.  I think this is because I usually relate the fixed mindset to students who don't attempt any task beyond what they are easily capable of (I used to be one of these students!).

3.  The relationship between speed and mathematical calculations

• In my background with math speedy calculating was always something that was valued, and it is one of the reasons why I disliked math.  Research now shows that expecting speed from students in mathematics is actually counter-productive and does not show the true potential of the student (in fact, stress from timed tests causes a block in the working memory where math facts are stored).  I wish they would have known this 15 years ago!

4.  The teacher's attitude is essential to how the students view themselves in mathematics

• This point is pretty obvious but I think that educators should be reminded about it often.  Young students are so impressionable and we can't allow any of our negative feelings about any subject affect our students.

After browsing this site I feel like I am not alone in my math experiences, and I definitely feel more empowered to teach mathematics in the way that is the most beneficial to my students.

What is Math?

When I try to summon my own definition of Mathematics, I tend to think of it in terms of the subjects it encompasses: addition, subtraction, geometry, algebra etc.  I knew it was much more than that so I  asked a friend what he thought the definition of what math might be to get a second opinion. After a long pause he said “Well, I guess it might be how numbers relate to one another”.  It is pretty clear to me that our definitions of math have been constrained by what we understood math to be in school, when in fact the scope of mathematics reaches far beyond that. 

So, to find out an all-encompassing definition of what Mathematics is, I turned to the internet.  I found a simple definition on Wikipedia:

Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change. (en.wikipedia.org/wiki/Mathematics)

Within this definition we find some words that we may not immediately connect to mathematics.  For me, these words are all of the ones that come after quantity.  When considering the definition it does make sense to include structure, space, and change as part of the study of mathematics, it is not something that many students are familiar with in the K-6 classroom.  

The internet was not so kind in my search of what defines "mathematical thinking".  There are courses one can take online to learn it, and books for sale on Amazon for purchase, but ne'er definition. So I'm gonna just go for a guess: Mathematical thinking is a set of skills that one is able to transfer to many disciplines.  Hopefully I'll be able to elaborate on this after Thursday's class!

P.S. If someone else finds a good definition, let me know.  Believe it or not I am not very good at googling.

How Schools Kill Creativity

One of the components of primary/elementary education that I am really interested in is the creation of school curricula. How do we decide what our children should be taught? How do we define "success" within this curricula? Sir Ken Robinson's talk "How Schools Kill Creativity" has made me consider these questions more deeply. 

The main point that resonated with me was the rigidity of our school systems.  We pass on a one-size-fits-all curriculum in the subjects that societal standards deem the most important, and our success is measured by how well we can conform to this curriculum. There is not often a place for risk-taking in the traditional methods of teaching, and as Robinson says we "... become frightened of being wrong". 

What does this have to do with mathematics?

Of the people that I know that enjoy math, most of them say that it is because math results in "one correct answer".  How do we reconcile risk-taking in math (or any subject) with this belief? Can we do it? I don't have an answer for that.... yet.

My Math Autobiography

My mathematics experience overall has been a series of ups and downs, with some years being more successful and some aspects being more difficult than others.  Something that stands out for me as a staple in the classroom from K-6 was long, double-sided drill sheets.  We would be given up to 30 problems on each side of the sheet to solve (with multiplication, subtraction and addition problems) where the speed of calculating answers was not explicitly, but rather implicitly indicated success.  

My best memory from mathematics happened in grade four when we learned our multiplication tables through song.  I still carry those songs with me to this day (although I still have a little bit of trouble multiplying numbers by 8, I was absent that day).  My worst memory would have to be in grade 5 when we were tracking the number of word problems that we completed on a community board.  Word problems were something that I wasn't very good at and I was in one of the last places on the chart, which was an embarrassing experience for me.  I was pretty neutral on my feelings toward math until that time, and continuous experiences like that in my competitive grade 5 classroom made me believe that I was bad at math until high school. I can't recall how my teachers felt towards the subject of math, but they may have facilitated the "competitive" environment that I always felt math was.

In high school I avoided math like it was the plague.  I didn't think that I would be capable of higher-level mathematics and only in my final year did I take the highest level required for entry into university.  As it turns out, the class that I so feared was the one where I felt the greatest success and where math became enjoyable.  The feeling of mastering a concept in math, when the process makes sense and answers become easier to find no matter how complicated, is very rewarding.  I think what made math work for me in that course was how the teacher explained WHY we did the things that we did.  This made the processes a lot easier to transfer to all situations.  A list of things that you must complete to come to the solution is no good when you come across an unfamiliar or slightly different problem.

Although I had a "math epiphany" I am still nervous about higher-level mathematics.  So far in university I have done only the two required courses for this program - Math 1090 and Math 1050.  Although I did well in these courses I was scared to challenge myself any further and ruin the good name I had given mathematics in my mind, and therefore did not do any electives.

I don't think I engage with math any more than the average person (calculating the cost of things etc.) and math isn't something that I feel strongly about either way, although I do appreciate its how it helps us to function in everyday situations.

Introduction

The purpose of this blog is to share my experience with mathematics and to reflect on the knowledge that I gain in this class. I am really excited to learn the strategies involved in teaching mathematics, and to see how they match up to how I learned math.