Putting my new techniques to the test!

This week I began working on the EQAO Problem Solving Assignment. The first part of the assignment requires us to solve two EQAO math problems in two or more processes. The second part requires us to find two volunteers to observe while they worked through the problems. We were provided problems at either the grade three or six level that came directly from tests of previous years. As I am currently doing my practicum in a grade seven classroom I was given grade six questions. In the beginning, I was a little nervous since we had only just begun our math class and as I stated in my last post, I don’t have the grandest background in math. It wasn’t so much about feeling unable to answer the questions (I was pretty sure I would be fine in that regard) it was more a slight worry about feeling confident enough in my understanding to provide proper answers for any questions my volunteers may have. However, I decided to take on the challenge with a positive attitude; because as they say, if every number in the alphabet were assigned a number from 1-26, knowledge would only equate to 96% and hardwork would only be 98% but attitude would equal 100%!

I began with the first question. It was a word problem that essentially required me to find the surface area of a rectangular prism. As I initially couldn’t remember the exact ‘formula’ I had been taught I decided to start fresh, and solve the problem the way that I felt looked the easiest.  To my surprise I had a really enjoyable time when I was able to deconstruct the problem to best fit my learning style. Even more surprisingly though, getting through the problem and finding an answer in my own way actually jogged my memory and all of a sudden, I could remember the formula I had once been taught! After checking the answers both ways I discovered that, my way, although a little slower, got me to the place I needed to be! The best part was, I didn’t have to struggle through some provided formula or search my memory trying to remember an exact set of steps. Instead, I was able to maneuver through the question in the way that made most sense to me, which in turn made remembering the formula that much easier.

After my experience, and how much enjoyment I got from discovering multiple solutions to the problem, I couldn’t contain my excitement. So I asked someone else in my household how they would answer the question. They responded with yet another process; which for me, just felt like another insight into how individual brains work. The household ‘student’ then asked ‘why are you so excited about this? I may have gotten the answer right but my work is all wrong” which caused a slight stray in my diligent work habits and promoted me to go on a long tangent explaining how important it is to encourage creative thought in problem solving. Needless to say my family is now very well versed in the importance of multiple solutions and differentiated learning.

In class, we have talked about how important it is for teachers to think on as many levels as possible to try and predict all possible answers that could be created by students. We’ve worked through multiple definitions and examples of how to solve a particular problem; but for me this was the first time I was really seeing it through my own experience. My work so far on the EQAO assignment has allowed me to put some of the concepts we have been learning in class to the test, which has really solidified my understanding of them and increased my confidence in my math teaching ability.

"New Math"

         When I received the first e-mail this summer about needing to complete a math refresher course I went into a state of pure panic. The last time I was in a math class, looked at a math test or read a math text book I was seventeen years old. I grew up in a family of "I was never good at math and I did okay, don't worry about it!". Not to say my parents weren't the most supportive people in the world, because they were (are), they just didn't classify themselves as 'math people' so neither did I. We believed we fell into the Arts category, which had to mean we didn't fall into the math one, right?

          Oh, how wrong we were...

          In the past two weeks I have gone from dreading all things math to actually feeling excited to teach it.  ME? Excited about math?! But how...

          The first two weeks of math have completely blown me away. Never in my life have I heard such positive responses from a math teacher (was anyone aware that the words 'yes' and 'brilliant' ARE a part of math vocabulary?). As a teacher candidate it is a fantastic confidence boost to know that todays students are not only given the opportunity but are encouraged to bring creative thought into their problem solving. This makes me extremely excited to see the shift in perspective that future generations have on math, especially since we will have the honour of taking part in this change.
One of the things that has interested me the most about 'new math' is the shift in focus that has occurred from the importance of the answer to the importance of the process. When we were in school it didn't matter how something was done as long as the answer was right. Yes, we were expected to show our work but this was more to ensure we were following the exact formula correctly. Now, the emphasis is on finding the solution that works best for you and understanding that sometimes there is no exact process. One example of this new technique can be seen through open questions. Open questions encourage students to find their own way to (one of many) solutions. They are not looking for an exact answer but rather they are trying to collect enough information to form one of the possible pathways that could lead them to a solution. This not only forces students to improve their overall problem solving skills (math or otherwise) but encourages them to learn how to collaborate. In 'old math' it was often a competition: who can find the answer first or who can create the most simplified solution. But in 'new math' the more you collaborate, the better the outcome.    Therefore creating a far more positive and pleasant math experience for all students!

The above image demonstrates the first collaborative task we were asked to do as a class, an activity called Four 4's. In small groups we were asked to use 'four 4's' to to create solutions that equaled all the numbers between 1 and 20. Being encouraged to rely on each other and work as a class to finish the task made it far more exciting and engaging then the typical competitive edge that accommodated the way I was originally taught math.

           One of my goals as a teacher will be to create a cohesive and positive classroom community. I believe that sometimes classroom cohesiveness can be disrupted by categorization. What I mean by this is students are stereotyped or placed in a certain group based on their skill set. Math in particular has always been a subject that people believe they understand or they don't, plain and simple. Being able to create a classroom where creativity in math is encouraged and their is no one answer would put me one step closer to the classroom community I am striving towards. Although this is a goal that goes far beyond a change in one subject, movement is still movement and every step will bring me closer to creating the best environment possible for my students.