Today I was working with my principal on the next assignment for the RMS Virtual Learning session we are currently doing as a school. Part of the session is solving some problems individually and then sharing with our colleagues how we solved the task. It is in preparation for the next session. The tasks have been focusing on how students develop towards multiplicative thinking and helping us to look at it from an LD learners perspective. This was the task for this part of the session:
In a bike-a-thon, cyclists will find
-water stations every two-thirds of a kilometre
-medical stations every three-halves of a kilometre
-bike repair stations every three-fourths of a kilometre
John has reached the first medical station, Alexa is at the second water station, and Sima is at the first bike repair station.
Who is further along the course? By How much?
Here is how I, my principal and one other colleague solved this task:
Mine is the top solution. The reason I wanted to share this blog is because recently on Twitter some educators had been sharing some fraction tasks with student work. People were discussing that they didn’t know what they didn’t know and the fact fractions have so many key ideas and levels of understanding that they were beginning to have their eyes opened to the content knowledge you need to have and understand to teach fractions is effectively.
Well I certainly would have fell in that boat, my schooling left me with a severe lack of understanding of fractions, a hate of fractions may better describe it. You can imagine how confident I felt then when it came to teaching it, which I feel many teachers are in that boat. When I had my math awakening and started researching and learning myself I began to feel more confident with fractions, then I moved into a Instructional leader position for my board. In my second year I had the opportunity to be part of the Fraction Pathway Action Research project that was lead by Dr. Cathy Bruce, Tara Flynn and Shelley Yearly and came to realize that I still didn’t truly understand fractions until I met and learned with this crew! Wow to say I made some leaps in my fraction sense is an understatement. If you haven’t seen their research check it out on edugains.ca under the Fraction Pathway.
This leads me back to the point of this post, when I looked at this question the fraction parts just made sense to me. I didn’t need to convert them to decimals as I was taught to do in school. Even the part that said the medical stations were every three-halves made total sense. I also kept everything on my number line mostly in proper and improper fractions to keep the unit fraction visible. I find it easier now see 4/3 and 6/3 then to convert to mixed numbers. I went straight to a number line which was never in my fraction vocab until I was part of the pathway research. I visualized my partitions and even for the last part subtracted fractions to find how much further John was along the course. It just makes me giddy to see how comfortable I am using fractions now when even 6 years ago I would have said it was a weak spot for me. And if you went back to when I was in school I would have been the student so frustrated with fractions that I wanted to cry and run for the hills.
As you can see both my colleagues went straight to converting the fractions to decimals and they both shared that they were confused with the wording of “every three-halves of a kilometre” in the beginning. They both shared they felt uncomfortable working with the fractions and it was because they felt they struggled with fraction sense in school and feel like they shy away from fractions. Many of our students are also in this boat but I feel many that are being taught using ideas from the Fraction Pathway, for example, focus on unit fractions, use visual models and build their fraction sense are going start to be more confident and hopefully not have to wait until they are in their late thirties to have a fraction awakening like I myself did!
Like so many concepts I have re-learned since I have become a math geek and started down this math journey to show students that math is awesome and that there are better ways to learn math then the rote procedures and memorization tasks I was forced to do and failed miserably at during my schooling, fractions can me learned in a way that makes total sense!