I have struggled with math for as long as I can remember. In high school I was the one who attended grade 11 and 12 math help three mornings a week and still shed tears over it every other day. Throughout my prerequisite math studies for my B. Ed. I failed a stats course (the only class I’ve ever failed…too bad it cost $300). Upon handing in my final exam I was certain I did not pass my Math 360 course, which used to be a mandatory B. Ed course at UVic. My life has been filled with many frustration filled math related tears and over time I have grown to strongly dislike math.
I am proud to say that the times, they are a changin’ over here in Mrs. Alleyn’s math world and that is largely to do with Nikki Lineham’s fantastic math website, Educating Now. Nikki is a brilliant middle school teacher leader in our district; Meaghan and I are both fortunate and grateful to have had access to her website through our respective schools. Nikki’s site is a business, and therefore runs by paid subscription, so I won’t divulge the inner workings of her lesson I’m blogging about today, but I do want to share how the lesson went for my grade 8s. I also want to share how Nikki’s work has turned me in to a more confident math teacher, which is something I never thought I’d ever be!
Today in math my grade 8s and I were working on the concept of “preservation of equality”, that is: “What does the = sign really mean?” My class came up with all kinds of answers to this question, but not a single student was able to tell me that the = sign actually means to BALANCE both sides of the equation. I was so pleased that no one was able to tell me that = means “balance” because it meant I had found a weakness in their understanding (and, my own understanding, if I’m honest!) We then worked with the concept of a scale/teeter totter and I ended up holding various objects in my hands, arms outstretched, pretending I was on one end of the teeter totter and Charlee, my 1.5 year old daughter, was on the other end. We talked about what would happen and came to the conclusion that because I am obviously heavier than Charlee, the teeter totter would launch Charlee high in the sky. We then discussed what might happen if Joel, my husband, joined Charlee on the teeter totter. Obviously his added weight would raise me into the air. We then discussed how we could even out the weight between my family on the teeter totter and decided that if Charlee came to my side, perhaps she and I would balance Joel. It was so interesting to me to use my family in the analogy because I had never thought of the = sign this way before.
Let it be known that my grade 8 class has a very wide range in mathematical competency – I’m talking a range from about grade 4 to grade 11. I think the best part of today’s lesson is what came next…
After some more work with numbers and teeter totters and balancing my grade 8s set out to complete their learning task, which was to create five questions solving for x, while using the teeter totter concept to help them answer their questions. Check out the differentiation that occurred once my students let loose:
Are you freaking out as much as I am freaking out over how awesome this learning task is? My struggling learners were able to use the teeter totter to help solidify what the = sign means; therefore, bringing them to a deeper understanding of algebra. My very advanced learners were able to differentiate the task to meet their level of ability, while still being challenged by the pictorial component (let me assure you, my strongest math students are rock solid when it comes to doing math in a procedural manner, but they do struggle when they need to show their work conceptually, as you will notice above).
As I sit here writing this post I am in awe that I taught this lesson today. I keep thinking, “I did this!? I understand this!?” Today’s lesson was a huge learning experience for me and for many of my students. I was not taught math like this, but our redesigned math curriculum calls for concrete, pictorial and symbolic representation of student learning, which is why I am so grateful for Nikki’s lessons and teachings. Nikki’s work has certainly made me a more confident math teacher.
P.S: Meaghan and I, along with a handful of our teacher friends, plan to take Jo Boaler’s new online, self-paced math course this August. Click HERE to check it out and let us know if you want to join our math posse. We are certainly interested in collaborating about math over the internet with our international teacher friends and readers!
Note: Tale of Two Teachers is in no way financially affiliated with Educating Now. We simply love their work and both use it regularly in our respective classrooms.This post was written with permission from Nikki Lineham, teacher in SD61 and part of Educating Now.