Ashley McCarl Palmer, Teacher Waterloo DSB

There is a growing momentum in the elementary panel to spiral subjects, especially math, which is now flowing into secondary schools. My board has been pushing the spiral math method in the grade 9 and 10 applied courses for the past few years and last year in September our principal asked us to think about our courses to see if spiraling could be beneficial there as well. If I’m completely honest, I scoffed at the idea at first.

Spiraling a course is a method of teaching where a base layer of information is given, and then the teacher comes back and builds on it over and over again. Many of us spiral already with skills, for example we may assign a lab report early in the course, give them feedback, and have them submit another one for a different lab, give feedback, and the loop continues. But to teach the content itself in cycles, instead of units is very different from the traditional model. If we use SPH 3U as our example, the motion unit could be shown in the diagram as red, forces as orange, energy as yellow. All the material is taught for the motion unit, it is tested and then left until the final exam. In spiraling, cycle 1 includes the introduction of all 5 units, which are tested and then all five are covered (and built upon) again in cycle 2, and so on.


Image used with permission from Aleda Klassen, author, September 2018.

I decided to give it a try in my SPH3U course second semester last year and found some challenges and some great successes. Students at first struggled with and complained about the model because they had never seen it before. The biggest change for them is it was much more difficult to memorize your way through a course that builds on itself. This negative start was overshadowed by the huge advantage spiraling offers us. For example, when we teach acceleration in kinematics we talk about this “gravity thing” but don’t really explain it other then saying “you’ll learn more about ‘what’ it is in forces”. A month goes by and we hit gravity in forces and you get questions about what causes it and you say ”save that for the energy unit!”

In the spiral model we can spend a whole week exploring gravity; Day 1 we could do a lab that explores acceleration and students find the ‘magic’ 9.8 number. The next day we would look at the force of gravity and derive where the 9.8 value come from near the surface of the Earth using the formula for universal gravitation. This then leads to conversations about what causes gravitational forces which is a great segue into potential energy. Many topics in the 3U course flow this way and the ‘ah-ha!’ moments were so amazing to see during these inter-connected lessons. So far, I think this is the biggest advantage to spiraling, as students are no longer told to “hold that thought” because the answer is coming later today or worst case, tomorrow.

So I had a working spiral layout I wanted to try but I was left with a really difficult question, how do I assess this??

In a traditional unit model we do quizzes and assignments and the lessons teach concepts that get progressively more complicated until we reach a unit test. We may do labs and activities to support their learning and all this is done to get them ready for a final exam. In cycles we can still have quizzes and a test (which would span 5 units of material in 3U) but because we are building, the Cycle 2 test includes material from Cycle 1, 3 covers 2, and honestly the Cycle 3 test is the same as the final exam. Did I just make all of my tests technically formative??!!

A lot of my time early on was spent in conversations with spiraling math teachers, board consultants, administrators and other physics teachers, trying to puzzle through the assessment piece. Assessment is a tricky and useful tool to recall information as Eddinghaus “discovered that without any reinforcement or connections to prior knowledge, information is quickly forgotten—roughly 56 percent in one hour, 66 percent after a day, and 75 percent after six days. [1] ”. Assessment timing becomes critical in cycling to make sure a topic is short enough that students are recalling and reinforcing material and not re-learning it. Another huge advantage of spiraling for me was that all of my assessments came under scrutiny… “Why am I assigning this? What is the point of this question? Are the answers that students give actually assessing the skills I want to observe?”…

I also realized that if a student failed the Cycle 1 test, they were really going to struggle in the next cycle, especially since we were building on that information. I ended up moving to a skills based assessment model where students would demonstrate a skill and if they missed it on the test they could demonstrate that skill to me at another date (before the next Cycle test). Students saw the added incentive that they could “boost their test scores”, while really all they were doing was taking the time to actually learn the material. Another added bonus was exam anxiety was reduced because they had just had their Cycle 3 test which served as a great practice tool for them.

Spiraling is NOT for everyone. I’ve seen many new teachers struggling with the applied math courses in our school when they are spiraled. I think you need to have taught the course at least a few times to start seeing how various topics are interconnected, understand the material and typical student questions and misconceptions, and what the long-term goals for the course actually are. Spiraling is very difficult if you cannot see the end of Cycle 3. At this point I would recommend teaching under the standard unit model to see what the course is really about first, and then take a look and re-shuffling.

While discussing my spiraling experiment with a colleague last year, he told me that the best test of something you do in the classroom is ask yourself, when you do it again, ‘what would you change?’. When it comes to spiraling my answer was actually nothing. The course flows and builds beautifully and I’m so glad I decided to take a rather unconventional leap which helps students learn, which in the end is what it is all about.

I’ve taken my look into my assessment practices even further and I am presenting at STAO this year (on Thursday) on how my current experiment is going so far. A group at my school is attempting to only give feedback to students, no marks (!), and I am attempting that with my 3U’s this semester while still spiraling. I’m happy to chat spiraling or assessment so feel free to come and find me in Toronto or I can give you an update on how the whole semester went at OAPT next May in my home base of Waterloo.

1. Youki Terada, “Why Students Forget—and What You Can Do About It,” Edutopia, September 20, 2017 [Online] Available: https://www.edutopia.org/article/why-students-forget-and-what-you-can-do-about-it [Accessed September 7, 2018]

Tags: Pedagogy