Growing Problem-Solvers: How to Spiral Curriculum for Long Lasting Learning

Tell me if this has ever happened to you…you’re about to launch a lesson on fractions and all of your learners exclaim, “We did this last year!” 

What about this: you start that lesson on fractions anyway, and maybe a couple of people remember the terms numerator and denominator, but most of them have them mixed up, and even though they “did this” last year, no one can really explain what a fraction is, let alone solve problems that involve them? 

Chances are that these learners worked with fractions by completing a sequence of classroom activities, leading to a unit test last year and haven’t thought about them again until now. This type of long-range planning is called “massed” or “blocked” and it is linked with poor retention. Learning Mathematics through these units is, unfortunately, exactly how I was taught, so it is no wonder that many educators struggle today to feel confident in our teaching when we didn’t have a lot of opportunities for deep learning when we were young. If you are concerned with providing deep, long-lasting learning in Mathematics so that your learners become genuine and critical problem-solvers, you need to try spiralling your curriculum!

Serendipity and “Sticky” Learning

My first encounter with the word serendipity was in Grade 2. It was the title of a levelled reader that I borrowed from my classroom library (that was way too much for me) and I don’t think I even attempted to read it before returning it. But the cover, with its furrowed Queen of Hearts character and magical title, captivated me. 

Without using Google now, how would you define serendipity? Does it make you think of that John Cusack movie? Is it about romance, the flow of the universe, or when things just fall into place? I think I have the gist of it, but after all these years, I never learned the true meaning and have to look it up as I use it. 

My Hero’s Journey as a Mathematics educator has, as it would happen, been very serendipitous. I have come across resources and mentors on and off over the past eight years that have been very valuable to me, all while I wasn’t looking for them. This blog post is inspired by one such mentor, a principal I’ve never actually met, whose motto, “Try something new, no one will die,” has stuck with me ever since I heard it!

In 2016, Kristin Phillips delivered a TEDxTalk (one of my favourites!) on what she calls “sticky learning.” This is that deep, enduring understanding we are always aiming for but that rarely happens. Turns out there is an ideal approach to achieving it, and we have been doing it the opposite way, especially in Math class, for way too long. 

When we spiral curriculum, instead of “teaching” and testing in units, we create multiple opportunities throughout the school year for learners to explore key concepts and experiment with strategies and tools. Spiralling allows for learners to do this in a variety of contexts which later translates to them becoming not only problem-solvers but critical thinkers! Instead of falsely demonstrating their ability to problem-solve right at the end of the unit, but not retain the ability the next year on, choosing to apply the right stuff from their repertoire and in new and increasingly complex situations is something that can happen when learners get to see content more than once in the year. In the 21st century, guiding learners to grow into these kinds of problem-solvers is essential. 

How I Spiral Curriculum In My Math Lab

At my school, we organise learning by sessions that are anywhere from three to seven weeks in length. When I began to plan for a year of Math Lab, I first laid out a foundational theme for each session and then selected activities from a variety of strands (in Ontario we have strands and expectations, in the US these are called domains and standards). My intention was to “space” and “interleave” important concepts and skills again and again throughout the year, because, like the fractions anecdote above, I know that learners need more than two weeks with something for them to be able to really make sense of it. Here is a snapshot of what our first four sessions looked like:

As you can see, I have quite a bit of freedom in my planning and it is may be alternative to your situation. I work at a school with a learner-driven programme where our guided Math Lab time is limited to one hour per week (they have a 75-minute block every morning where they pursue Mathematics learning and other foundational skills independently at their own pace and level). With such a small window for me to guide, I selected problems that would touch on a variety of strands each session, with each successive session spiralling deeper. 

For example, let’s review the Spatial Sense and Measurement pathway we have followed so far. In Session 2, the learners took on open-ended problems like “The Broken Ruler” or “Mowing the Lawn” and uncovered concepts like how to use a ruler, and measure perimeter (and calculate area for the older group). Then, in Session 3, they had to recall this learning and extend it in new contexts like finding enough materials for “Framing Photos” or making Metric unit conversions in “Cutting Paper.” In Session 4, these skills were needed again, although this time in the context of a longer-term real-life based project such as working on a farm and designing new livestock pens or planning an agricultural conference venue with enough space for vendor booths. 

Next session we are moving into the theme of Entrepreneurship and our learning focus will spiral back to Financial Literacy. In Session 1, the learners explored basic Canadian currency and later in Session 4 started to make calculations with money amounts. Building and running our own businesses over the next several weeks will take us even deeper into finances, from evaluating and managing costs and revenue, to calculating taxes and interest. 

The case for spiralling the Mathematics curriculum with your learners is pressing but, I’m sure, also daunting. It is my hope that this blog has made it feel at least the tiniest bit more accessible, even mid-way through the year. Maybe you’re even experiencing a little serendipity of your own right now, like you needed a change but didn’t know what! 

Start small, perhaps by choosing just one skill or concept that you know your learners struggle with – how could you connect to this more often throughout the school year? Check out the resources below for more ideas and examples and please feel free to comment below and let us know how it goes! 


For the readers:

Kristin Phillips’ blog:

Scientific American article on interleaved learning:

For the grab and goers:

OECTA Slides on Spiralling:

Elementary Long-Range Plans from Ontario Ministry:

Sample Secondary Long-Range Plan:

Melanie Duncan is an Ontario Certified Teacher (OCT) and IB qualified educator based out of Ottawa who also works as a tutor, organizational coach, artist and blog content writer. She is a Primary/Junior Mathematics Specialist and she is on a mission to make math your new favourite subject! You can follow her other adventures on Instagram @mduncanart

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.