Why a Spiraled Curriculum

A "spiraled curriculum" involves going through ALL course material at the start of the course - in a limited way. Then again, but more in depth, then (perhaps) yet again for mastery. All of this, done in the same amount of time as regular "linear" teaching. Perhaps you know these concepts by other terms; either way, it's a good idea.

I'm not there yet.

When you spiral, there is no end.

Credit for my awareness goes to Bruce McLaurin (@BDMcLaurin), and if you only want the quick version, read session 2 in my OAME 2013 Day 3 post. A more in depth version is below, where I'll also explain how I'm starting to approach it in my Grade 11U course.

FLAWS IN TRADITION

The traditional way to approach a course (I'll use mathematics in specific, but this could work in general) is to break it down into units. Like an essay: Tell them what you're going to say, say it, then tell them what you said. Let me highlight a few reasons why that doesn't work so well in present day.

1) Semesters. In most schools (in Ontario at least), students no longer take the same subject year-round. They take a course from Sept-Jan, then other subjects from Feb-June. So it's possible to finish your math course in January 2013, then not have math again until February 2014. No wonder students forget things. As such, constantly bringing a topic back over four months is better than doing one full week and moving on.

How can there be anything be more important
than doing math after school?!

2) Cramming. It may simply be my perception, but students seem to be doing a lot more cramming these days. Some of it is self-inflicted, due to online games and constant texting, but there's also part time jobs (to pay for post secondary), more extra curricular activities than ever (for things that didn't exist 20 years ago like "Anime Club" and "Free the Children") and time spent on fundraising events (because cutting taxes takes precedence over funding education). Meaning if there's a test tomorrow, the student crams, perhaps even does well, then the knowledge is GONE - until the exam, which involves more cramming. But if the topic cycles back more often, there's a reason to invest time over multiple evenings.

3) Unit Evasion. Similar to cramming, there's often that one unit (say, Trigonometry) that a person can't wait to be done with. In a traditional procedural curriculum, once you're past the Trig, an "out of sight, out of mind" mentality can take hold. Perhaps the student won't even study that topic for the exam, figuring as long as they do really well elsewhere, the lack of Trig won't matter. Until next year! However, if the topic is constantly spiraling back, there's more incentive to actually (if grudgingly) understand, and remember.

Thus I'm on board with the cycling idea. A couple of teachers in my school are even implementing it in Grade 10, with success as far as I can tell. (I believe they started by looking at all graphs, be they lines or parabolas, and after handling visual patterns, cycled around again to focus in depth on the algebraic forms. I could be wrong.)

Either way, I'm still wrapping my head around this. It's hard because I'm excessively organized, mentally putting things into their individual strands, but here's my first kick at the can.

GRADE 11U

Quick background: The Grade 11 3U course ("Functions", University level) consists of four strands, and typically 8 units. Those are...
Strand 1-Functions (Functions, Parabolas, Rationals);
Strand 2-Exponentials;
Strand 3-Discrete Math (Sequences, Finance);
Strand 4-Trigonometry (Periodic, Triangles).

If you think a teacher always teaches the same course, in the same way, with the same lessons, in the same order, welcome to a reality check. 

I've played around quite a bit with the order. Strands used to go 1,2,4,3; Discrete was crammed in towards the end over less than 2 weeks, and the Summative was Financial. Parabolas were typically done last within Strand 1 - in theory a return to the familiar of Grade 10, yet always somehow a bloodbath.

Last year I think I finally found my rhythm. Parabolas, Functions, Rationals, Exponentials, Sequences, Triangles, Periodic, Finance. Thanks to a colleague, the Summative also tested Graphing while the Exam tested everything else. But that's still strand-by-strand, using relative weight depending on volume of material.

This past semester, I didn't do that.

I didn't spiral either, but my units went as follows: Parabolas, Functions, Exponentials, Rationals, Periodic, Sequences, Triangles, Finance. In other words, I would leave a STRAND, then cycle back to that STRAND later.

What worked:
- Periodic functions before triangles makes SO MUCH SENSE, I don't know why I didn't try it sooner. (Actually I do - Periodic usually goes better, thus do the challenging stuff first.) This time though, when I got to triangles, I could relate solutions back to the graphs.
- Sequences needs exponential knowledge (for geometric patterns), so I liked using that unit to split Trigonometry.

Root

- I even touched on Exponential and Sinusoidal curves in the Functions unit. I'd do that again. Refinements are needed though, since they come back, whereas functions like Root do not.

What didn't:
- I gave a task after/in Periodic functions that touched on all functions to that point. Then realized I had no idea how to record it, since it bridged THREE strands. I ended up giving THREE marks on the one assignment, per each strand, which took me a month to work through and felt painful. Advice welcome.
- The fact that it's not true cycling, only juggling the order. I also have no real way to compare this order to my prior ones.

So there it is. If you see good way to do this that I don't, or think there's merit here, feel free to let me know in the comments! Similarly, if you DON'T think there's merit, that could be a good discussion too. And I should get back to marking Summatives now. >.<