This semester was my first go at spiralling a course through problems instead of units. Traditionally we teachers follow the chapters and sections from the textbook. Well why not? It’s all laid out and organized nicely….most times in 1 day chunks….no planning needed, am I right???

How exciting is it though? How much do students really need to think? Are they really solving problems and learning mathematics.

After reading about spiralling from Alex Overwijk and bouncing ideas back and forth with Kyle Pearce we decided to give spiralling 1P math with 3 act tasks a try.

Each day or two I would introduce to a new 3-act math problem (read Teaching with 3-Act Tasks) to solve with students. We would use that to stimulate wonderings and finally narrow down to a particular goals I wanted to cover. Each of these lessons is taught with a 4 part math lesson (From Kyle Pearce) which always has students working on solving problems on their own FIRST, and then we step in and teach skills (“math teachery” way) after.

We did not teach within units. We mixed up our 3-Act tasks and problems throughout the semester.

I kept a list of all lessons, and order I used, along with any resources like blog posts, video files, handouts, etc. I wanted to share that list below.

Spreadsheet design was by Kyle

The spreadsheet shows for each day,

- the strand we covered,
- the learning goal (LG – for my assessment sheet),
- the topic, notes for planning,
- the inquiry lesson portion (3-Act math problem(s))
- connections to other strands (a place for me to remind myself to tie this piece to other strands)
- the consolidation/practice resources/links
- other resources like blog posts, handouts, links, tweets, etc.

You may notice the bright pink row. These are our assessment/mastery days. We had one whole class each week for this.

The first half of an assessment/mastery day class was handing back of past paper assessments that look like:

Each one consisted of 4 questions that covered the learning outcomes of the last week or so. I wrote feedback for any question that weren’t completed perfectly. They were to read the feedback and re-do those questions.

I let them know that everything counts…..I consider all our conversations, my observations and anything they hand in for their grade.

Also during the first half of class students worked towards upgrading their skills. They access their customized spreadsheet which shows their achievement on each of the learning goals. They choose a learning goal to upgrade. Based on their prior achievement they are given another task to try. After I assess this new task I go and change the mark for that learning goal.

Both Kyle and I have written posts on this sheet a few times. (here, here, and here). An idea we extended from Alice Keeler.

We spend a good chunk of time working at getting better on our skills always promoting growth!

The last half of the class we do this week’s paper assessment (that looks like the one above). I mark it and give it back so that next Tuesday we can do that all over again.

Here are some benefits I have noticed from both spiralling and teaching through problem solving:

- Almost no need to review at the end of the year. We reviewed all through.
- Students see how math connects together. (Proportional reasoning shouldn’t stand as a lone unit when you have linear relations and algebra to teach too!).
- Students were more confident in math than I’ve ever seen them. (And for 1P’s too!). When teaching in units, students know that whatever problem we will solve today HAS to do with what we learned yesterday. When we teach through spiralling students are always wondering what math they can use to solve the problem at hand. My students became great at risk taking! They would try! How many times has it been where we give a new problem to our students they complain that you haven’t shown them how to do this. My students were given new problems everyday and they became great a trying strategies. Whiteboards help immensely with this too!
- A time saver! You may think that I would run out of time teaching this way…..I couldn’t possibly teach through problem solving and still cover everything, let alone booking a whole day dedicated to growth EACH WEEK! We had lots of time. Since each lesson tied multiple expectations and learning goals together, we could cover more in one lesson than we could in two lessons the old way. The growth/upgrades each week allowed students to practice skills from all over the course. Around mid-term time I gave my students an old final exam to see how they would do, and they did great!!! I was amazed. We still had half a semester to go!

Since we are coming close to the end I wanted to share my experience! Feel free to check out my daily plan from grade 9 applied

As always, if you have any recommendations or feedback for me I would love to hear about it!

Hi Jon. I was just wondering if you had a doc that has the learning goals written out since this just refers to them by number.

Thanks for the inspiration!

Here is a sample of what I am using to track marks according to learning goals. The learning goals themselves are just our curriculum expectations or standards. https://docs.google.com/spreadsheets/d/1DDmfG8zVOkjWG8f0X_bW5GQoiT1xscD5nP2S-MZBnTA/edit?usp=docslist_api

Hi Jon! You and Kyle are doing amazing work! My question concerns assessments – do you have to administer “common assessments” with your colleagues that teach the same course? I was curious about how that looks, and whether your administration has any expectations about you being “lock-step” to an extent with those who also teach this course. If so, has that presented challenges? Do your colleagues embrace the idea of dissolving units in favor of spiraling? (I ask from the lens of being required to give “common unit assessments” so, if I were to dissolve the concept of units, that might be challenging for me, knowing my teacher counterparts might still be teaching units from a textbook.) Thanks, as always, for sharing!

Hi Cathy, Great questions.

For the last few years I have been the only one to teach this course at my school. And since this is the first time I’m spiralling the units this way having common assessments hasn’t been an issue. My department does embrace this idea of spiralling but are hesitant to try, so next year I have arranged for a teacher to teach another section along side me so we can work it out together. We will have common assessments, and we will have a common final exam. I can see where there might be concerns if admin wants everybody to stay together. I’ve been lucky in the past with other courses where my admin has been flexible and allowed people to try things as long as communication was kept open.

I might try asking admin for a “pilot” spiralling program where your section is doing this and the others are staying “lock-step” together. Maybe after, the other teachers might want to jump on board?

Sorry I don’t have more experience to share with spiralling and common assessments.

Thanks so much for your insight, Jon!

When I tried to save the scope and sequence it was a PDF file. Do you have it as a Google Forms copy that I can edit? THanks.

Jon thank you for sharing your reflection of your journey! I am teaching MFM1P for the first time since my first year of teaching (so basically for the first time LOL) and was thinking about doing a spiral, but at the very least will be doing lots of problem solving based activities (plan on trying some of your & kyle’s 3-act tasks). Also hoping to go gradeless! (Between this and starting a spiral in MHF this year for the first time spiraling MFM1 would probably be too ambitious – but I look forward to finding this post again when I need some inspiration!)

Thanks for sharing Heather! Good luck

Have you tried Spiralled 3-Act Tasks with coursed like MHF4U OR MCV4U? If yes, can you share some of your resources.

I am spiralling with MHF4U now…not so much with 3 act tasks as they are hard to come by for this course. Check out this link from Al Overwijk and Janice Bernstein. https://sites.google.com/a/ocdsb.ca/spiralling-in-mhf4u/course-plan

Jon, thanks so much for sharing these resources! What a tremendous amount of planning and time that you are sharing with the greater community!

I have looked at the spreadsheet doc that you shared above in these comments, and the LG’s listed on that do not correspond to the Course planning spreadsheet shared in the web post. (e.g., LG # 14 has to do with the sum of angles in a polygon, but the lesson for LG #14 is about collecting like terms…) Are the particulars for these two documents for different iterations of the course?

Hi Jacky, yes, the LG numbers have changed from semester to semester. Glad the resource is helpful to you.

I am interested in spiralling MCR3U and am inspired by the re-visioning, but unsure of where to start. If I wanted to blow up my course where should I start? What do I want to look for in a 3-step task?

Hi Jon,

For the assessments, I noticed you give students opportunity to master learning goals with something like “Task to improve to L4”. I was curious as to what you use for those tasks, where you get them or how you make them. Thanks!

Nathan, those questions for the most part are our typical test questions and some are our released standardized test problems (EQAO).