spiralling

Gaining Insight

by Jon Orr

As the year closes down I think back on 2017.  I was curious about some of the stats on this site and was blown away at some of the numbers. I never thought that when I started sharing what goes on in my classroom that I would have over 150000 views in a single year! Amazing….and thats all because of you! I dug a bit deeper and found the three most popular posts from this year.

  1. Angry birds Parabolas
  2. Flippity Flip Bottle Flip
  3. Spiralling Grade 9 Math

At first glance I thought, “Yeah, those top 2 posts make sense. Their kinda gimmicky and fads. We search for those relevant topics our students are into; games and bottle flips! I’m sure if I wrote a post on fidget spinners it would be up there too.”But after thinking back on those activities and comparing them I think both their value come from being able to gain great insight into student thinking. And it’s that ability to assess our students deeper thinking here that teachers are drawn to.

Take the Angry Birds lesson for example, the creativity that is embedded  throughout the lesson is everything. Students get to choose how their flight paths look and act. There’s a story behind every arc they put into their activity. Their thinking can’t help but spill out all over, and I get to use that knowledge I gain to help push them along. Take away the angry birds and you still have a great creative lesson.

Replace it with a drawing, or trace of a picture or even a marble run and students experience the exact same creativity and learning goal expectations. The activity still allows me to have those insightful conversations.

The bottle flipping activity is a formative assessment gold mine. Again take away the bottles and replace with paper balls or card tossing and this lesson is identical, and I have just as much success at seeing into my students thinking.

It’s this insight that we all want. It’s this insight we need. Insight allows us to what Kyle Pearce and I have been calling ignite our moves. Seeing how a students thinks in live time allows us to act. We may act to address a misconception. We may act to push learning further. We may act to plan our next lesson. We may act to change our planned lesson into something that the students need at that moment. Lessons that allow insight into student thinking must be our norm.

This fits with the 3rd top resource. Spiralling Grade 9 Math. The file found on this post give us a day-by-day to teach with lessons just like the ones above. Not gimmicky lessons —  Lessons that spark curiosity! They are lessons that provide great insight so I can ignite my moves and fuel my students sense making. And fuelling sense making has to be our main purpose.

Have you used any of these resources? Comment below to share how?

Assessment in MFM1P – Update

by Jon Orr

Here’s a short update on my grade 9 applied course. I’ll try to explain this as clearly as I can…bare with me.

An integral part has been our weekly mastery days. I’ve written about those days along with the tools that make them possible here. These days have been so important to our learning and we will definitely be doing them again next semester.

Allowing For Differentiated Learning and More Student Accountability.

Having these days allows students to have more responsibility in their learning not less! We are using a web based and app based tool called Freshgrade (You can read about how I set that up for mastery days here – this post will be mostly about the benefits). On our mastery days students have to scan through their portfolio and decide which learning goals (expectations) to improve on….then, they, the student, has to go and make that improvement happen (Each LG in Freshgrade has links to questions for them work on). So our mastery day is filled with students all working on different expectations from the course — according to their need. With the encouragement I give them they know it’s up to them to work towards mastery on each learning goal.

Student view of a learning goal to improve:

An activity in Freshgrade I’ve called a learning goal. Each one shows student achievement and next steps to improve.

Capturing Growth Informs Instruction & Assessment

The portfolio tool in Freshgrade is amazing. It captures and holds all of their work. It provides me great insight into their learning. As students work to improve their learning goals (expectations) they upload pictures of their work through the app. I get to see that work and provide audio or written feedback also through the web/app or in person. What I love is that I get to see all that interaction for each learning goal (expectation) forever. I can see the growth that my students are making. My old spreadsheet tool never tracked past work…only most recent. I love being able to see a student’s thinking progression as they attempt problems. It makes me as a teacher more confident about that student’s ability on the course expectations.

For example, this student uploaded a picture of their work on solving a proportion. They were confused on the nature of proportional relationships. After a comment and talking with the student they made corrections and re-uploaded. Their next step is to attempt a new problem to show consistency. That progression of learning stays in their portfolio for us both to see!

A student view of their portfolio:

Can’t see the video? Click through to the post

Capturing all of their progress and achievement in Freshgrade also provides me a ton of data. Since I set up the categories in Freshgrade to be the strands from the curriculum and each learning goal is assigned to one of those strands I get to see my class’ achievement on those strands. For example, If I filter the activities (learning goals) to only see the ones for linear relations I can see if we need to work more on linear relations. This has been great in the spiralled course. We can spend more time on what we need.

Gradebook view showing learning goals and student achievement.

I hope I explained our mastery day process clearly……now, onto an updated day-to-day plan for MFM1P.

Planning:

Each semester I’ve spiralled I’ve kept a spreadsheet that outlines my day-to-day. In the links below you can see those outlines in detail. I’ve included each semester on it’s own tab.

Webpage view of the outline

Get your own copy of the Google Sheet (You’ll need a Google account).

Sign up for a free Freshgrade account

Spiralling in Advanced Functions (MHF4U)

by Jon Orr

I’ve been spiralling my courses for the last few years, but this last semester was the first time I spiralled the Advanced Functions MHF4U course. If you’re new to the spiralling idea check out the blog post from Mary Bourassa and the MHF4U website from Al Overwijk and Janice Bernstein. They’re great resources to get you going.

This post is really to remind my future self on what I did this semester and for anyone else asking spiralling questions.

On Planning

Occasionally I will get an email from a teacher who is interested in trying spiralling and the question they usually ask is, — Where do I start? I think most of us need someone to shine the flash light down the path for us to see where to head. I usually start with a table that shows the strands of the course and where the major skills (overall expectations) fit in. I try to group them by themes. This year I my cycle one was about introducing the functions and focusing on graphing characteristics. Cycle two focused on linking algebraic representations with graphical. See below.

From there I keep an ongoing day-to-day plan.

Click to see the live version

On Homework:

In the past I’ve given out homework in a very traditional way, “Tonight, complete page ___ Questions #__ to ___. Tomorrow we’ll take them up.” And what did homework take-up look like in a grade 12 course? Well, for me, it was always “What problems did you have trouble with? Number 8b? Ok, does anyone have that one completed? Kearra can you put that solution up on the board?” If no one had that question right, then I would put up a solution. And everyone watched, twiddling their thumbs (or more realistically — texted) while I put that solution up….or we all watched Kearra put the solution up. Not a great use our of time.

I’ve changed that process over the last year or so. For me, giving out homework comes in a homework set. I got the idea from Al Overwijk and Mary Bourassa. The sets not only have practice problems from the ideas from that day, but also practice problems from other areas of the course. Each night of homework they are practicing most strands of the course. It keeps concepts fresh in their minds and keeps practice going all semester.

a typical homework set

When students come to class they get a playing card that randomly assigns them a partner. Instead of asking which question we should put up, I choose two or three from the set and the pair has to put them up on the vertical whiteboards/blackboards around the room. They are only allowed one piece of chalk or marker between them. I circulate around the room to give feedback and check for understanding/thinking. I’ll routinely yell out to “switch the marker” which forces students to communicate, error check, and defend their work. A better use of our 10 minute homework take-up time. After, students hand in their homework which allows me to check their understanding and gives me insight on what skills we need to improve on (I choose one or two questions to focus on). Gone are the days where I give out homework and I don’t find out what they really know until test time. Now, I know daily. Is it more work for me? Yes it is. But it’s worth it.

Can’t see the video? Click through to the post

After homework take up.

Whiteboards & Note-taking:

Most of our problem solving and practice work in class this year was done on non-permanent surfaces. For some students, parents, and teachers this is a concern since they are wiped away and there is not a record of that work. Here is an email response I sent a fellow teacher this year to address the concern:

“Do your students need the note? Are they asking to take notes? If so, have a conversation with them about what they need and teach them to take pictures of what they need or make notes for themselves. Or have them summarize what they’ve learned after doing the problems as an exit slip.
I sometimes do “important” solutions on chart paper and then they stay up in the room so we can refer back to them.”

Changes:

As always I’ll be making changes for the next time I teach the course. I want to include solving equations earlier in the course. This year I didn’t bring it in until cycle 3 and I feel like we could have benefited from more exposure. Also, radians need to be introduced in cycle 1 so that it can fuel all of trig for the rest of the year. I feel like it was crammed into the last cycle.

Day-to-Day Outline and resources for MHF4U

See the outline as a webpage

Get your OWN copy of the Google Sheet to modify.  – You’ll need a Google account

Updating the MFM1P Spiral

by Jon Orr

“Have you taught for 25 years? Or have you taught one year 25 times?”

I don’t think I’ve taught the same course the same way ever. Why would we? We don’t have the same kids in front of us. And especially with the resources at our finger tips from our colleagues inside and outside of our schools. I’ve wrote before about the power of #mtbos and it changes the way you teach.

I started spiralling the MFM1P course a few years ago with Kyle Pearce. Since then I’ve taught that course 3 or 4 semesters in row…..and never the same way. New amazing lessons and tools are springing up. For past lessons I wasn’t completely happy with I’ve got to see if this new lesson or that lesson will help my students understand the concepts more deeply.

One change I wanted to make was to include solving equations earlier in the course. In my old plan I waited to introduce it after introducing linear relations. But, after teaching solving equations using the Double Clothesline and the puzzle nature of learning it that way….I can introduce it now and continually practice our skills through warm ups.

If you want to follow along as my day-to-day plan unfolds follow this link! If any of you have been spiralling MFM1P I would love compare notes, or see your plans.