A Summary of Spiraling through the Curriculum with Activities

At TMC14, Alex Overwijk and I shared our experience spiraling through the curriculum using activity-based teaching. I'm going to attempt to summarize what that entails. The PowerPoint is on the wiki.

Let me start by giving credit where it is due. Alex and Bruce McLaurin (@BDMcLaurin) started spiraling at their school 5 years ago. They are the experts on it now and are sharing the experience with teachers far and wide. I got involved this past school year when I spiraled my grade 10 applied math class, second semester. Alex wanted to collaborate on this with me and Sheri Walker so we met 3 times during the semester to figure out what we wanted to do, try some things out and plan each cycle. We took the lead from Alex on which activities to look at and added a few things of our own. This was truly jumping in the deep end of the pool, but I firmly believe it is the only way to do this successfully. At the end of our session Alex said that if you try to do it slowly and incrementally, the kids will drag you back down and you will go there because that is your comfort zone. I agree, so jump on in!

A bit about grade 10 applied math. The students in this course have generally been unsuccessful at some point in math and most do not like math. There are a lot of behavioural issues and I would guess that in the average class, over half of the students have an IEP. Asking these kids to sit and take notes then do homework is a recipe for frustration all around. Instead, we tried to get them up and moving, doing math in context, even if it was a contrived context, and assigned no homework. There was no point assigning homework - those who would do it are the ones who didn't need to and the ones who needed to wouldn't do it. So no homework, no textbook; we created worksheets for practice which some students finished and others didn't. They did what they could in 75 minutes each day, which was different for each student.

Here is how it was structured. Over the course of the semester we did 4 full cycles and a bit extra at the end. This means no more units. Each cycle covered each of the overall course expectations (they start on page 53) and we tested all of these at the end of each cycle. 

We uncovered the material through activities. Hands-on as much as possible, with manipulatives, graphing technology and whatever "stuff" we needed - spaghetti, pennies, linking cubes, algebra tiles, cups, etc. The activities started out very scaffolded and become more open-ended and richer as the course progresses. I blogged about it all starting here and I will link to Alex's blog posts below.

The first cycle started with the 26 Squares activity which took about 3 weeks. We hit all 3 strands of our curriculum. Next we did some toothpick activities to work on linear modeling and equations. We did Andrew Stadel's File Cabinet 3-act next to hit on some of the measurement strand. We used Smarties, Jujubes and pennies to solve systems of equations. That is where we ended cycle 1.

Please note that these are Smarties:

These are actually called rockets:

During the 2nd cycle we did Spaghetti Bridges for linear modeling/solving, a series of activities including High Fives and Frogs for linear and quadratics, found inaccessible heights for similar triangles and trig along with a roof truss task for the same expectations, then I did some work with surface area/volume of prisms and pyramids (I think Alex and Sheri did something different). Then came test #2.

The following chart, although hard to read, gives you an idea of the number of activities and which expectations they are hitting.

Alex also did a card tossing activity which we got participants to try out at TMC14. It is a lot of fun to do and hits a lot of curriculum expectations. I find that the more of this I do, the more I can see how to extend an activity to get more out of it.

(thanks to Nathan Kraft for the photo)

Throughout the course students saw the same concepts several times. For example, in cycle 1 they solved systems of equations only with manipulatives. They did not even write equations to represent the situation. In cycle 2, they did the same but also started to write something to represent the situation - some wrote equations, some used symbols or pictures. In cycle 3, they learned how to use elimination through a very logical progression of questions that made sense in context. And we reasoned through the answer. They may not have been able to present a beautiful algebraic solution, but they could solve the system and could explain to you how they did it. They were not following an algorithm - they understood what they were doing. In cycle 4 they solved systems to work through the cup stacking activities. We created a solid foundation and built upon it each cycle.

The benefits from the PowerPoint are shown below, but one of the big ones for me is time - you have time to get through the course - in fact they see most of the the curriculum in the first 6 weeks; you don't need to feel rushed to get an activity done - if students need an extra day, take it; if someone is away for an extended period of time, they miss an activity or maybe 2, but we will cycle back and see it again.

As a side note, I got comp books for my students because I enjoy structure a little more than Alex. (By "enjoy" I really mean "need".) For each topic I would print out an example or fill-in-the-blank type of sheet for students to glue in their comp book and fill in. This way they all had a resource to refer to. Some students took their comp books home to help them study for tests and they were allowed to use them for the end-of-year summative task.

I hope this helps shed a little light on what is involved in spiraling through the curriculum with activities. Please throw any questions my way in the comments. Perhaps the strongest endorsement I can give is that I will never teach this course in a "traditional" way again, and that I have volunteered to teach it (the course that no one wants to teach) both semesters next year.

Why I Go to Twitter Math Camp

It’s funny – a year ago, after TMC13, I wrote a blog post entitled “TMC 13 - Minus the Math”. I find myself again not wanting to talk about the math that surrounded me at TMC14. It’s not that there were not great ideas presented or innovative ways of doing things, but more that the reason TMC is so special for me is due to the interactions that happen around and outside the math. Being constantly surrounded by up to 150 people for 4 days should sound a little like hell to an introvert like me, but it is truly the most deeply fulfilling professional, well, anything I have taken part in. I have presented workshops in a lot of places, in a lot of formats, and other than Exeter, nothing even comes close to TMC. The connections that exist before those magical 4 days get strengthened and new ones are formed, and (this is the thing), they continue to grow after we all head in different directions geographically. Each of these connections helps make me a better teacher as they encourage me to share, try others’ ideas and stay connected to the greater math world around me.

I cannot possibly do justice to how I feel about my tweeps. The fact that I feel comfortable even calling them my tweeps is remarkable. I do not ever make assumptions that people are going to like me or think highly of anything I do, but I feel that some teachers on Twitter really do value me and my work. This is remarkable.

I want to mention a few people that had an impact on me at TMC14. It was such a pleasure to have spent time with many others, but this post might never end if I list you all…

Pam Wilson (@pamjwilson) may be the nicest person on the planet. She makes me want to be a better person and teacher and continually motivates me to do more math ed reading to continue learning. She is amazing. She also reads my blog and has always been kind and supportive which means so much to me.

I was actually too shy to talk to Nathan Kraft (@nathankraft1) last year, but am really glad that I got to spend some time with him this year. He is genuinely a good person and I feel fortunate to call him my friend.

I enjoyed a conversation with Viktoria Hart (@Viktoriahart) and the always awesome Justin Lanier (@j_lanier). Viktoria has 1 more year of school left before she becomes a teacher. Wow! She is going to kick ass when she gets in the classroom.

MaryAnn Moore (@missnarymm) was kind enough to chauffeur us around. She is simply lovely and I look forward to continuing to get to know her on Twitter. She said it well when she tweeted this:

I had the pleasure of two dinners in the company of the Memphis trio: Kevin Mattice (@kjmonopoly), Matt Bigger(@mwbigger) and Seth (@melroseharkins) along with Levi Patrick (@_levi_) from  Oklahoma City. I was lucky enough to get to work through Park Central (or was it Central Park?) with Levi and have to tell you that he is sharp, funny, kind and passionate about what he does.

Kate Nowak (@k8nowak) was kind enough to help us find a quick lunch on Friday and it was really refreshing to talk to her. I have admired her work from afar and feel fortunate to now have gotten to know her a little bit. She later tweeted that she would like to know more about the spiraling work that Alex, Sheri and I have done so I sent her the link to my blog. I think this may be the best tweet I have ever gotten:

I can’t not mention getting to see, talk to and hear Eli Luberoff (@eluberoff). He continues to impress me with his passion and commitment to making a product that is as good as it can be for students and teachers.

Most notably though, I brought Alex Overwijk (@AlexOverwijk) and Sheri Walker (@SheriWalker72) with me to TMC14. There are now two people that I collaborate with at home who get “it” – the “it” that makes TMC so special. The passion of all the educators, the friendly nature of all who attend, the collective need to improve as teachers that is second to none. I got to share that with them and that is huge. I am so glad they were able to make the trip with me. I love them both and they defined TMC14 for me.

There was a chunk of time that was not my finest hour, so to speak, and I appreciate all the concern that was expressed. I should know that I cannot be “on” for 3 days straight, especially on little sleep, especially, especially with no lunch on the day I am presenting. The intersection of those (and a few other) things left me unable to give any more when asked to do something that would have been very difficult for me even on a good day. I hope I didn’t offend anyone and am truly sorry if I did.

I leave TMC renewed in my passion for teaching, knowing that I belong to an amazing group. Being part of this community makes me feel complete. Thank you to Lisa and Shelli for making this possible. You will never truly know how much this means to me.

See you at TMC15.

Not a TMC14 Post!

I am really just testing out a theory here. While I do that, here is a picture of one of my dogs.

TMC14 - Thinking Through Day 1 of Algebra 2

I feel very fortunate to be back at Twitter Math Camp. It is so great to see the Twitter friends I made last year and to meet so many fantastic new (to me) people! For the morning session (2 hours/day for 3 days), I chose Algebra 2. Being Canadian, we do not have a course called Algebra 2. In fact, the content from Algebra 2 fits in grade 10, 11 and 12 courses within our integrated Ontario curriculum! Therefore talking about the flow of the course or the connections within the course is a little less relevant for my situation. However, I am taking pieces and figuring out where they do fit and how I can adapt them to help my students make more sense of math.

Glenn Waddell (@gwaddellnvhs) spent a large portion of the first day showing how he ties all of the algebra 2 functions together through a common algebraic form. 

The one of these forms that most teachers likely don't use is the linear one: 
y = a(x - h) + k. 

Glenn has blogged about it here. I like the way this connects to the other equations which we do use. I like it, yet it bugs me and I'm not sure why. It makes a lot of sense and is a very useful form. 'a' represents the slope (or rate of change) and (h,k) is a point on the line. Slope-intercept form is great for graphing, but Glenn's form (I'm not sure what to call it) is so much more useful when trying to find the equation of a line given the slope and a point on the line or two points, etc. Once you determine the slope, substitute the point for h and k and you have finished! Here is an example using Desmos.

The more I think about it, the more I think that my discomfort with this form is simply that it is not what I am used to seeing, and perhaps, that it can be simplified (and I kinda like my functions to look tidy). But it really is a smart way of tying together so much of what we do with functions and their graphs. I think I will work with this at the beginning of my grade 10 academic class in September. They will all know y = mx + b and will be working through transformations of quadratics before long, so it seems like a natural fit. Thanks, Glenn!

Change is Hard

In my last post I eluded to the fact that getting away from a lot of "direct instruction" (there are so many connotations of that terms) is hard. I teach in a department where everyone is expected to teach the same thing, in the same way, on the same day. This stemmed out of necessity. The school population used to be much smaller so when there were 2 sections of a course being offered, the teachers would work together, taking turns making up lessons. They would both teach the same thing on the same day as they had both contributed to creating those lessons. We still do this and also take turns creating tests and test on the same day. But times have changed. Our school population is over 1100 and there are generally 2-4 sections of each math course each semester. However, getting away from the SMARTboard lessons we all share is not an easy task. The thing is that you can't formally teach a lesson at the board (show concept, work through examples, repeat) AND do activity-based learning. Both require time and I can't do justice to an activity if I also have to "teach" the lesson. In MFM2P it was rare for me to do any direct instruction, and when I did, I disliked it. You may be able to cover more, but many of the students are not taking that journey with you. How many times have you found yourself saying "but I taught this!" when students don't know how to do something? Just because we teach it does not mean they learn it. Why it has taken me so long to figure this out is beyond me. Anyway, I want to change the way I teach in my academic classes, but I don't want to rock the boat too much. I value the collaboration I have had with some of the teachers at my school and don't want to upset anyone. What works for them is great and I don't wan to change anyone else (except if they are teaching kids in the MFM2P stream!), but I know that I could connect with more students and do a better job of engaging them all. And I'm okay with doing more work...

So my thought is to stay on track with testing at the same time as the other classes (which rules out spiraling), but do activities for the majority of the days leading up to the test. There will be some skills that I will have to teach, but I'm going to work on making that the exception, not the rule. I will also blog about what I'm doing so if anyone wants to try what I'm doing, it'll all be there. Change is hard, but change can be very, very good!

Reflecting on 2013-2014

In the fall of 2013 I started trying a few new things in my classroom. I did counting circles with my grade 9s (MPM1D) and I think that really helped set the culture of my classroom. Some students loved it (perhaps because they didn't consider it "work"), while others hated it. It took me outside my comfort zone, but I know it was a good thing. Making everyone say something every day is big. I try to involve all students every day, but this forced the issue and may have made some more comfortable to share ideas along the way. I hope it helped improve some students' number sense too. I tried to do math talks with that class, but got swallowed up in the "I have to cover this curriculum by this date so I don't have time to do anything extra" mentality. I need to lose that! I did throw in more activities and tried new things, but not enough. In the fall I also had a grade 10 academic class (MPM2D) and a grade 12 Advanced Functions (pre-calc-ish) class (MHF4U). I also tweaked them (I have taught all these courses before) and added cool stuff where I could make it fit, but still, there is much more I could do. In all of these classes there was still way too much of me teaching and them taking notes, then working through examples together. This, I feel, needs a whole separate blog post...

Second semester I had a grade 10 applied math class (MFM2P) along with two sections of grade 12 Calculus & Vectors (MCV4U). The Ontario math curriculum documents are available here: grade 9 & 10 and grade 11 & 12. I have to admit that I didn't do too much to make MVC4U better - a few added investigations, a few more station activities, more use of whiteboards, but not a big overhaul. It works and it is the course that I'm least likely to change in a significant way. The grade 10 applied class was a whole other story. I ditched pretty much everything I had done before and started fresh. I was very luck to have the opportunity to work with Alex Overwijk and Sheri Walker throughout the semester and successfully spiraled through the curriculum with activities. I blogged about it all, starting here, so I'm not going to go into the details of what I did. I will say that it was exhausting and exhilarating and at times frustrating, but it was good. My students learned math, despite not wanting to, in many cases. One student in particular complained about having to do work, said things like "can't we just have a lesson?" and often said that he didn't know how to do whatever we were doing, but with a little nudging always got there. He told his guidance counsellor that I "wring the math out of him". I like that. And it is an apt description of what went on in that class. They often tried to quit but I never let them. They may not have worked as hard as they could have, but they all worked every day. They were not spectators. They learned to persevere. It was not perfect, nor will it ever be, but I think it is on the right path. This is what they left on the board for me:

(yes, some of them called me "b-dawg" - so not me, but I grew to like it)
They were a great class and I feel fortunate to have spent the semester with them.

Next year, I volunteered to have a grade 10 applied math class each semester as I am very invested in teaching this course this way. I am looking forward to actually having some idea what I'm doing from day to day (!) and learning from what I've done. Blogging about it has already proven itself useful to my two colleagues who will be teaching it the same way next year along with me. I'm sure I will also be reading my posts to remember what did and did not work. There are definitely some things that I will change, but I am so thankful to Alex for sharing his time and work with me.

I also want to make changes in the other courses I will be teaching. That goes back to needing a separate blog post so I will leave it at that for now.