(If you would like to run your own math party, HERE ARE ALL THE RESOURCES you will need, as well as instructions for printing and set up.)

In my last post, I vowed to keep things short and sweet, then proceeded to ramble on for 599 words. So this time I’m going to do my best to get to the point. Here goes…

I tried something a little different recently. As a way of practicing/reviewing for upcoming test on similar triangles and right triangle trigonometry, our class had a Math Party!

First and foremost, there was food! I’m not sure I could’ve called it a “party” without snacks of some sort. As student came into class, they were given a white board marker and a name tag containing the name of a famous mathematician and a number.

The first thing I had students do was research their mathematician, then speak to other students about what their mathematician accomplished. Then for the rest of the class students walked around and attempted to answer the problems posted around the classroom on the whiteboards, Wipebooks, and windows (yes, windows! Give it a try, students love it and there’s no mess). However, there was a catch! Each problem had a famous mathematician’s name where a number should have been, so students needed to seek out who in the room had that particular name tag in order to find the missing number so they could proceed in solving the problem.

I’m so happy with how this turned out! The room was abuzz with students working on problems, asking each other questions, talking about about famous mathematicians, and of course, eating lots of food! I can’t wait to try it again with my grade 12’s during our upcoming vectors unit.

If you’d like to run your own math party, please feel free to use/adapt the resources linked above. Thanks for reading.

I’m trying something new with this post. I’m going to try to keep this short and sweet. Get in and out quick. Get right to the point. No more long-winded, drawn out, over explained blog posts. (I’m not off to a good start am I?)

I’ve been trying something in my calculus class lately. It involves VNPS. This stands for “Vertical Non-Permanent Surface” and the goal is to get students up on their feet working working on a surface that easily erases, which means they don’t have to be afraid to make mistakes (see image below). I’ve had students do VNPS individually sometimes and in groups other times. When I use groups I have the students draw cards to determine their partners. I do this based on the recommendations of Peter Liljedahl in order to ensure fairness, that students work with others they wouldn’t normally choose to work with, and mainly to avoid the constant complaints 🙂

VNPS is nothing new. Many math teachers all over the world are using it in their classrooms. So how have I been using it specifically?(FINALLY THIS GUY GETS TO THE POINT! So much for short and sweet!) I’ve been giving my students the skeleton of problem and then I have them choose their own values for the constants and exponents I’ve indicated. The image below is an example of this.

This way each student/group has their own unique problem, whose answer will most likely not be “nice”. Interestingly enough, the feedback from my students has been that they like having to work through problems with “not nice” answers, unlike the problems in their textbooks.

So how do I check their answers? I’m so glad you asked. Desmos of course! I type in the equation I gave the students with the constants a, b, c, etc. and Desmos allows me to create sliders for these constants (careful not to use certain letters that already have pre-programmed values like e and i). When a student wants their answer checked, I simply input their a, b, c, etc. values and Desmos tells me the answer immediately (see image below). Here is the Desmos graph I used if you’d like to play with the sliders.

Here are a few shots of what my students came up with.

Another example of when I used this was during a product rule lesson. See image below.

I realize these are 2 calculus examples but this can work in any math class. Off the top of my head…

Grade 9 – Have students choose 2 random points and determine the equation of the line passing through them. Set up Desmos to calculate the slope and y-intercept automatically.

Grade 10/11 – Have each student solve their own intersection of a parabola and a line problem. They choose their own a, b, c values for a quadratic in standard form and the slope and y-intercept of the line, then solve the system. Have Desmos graph the two functions and then click on the POI’s. (You could also start the quadratic in factored or vertex form to add a challenge. Now that I think about it, this is probably better because it’ll be easier to ensure that the system has solutions.)

Grade 12 Advanced Functions – Set up a general polynomial in factored form, with some factors having powers or 2 or 3, then have them choose their zeros and sketch their unique graph. Have Desmos graph their function and compare.

Ok, I think I’ll stop my rambling here. It wasn’t exact short and sweet, but at least there were pictures 🙂

If you’re interested, I have also blogged in the past about other things I’ve tried. Here are a few links:

Lastly, I’m going to call on my fellow Cohort 21 mathies to share something they’ve tried in the last year or two, no matter how small. Either leave a comment below or write your own blog post about it! Let’s all help each other out by highlighting and sharing our successes.

So I tried something new this year. Every morning, I’ve taken a few seconds (sometimes minutes) to reflect on what I am grateful for that day, and I’ve been writing it on the board in my classroom for my students to see.

Here are what I would consider the “results” thus far:

It has helped me start each school day with with a smile.

When I have a stressful day ahead, it gives me a moment to breathe and consider the bigger picture of just how lucky I am.

It’s helped me to be grateful for small things, like being able to see my friends at hockey each week.

It’s helped me to be grateful for big things, like my family and all the support they provide.

It’s sparked conversations between myself and my students (eg. “Sir, why are you grateful for an after hours vet? Is your dog okay?”, which led to some great chats about their pets).

I even overheard some grade 12 girls who were working in my room, prior to starting their study session, go around the table and each say what they were grateful for.

Another approach I’ve trying this year is emailing/texting people to thank them and/or congratulate them. I’ve mainly been doing this when my stress levels have been off-the-charts as a way of forcing myself to take a breath and gain some perspective. Also, selfishly, writing these messages just makes me feel happy.

AND NOW FOR MY CHALLENGE!

I’m asking everyone that reads this post to take a minute to reflect on what YOU are grateful for and write it in the comments section below. Let’s see how far our gratitude can spread through both the current Cohort 21 members and alumni, and hopefully beyond.

The thing that’s been pedagogically “stuck in my craw” recently is my students’ daily homework, specifically, how much math homework is enough?

Our math department’s current homework model is shown below. We have every section’s homework broken down into the categories “Minimum Expectation”, “Further Practice”, and “Challenge Questions”. The problem we continually see is that students attempt the “Minimum Expectation” questions only, then stop, regardless of whether they got the questions right or wrong. This is problematic to us for 2 reasons: First, there are good questions being ignored in the “Further Practice” section, and second and MOST IMPORTANTLY TO ME, my students are not even attempting the “Challenge Problems” which are the Thinking/Inquiry problems defined by KICA, which make up about 20% of our courses. Of course we tell them repeatedly that they need to be consistently trying all the homework questions, but our message only gets through to some of our students.

So we’re looking to revamp how we assign homework (in fact it’s one of our departmental goals for this year) and I’m looking for feedback from the Cohort 21 community (and beyond) on what is the best way to do this.

First and foremost, I think we can go from 3 categories to 2. Something like “Standard Expectation” and “Further Practice, if needed”, and in the “Standard Practice” we could include questions from each of the KICA categories at various levels, thereby ensuring that all students are attempting critical thinking problems on a daily basis. Then, in the “Further Practice, if needed” section, recommend more practice for those who struggled with the initial problems. I’m in the brainstorming phase on this right now and I have some concerns:

How many problems is enough practice in the “Standard Expectation” section? This is really hard for me because I’ve got 2 competing beliefs in my head. First – Lots and lots of practice creates a solid foundation of knowledge, but, Second – overloading students with too much homework that has repetitive questions makes math not enjoyable.

Will students (especially grade 9s and 10s) take it upon themselves to try the “Further Practice, if needed” problems? I hate to be glass-half-empty on this one, but in my experience, especially in grades 9 and 10, students actively strive to have as little math homework as possible.

How can we be more explicit with the “Further Practice, if needed” section? For example, if a student struggled with #8 in the “Standard Expectation” section, how do they know that #10 in the “Further Practice” is similar and should be attempted?

I just read Jen Weening’s blog post (@jweening) on using google forms to ‘create your own adventure’ and I’m excited about the power of this to help direct students to the proper problems for them, but also feeling overwhelmed at the prospect of having to create something like this for each unit in each math course.

I also tried something called Homework Trees last year (I even wrote a blog post about it) which were somewhat successful, but in the craziness of the Spring term last year, I didn’t commit to them every day in every course.

So in conclusion, how might we:

Make homework purposeful?

Ensure homework provides enough practice without being repetitive… Unless a student needs it to be repetitive?

Have our students self-assess when they need extra practice and how to locate that extra practice?

As I said earlier, I’m looking for help on this one, so please leave any feedback/comments/suggestions you may have. THANK YOU!!

Hello new Cohort 21 members and welcome to your new life-long professional family! You are about to embark on a professional development journey that will excite you, challenge you, at times overwhelm you, and ultimately, improve you as an educator. As a recent graduate of Cohort Season 6, I thought I’d pass along my 10 tips for new Cohort members (it was going to be 21 tips – get it? – but I quickly realized that 10 was my max). Here goes, in no particular order:

We are all on this journey together and it’s OK if you are not as far along as some others. I need you to remember this throughout the year because you are about to meet some Educational Rockstars who are in a league of their own, which can be very intimidating if you’re the person still searching for their Action Plan in mid-January (*cough* like I was last year *cough*).

Give Twitter a chance. I get that it’s not for everyone but please come with an open mind on Saturday, get signed up, install the app on your phone, follow all your fellow Cohort members and teachers/admin at your school, and see what happens. I, myself, am not a big “tweeter” but the number of ideas I’ve got from the people I follow is well into the hundreds now (when I see a tweet, article, or activity I want to remember I press the “Share Tweet Via” button and then email it to myself).

When your students are doing something “picture worthy”, remember to take the picture, then tweet it out. Letting your fellow Cohort followers into your classroom can help us all in so many ways.

Don’t become paralyzed when writing a blog post. Yes, it can be stressful to officially push “Publish” for the world to see but the pride you feel when you do is incredible! (Plus the supportive feedback you get from the Cohort community in the comments section just makes you want to write more.)

Blog posts don’t have to be 5000 words long and change the education system as we know it. They can be a quick “I tried this new activity today and it went really well”, or “I tried this new activity and it didn’t go so well and now I want feedback in order to improve it”. Heck, you’re currently reading a blog post that is a list of 10 tips. Not exactly life altering!

When you do blog, please tweet the link to your new post to make it easier for all of us to find.

Try to read and comment on others’ blogs as much as you can. We’re all so busy but even a quick 1-2 sentence comment can help others more than you know.

Circulate your blog amongst your peers, coworkers, bosses, friends & family. It’s amazing how feedback can spark a new idea or can snowball into an encouraging new perspective.

Go to the socials after each of the face-to-face sessions.

Garth, Justin and all the facilitators are AMAZING! (Not a tip, just a statement of fact that cannot be said enough)

Hopefully this was helpful in some way. I can’t wait to see everyone this Saturday!

CLICK HERE for a brief overview of my action plan, what I learned, my next steps, and my biggest take aways.

Part 1: How My Action Plan Came To Be

When I reflect on my Cohort 21 journey, I’m reminded of the famous line in The Godfather III.

In my head, the line goes something like, “Just when I thought I had a perfect action plan, Cohort 21 pulls me back in and makes me go deeper!”

At our November F2F, I crafted what I thought was a perfect action plan centered around student retention of math concepts, and went to work exploring how to improve this. Before I knew it, it was January and I was sitting among my new friends again, questioning how important retention actually is. Please don’t read this as “this math teacher doesn’t believe his students should retain anything he teaches them”, I’m simply wondering if retention should be the main focus of my practice moving forward and, to be honest, I don’t think it should be.

Recently, for the first time since January, I looked at my place mat booklet and I thought I’d share one of my responses:

If you can’t make out my chicken scratch (pun intended, if you were able to read it), it says:

Question: What is the urgency behind your action plan?

My Response: It’s not super urgent, instead it’s more of a slow philosophy change where we promote the gaining of foundational knowledge on a deep level in order to have success on ‘big problems’… but which comes first? (Chicken or Egg?)

What I realized in January is that students are only going to retain math knowledge if the concepts being taught mattered to them and/or they enjoyed what they were learning. I also think retention is helped if students enjoy math class as a whole.

So this is where I’ve landed:

How might we ensure that students have a positive outlook on their math class and are engaged by the concepts?

Part 2: What I Tried This Year

I struggled with what to say in this section because, although I have tried new things this year, I feel like listing them comes across as showboating and “braggy”. However, I often think back to our first Cohort 21 face-to-face session where @gnichols showed this video:

I’ve got almost all of my ideas this year from other educators who have been willing to put themselves out there and share details about their practice (through blogs, Twitter, etc). I can only hope that sharing my ideas (below) can help others have their light bulb moment. So, here I go sharing some of the things I’ve tried this year…

“Math is Fun Fridays” – I wrote a blog post about this earlier this year. HERE is the shared google doc with all the Fun Friday activity ideas. (Feedback – students love this! The only problem is that it’s April and I’m running out of fun/interesting activities!)

“Are you ready for calculus” diagnostic – I wrote a blog post about this earlier this year. (Feedback – This motivated some students at the beginning of the year, but as we moved into the winter term, they stopped wanting to continue to work on their core skills. I’m still wondering how to change this in the future.)

A full PBL unit on right triangle trigonometry – Students examined existing wheel chair ramps on our campus, researched the maximum legal steepness, and built a prototype of a ramp into our school’s main office. (Here is a link to the student presentation created for our Head of College). (Feedback – In the future I need to insert more quick assessments throughout the unit to ensure each student is meeting the key targets along the way.)

“The Story of a Limit” (idea from @hpalmer) – Calculus students created children’s stories explaining the concept of a limit. The video below has some of the highlights. (Feedback – Students were able to let their creative side shine and I was really impressed by some of the stories).

“The Smarties Project” – Calculus students redesigned the existing Smarties box such that it had a golden rectangle face and held the maximum number of Smarties. Link to the full project is here. (Feedback – I had several students tell me they enjoyed the challenge of this project because the numbers “weren’t nice” which made it feel more authentic. The “I need help zone” (see below) helped struggling students a lot. In the future I might make everyone’s rectangle face a different ratio so everyone isn’t getting the same final result).

“I Need Help Zone” – I wrote a blog about this earlier this year (link is here). (Feedback – I really like how this worked during an in-class activity. It forced students to talk about math instead of writing out all the steps for their friend).

“The Homework Tree” – I wrote a blog about this (link is here). (Feedback – I only tried this a few times this year so I don’t have a good feel as to the student point of view of the trees, but I do like how they are personalized and less time consuming than our current model).

Lastly, I used various online tools such as Quizlet (thanks @amcniven!), Quizizz, Kahoot, and Teacher Desmos on a more consistent basis. (Feedback – In my opinion, Quizizz is a better version of Kahoot because you can set it so speed doesn’t earn you more points, and you can download the results to Excel when it’s finished. Also, I LOVE Quizlet and so do my students. They work in groups to finish first but everyone has different answers on their screen so no single student can just take over and do all the work. Lastly, Teacher Desmos has awesome activities that allow students to discover concepts rather than be told. A lot of activities are not searchable on Google, however. I found that John Orr has good ones that he’s shared on his blog here.)

Part 3: What’s Next?

If I want students to have a positive outlook and be more engaged in their math class, these are the first things that pop in my head that I could do more of in the future:

More hands-on activities

More group work

Have homework be less time consuming for students

PBL (or at least, incorporating more elements of PBL in some units)

Start with ‘big problems’ and let the core skills develop out of necessity

Spiraling in grade 9 and 10 applied math

I think bringing more of these things into the grade 9/10 math programs will develop a strong core of knowledge and a positive outlook towards math which should pay off in the senior grades. (Obviously we can look at doing more in grades 11/12 as well, were applicable).

Lastly, this Cohort 21 experience helped me reflect on my personal practice, and doing so I learned that I am hesitant/resistant to change for fear of the unknown, specifically, fear that the new way will not be as good for my students because I can’t see the final result. However, this experience has helped me to push past this and trust myself.

However, when I consider the question another way, why are students not engaged in the concepts?, I started to consider how we assign homework.

For our senior school math courses, we assign homework this way:

Their homework is broken down into a minimum expectation, a standard expectation, and challenge problems which we ask for them to attempt, at the very least. We often encourage students to skip certain questions if they are understanding. For example, if #6 has parts (a), (b), (c), (d) assigned and a student can correct answer questions (a) and (d) and feel confident, then they can skip questions (b) and (c).

However, what I’ve learned is that this is not happening. Most students are trying all the listed problems and become either overwhelmed or bored and quit prior to the challenge problems (the problems we, as teachers, want them to try the most!). Other students see upwards of 20 questions listed and instantly feel defeated so they don’t even start.

I want to make homework more manageable for students and also in line with their current ability. My working prototype to do this is what I call a Homework Tree.

I wanted to make homework be a positive experience, which means different questions for different students. My hope is the following:

Students who answer Yes after the first 5 questions will gain confidence in their abilities

Students who answer No will realize they need extra help quicker than before.

If students answer No often, they will be motivated by this to want to be in the Yes category more often.

This can help with goal setting. Students who answered No a lot in a previous unit can set a goal of being in the Yes category more often next unit.

I’m hoping this way allows students to get to the challenge problems faster so they attempt these problems and improve their critical thinking skills. (I want to warm them up for these problems, I think our current way sometimes burns them out).

A student who struggled with the first 5 questions (and therefore answers No) is given a challenge problem they can handle. Again, trying to build confidence.

As I said earlier, I’m still in the prototype phase so any and all feedback is welcome!

You may only get help in the “I Need Help Zone” (located at the back of the classroom). Only one sheet of paper is allowed during this meeting.

Example Scenario: Jimmy asks Julie to meet him in the “I Need Help Zone”. Jimmy brings his paper only (no writing utensils) and Julie brings NOTHING. Jimmy asks his questions and Julie does her best to help him using only her words.

I tried this new strategy in my calculus class while they were working on their Smarties Project. It was an open-book in-class assignment where students could only get assistance from their notes or from a peer in the “I Need Help Zone”.

I’m happy to report that it was a major success! At first, students were a little embarrassed (no one wanted to be the first person to need help), but that faded quickly. I’d say there was almost no time during the period that some students weren’t using the zone.

I love how this worked out and I’m hoping to use it again soon. Obviously there is a benefit for the student receiving the help, but there is also a huge one for the student giving it as well. Having to look at someone else’s work and diagnose what’s wrong, why, and what to do next, using only words, is a massive critical thinking exercise that, in my opinion, students need to experience more of.

Has anyone else tried something similar to this? I’m thinking my next step is to use this strategy during a flipped unit when students are using class time to complete assigned problems.

(Image courtesy of https://ronniemcbrayer.org/2015/09/21/more-than-we-can-bear/)

Since our last F2F meeting, I’ve been wrestling with this idea of retention. Of course I want my students to retain what they’ve been taught, but I think I need to get more specific. Do I need my calculus students to have memorized the quotient rule, or am I satisfied if next year in university they are able to look up the formula and know how to use it? Do I expect my grade 10 students to walk into grade 11 math and remember every factoring rule, or am I happy if they have some recollection what’s happening and, with a little bit a practice, can get themselves right back up to speed? … Serious question – did these two examples just describe students who have had good retention of knowledge? I think I’m confused by my own action plan! What is good retention? Is it remembering how to use a learned skill immediately with no assistance? This isn’t how the real world works. Do we expect professional Engineers to remember everything from their 4th year classes? No, they would be able to read, research, and get assistance from colleagues to help solve the problem they are tasked with.

Although I haven’t exactly landed on my true focus, I have tried a few new things to this point and I’m curious to find out if they help with retention of knowledge.

In calculus this year, I assessed our first unit on limits and the definition of a derivative with a traditional assignment and test. Students haven’t seen these concepts since early November and I wonder how much they’ve retained. So, I plan on surprising them on their first day back in January with the assessment below (shhhh, don’t tell them). I’ll be sure to update this post once the data is collected.

Recently, I tried a more authentic form of assessment that I like to call The Smarties Project(please feel free to use it and/or pass it on to your colleagues). I’m hoping this way of learning about optimization will stick with my students longer. As part of this project, I tried grading it using the single point rubric, hoping that my students will engage more with the feedback I am providing. I’m planning on doing another “retention research assessment” about optimizing volume in a few months, afterwards I will compare if retention improved.

A few other non-traditional things I’ve tried this year are:

“The Story of Limit” (thanks to @hpalmer for the idea!) – my calculus students wrote children’s stories that tried to explain the concept of a limit to children who are at least 7 years old. We then visited Junior and Montessori school classes where my students presented their stories. They are now on display outside our Senior Learning Commons (see picture below).

PBL in grade 10 applied math – my students investigated how wheel chair friendly the older buildings on our campus are, measured current ramps on campus to see if they were below the legal angle (they were!), designed a legal wheel chair ramp for one of our school’s office buildings (see picture below), and lastly, presented their findings to our Head of College.

In the New Year I’m hoping to teach vector addition with the help of billiards (thanks to @rutheichholtz for the idea!)

I honestly have no idea if these non-traditional ways of learning will improve a student’s retention of knowledge or not. Something I’ve been considering more recently is should I be focusing more on the skills required for good retention? Essentially, if a student has not retained a concept fully, what avenues can they take to help correct this?

If you can’t tell by now, I’m in desperate need of another F2F session! Hopefully my fellow Cohort 21ers can help straighten me out.

Lastly, here are some articles/blogs that have me reflecting on my current practice:

Is it Saturday yet? I need some of that “Cohort 21 Face-to-Face” magic.

Since the last F2F, I feel like my head hasn’t stopped spinning. Aside from Cohort 21, I’ve got 4 preps (never experienced this before), I’m trying to get comfortable in my new role of Subject Coordinator for senior math, and I’ve got a 2 year old at home who is the most fun kid you’ve ever been around (okay, I might be a little biased here. Side note, he can now count to 6 and correctly identify a hexagon! … Sorry, I’ll move on now). All of this would have been enough to keep me busy this year, then Cohort 21 entered my life and has me questioning everything I’ve ever done!

I’ve really enjoyed Twitter so far – everyone’s willingness to share their thoughts and ideas has been inspiring. However, the downside can be educational opinions overload. Every time I look, someone has posted or retweeted an article about how education needs to change. Some of these speak to me and force me to reflect on my practice, and others I completely disagree with, but then I stop and wonder if I should be more open-minded?

As part of reflecting on my own practice, I’ve been reading the blogs of other teachers. I read about a calculus teacher who has stopped giving grades and gives personalized assessments. I feel inspired reading his thoughts and the testimonials from his students, but I’m left to wonder if I truly believe his methods are best for my students, or am I suffering from recency bias? In short, is this lust or love that I’m feeling? Should I jump in the deep end starting tomorrow, or should I try one new approach in our next unit and see how it goes? As I said before, my head spinning.

As overwhelmed as I feel right now, I can’t remember a better time in my teaching career! I’m inspired by what my Cohort 21 colleagues are doing and it drives me to be better for my students.

Do I have too many ideas? Yes. Can I try them all tomorrow? No. Okay then, which ones should take priority? Which would benefit my students the most? Which could inspire my colleagues the most?