Monday, 21 October 2013

Introducing the Radian Measure

As I've posted before, I'm teaching grade 12 Functions and am working on making better use of a great outline put together by the OAME. I think this is good practice for me as a new teacher because it should help me be more efficient in my lesson planning, ensure that I hit all the curriculum requirements (because this outline was built based on them), and keep me from leaning on the textbook for examples and questions. One of the skills I want to develop in my students is to help them begin to use the textbook as a reference. It will be a much better supplement if the examples and descriptions in it are not word for word what the student has already seen in class and has in her notes.

I'm feeling good about this because I think I have a BIG improvement over the lesson for introducing radians. The lesson outline really just has students think of radians as an alternate unit for angles with an easy to develop pattern that leads into an easy to use formula for converting. Just like it's better to actually spend some time discussing the differences, pros and cons, etc between the metric system and the imperial system I think it's better to start students working with radians before they even know it and have them be useful because they are connected to other areas of mathematics, then get them to find the pattern for the easy conversion formula. Hopefully I'll also remember to talk to them about how any conversion formula relies on multiplying by 1 and "cancelling" units; in this case

I'm going to use the formula for circumference and unit circles. Oh, yeah, I'm planning on writing "Matt loves circles" on the board as my hook tomorrow. If I remember I'll be bringing my pi coffee mug too. I want to lighten things a bit right after the midterm and while I also set up for student conferences where I will make sure each and every student knows how they are doing at this point and I can get some 1-1 feedback and help them set realistic goals for themselves (unfortunately some came to me pretty unprepared and the goal might end up being "learn as much as I can so I get a better grade when I take this class again"). I'm going to ask them to spend some time trying to figure out why there are 360 degrees in a circle. I'm posting that question to twitter now too to see what other responses I can get. 

By using the unit circle, the circumference is 2pi and it shouldn't be a big jump to get students to tell me how far they would have to walk to get around half the circle and a quarter of the circle and 7/12ths of the circle. These being the arclengths associated with that ratio of the unit circle. I did a really quick modification to one of the included worksheets and am going to ask my students to tell me the arclength of the highlighted portion of the unit circle, as well as the angle in degrees between the terminal arm and the x-axis. (Next they'll get the formula). I tried using a highlighter at first but it didn't show up in the photocopy, so I reached for my favourite green sharpie and voila.

On a black and white photocopy the whole circle is still visible but the green is really obviously highlighted. If I keep teaching this course I might remake the page, doing something "nicer" on the computer for the same effect, but I also have some serious improvements to past portions of the course that I would want to make first. The instructions at the top of the page are not 100% accurate to what we're doing with the worksheet and in the future I will block that out to be more clear. I'll have them work on the new pairs I'm setting up for tomorrow - I've left a couple of students who need more attention at the back corner of the class for far too long already so they're going to move up and towards the middle starting tomorrow!

Today was the midterm, so tomorrow my students begin our unit on Trig Functions. It should last about 2 weeks at our accelerated pace (10 hours per week of class) which works out to about 2 of the outlined lessons per day, but I plan on putting some of them together and getting into a worked example of where a trig graph might come up (I'm thinking average monthly temperature for different cities with universities in Ontario and/or Canada where my students might want to go).

Almost forgot; the unit, lessons, and worksheets are available here.

Tuesday, 15 October 2013

Following a Plan

I guess it's normal for teachers to feel like they are starting from behind and trying to catch up. That's how I felt my first few weeks, first month, and still feel now almost half way through my short semester. For me it was a combination of being a new teacher, being hired at a school I'd never heard of right at the start of the semester, then trying to match the conflicting outlines of the other teachers who are also teaching the same course as me. My semester is also short - running from the first week of September only to the end of November.

My teacher education program and experience at my placements did a really great job of encouraging us to not try too hard to recreate the wheel too often. There are great lessons and resources all over the place and in particular all over the web. Many of which have been created by experienced teachers, with access to time, research, and other tools that we don't have. A lot of them have even been paid to make them - others, of course, have been shared by teachers out of the goodness and kindness of their hearts and in the interest of making us all better teachers. Regardless, there seems to be no excuse for teaching from the textbook alone or for having to make up class notes and activities from scratch everyday.

Two places we were most often directed to were the EduGAINS (mathGAINS) and TIPS4RM wesbites. My focus during my teacher education was on the intermediate grades, because I was more familiar with the high school and university material, students of that age group, and because my placements were in a grade 6 class and a grade 7/8 class. Now that I'm teaching a grade 12 course I've come back to these sites and had a closer look at the material for high school courses and I think it's just fantastic. I wish I had put together that the two sites can be seen to work in tandem but that they actual don't repeat much material. The formats for the lessons are the same and both use the titles GAINS and TIPS4RM so when I was first looking them up this Fall I thought they would have repeated the same material in two different web locations. NOT THE CASE!

By searching for "tips4rm, mhf4u" I came across this site here which includes a nice outline of the course and an outline for each unit along with some projects and some pedagogical explanations for why things are done the way they are. By searching for  "edugains, mhf4u" I come across a link to here which includes the same basic outline (but not some of the projects) AND has detailed lessons for most of the topics covered. I WISH I HAD FIGURED THIS OUT SOONER! But really, I'm just glad I got myself set up on it now. Because I'm teaching the Ontario Curriculum and these were written by the Ontario Association for Math Educators (OAME) (@OAMEcounts) it's really helpful for making sure I cover all my expectations and for putting together my lesson plans in a sensible fashion (I plan on teaching this course again and as a private school I will have at least one inspection by the Ministry who will likely ask about my lesson plans, how I am tracking expectations, and things like that).

My big idea for improving my teaching, reducing my planning time, increasing my time spent reflecting and improving (through this blog and twitter with the help of other great math teachers) is to follow these outlines as a starting point. I will modify them like crazy when I want to or need to. I have already used a great activity called "Light It Up" from the Illuminations folks too and plan on using more of their stuff so I am not going to limit myself to GAINS/TIPS4RM course either, but it means I have a great starting place that is not just teaching from the book because one of the most important skills we can develop in our (especially senior) students is the ability to use their books as resources, to use the index and glossary and look things up and then to look them up online too. That's how it works when you want to do something you don't know how to do and it's not for school. If I can teach my students how to teach themselves then I'm getting somewhere and it doesn't really matter if they ever use the math in real life....

My Context

I'm a new teacher. I did a math degree and spent a few years tutoring before attending what I believe to have been a fantastic Teacher Education program in Ottawa, ON with mostly amazing faculty about a year and a half ago.After moving to Toronto I have continued to tutor and spent a good amount of time tutoring (and pre-teaching) the Functions courses (grade 11 and 12) and the Calculus and Vectors course. When I got the last minute job offer to teach high school math a private International school I jumped at the chance to teach, to put teacher on my resume and to have a paid teaching job. I'm teaching two sections of Grade 12 Functions (MHF4U under the Ontario Curriculum). I'm very comfortable with the material, with connecting one idea to the other and with cycling back to reconnect to past topics. In short I know I can and will be a good teacher. I want to be a great teacher, but I know I'm not there yet. Right now I want to be a good teacher day in and day out and I'm getting there.

The set up where I work is different from other schools. I have small classes. I had 14 students between two sections to start and am now at 11 between the two. Unfortunately the split is 10 in one section and 1 in another. The classes can't be combined because they actually take place in different physical locations. Next week I may lose a few more students from my class of 10 as some are working well below the grade level. I wish there had been more intervention I could have done for the students who are not prepared for the class, but for a number of reasons there wasn't. I'm going to try harder at that next term and in future Septembers when there are students new to the country and new to our education system. I really like the small class size, but the class of only 1 is too small so to build in interactions with other students I'm going to connect to the class of 10 using a wikispaces page and encourage her to connect to other students through the Open Study site (

I'm excited about being in an English Language Learning (ELL) environment. It is really great AND really challenging to realize just how high the literacy demand is for math at this level (word problems and explaining abstract concepts like limits and infinity). I'm working at reducing this demand and also at building up my students math vocabulary most every day. I have a real advantage over public school ELL situations because all of my students share a mother tongue. The international school is fed into from China and all my students speak fluent Mandarin. (So far I have failed to learn anything - I want to know the first few numbers at least by the end of term.) So our word walls have an English column and a Mandarin column and in group work I encourage the stronger English speakers to help translate and explain concepts in Mandarin to their peers. I want to keep finding ways for peer learning and instruction - another reason I'm pushing a wiki on them. If they take it up it will be a great place for them to store and share resources in Mandarin that I can't find or understand. (The only place I have yet to find anything translated from English to Mandarin and with descriptions in both is through the Khan Academy; but not much of my material is done yet and their stuff is very computational based. It's necessary, but far from sufficient for success at this level.)

More to come!