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Links...

Visual Patterns
Andrew Stadel's 3-Act Catalog
More 3-Acts Livebinder
Tap into Teen Minds (3-act math tasks sorted for Ontario Curriculum)
Math Mistakes
Nathan Kraft's Toothpicks Video

Blogs Worth Following...

Fawn Nguyen
Andrew Stadel
Dan Meyer
Nathan Kraft
Sam Shah
Nat Banting

November 20, 2012

A Day in the Life of this Math Teacher

5:10 am Alarm. I get up and do 20 minutes of yoga. Well, actually I think about the fact that I should be getting up and doing yoga for 20 minutes while lying in bed. Then it’s too late to do yoga.

5:30 am I actually get up. I get myself ready and have breakfast while getting my lunch together and finishing up the kids’ lunches. Make sure they are all awake and getting ready. It’s pajama day at their school so my eldest has her pjs and bathrobe on. The boys don’t want to wear pjs to school (???) so the alternative is to wear blue (???) which they do. My youngest, who is 3, will not start school until September, so she can wear whatever she likes as long as she gets herself dressed!

6:30 am Out the door. Well, not really. They are never all ready when it’s time to leave. But there is not too much fussing this morning and I don’t have to carry anyone to the van without a coat or shoes so it’s a good morning.

6:45 am Drop the gang at daycare (which is 2 minutes from home – you do the math on how long it took to get them all out of the door on a good day!) and get hugs and kisses times four.

6:55 am Stop at the store to buy a litre milk. Only 4 litres of milk are sold in bags (each containing 1.3333333333L of milk) – the 1 L size comes in a carton. (Milk sold in bags seems to be a weird thing to the rest of the world.)



7:00 am Arrive at work. Nothing in my mailbox, as usual. Go upstairs and open my classroom and turn on the computer (there is heat in my room today - yay!) along with five other classrooms. Teachers like to arrive to an open room – just a little thing but it seems to be appreciated. It also keeps the kids from piling up in the hallway. The math/English bowling alley (office) is actually not completely like a freezer today as it was yesterday. Life is good. Fill the kettle and Tassimo with water and make myself tea (that’s why I needed the milk) then settle in to look at what I am teaching this morning. Completing the square in grade 10 academic. I actually knew that because we did it with algebra tiles yesterday and they really wanted to know how to do it without the tiles. Colleagues arrive, check my emails and twitter briefly, then head to class.



7:55 am Warning bell. Classes start at 8 am. As I teach at a rural school, all of our students take the school bus so, in theory, no one is every late to class. This holds true the vast majority of the time. The kids arrive in class and drop off their homework on my desk. I know that giving homework is controversial these days, but I still do. And I check it every day in every class. We start completing the square. With tiles to begin to get them on track then we use charts and flow into the algebraic equivalent. And I LOVE teaching this. I’m not sure that any of them will ever need to know how to complete the square or if we should still be teaching it, but that’s a whole other discussion. It’s in our curriculum therefore we teach it. But teaching it this way, where we move from the concrete to abstract while linking the two is so much more powerful than having them learn an algorithm. I think that my students could all tell you why we divide the coefficient of x by 2 and square it. I think they could tell you why it’s called completing the square. I think they get it. And they understand why a parabola written in vertex form is more useful than one written in standard form. We work through some examples together. They work through more on their own and I circulate helping those who are stuck and giving stickers to those who got it. Yes, I give stickers. They love them. So it was a good class.

9:15 am Class ends and I have my prep period next. I work through some calculus questions. I am tutoring a student who graduated last year. I didn’t teach her while she was here but she’s a really nice girl and works hard but struggles with calculus. In calculus for life sciences they look at Discrete Time Dynamical Systems (DTDS) a lot. I have never heard of them. So I am learning. Ugh. Posted some lessons on Edmodo. Worked on a few other things that were clearly not important enough to remember.

10:45 am Lunch. Yes, lunch is at 10:45. It’s amazing how quickly you get used to eating lunch at 10:45. When daylight savings time ended, we were all starving at 9:45 am. It was terrible! Pita, cheese, veggies, fruit, water. All while catching up on Twitter. No one asked for extra help at lunch. Weird.

11:35 am Grade 12 Advanced Functions. This group is hilarious. They decided it was no-desk Tuesday so they pushed all the desks out of the way and sat on the floor in a circle (I took a picture of them but am not sure if I should post that). This is the same group that uses Edmodo to organize pot lucks for review days. One of the vice-principals came by and stopped in and they asked her to tell them a story (since they were having circle time) and she did. Then we evaluated a lot of logarithms and they “discovered” some new rules. One student kept getting phone calls so I took his phone away. Turns out it was another student in the class who was calling him. Ah, teenagers! All the desks were back in place by the end of class at 12:50 pm.

1:00 pm Grade 10 applied…test on quadratics. Well, it’s the quietest they have been for a while.

2:15 pm End of the school day. Busses leave at 2:27. I head to the office to do the discrepancy report – a printout (yes, let’s kill more trees) of any absence discrepancies for the day. For example, if a student is marked present in 3 out of 4 classes, that will show up and the teacher of that other class can correct their mistake before a synervoice goes home saying that the kid skipped a class. I don’t make mistakes so I just initial it and hand it in. To clarify, I make lots of mistakes. But not with my attendance. I got that figured out.

2:30 pm I have tests to mark so that’s what I do. I always return tests the class after they are written. I’m a “do it now or it might not happen for a long time” kind of person.

3:30 pm Leave my school and go to my kids’ school to pick up kid #2 at 3:45 pm. I get hugs from kids #1 and #3 while I am there then we head to Jiu-Jitsu. This is his thing. He is 7 and has his blue belt. He goes to four classes a week and helps with another four. His older sister started in August so she still has her white belt. I am at the Dojo on Monday, Tuesday, Thursday, Friday and Saturday. I insisted on taking Wednesday off as that is the only night off for the week. We hit Starbucks on the way there. He helps with the Little Champions class at 4:30 then has his own class at 5:00. I mark those tests. The other parents at JJ ask me what’s up when I’m not marking. Hmmm… He takes forever to get changed afterward because he is goofing off with the other boys in the change room. We make it home by 6:30 and supper is ready. Food, cleanup, baths, stories, bed. With a little mayhem and chaos thrown in for good measure. Somewhere along the way lunches get made, dogs get fed, toys get put away. Some of the toys get put away. And they are all in bed by 8-ish.

8:15 pm Since I finished marking today’s tests and I feel like I caught kid #4’s cold, I think I am not going to do any work tonight. Instead I am writing this. And then I’m actually going to post it. Unlike the other unfinished blog posts I have sitting on my desktop. Then I’m going to do something crazy like watch tv and sleep. And tell myself that I really need to get up and do yoga in the morning.

August 31, 2012

Perplexing Polynomials

I have recently been attempting to make working with polynomials easier for students to understand. We tackle this early in our grade 9 curriculum, in both the academic and applied streams. We relate it back to working with integers, use manipulatives and on-line tools, developing a solid understanding of each of the pieces. That ‘x’ terms can represent length (1 dimension), ‘x2’ terms represent the area of a square (2 dimensions) and ‘x3’ terms represent the volume of a cube (3 dimensions). That we can use algebra tiles to add and subtract units, ‘x’ terms, and ‘x2’ terms. How the zero principle helps us. That each part can have meaning, can represent something concrete. Then we put it together and suddenly we have expressions like ‘2x2 – 3x + 5’. What does that mean? Students have just learned that you can’t combine terms unless they are like terms – the ‘x2’ terms go together because represent the area of squares so you can combine them. But you can’t combine ‘x2’ and ‘x’ terms – one represents area and the other length. So what do expressions like ‘2x2 – 3x + 5’ mean? The world of math just became incredibly abstract. It quickly becomes a case of learning the rules to follow in order to be able to add or subtract polynomial expressions. The rules were “discovered” by looking at like terms separately, but when terms get combined and then we take a step further and introduce multiplication (and the exponent laws that go with it), the whole simplification process becomes very confusing for many students. So this is where I am now. Only by working through this and trying to come up with a meaningful reason for combining these polynomials have I truly understood why my students struggle so much with simplifying polynomials. It is completely abstract with seemingly different rules – if you add terms the exponents don’t change but if you multiply you add the exponents. I don’t want my students to memorize rules, because, as we all know, they will forget them or use them incorrectly. I want them to understand why they are doing what they are doing. I want it to make sense to them; I want them to understand how the pieces fit together, to almost intuitively approach a problem because they really, really, understand all the pieces and can put them together. But I don’t know how to get there. I don’t know how to make simplifying polynomials less abstract, how to tie the pieces together into something cohesive that makes sense. I would love suggestions! Help, please?

August 17, 2012

Working Backwards?

I have been trying to find a good context for a particular topic in grade 9 math – something that will be relevant to students and will illustrate why using math is helpful (essential?) to solving the problem/answering the question. The way this is structured - in this lesson they must reach these learning goals, in the next lesson they will reach other specific learning goals – seems backwards. I realize that this is not a novel thought on my part, but this process is really backwards. We should be finding good, interesting, engaging questions and pulling the math out of them, in whatever order it comes. Students should ask “How can I do that?” before we teach them a new concept so that they drive the learning process and see the relevance of what we are doing. This process would mean that as teachers we have to find great questions. That is a fantastic reason to have a PLN. We need to share ideas and help each other grow those ideas and the ripple effect of other ideas that come out of them.

August 13, 2012

Hiding Behind the Hat

For some time I have been working up to this, slowly peeking out from behind the metaphorical hat (that is my 3-year old in the picture), to create a greater digital footprint. Those who know me know that I am a self-avowed geek and huge advocate of technology integration in the classroom. But I’m also an introvert so this is not an easy process. A huge thank you goes out to Tony Baldasaro (@baldy7) for his many posts on the subject which have helped me enormously and to Will Richardson (@willrich45), who is something of a rockstar to me, who admits that even he still has that feeling in the pit of his stomach when he publishes a new blog. So here goes. Thinking and planning for the upcoming school year leads me to two big goals. One has to do with the use of technology, the other more generally about how I teach.

Last year I started using smartphones (for those students who had them) and iPod touches (on loan for the semester) in some of my classes. I would describe my efforts as a failure. But that is how one learns. I think it’s important to reflect on the good and the bad and I know that I need to make a greater effort to improve. In addition to mobile technology, I have a class set of TI-Nspire graphing calculators, use a SMART board and my iPad to control my computer so determining the best use of resources was, at times, overwhelming. As is the quantity of, well, everything out there in the wired classroom. It seems to me that using mobile technology should be seamless and natural for students but, perhaps due to the fact that many teachers do not allow them to use these devices and definitely because of my inexperience, that integration is not happening smoothly. I have learned that I need to do a better job of planning when and how students will be using their mobile devices. I need stay focused on small goals and build one step at a time as I learn what works. But the bigger picture here is that it should not be so much about what technology we use, but about how we use it. Which leads me to my second goal.

Grant Wiggins’ (@grantwiggins) talk at Exeter along with Dan Meyer’s (@ddmeyer) workshops/posts have pushed me to rethink how I teach… I think we need to ask big questions, allow them to think and discover, not lecture and have students do exercises. This is especially true for those students who are less mathematically inclined. As I read somewhere – do the non-Googleable stuff in class. Make the most of that 75 minutes every day – make it count (no pun intended). In Ontario high schools there are two major streams in 9th and 10th grades: academic and applied. These courses are generally for students who will go on to non math-related university studies or to community college. Making the curriculum relevant for them and engaging them can be challenging so this is where I want to start making changes to the way I teach. I already do many hands-on activities with my students, collect data and use real-life situations, but I think the balance of “sit down and let’s go through this lesson together” and “discover some cool things for which you need to use some math” is off. So I will create and search out good questions. Finding folks like Nat Banting (@natbanting) is a great start.

So my intent is to blog about my progress toward both of these goals and to post anything from which I think others may benefit. And I may talk about my kids because it’s hard to not talk about my kids. I welcome feedback so please comment below. Thanks for taking the time to read this!