## Sunday, November 29, 2015

### More than one way to learn. I mean divide.

Happy Thanksgiving "break"!

I just spent 4+ hours grading quizzes that I gave last week on Polynomial Operations. They turned out pretty good, so I was happy. A lot of the mistakes were predictable (subtracting with negatives is always such a problem!), and the kids did well with the division of polynomials.

Some surprisingly so, especially considering the uproar that division caused in class. It helped that I told the kids to use whatever method "worked" for them. This student used long division for one problem (and messed up some subtraction) and "the box" for another. Can you see that she actually did it twice because she wasn't sure of the decimals?  I guess the second time through convinced her.

The day before the quiz I showed the kids what would happen if you did synthetic division when there's a leading coefficient...

While I had told them that they "couldn't" use synthetic because of the leading coefficient, once I showed this type of example several kids saw the relationship in the answers. The correct answer (via long division) is twice the other, though the remainder is the same.

It was kind of neat to see that several kids took advantage of this and used synthetic division on the quiz, then divided out that leading coefficient from their answer.

Saw this the other day from @dmarain:

It amazes me that people think that there's only one way to do so many types of problems. Is it arrogance? Fear of not being the sole ownership of the learning? So sad.

## Thursday, November 19, 2015

### Using the boards...

I finally got around to using those nice white boards around my room today with the kids.

Yesterday they learned how to do synthetic division (to everyone's relief) so today when they came into class I asked for 4 people to put their work on the board. Once I had a volunteer I asked them to pick a friend. Those two went up together and worked out the problem with both synthetic and long division.

It actually worked out very nicely! Some kids were happy to volunteer and even more excited to pick a friend... the friends weren't always that thrilled, but they were working in pairs so there was support built in.

I originally thought about asking for 8 volunteers but knew it would be a stretch in some of my classes, so the "pick a friend" thing worked out great. It got kids up there that never would have offered.

In one class a student who wasn't here yesterday for synthetic volunteered (?) then chose another student who was a little shaky. We ended up recruiting a third student to jump in with them.

More division tonight, so I'll probably do something like it again tomorrow. And it gets me out of just projecting the answers. :)  Maybe I'll try asking for one volunteer and letting them choose the next person. And letting that person choose the next. Etc.

We'll see.

## Tuesday, November 17, 2015

### Polynomial Long Division.

It certainly would be easier to divide polynomials if the kids knew how to divide numbers using long division.

Many claimed they never learned.  It's always the teacher's fault, right?

So long division today; I was hoping to also get to synthetic division but that certainly didn't happen. Hopefully once they see it they'll forgive me for the long division pain. :)

What was interesting was that I actually had kids asking me if I'd make a screencast of a long division talk-through. I'm at basketball practice then an indoor soccer game tonight so it's not going to happen, but I did find a video on YouTube from PatrickJMT that I thought did a nice job of explaining.

I also was playing with Anna Hester's box method of dividing, which is super nice.  It's based on the kids using the lattice (area) method of multiplication but working backwards. So many of them like to multiply that way that hopefully dividing that way might be nice too.

Here's Anna's explanation:

## Monday, November 9, 2015

I remembered last night while lying in bed (in those 30 seconds that it takes me to get to sleep because I'm always so tired from getting up at o'dark-thirty) that today we were starting trig in precalc class. Which means radians! Which meant I needed to find my favorite pi shirt (and earrings) to wear today.

So that set me on a scramble this morning to find that box that had all of my random clothes in it. Because we've moved since my last opportunity to wear a pi shirt.

Anyway.

I don't know how much trig my precalc class has seen. I have students coming from 3 different places (Honors Algebra 2, Honors Math 3, and Trig w Functions (which does very little trig, btw)) so I'm going to go through my normal trig unit like I have in the past. If I see that they "got" it I'll adjust on the fly.

Today we started with a quick warm up with adding and subtracting fractions - I'm sure they were like, "Seriously?!" and then went over the little special right triangle review that I'd given them Friday. Then we moved into the idea of measuring angles... why is this one 120 degrees and not 240? Why not 480? Enter the coterminal angle.

And now, just for fun, what if we throw in another unit of measurement? Who needs to stick with degrees anyway.  I pulled out my "very expensive, very accurate measuring tool" (aka The Smartees) and had the kids measure a variety of circles. Then we took those smartees and placed them along the arc of the circle to create an angle. That, my friends, is one radian. Now do it again. And again.

Have we gotten halfway through the circle? Almost. (Some kids had. They must not be very well trained in the art of smartee-arc measuring.)

This brought us to the idea of pi radians equaling half of the circle... and off we went from there.  I also showed the radian gif that's on this site that looks a little nicer.
That is the first time I've ever embedded a gif. So that's cool.

Anyway, my class went on from there. We labeled some angles we "think" we might use in the near future and talked about coterminal angles in terms of radians. And then the bell rang. (ugh)

However, on the way out, the kids were talking about the next class they were going to. One of the girls said she's not a fan of her next one because it's boring. And then she said, "This (precalc) is the only class where I have to think. But I'd rather think than be bored."

I think I'm doing my job.

## Friday, November 6, 2015

My sister-in-law and her family were visiting us a few weeks ago. She'd planned to leave after a doctor's appointment on Friday afternoon but then her hubby ended up stuck at work longer. She texted and apologized because they weren't sticking to their plan. Of course it wasn't an issue (and I told her that), then she thanked me for my flexibility.

Isn't being flexible a necessity for our lives these days?

Or is it just me in which plans don't always work out the best?

I had a plan for my Math 3 classes today, and because I was being observed I had to articulate what they were.

Original plan:
1. Warm up problem
2. Review HW
3. Split into designated groups to work through some applications of quadratics problems. Present to each other on the board.  (I had planned for groups of 5 - 6 and even rearranged my desks yesterday.)
4. Finish problems for homework.

What actually happened:
1. Warm up problem (which we solved twice because I wanted to show that completing the square and the quadratic formula got you the same answer)
2. Review HW - took longer than I had anticipated, but again I wanted to make them aware of the choice they had in solving quadratics. Plus we solved a couple because there was some confusion.
3. Split into designated groups to work on one problem (which I assigned). The hope was that we could come back together to our normal table groups to present the problem to their group.  After thinking on it I changed my mind on group size and quickly put my desks back into 4s. So then I had to re-design my groups so they represented a variety of strengths.
4. Some groups finished their problem relatively quickly, so I told them to work on another problem from the worksheet. Some groups were still finishing up as the bell rang.

So, most kids got one problem done today. Am I ok with that? Yep. I'm hoping on Monday to have the kids present their one problem to their group and take a look at some of the ones we didn't get to.

In working my way through 2 brand new courses this year, flexibility has become my middle name.

## Thursday, November 5, 2015

### I'm giving them choice and they don't like it.

We've been solving quadratic equations in my Math 3 classes for the past couple of weeks.

After starting with solving by factoring, I segued into radicals, completing the square, and quadratic formula (with a detour to show graphing).

(The word segue looks so weird.)

I've been very careful to emphasize the choice that the kids have to make when solving and haven't told them when to use which method. (Except for last night's assignment on the Quadratic Formula, when I wanted to make sure they used it for practice.)

Today's work was a chart - the kids were given 16 quadratic equations and told to assign 4 to each of our 4 solving methods (then solve 2 of each).  I really wanted them to think about how to solve each one.

And you know, for as much as kids want to complain that they don't get a choice in life, they don't like it.  They want to be told what to do when (wish my kids at home were like that!). They want to be spoonfed, and I'm refusing to do that. I want them to be able to rationalize which method makes the most sense, and if they use the quadratic formula on an equation that will factor, so be it.

I'm hoping that will work out better for them (and me, honestly) in the long run.

## Tuesday, November 3, 2015

### Rearranging and the Harkness Method

Four years ago, several of us were "talking" on twitter about getting together to work through some of the Exeter problem sets. There's an intrigue to how they run their math programs there and we wanted to try some of the problems.

The rest is history.
(If you don't know what I'm talking about, check out Twitter Math Camp and I'll hopefully see you in Minnesota this summer!)

Anyway, the method of instruction that they use at Exeter is called the Harkness Method, and there's a local teacher that has adopted it for both his Honors Precalculus and Algebra 1 courses (his name is Johnothon Sauer and he blogs about it here). I heard Johnothon speak a few weeks ago at OCTM and then had the opportunity today to visit his school with several of my colleagues to observe. We were split among a couple of different teachers and I didn't actually get to his room, but I was able to see one of his coworkers and his Honors Precalculus class.

The students were getting ready for a "Checkpoint" (aka, a test) and were leading themselves through review problems in their groups. From what I could tell, the problems dealt with rational functions, logarithms, the difference quotient, and sequences and series. The kids were moving from one problem to the next on white boards, working together, instructing, and asking each other questions. The teacher observed and jumped in to clarify as needed. Tomorrow they'll take a practice test (individually), then Johnothon was telling us that he has his kids grade each other's work before Thursday's Q&A session. Friday is the 5-question (with multiple parts) checkpoint.

It was very interesting.

The kids were active, involved, and interested.

Converting to using the Harkness Method would mean an awful lot of work this summer; the teachers made a ginormous packet of problems that the kids work their way through during the school year, 6ish problems a night. These problems spiral in difficulty and jump from one topic to a next, which keep the kids fresh on everything at once. I'd imagine that reviewing for a semester exam is a breeze!

Anyway, I headed back to school this afternoon pondering what to do next. At minimum, I need to get the kids working together more and discussing more. I wanted to create more white board space for them to work on (and make them work on it).

So I went back to school and talked about it with a colleague who had also observed. She had just gotten 2 dry erase-type things on wheels (that look more like shower doors) and offered me one. We ended up putting a tape grid on them and are going to use them to write our weekly agenda, which frees up a big white board in each of our rooms. I also ended up moving my desk to the other side of my room because it was halfway blocking another white board.

It feels like a completely different room!  The kids are going to be so confused when they walk in tomorrow.