Completing the Square

It's amazing what a difference a change in teaching technique can do.

Taught my 20-1 honors class completing the square today.  You know, the thing that you do to get from standard form of a quadratic to vertex form.  Yeah, I can feel you cringing in your seats right now.  See, when I was taught completing the square, I had no idea why you  had to do any of the steps.  It made absolutely no sense, but being the good math student that I was, I went along with it and eventually got good at completing the square.

I had no idea why I what the process meant.  I just got very good at following steps.  What an awful thing to impress on kids.  "Don't question this, just know that it gets you the answer.  You don't have to  understand, just do it."

Ugh.

And the sad thing is, that's exactly how I taught it last year.  These are the steps, do it 100 times until you get good at it.  Got it?  Good.  Let's move on.

Today I changed things, I decided to teach completing the square using algebra tiles.  Students could see that you were literally COMPLETING a SQUARE.  This was something that I could never get students to  understand, why you have to divide the middle term and square it to get the final term.  My students now get it, they understand that they have to have enough 1s to make a square, and then to subtract whatever they added to keep it balanced.

They get it.

They don't just get how to do it, they get why.  And that, ladies and gentlemen, is math.

Granted, I'm still teaching them this very arbitrary thing of finding a vertex form of a very specific shape (parabola)...but one step at a time.  I consider this a mild success.

Still boring, getting better

As the title states, I'm still doing a lot of really boring "me talk and you write" type of teaching.  But it's getting better over time.  I find myself being more adventurous in my attempts to put more types of novel learning activities in with my regular, comfortable, teaching style.  I've tried things that have worked better than I anticipated and that has been encouraging.

Specifically, doing a lot of things with Perms and Combs and my 30-2s is really encouraging to be engaged.  McDonalds and DQ both have combinations involved in combos.  Oreo permutations are today and I am hoping for good results.

Still having issues with my higher achieving class, 20-1 Honors.  They work hard, but don't really want to share their thinking, or answer questions.  Maybe fear of wrong answers?  Maybe I'm asking the wrong questions.  Probably.

Some of my 20-2s come into class with the conviction that they will not do anything.  I think their first unit exam will hit them hard.  I hope it doesn't damage their confidence but I think it will be a good wake-up call. Many of them think they can achieve the objectives, so they don't do the examples.  They write down what I do and talk the rest of the time and think they "get it".  At some point, they will look at me and say "I don't get it at all, I'm confused" and then sit there and do nothing.

I find that interesting, the polarization.  Either they "get it" and don't need to do it, or they "don't get it" and don't need to do it.  Not getting it is not a sign to them that they need help, but a ticket out of doing anything. They sit there on their phones and talk to their friends and then exclaim "this is too confusing!  I don't get it!" when I ask them why they haven't done anything.

Yet they have made no effort to understand.

Is this a behavior that we, as teachers, have trained into them?  Or is it just individual students that have this type of attitude?  I'm not sure.  Need to make my lessons more interesting to try and engage these kids, but sometimes they just have to buckle down and do the work.  Not sure if some of these kids are capable of it, and it's going to catch up with them.

Moderate Success

Had some success with the 30-2s and the Set Theory Unit, they have their first Unit Exam next period.  After giving them a formative assignment where they were to create their own Venn diagrams, I realized that they were really having trouble.

Created an interactive Venn Diagrams smart board activity.  Made a bunch of colored circles and infinite cloners of set theory terms (A, B, C, \, ', U etc).  Had students move around the circles and answer questions.  I saw significant improvement from the students afterwards.  Gave them a hard assignment after, the ones who persevered were the ones who I felt got the most learning out of it.

Found 2 really awesome games/applets that I did with them.  The sets game is really amazing (google sets game).  Students really got into it, I think I might make it a weekly challenge to beat our best time.

Been mostly successful in keeping my lessons short (< 30 minutes).  I find that if I have short periods of teaching interspersed with activities, they stay attentive longer and are more engaged.  Surprisingly, it reduced my classroom management issues.  All it takes is a few seconds to get their attention again and it has increased on-task behavior...monumentally.  Really.  Seriously.  Students are 100% more on task.  And it allows me to guide their learning by walking around and helping them.

20-2s are doing a unit project instead of a unit exam for their first unit (logic and reasoning).  I think having them do a project is better than an exam for logic.  Assessing them on their actual application of logic and reasoning is better than answering multiple choice questions imo.

I'm rambling.  But this blog is for me to reflect so I don't really care.

20-1 (honors) are awesome.  Classroom management isn't an issue.  On the other hand, they tend to be somewhat less willing to be creative/take risks than my other kids.  It's hard to get them to share their ideas, or volunteer to demonstrate their solutions in front of the class.  Have to find a way to get these kids to take risks.  They are also addicted to having a clear-cut way to solve a question.  Demonstrating 2 different approaches baffles them and they panic.

"I did it the second way.  I don't understand the first one." 

"That's fine, the second way works too."

"But the first way confuses me."

"Then use the second way."

"Can you only show us the way that's on the formula sheet?"

"..."

I wonder if this is common with higher-achieving students or if it's just me?

Day 1

First day of school today.  For me, it's the second half of my first year of teaching.  I started teaching last year in February.  Mostly today consisted of housekeeping items, a little bit of review.  Going to be working through review booklets for a few days and then getting into the good stuff.

I think the stuff I have written for 20-2 and 30-2 are pretty good.  Realistic examples, lots of multimedia, different activities.  Going to try and keep all my lessons under 30 minutes.  Definitely going to time myself once I start actually teaching.  I think that way, students have time to ask questions, clarify and work on homework in class.  The more they work in class, the better for them overall.

My class sizes are ballooning.  A class that originally had only 21 kids (omg yay) at the end of June now has 30.  And growing.  It's a 30-2 class, so the students can be a bit chatty.  Working on keeping them motivated to learn.  A lot of students in the 30-1 class are getting scared and dropping into mine.  My worry is that they think 30-2 is going to be a cakewalk, which it isn't.  I'm thinking that overconfidence might prompt them not to work as hard as they should for a diploma course.  Hopefully it doesn't affect them adversely.

Meeting new kids, seeing new faces, talking to students I've had before...its exhilarating.  I love starting fresh, learning more and revisiting things I've done to see how I can improve.

All in all, a good day.