Confidence

So I watched an interesting video of a speaker during our PD day today and I thought I would blog about it while it was fresh in my brain.  The speaker talked about how we can get what we want by changing the way we think, and I think that there's a great deal to be said about student success in regards to that.

I am not perfect.  I am not even close to perfect.  Hell, some days I feel down right awful about what happens in my classroom.  But I'm working towards changing the things that I don't like and one of those things is how I treat my students in order for them to feel like they will be successful.  Deep down, I know that all my students can't be successful.  Hell, half of them are only in this course because their parents forced them to.  Many of them have such deep mathematical misconceptions that they are essentially innumerate in Grade 11.

But I think it all comes down to confidence.

The students who are successful are the ones who think they will be successful. I'm not saying that all students who think they can succeed will.  Obviously it is not enough to simply be confident if there is no evidence of understanding or mastery.  However, if you think that you will fail, then you probably will.  So here is my plan:

Step 1: Changing the way students think.  Focus on what you want to happen, not on what you don't want to happen.  If you want to understand the concepts, then visualize it happening.  When you say things to yourself like "I'll never get this."  "This is too hard"  "I don't get it, I give up" then your brain looks for evidence to support that.  If you instead think "I will understand this."  "I just need a little more practice" "I think I just need help with this part and then I'll be able to do it" then you set yourself up to be successful.

One of the most famous people in the world with this kind of thinking is Steve Jobs.  He constantly did things that no one thought was possible because instead of thinking about how something wouldn't work, he thought about reasons that it would.  

Step 2: Students who want to be successful, act like successful students.

 Sow a thought and you reap an action; sow an act and you reap a habit; sow a habit and you reap a character; sow a character and you reap a destiny.   

If you want to do well, act like people who do well.  Look at the people around you that you admire, what do they do?  If you behave like them then through actions, you create habits.  Those habits will lead you to success.

Step 3: Let students be receptive to success in all ways.  Sometimes success doesn't come the way you want or expect.  I don't think that the traditional methods of assessment (tests, exams, grades) can really test what a student knows.  I want my students to focus more on the journey of learning.

I had a conversation with a student who consistently uses negative thinking in math class.  "I don't get this.  You aren't making any sense.  You  have to teach it to me again, I didn't get it."  The other day I stepped back, I let them struggle through it.  I gave guidance and examples but I didn't let them cop out of trying.  By the end of 80 minutes the student still looked a little defeated.  I pointed at the first question on the page.

"How long did it take you to do that?"

"Like twenty f--ing minutes."

"What about that one you just solved?  How long did that take you?"

"Not that long, actually.  But I got it wrong."

"But the one you just worked on was harder.  Do you see how much you improved?"

"Yeah I guess"

It's the first step.  I hope that all my students will be successful, but I know that some will fall.  I guess I just have to be there to help them stand up again and keep walking.  After all, life's is full of things that will rise up and trip us.  I guess it's not really the falling that matters, it's the getting back up.

The best task!

In my few years of teaching, I've shown a number of 3Act tasks or similar and I have gotten mixed results.  But there is one task that I've always had a lot of success with.

Tell students that they are getting a contract of employment.  The contract is going to last 30 days, 5 days a week.  On the first day of their contract, they get $0.01. That's right, 1 cent.  On the second day, it doubles. Now they get $0.02.  On the third day, it doubles again and so on and so on.

Goodbye, Canadian penny

How much money do you think that you will make after 30 days?

I usually start off by handing out the contract, having kids fill it in and then asking them to write down their best guess.  Answers usually range from $10 to $1000, but not much over.  Then I ask them to fill out a chart with how much they are getting paid per day and how much they're getting paid all together.  They start to get to work because they all have calculators and it just seems like easy button pushing.

Then the  magic happens.

At some point some murmuring begins to happen in the classroom.

"Is this what you  have?"  "This can't be right" "Oh my god" "This is crazy!"  "I want this job"

Not a single student isn't frantically trying to figure out how much money they're going to make.  Every single one of my students is engaged in the task.  Everyone wants to know the answer.  How much money are you going to make?  On the last day you make about $5 million.  Altogether, about $10 million.

I do this task every year and I always get great results.  I attribute it to a couple of things:

1. Low risk.  No one knows what the answer is so everyone's guess is equally valid.

2. Simple calculations.  Not everyone can calculate terms in a geometric sequence or series, but everyone can type *2 on their calculator and hit enter.

3. Interest.  The task is genuinely interesting, students get invested in the idea of getting paid this way.  Some even propose that they're going to suggest it to their boss.

This is an extremely powerful task for introducing geometric sequences or series.  The follow-up question is: Is there an easier way to figure out how much you can get for the 30th day without having to write out all the previous days?

It's fantastic, I love this task.

It's interesting what happens when you have 3 sections of the same class.

The first lesson of the day is generally not as good as the last.  When you teach the same lesson multiple times, you make adjustment and get better each time you do it.  It's kind of unfortunate that the first class is the guinea pigs, and then the last class always reaps the benefits of your experience.

Toothpick triangles went quite well, we started it last day.  Today I plan on tackling the terminology used in sequences and the formula for an arithmetic sequence (going to try and have them derive it) as well as the arithmetic series formula (again, have them derive it).

Looking forward to geo sequences/series.  Have a great introduction activity planned for it.  Hopefully the leap from concrete to abstract isn't too jarring from them.  I have a feeling that these kids are still, really, 10th grade math students with a 10th grade mentality.  It's going to be a shock for them when sitting and paying attention won't be enough to get them through.

How do you get students to participate more in class?  I think a lot of it is making the contribution low-risk.  That's why I want to start using Socrative more.  It's a low-risk way to contribute and get feedback.  It especially helps me, because I can really see how the class is doing as a whole.

Still trying to think of ways to deal better with my biggest class of 33.  Will have to implement a seating plan, firstly.  We'll have to see how that works out.  They really have trouble stopping the talking when I need to address something at the board.  Most of my class is spent with them working so it's not like I demand them to be silent for 90% of the class.  More like...30%?  Or probably less actually.

New Semester

This blogging thing is turning out to be more work than I thought.  Haven't really been forcing myself to keep up with it, which is a problem for me.

I wanted to try something new (again) with my 20s.  Working with my beliefs that active learning>passive learning.  And real life problems>worksheets.

I'm starting off my first day with Dan Meyer's "Toothpick Triangles" as an introduction to arithmetic sequences/series.  Start by posing a problem, have kids ask good questions (something that they have to practice) and then developing terminology and formula out of neccessity, or to make things easier.

I think having kids generate the problem forces them to be invested in the process.

I'm also going to start using Socrative as a tool in my classroom.  I just had an introduction to it recently and I absolutely LOVE the idea.  After all, 90% of my kids have cell phones.  It's honestly amazing how quick and easy it is to get feedback.  Love it for formative assessment.

I will hopefully blog about this lesson over the weekend.  Who starts semester 2 on a friday anyway?!

Hate

If I hate my lesson, my kids will hate my lesson.  End of story.

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.