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.

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?