Monthly Archives: June 2013

Math Council

This is a group activity I created and have a lot of fun using in my classes.  It can be used as a review activity at anytime because all you need to do is create 10 or 12 problems.  It came from a desire to have a collaborative activity where each person in the group had their own distinct role to play.

The Overview

Students form a Math Council in groups of 4.  Each student then gets or chooses a role to play.  Each role has unique things that they are graded on.  The end goal is to create a poster that highlights the problems that the group worked on.  But in the creation of that end product, each member of the council has certain responsibilities.

Each student must do every problem on their own paper.  Then as a group they decide what the right method was and then that gets transferred onto a poster.

There are four roles:  Leader, Scribe, Sage, Runner.  Here are descriptions of each:

The Leader is in charge of making sure the poster finishes, as well as selecting the problems that group works on.  Each group is initially given an envelope of problems and the Leader chooses which ones the group works on.  Typically the envelope will have about 10 problems of which the leader selects 4 or 5 for the group to work on.  Interesting for me to see which ones they choose.

The Scribe is in charge of the poster.  Other members can help work on it, but their grade is most directly tied to the quality of the poster.

The Sage is responsible for coming up with key points for each problem.

The Runner is the only person who can ask me a question.  The Runner must report my answer back to the group.

Leader2

The Advice

– I do not answer any of the Runner’s questions near the group.  I make the Runner come to me and report my answer back to the group because I want to make sure that the group must rely on the Runner to explain to them what I’ve said, rather than them simply hearing me say it.

– I give each group an envelope with lots of problems in it, and then have the leader choose 4 or 5 for the group to work on.

– Each student must complete every problem on their own paper.  That is the “work shown” grade.

The Executive Council

This is a fun thing I added to mess with the students help students work on their collaborative ability to adapt to changing circumstances.  I have what I call the “Executive Council” and they call me periodically during the activity and make new demands upon the students.  I pretend to be receiving a phone call and then announce that the Execute Council just contacted me and they now want this or that.  Here are some common things the Execute Council calls for:

– They demand that every council has a name and that name goes on the poster.

– They require a certain problem out of the bunch to be on every poster.

– They require the Sage’s key points to be on every poster.

– They want a picture of a penguin drawn on every poster.

– They give extra credit for their favorite posters.

It’s pretty fun – after awhile when I act like I’m getting a phone call the students will call out “If that’s the Executive Council don’t answer it!”.  They will continuously ask who the Executive Council is – but of course I am not allowed to reveal that.

The Goods:

Leader

Runner

Sage

Scribe

Advertisements

Motivation 101 – Define Success

I tell students that success in our class means everyday you leave better than you showed up.  And to leave better means you learned at least one thing about algebra.  It doesn’t matter if you have an A or an F, that simply measures how you have done in the past – but today you are success if you can learn one thing.

Everyday I write the goal for the days lesson on the board.  The goal could be to simplify rational expressions, but I always remind the students that the actual goal is to learn at least one thing about algebra.

I tell students to look for things they don’t understand and be excited when they encounter them because it is precisely those things that are going to make them a success.   If I’m helping a student and they get it – they go from a place or not knowing to knowing, I tell them “good job, you’re a success today, keep it up”.

At the end of class I always recap the day for the final couple minutes, and I provide them with time to reflect on what they learned.

Look I guess what I’m saying is that you want to define success in such a way that allows every student to feel good about themselves everyday, regardless of past performance.

Why Algebra? – The Basketball Analogy

“I think less of us would drop out if we just knew why the hell we needed this stuff”

That was said by a student who was simplifying rational expressions.  I had a positive relationship with her so the quote was simple honesty and not some veiled attempt at making a teacher feel bad by calling their job pointless.  I knew at that moment I needed to be more purposeful in my attention to the question of ‘Why Algebra?’.

Periodically throughout the year I dedicate a few minutes to tell them why Algebra is important.  I always remind them there are many different reasons, and that no reason by itself will feel sufficient because we are all such different people.  But when we take all the reasons together, the total picture will hopefully be able to answer the question for each student.   I usually start with a basketball analogy because I used to coach basketball.  It’s how I explain that you will need to use algebra in more advanced math.

We learn algebra differently that we learn most things in our life.  For example you generally play basketball first.  And then you decide you want to get better so you practice some rebounding drills.  Then you realize that you need to be able to dribble the ball and you start doing ball handling drills.  Algebra is typically constructed the other way around.  We practice algebra drills without ever playing math – essentially we are practicing dribbling drills without ever playing basketball.  This of course is not always true in algebra class and we are playing math as much as possible in my class – but I’m not trying to spend a lot of time in gray areas to make this point.

With that setup I show the students this video of MIT Instructor Lydia Bourouiba (I begin it at the 1-minute mark) going over a Separable Equations problem in a Differential Equation class.

There are multiple places in this video where she does algebra steps.  Like at the 1:09 mark when she puts all the y-variables on one side of the equation, and the x-variables on the other.  Except she doesn’t show any of her work, she just does it.  In basketball you don’t think about how to dribble, you just dribble.  So here I pause the video and do that step like we would in our class, I multiply both sides by dx, canceling the dx’s on the left.  Then I divide both sides by y^2, canceling the y^2 on the right.  Students are surprised to see that they understand something Lydia is doing, and also wondering why she didn’t show her steps like I did.

I end up pausing the video in several places.

I’m basically showing the class that someone in a multivariable calculus class is using the exact things we practice.  Except that the algebra she uses is not an end unto itself – rather it is another step towards a greater purpose.  She is using algebra in the process of resolving a larger question.

Here’s an exchange I had with a student after I made the points above:

MM – “Similarly, in basketball you practice your cross over dribble because its going to help you in the game.”
Student – “Yeah Mr. Miller, but how are we suppose to remember what we are doing here 10 years from now?”
MM – “Do don’t have to remember it, because you’ll just do it.  When you are playing basketball you don’t remember that first dribbling drill you did 10 years ago.  You just dribble.”

And I shit you not – I saw and heard multiple aha moments around the room.  And then the closing line:

MM – “I know what you are all thinking.  I know if I was you, when I was your age, I would be thinking to myself ‘That’s fine but I still don’t care because I am never going to take that class.’  (pause for laughter and general agreement from the class)  But you never know.  I ended up taking that class”.

That takes a few minutes – and then I begin the days lesson.  Are students instantly motivated?  No.  But at worst the student who honestly thought there was no reason – now knows there is some reason.  Maybe they don’t think that reason applies to them, but they know its there.  And if your students do not embrace the unknown quality of their futures; embrace the fact that they don’t know where these open doors lead – then your job as a motivator is not done yet anyway.