Upsidedown Math

I am intrigued by Dan Meyer.  If you don’t know who he is and you happen to be a math teacher, you should really get aquainted.  Will take you to his Ted Talk.  Will take you to his blog.

Next year I’m about to embark on a journey, along with a partner middle school teacher, into a world where we are going to turn the way we teach Math upside down.  Why?  Because the way I teach it right now isn’t the way I think my students learn best.

In coversations I’ve been having with twitter pals Dave Martin, Joe Bower, and Paige McClement I am intrigued by the idea of building student engagement in my math class by turning it upside down and backwards.

Here’s what my math class has looked like for many years:

Day 1:  Intro concept, direct teaching, textbook question practice.

Day 2:  Worksheet that practices concept.

Day 3:  Second unit concept intro, direct teaching, textbook question practice.

Day 4:  Challenge questions using 2 concepts, quiz.

Day 5:  Project with Concepts 1 and 2.

And if this is what your classroom looks like I am not criticizing you or saying it’s wrong.  BUT what if I turned this upside down and instead my classroom looked more like this:

Day 1:  Major project/concept introduced.  Students make a list of what they will need to know in order to solve the problem.

Day 2:  Students come up with a list of skills they need to solve the problem and check off if they already know it, can find out on their own, require teacher help.  Teacher teaches tutorials to small groups based on what they have outlined they need instruction in.  This is based around the idea of teaching as necessary (learning as you need it).

Day 3:  Student Work Time

Day 4:  Check up to see who is progressing and who is stuck.  More mini-lessons to the groups that require it.

I think I’d get far more engagement with my “upsidedown” math design than with my more traditional way.  And of course I still need to do some direct teaching.  It’s tough to get away from that in a math classroom.  But not ever student needs direct teaching.  Some of my students function very well learning all on their own.  I almost hold them back by making them sit with the full class and making them sit through the lesson I’m teaching when they could have picked it up on their own in 5 minutes.

I thought I was doing a good job by simply giving them the worksheet early so they could just simply work on it while I was teaching.  But I wasn’t challenging them at all.  And that’s my fault. 

I have been developing some new ideas that I’m having success with and I’d like to keep them going for next year. 

1)  Student filmed tutorials:  With the aid of a flip camera I have some students filming short instructional videos on basic concepts like “What is a perfect square?”  We’ve been posting these videos so that when other students are at home and working on a problem involving “perfect squares”, they can click on the tutorial for help if they’ve forgotten the concept. 

My theory:  Those who can teach, truly understand.

2)  As-You’re-Ready-For-It Math:  Instead of giving them assignments one at a time, I gave them all in a package.  Students who worked quickly advanced to the “Math Challenge” portion where they completed the “Amazing Math Task”.  If they solved it successfully they then became the panel experts to help their classmates as they slowly reached the same point.  I now had a group of mini-teachers who could help when I was elsewhere in the class working with those having diffiulty. 

My experience:  My academic students are usually first to join the “panel” but I’m starting to see others strive to get there and my panel is growing.  In my volume unit I wound up having a 1:1 ratio of panel “experts” to working students.  They are also starting to see that everyone has strengths in math somewhere.  Students who excelled in linear relations struggled with geometry.  Here I had new stars that rose up and they weren’t necessarily who you might expect either.

It’s true that math is one of the classes that allows kids to gain some immediate feedback about being right or wrong and if they are right, it provides and immediate feeling of success.  So I’m going to delve further into Dan Meyer’s ideas now and try to capture their interest by offering real life challenges without scaffolding my way up to them.

Present the big problem and let the students figure out what the smaller pieces are that they need to know.  I figure probability is a great unit to start with.  Afterall, who hasn’t wondered at some what the odds were about something.  Winning the lottery?  Taking the next card and risking breaking 21?  Passing the guaranteed parking spot in the hopes of getting a closer one?

While I’m experimenting with this year’s Grade 8 class, next year I’m jumping in full tilt.  My goal:  To completely eliminate worksheets from my math class, present math in terms of real life challenges (not by linear concepts and strands), to combine with other subjects so students stop seeing math as an isolated course.


It wasn’t amazing because of the project, it was amazing because of what I learned.  I gave my students an advertising unit project where they had to invent a drink and then advertise it.  But they also had to make the drink and sell it.  In order to prepare the drink they had to do conversions from ounces to mL in order to buy the right amoung of ingrediants.  They had to figure out how much they needed to make one drink and then extrapolate that to figure out how much they needed in terms of juice/pop/icecream/drink mix, etc.

They were essentially completing the unit on ratio/unit price/proportion that I had taught earlier this year but in a much more meaningful way.  So why do I need to teach that unit?  Why can’t I just do THIS project (that they loved and gave me 100% student engagement) and save myself some time?

Well, hopefully that’s what I will be doing next year…..


About Cherra-Lynne Olthof

I've been a middle school teacher for my entire career (which began in 2001). Like my students, I too am a life long learner. My goals include helping my students to achieve their goals, support them in their learning, and to encourage them to think "beyond the grade".
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