Wednesday, December 21, 2011

Camera, Set, Mathematics!

To remain competitive in the global economy, our students "... should be able to use the logic of Algebra and the spatial reasoning of Geometry to understand and solve real-life problems. These mathematical practices equip learners with the ability to solve complex problems and think critically about issues unrelated to mathematical concepts. With these skills, our young people will have the potential to do amazing things – in math, in science, or whatever field they choose to pursue." -

If we want our students to become productive, contributing citizens of the United States, then we need to change the way that we are currently teaching math in our schools! We need to integrate inquiry, problem-solving and real-world application into our math curricula. Students should be engaged in creative, critical thinking when they are solving problems. Teachers should articulate that there are multiple ways to arrive at the same solution to any given problem and allow students to struggle in order to make discoveries on their own with guided facilitation and appropriate scaffolding.

Dan Meyer, an inspirational writer, speaker and teacher (whom I met at the Siemens STEM Institute), is helping math teachers across the country stimulate the curious minds of our students. Meyer proposes that teaching mathematics should be like having your students watch a movie. In a typical movie, there are three acts. Act One engages the audience. Act Two is when the conflict surfaces and the plot develops. Act Three is when the conflict is resolved and a sequel is expected.

To help math teachers understand Dan's analogy of teaching math to watching a movie, I am going to analyze his resources that he provides on his dy/dan blog:

Act One

Introduce the central conflict of your story/task clearly, visually, and viscerally, using as few words as possible.

Your first act should impose as few demands on the students as possible — either of language or of math. It should ask for little and offer a lot.

Here is an example of Act One.

Act Two

The protagonist/student overcomes obstacles, looks for resources, and develops new tools.  What resources will your students need before they can resolve their conflict? What tools do they have already? What tools can you help them develop?

  • What is the height of the basketball hoop? 
  • The distance to the three-point line? 
  • The diameter of a basketball?

Here is an example of Act Two.

Act Three

Resolve the conflict and set up a sequel/extension.

The third act pays off on the hard work of act two and the motivation of act one.

If we've successfully motivated our students in the first act, the payoff in the third act needs to meet their expectations.

Here is an example of Act Three.

The Sequel

Make sure you have extension problems (sequels, right?) ready for students as they finish.

  • How would the equation change if Dan shot from the free-throw line?
  • What would this new parabola look like?

Need another example? Check out the Three Acts with Video Implementation.

Act One

Which do you think is cheaper: a shower or bath? Why?

Act Two

What information will you need to know to solve the problem?

Act Three

Have your students solve the problem

The Sequel
  • How would the situation have to change for the answer to reverse itself?
  • How long of a shower can he have with the same amount of water he used for the bath? 


Many math teachers take act two as their job description. Hit the board, offer students three worked examples and twenty practice problems. Its clear to me that the second act isn't our job anymore. Not the biggest part of it, anyway. You are only one of many people your students can access as they look for resources and tools. Going forward, the value you bring to your math classroom increasingly will be tied up in the first and third acts of mathematical storytelling, your ability to motivate the second act and then pay off on that hard work. - Dan Meyer

To demonstrate Dan's Three Act instructional method, I am going to use a word problem out of a math textbook: 

Word Problem

Sunjana works for a delivery service.  She is paid $5.15 an hour, plus half of her cost for gasoline.  Her car is old and gets only 21 miles per gallon of gas.  If she drives a total of 86 miles one day and gas costs $2.59 a gallon, how much should she be reimbursed for gas?

Now, the context of this word problem is plausible, because it is a real-life situation and is relevant to the workforce (which, to be honest is better than most word problems).  However, the issue is that the question, or hook is typically at the end of word problems, when it should be at the beginning.  The question in the word problem, "How much should she be reimbursed for gas?" should be the introduction to the problem in order to hook and engage the students.  This delivery method stimulates inquiry by having the students ask their own questions in order to solve the problem.  

Let's break this down into the Three Act Model.

Act One
How much should she be reimbursed for gas? (students are now engaged and invested in the problem)

Act Two

Students begin to seek information that is needed to solve the problem by asking questions such as:

  • How much money does she get paid per hour?
  • How much does gas cost?
  • How far does she have to travel?
  • What is her car's gas mileage?

Act Three
Students use their collected information in order to solve the problem.

The Sequel
How much money will Sunjana save her company if she drives a car that gets 35 miles per gallon of gas?

Watch Dan in Action giving his TedTalks Presentation

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