Realistic Math Education: Defining the “real” in real world

Dan Meyer recently posted about how students aren’t easily fooled by attempts to make make tasks “real world” by placing a photo next to them.

I found myself nodding along at what he described.  I once naively asked a fourth grade class to write real world problems about fractions and received the following response:

The Knicks scored 12 ½ points and the Nets scored 13 ¾ points.  How many points did they score all together? 

When I asked the student how it was possible to score ¾ of a point or why you would want to know the combined score of two opposing teams, he looked at me like I was crazy and said it didn’t matter–“you told me to make a problem with fractions so I put fractions in it.”

Even at young ages, students learn there is a game teachers play where they make “real world” problems.  Kids pick up pretty quickly that these aren’t about the world they live in–they are a special type of problem in math.  So they skim the word problems.  They pull out the numbers and assume they should try some mathematical operations they recently did in class.

So I agree with Dan that spreading the “real world” over a task doesn’t fool students–even our younger ones.

I do believe in building off students’ experiences . Although math tasks don’t have to be real world, they need to build on what students know.  An activity they can do.  An experience they had.  An operation they already understand mathematically.

As I was reading the post, I thought about Realistic Mathematics Education (RME), developed in the Netherlands over thirty years ago.  RME is strongly based on Hans Freudenthal’s philosophy that students should be guided in a process that allows them to “mathematize” the world around them.   They should be provided with tasks that allow them to use mathematics to organize and solve a problem.

What’s interesting is that many people incorrectly assumed that this meant real world problems of the kind Dan showed.  However, realistic in RME referred to situations students could imagine, not necessarily something that would happen in real life.  As a result, “the fantasy world of fairy tales and even the formal world of mathematics can be very suitable contexts for a problem, as long as they are real in the student’s mind.”

Making it clear that real is about what is real in the student’s mind can be helpful when thinking about how to select appropriate tasks for students.  Unfortunately, it’s much harder than simply throwing a real world picture next to the problem.

Want to know more?

Check out the Freudenthal Institute’s page:  http://www.fi.uu.nl/en/rme/

Read about Freudenthal and RME: Gravemeijer, K. & Terwel, J. (2000): Hans Freudenthal: A mathematician on didactics and curriculum theory, Journal of Curriculum Studies, 32(6), 777-796.

Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational studies in mathematics, 39(1-3), 111-129.