Bringing the Problem to Reality

Quick Links to Physical Reality Lessons

Quick Links to Virtual Reality Lessons


When  you want to build a deck, you have to decide how big you want it to be, find out how deep the frost goes in the winter where you live, find out about hand-rail laws in your town, and research lumber prices.  You have to figure out what data you need, and then you have to get it.  Reality does not provide a list of the data required to solve this or any other problem.

Even real problems in pure  math do not come this way.  Do you think Pythagoras’ teacher gave him a worksheet like this?

"Question 3) Find c^2 in terms of a^2 and b^2. Then, publish and become famous."

Yet our text books look like this, and our test problems look like this, and most of our lessons look like this.  Even when we present problems in an open-ended way, we have to choose what to present, and this decision gives our kids some artificial data to work with that steers them towards the answer we want them to find.

This is not our fault.  This is a reality of verbal communication.  It is a design flaw in language: when we describe an idea, we must describe the important parts, because otherwise we haven’t described anything (or may have described multiple things).  Language is not flexible enough for us to describe a situation without explicitly identifying the important parts.  Written language has it even worse, since it isn’t interactive.

We can break free of this limitation by constructing an environment for our kids that they must explore themselves, without verbal communication with us.  The kids have to ask data of the environment instead of asking the teacher, and to do that they must figure out which data they need and how to ask that question of the environment.  For example, if they need to know how high a ball is, they need to a) realize that and b) go get a freaking ruler and measure it.  An environment of this kind provides no hints, but does provide instant and accurate answers to questions well asked.

When students are “fluent” in an environment, and have the confidence, skills, and tools to ask questions of it, they can do real problem solving.  Anything else makes them dependent on another person.

In presentations, the teacher decides what to present and what not to present, which gives hints to students.  In environments, the teacher makes a place where nothing is said but everything can be measured, which requires students to think for themselves.

It is really hard to create an environment like this that focuses on the curriculum-mandated skill you want to teach your kids.  You cannot use this in class if you are teaching factoring today and have to be on to the factor theorem for polynomials by Tuesday.  Even I, without harsh demands on what I teach, cannot do this every day – I just can’t think of a way to invent an environment in which a student might discover, say, the binomial theorem.

But we can use create these environments sometimes, and I would encourage you to look for those opportunities and take them when you can.  Every time I think of an easy way to do it, I’ll write about it here for your consideration.  I’ve already got a few.  Check back for updates occasionally!

6 thoughts on “Bringing the Problem to Reality”

  1. thanks for all the work you have done. I am a first year teacher and I am truly inspired to be a better teacher because of people like you. Thanks again

Leave a Reply

Your email address will not be published. Required fields are marked *