I’ve seen people using the terms “inquiry based learning” and “discovery based learning” as though they are interchangeable. They’re not. And here’s why….

Let’s forget about that fact that discovery learning doesn’t actually exist for a moment and pretend that it does, at least in the way that some people believe it does.

I think when people use “discovery based” learning they are thinking that we throw kids in front of a bunch of visuals and hands on materials and basically say, “Here. Now go learn subtraction. Come back to me when you’re done.” I think people are assuming it’s a model where there is NO direct instruction and kids just simply learning things by figuring it out themselves.

And this is why inquiry based learning gets a bad rep when it’s not the same thing at all. So what is it?

The inquiry model begins by asking a question. A meaningful question, not something as lame as…….If Johnny drinks 4 glasses of water and Sarah drinks 9/2 glasses of water, who drank more water? (By the way, my Grade 6’s answer to this is…..”Who talks like that? Who says they drank 9/2 glasses of water? Seriously?”)

No, what I mean is that instead of doing mini lessons that lead up to a culminating project, we begin with the “project” and go from there. For example, when I taught about Pythagorean Theorem I posed the question…..“So if a well built building is made of walls that make perfect 90 degree angles, is this school a well built building?”

**2. A Shift In Who Asks The Questions**

Kids are more likely to pay attention to you if they ask the questions themselves. This way they are invested in the answers. In a standard math classroom I think a teacher stands up at the front of the room and says, “Ok, today we are going to learn how to calculate unit price.” And then proceeds to teach.

However, when kids are faced with a project where they have to create a drink and sell it to maximize profit, suddenly THEY want to know…..well how do you figure out how much it costs per glass. And now that I have their attention (because they honestly want to know the answer), I can engage them with some direct instruction as to how to do so. Yes, notice I said DIRECT INSTRUCTION. I do indeed use that in my classroom, although there will be some kids who will never ask the question because they do indeed figure out how to do it on their own. Shocking, I know.

Inquiry based learning is not so much evaluated based upon correct vs incorrect but rather on how well did your process work. And here’s where people freak out. Yes, we do allow for the fact that there is more than one correct way to do something.

**4. The Development of Understanding**

I am a product of the “old” math generation and I was an excellent math student. I was in the top five percent of my class and while I hated my math classes, I was very good at them. But here are a list of things I couldn’t have explained to you if you has asked me…..

a) Why we invert the second fraction when we divide.

b) Why the whole a² + b² = c² thing worked.

c) Why when testing for equivalent fraction if you cross multiplied and got the same answer it proved the fractions were equivalent.

d) Why when looking for a missing number within a pair of fractions the whole “cross multiply divide” thing worked…..

e) Why when changing a mixed number to an improper fraction you multiple the denominator by the whole and then add the numerator.

And there’s more but too but I think I’ve made my point. I was simply taught these methods and since they worked and I had the process memorized, I got the correct answer ever single time and that was good enough.

Do you know when I finally learned the “WHY” behind these things? When I goat job as a math teacher and had to teach it to my students. Now some people are ready to slam me in the comments (oh yes you are) and say that I obviously wasn’t a very good math student when I was a kid. And here’s the part that might shock you…..I agree. You’d be absolutely right, I was a horrible math student because I didn’t have a clue why I was doing the things that I was doing.

There’s a possibility that I asked why somewhere along the way and likely I may have even been told, but since I didn’t need to know the why to get the answer I likely forgot it. But man I sure rocked those 30 math questions on that worksheet. 30/30. Almost every single time……

Some people would argue that we now spend too much time explaining the “why” to kids and not enough of symbolic representation. Well…..I took a University level math course (just one, the introductory course) and after battling with nothing but symbolic representation for an entire semester, I never took another. I got a B in that course, which I was pretty proud of. However, the truth was clear. Though I had been “good” at math throughout school, I was not a good math student and so I never took another math course again. And to this day everything I did in that math course on derivatives and logs are completely lost on me. I recognize it when someone puts it in front of me, but all it is to me are numbers and symbols that make no sense. And I think that for many of our kids today…..it’s the same thing.

Because it has no meaning.

Inquiry base learning can often give kids that meaning. Or at least the desire to understand the meaning and from there they internalize more of what it put in front of them.

Being an inquiry based teacher is hard. You have to be good at it. Damned good at it. And I’m still working on it. I do know that the inquiry system has resulted in a much higher level of engagement within my classroom and when kids ask the questions instead of the teacher, they learn so much more.

In an inquiry based classroom, the kids spend more time talking than the teacher. And that’s the BIGGEST shift of all……….it has nothing to do with “discovering” how to multiply. It is driven by the desire to know WHY when you combine these two numbers something magical happens and they become this whole other number.

Too often I think we suck the life out of the math classroom with lectures, worksheets with 30 problems to solve, and kids who do nothing but sit in desks and write on a pice of paper. It’s time to breathe life back in and get our kids to buy back in as well.