Tag: understanding based teaching

Understanding Math — Let Kids Fake It
There’s a lot of talk about making sure kids understand what they are learning — instead of just practicing some arbitrary set of steps. I’m a proponent of this myself.

I copied and laminated this back in 1998!

But how well a child grasps a concept is based on how well he or she connects with it.

The learning style and interests a child has has an impact on if (or how well) he or she will understand a concept. And, as far as I know, there’s no rule on figuring that out.

You keep explaining it in different ways until you see the “aha moment.”

Except there are some times when understanding is too far out of reach. Or the child’s way of learning requires a deeper understanding than what’s available or possible at that point.

So what do you do in those cases?

Do you delay teaching that piece for understanding? Do you go on to something else and skip it altogether? Can you go on to something else?

Before making that decision, consider three points.

1. Nobody understands everything.

The way all the pieces of math work together is amazing. Nobody knows how they all fit — even the most famous of mathematicians. Everyone has something missing. Some of us have much missing.

So if your child is lacking in understanding for a few things — or even many things — that’s okay.

2. There’s more than one way to “understand” something.

Take any math concept and you’ll find that the applications of it are vast. It’s likely that you can use it in business, in fashion, in your yard and kitchen and in the toy box. So you can explain the concept — and inspire understanding — with any of the applications.

You can also explain a concept with metaphors to other math concepts and even metaphors to non-math concepts.

3. But they’ll get it, eventually.

Back in 1998 I photocopied an article from an AMS Notices journal called “Eventually” by Marianne Freundlich. I laminated it and hung it on my office wall.

It’s moved offices a dozen times at least, but has remained an important reminder: “When learning something new, you may not get it now, but eventually you will. Just stick with it.”

The “fake it ’til you make it” principle works in math too. It’s okay for them to practice something that they don’t understand.

But kids need you to know they’re faking it.

Often kids fake their learning. But they’re also trying to fake out the instructor. It turns into a big dirty secret that they keep inside. Like this:

“Mr. Smith, I don’t understand this. I think I can do the problems, though.”

“Well, Joan, let me explain it this way…”

Mr. Smith explains another way. Joan feels uncomfortable because he’s spent so much time on her and she still doesn’t get it.

“Okay, I think I understand now.”

“I’m glad. It’s important for you to understand before we move on.”

Joan thinks she’ll just keep practicing and hope that something clicks before the test. She doesn’t want to ask for more explanation.

Fake it like Fermat!

(That’s supposed to be a play on “Bend It Like Beckham” — I’m not sure it works.)

A well known phrase in math graduate school is, “Okay, I don’t understand that, but I’ll go with it for now.”

Mathematicians fake it all the time. They come back later to see if they can work out the details (and don’t publish or approve of something until they do). But they announce out loud that they’re faking it.

And kids should be allowed this too.

“Mr. Smith, I don’t understand this. I think I can do the problems, though.”

“Okay, Joan, that’s fine. Perhaps after you do it a while, you’ll get it. “

“It’s possible.”

“No problem, if you don’t get it now, you’ll get it eventually. As we move forward, when you come to something like this, just keep doing the steps. That might help you understand, too.”

“That works for me. Thanks, Mr. Smith.”

“Feel free to ask me any questions about it and we’ll continue the conversation until you do get it.”

Not understanding is totally okay — but the child must know it. And, more importantly, they must know that you know it!

So let them fake it!

When understanding is too far out of reach, encourage some rote practicing of the steps. And let them admit, out loud, that understanding isn’t there — even be happy for it.

Anticipate the understanding and be excited that someday it will come.

And if your child wants to move on, do it. They’ll get that other stuff eventually.

Share your thoughts in the comments or on twitter/x.

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August 13, 2012
Math Skills in a Math Toolbox
We don’t teach each new math skill just to have something to do during the next math lesson. And yet textbooks make it look like we do.

Math skills are presented in bubbles called sections. The section doesn’t show how the math rule being taught connects to past or future lessons. Nor does it point out what previously learned skills or rules are currently being employed.

Okay, it might note that this section is similar to the others in the chapter. But how often do you see a section point out how you’re going to use the skills you learned in a previous course?

Kids rarely understand that each level of math is taught so that the tool that’s being practiced can be used later – in another math lesson or math situation.

They don’t see the long term growth of math skills and math maturity – their math toolbox.

Math skills are tools.

Take a look in any man’s garage and you’ll see a plethora of tools.

Point one out and ask the owner these things:
1. What is this?
2. Under which situations will it function (and under which won’t it)?
3. In what situations would it be helpful to use?
4. Do you have the confidence and ability to use it when you need to?
5. Have you ever used it when there was something else that would’ve worked better?
Chance are, he’ll have thorough answers for 1, 2 and 3. And for number 4 – he’ll look at you like you’re nuts and say, “Well, yeah!”

For number 5, he’ll say, “Well, of course. Sometimes I’m not sure what will work best, so I just pick a tool that I know can work. If it turns out to not be the best tool for the job, it’s no big deal. It might have taken a little longer, but it still got the job done.”

Tools accumulate – and add to each other.

Mr. Garage Owner didn’t collect a whole bunch of tools that he’s clueless about. He likely wanted to build one thing and realized a tool could help. So he bought it.

He learned how to use it, then hung it on the wall. Probably on a pegboard with the shape of the tool outlined.

Then he wanted to fix something else. He could have used his tool, but if he had another tool as well, it would make it even easier.

So he bought another tool.

Together with the first tool, he fixed his gadget then hung the new tool on the wall.

He continued this way until his pegboard was full and he was building more tool storage space in the back yard.

Now he knows each tool, when and how to use them, and confidently pulls them out each time it’s necessary.

And if he chooses the wrong tool for the job, he gets over it quickly.

Teach math like the kids are accumulating tools.

When you start a new section in your math lesson, review the math rules that they previously learned. Show how the newest problems may (or may not) be solved with the old math skills alone.

Present the new skill or math rule thoroughly. Be clear on what it is, how it can be used and under what circumstances. Also point out where it can’t ever be used. Like “adding to both sides” can’t work when there’s no equal sign.

Point out some areas where the new math rule might be helpful. Point out some areas where the new rule might not be the best for the job, but it would still work.

Show how to use the new math rule along with the old rules (pointing them out everywhere) to achieve results.

Have them make a list of all the math skills they’ve learned – a pegboard outline – so they can be kept handy.

Let them play.

Math is typically thought of as the subject where “there’s only one way to do it.”

BAH!

Just like Mr. Garage Owner, using the non-optimal tool for the job still gets the job done. As long as it works (can’t run an electric drill in the rain, after all).

So let them play. Turn your math lesson into a time where they can use any math rule they want. Let them discover their own confidence in choosing tools.

And let them try out tools that might not be the best for the job.

As they grow their math toolbox, they’ll grow in math maturity and confidence!

Share your thoughts in the comments or on twitter/x.

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June 12, 2012
Curiosity Based Learning with 100 Floors iPhone App
From Floor 1, you can tell what you have to do.

I’ve become slightly addicted to this free iPhone game called 100 Floors. It has strange and interesting parallels to leraning math.

It has no instructions and no hints. And upon first entry to the app, you feel lost, confused and annoyed. (Already starting to sound like a math problem, right?)

Based on the name of the game and the view of “Floor 1,” it’s clear that the idea is to open each set of elevator doors.

But with just a bit of patience and curiosity, you find yourself challenged just enough on each subsequent floor to keep going.

And you have no idea what to do next.

With each floor you’re not sure what to do.

So you start doing seemingly random things. You notice yourself bumping the phone. Tilting the phone. Shaking it. Blowing on it (I know, that isn’t a feature yet, but I tried anyway).

You tap and drag everything on the screen – including the ads.

(I even yelled into it – just in case that was the key to getting the doors open.)

And sometimes you just stare at it. Curious.

Remember – there’s no punishment for failure.

This one is my favorite!

If you can’t get the doors open immediately, no big deal. If you look, shake, yell, bump, tap and tilt with no results… okay.

So what? Who gives a fuzzy red rat’s tail?

You might turn off the phone and go mow the yard.

But those closed elevator doors stay in your mind. So you’ll come back at some point. You’ll open the app and check it out.

Just one more time.

Just to see…

And when the doors open – yippee!

There’s no prize. There’s no grade. There’s no money.

But the excitement you have from getting those crazy doors open and seeing the green arrow is unimaginable!

“Cheating” is allowed.

Sharing a tip is something you do only if you want. Giving or getting a solution isn’t prohibited, but it’s fun to try to get the solution yourself.

So you choose what to share and what to ask for. Based on your own desires and curiosity.

And it’s the same as learning math.

This one almost killed me. Had to go do something else for a while and come back later.

So far I haven’t found an official math problem in the game. But the tactics, patience and curiosity that you use are exactly what learning math is all about.

In each new math problem, students may wonder, “What the heck do I do with this one?” Just like you do with those elevator doors.

And if there’s no punishment for trying nutty things, their curiosity will take them places.

Tapping, dragging, shaking and yelling into the phone might have made me look goofy. But Husband was nestled in his chair doing equally insane things to get his elevators to open.

But there IS punishment in learning math.

That’s where things diverge.

Performance based teaching is the basis of the typical math lesson. Math problems are given to the student. And the student is expected to give back the right answer.

If the right answer isn’t given, there are repercussions. Points are deducted or the failure is publicly noted. Or both.

And if you don’t have the right answer, you’re just not learning math.

Period.

(BTW – that’s a horrible myth!)

And “cheating” is all or none.

This one sort of turns out to be a math problem.

Either the teacher coaches step-by-step, or there is no tutor or teacher at all.

Think about the last time you did a math problem from a textbook with a teacher watching.

If you took the wrong path, you were quickly guided back on track. This was either with words, “Are you sure that’s what you need to do?” or with facial expressions.

Math students aren’t allowed to take or leave tips at will. And they sure aren’t allowed to give them when they want.

That’s cheating.

But isn’t that what grownups do when they “guide” students?

How do we change this?

How can we make learning math more like playing 100 Floors? How can we get students into the adventurous mode – tapping, shaking and doing anything they can to a math problem?

How do we get them to cheat on their own terms? And how do we get grownups to stop over cheating?

Share your thoughts in the comments. And share this article on twitter!

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May 8, 2012
Differentiated Instruction
I just learned what the phrase “differentiated instruction” means. Jeanette Stein told me on #MathChat that for her, differentiated instruction is

Meeting kids where they are at to take them where they can go.

I love it!

So I read the article Jeanette shared from Teach-ology. Seems differentiated instruction is a fancy term for focusing on the individual students rather than the teacher.

I’ve been doing it for years!

The first few semesters I taught math (back in 1996), I would lecture. I mean straight up, lecture. But soon I learned that it wasn’t about me.

Over the next 16 years I watched the students. I quit spending so much time and energy on preparing lectures and much more time and energy thinking about the comments and questions I got from the students.

I learned how students get quickly confused by the simplest of things – like solving an equation in one variable with four terms.

I learned that the way something is said is much more important than what the words are.

I learned that many of the “math rules” were merely tricks some clever person thought of as a mnemonic device. And that if these tricks are forced on certain students, they’ll likely never understand what’s really happening.

The biggest trick/hoax is PEMDAS or the Order of Operations. Other math rules that get highly confusing are the Zero Product Rule and cross-multiplying (a term I personally despise).

And most importantly, I’ve learned that creating a safe and inquiry based learning environment is the key to differentiated learning.

And there’s more!

In considering my classroom experiences, I’m finding many other instances and examples of differentiated instruction. So this is the first in a series on tactics to improve your own differentiated classroom. Here are the proposed topics/titles:
- Eliminating the Fear – How to Engage Students without Calling on Them
- Show Your Work! – What’s up with that?
- Grading in a Differentiated Classroom – Why Teaching Math Is Harder than Giving Birth
- “It’s Your Education!” – How to Empower Your Students
- If Shakespeare Taught Math – How to Use Metaphors to Teach Math
- If Picasso Taught Math – How to Use Drawings to Teach Math
- How to Teach Your Students to Think Like a Mathematician
Wow – that’s rather ambitious of me, isn’t it?

I’ll shoot for these once a week and you can find a link to the series (this article) in the sidebar under “Quick References.”

If you have any requests or ideas, let me know in the comments. And don’t forget to share this series with your PLN on twitter!

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May 4, 2012
Education vs. Technology – One Advances and the Other Doesn't
Wil, the research guy, notices how technology has advanced, but education is being left behind.

While on vacation recently, I met an English professor who was using a 70s era computer programming punched card as a book mark.

During a brief exchange, he said “Forty years ago we never imagined we’d have things like this,” pointing to my iPhone.

What struck me was the manner in which he offered anecdotes of the days in which they were still in use. He didn’t imply loss or anger. He didn’t express any resentment for discontinuing the now antiquated and obsolete programming medium.

On the contrary, he jovially stated, “Now, I use them as bookmarks and my wife uses them for her grocery lists.” Talk about recycling!

Embracing change.

I began to wonder why advances in technology have been embraced so well and completely, and why we are still in the “punched card” age of education.

Many “upgrades” to effective learning are not universally applied… yet.

For a considerable number of our public schools, we still approach the teaching-learning interaction in a way that is decidedly contrary to what research has not only indicated, but has, in many cases, shown to be true.

It’s not just data transfer.

Some still believe that education means opening the knowledge portal of students (whatever age) and simply depositing information. This is unrealistic and grossly simplified. Education – learning – must be received more than it can be given.

Let them lead.

Autonomous students not only having a say in what they engage but to a large degree feel their education is self-directed. This has a huge impact on their motivation, level of focus and ultimately how much they learn.

Support with information, and don’t forget the “Way to go!”

Research has provided us with concepts such as scaffolding to help children with mastery.

Less acknowledged and utilized (perhaps due to less educator proficiency) has been emotional support and encouragement. But this is just as important in a child’s education.

You may have the best information in the world for how to do something. But if the student is disengaged, it’s just not going to happen.

Start with a conducive learning environment.

This could be a post all by itself. The jist: it’s less about giving something, and more about ensuring the student is engaged. So the educational paradigm must focus on how we can facilitate the student’s learning, whatever that looks like.

This means focusing on the student and HOW they learn right now. Instead of “he just needs to pay attention” or “she needs to work harder”.

Back to the punched cards.

We’ve been given these specifics that have been presented to us over and over in the research. They are being applied with successful and definitive results. So why are we resistant? And who are the “we” we are talking about?

Look at the inevitable and constant changes in technological advances. Now consider the stagnant, upgrade-resistant public educational system. What’s the difference?

What you can do.

Be informed. Ask questions. Request and support educational “upgrades” in your schools.

You and your children are the customers. Only you can create the demand for improvements in your child’s education.

Have a voice. Be the squeaky wheel. And support schools when they move in that direction.

They may already be doing so. If they are, let them know this is what you want.

For more on how to support your schools in embracing conducive learning environments, contact us or leave a comment.

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March 27, 2012
Anxiety Safe Learning Environments
Would you like to create a safe math learning environment free from anxiety? What would that look like? Let’s first peek at what it doesn’t look like:

Okay class, what’s the answer to number 12?

I think it’s 75, Mr. Jones.

No, Emma. That’s wrong. Have you been paying attention?

Unintentionally or not, this is often taken as ridicule by Emma and her classmates.

They quickly learn to avoid this verbal punishment and the anxiety it causes.

And the easiest way to avoid it is by not trying.

There is a power-dynamic, a vulnerability, that goes along with any instructor-student relationship. In these situations, students must feel safe to engage. Encouragement and support are ideal. But more importantly, the learning environment must be free of criticism, shame, or overwhelming frustration.

If a student feels that there is threat of criticism, shame and frustration in a math class, it’s curtains. Even if forced to “stay in that chair and listen,” they won’t mentally stick around to learn much of anything.

So how do you get your learning environment safe from anxiety?

Praise the “wrong.”

Being wrong means the student’s trying. Trying means they are engaged. Engagement gives an opportunity to learn.

Without the opportunity, learning can’t happen.

When you praise the incorrect answers, you praise the trying. When you praise the trying, the students are more engaged in math class. They have an opportunity to learn.

So when they’re “wrong” – praise them.

Exercise patience

You may say, “But they didn’t give the right answer!”

Got it.

But before performance, or getting the right answer, a student must take in and process information at a pace where they can retain it. Getting the right answer is only an indicator of understanding and effective learning of math. A confirmation. It’s not the learning itself.

Letting them be wrong and process how they got the wrong answer is part of the process of learning. And sometimes this can be slow.

But giving a student time to think about and mull over questions and answers is more effective for learning in the long run, than requiring the right answer.

Yup – you’ve got things to do, kids to teach. So it might leave you feeling frustrated when you allow wrong answers and give them time to ponder it.

So when your patience is running thin, step away. Adults need breaks, too. Take one to avoid a damaging experience.

Learn from the “wrong”

When an incorrect math answer is given, ask them how they got there. Get them thinking about it. There are more learning opportunities in the wrong than the right.

Right answer given. Say: Good job! Let’s move on to the next one.

Incorrect answer given. Say: Excellent. Let’s talk about how you got there…

We can praise the attempt and find something in the incorrect answer to build on and learn from.

Think about the teaching implications of this. How many more folks would be willing to try something if being wrong is okay? How many more kids will you engage if there’s no criticism or humiliation to avoid?

Be ready, don’t force it

Your students might have been trained to avoid verbal punishment by not trying. Remember Mr. Jones from above? Mr. Jones is everywhere. So take it easy when creating this “anxiety safe” environment.

When the more vocal students get wrong answers, praise like crazy, be patient and help them learn from the wrong answers. The rest of the students will follow.

And whatever you do, don’t be Mr. Jones.

Your turn…

How do you create a learning environment safe from anxiety? Have I missed anything? Share your thoughts in the comments.

William Devine is a licensed professional counselor in private practice. He has joined the MathFour.com team as the Director of Research. Connect with him in the comments, on the contact page or via twitter @MathPsych.

Feature image adapted from an image by Marshall Astor – Food Fetishist | Flickr.com | CC BY SA

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February 8, 2012
Teach a Man to Fish… Really?
This idea was inspired by something Tom with Leaving Work Behind wrote in an article about success months ago. He wrote:

Principles are timeless – techniques are not. Would you rather I give you a fish, or teach you to catch your own?

Here’s a week in the lives of Tom and me… “fishing”…

Monday

Bon: Hey, whatcha doing?

Tom: I’m fishing.

Why?

Because I’m hungry. You can eat fish.

Bon: I’m hungry too. Will you share your fish?

Tom: Sure!

Tuesday

Bon: I wonder where Tom is. I’m hungry.

Wednesday

Bon: Hey Tom!

Tom: Hi Bon!

Bon: I’m hungry. I haven’t eaten in two days. You weren’t here yesterday.

Tom: Well, I’m fishing now. Watch how I do it and if you ever need to, you can do it yourself.

Bon: Swell!

Thursday

Bon: I wonder where Tom is. I’m hungry. Good thing I watched him yesterday. Now I can catch my own fish.

<pause>
Bon: What’s going on. I’m not catching any fish. And I’m doing it exactly as Tom did! I’m so hungry!

Friday

Bon: What’s up, Tom!

Tom: Hey Bon. How are you?

Bon: I’m SO hungry. I tried to fish yesterday but I couldn’t catch anything. And I was doing it exactly like you did.

Tom: That’s strange. How about this. I’ll let you do the fishing today. Together we’ll see what you’re doing and adjust it so it works for you.

Bon: That sounds great!

Saturday

Bon: Bummer. Tom’s not here. But I was successful catching fish yesterday so I’ll have no problem catching fish now!

Sunday

Bon: Hey Tom!

Tom: How’s it going Bon?

Bon: Excellent! Hey – wanna join me for lunch? I’ve caught enough fish for both of us!

Do you really want to teach someone to fish?

There’s a difference between teaching someone to fish and helping them learn to fish. In the case of Tom’s teaching medium – his website – he can only teach. Likewise, here at MathFour.com, my writings can merely teach.

But when you’re face to face with a student, teaching isn’t nearly as valuable as helping them discover.

Indeed, if you’re going to teach a child who really needs help learning, you might as well just give them the fish.

Do you teach your kids to fish – or help them learn?

Share your thoughts in the comments.

Images by Tony the Misfit on Flickr, CC BY.

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January 27, 2012
Improving Creativity with Technology
This article is based on the talk “Improving Creativity with Technology” given at the University of Houston teachHouston T3 Regional Conference.

Traditionally we give a concept or algorithm to the students and ask them to memorize, understand and use it. And by “give” I mean we serve it to them well done, fully baked, nothing left to do but eat it.

Piaget’s research (and subsequently others) suggest that allowing students to discover or create the methods is more effective than handing them the method and asking them to take it, eat it, no questions asked.

But how do you let them discover it?

Since the math we teach in middle school and high school is based on real numbers, every concept can be demonstrated with “plain” numbers. Which means it can be discovered by playing with numbers.

Calculators make this playing or experimentation fast – giving a student the ability to quickly see patterns and construct concepts.

Introduce the topic with numbers.

When you introduce a topic, give 10-20 “examples” of it with real numbers. Ask the students to play with them and notice any patterns they find.

Notice you’re creating an inquiry-based learning environment, an Inquiry Zone for Math Learning. Remember to maintain positive body language, ignore negativity, and super-validate what any student says.

Give the students the power!

Until the student decides differently, everyone is wrong. Even the teacher and textbook. They get to validate it for themselves – and they can do this with real numbers.

Ultimately, if they grow to be mathematicians, they’ll learn that verifying with lots of real numbers doesn’t mean “proving” it – but for the time being, this works fine.

Giving them this power lets them experiment as much as they need, and only as much as they need, to verify a concept for themselves.

Use the Play & Say method.

You’ve heard of the “Plug & Chug” method? You take a formula, plug in the numbers and chug through the arithmetic. Plug & Chug is a non-discovery based practice tool. The practice is good, mind you, but the formula is given, not discovered.

Remember, something discovered is more likely to be remembered than something given.

So use the “Play & Say” method. Each student plays with the numbers until he or she can say what the formula or concept is.

Caveats

If you’re trying to teach a concept with this and one student discovers a different formula or concept. Run with it – as long as it’s mathematically sound. Don’t discourage the discovery of anything, even something not on the current curriculum.

If a student gets frustrated, don’t force them to discover it themselves. Give them the concept or formula and encourage them to experiment later with it.

Suggestions

If you find there is a big difference in how much time each student takes, send the experiments home with them. Give them five minutes at the beginning of class to play – the students who realize they need more time will have done more the night before.

How will you do it? Share your thoughts and experiences in the comments.

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January 21, 2012
How to Create an Inquiry Zone for Math Learning
In a previous article, I suggested two ways to introduce inquiry-based math instruction into your teaching structure. One of them was to create a safe discovery environment – an Inquiry Zone. This is where students could ask anything and not be held responsible for performance.

It can be a location or a time – or both. It can be announced or understood.

As the facilitator, here are some things to do to create the safe Inquiry Zone.

Maintain positive body language.

When a student asks a question, make sure your body language and facial expressions say, “Wow, that’s a very smart thing to ask.” Do this regardless of how you feel about the question personally.

Ignore negativity.

If other students laugh at a question, ignore them. Instead validate the asker and the question through words and body language. Chastising the negativity only validates it.

Super-validate every question.

Follow up every question with a similar or extended question. If you can’t think of one, say, “That’s really interesting. Let’s write it down so we can look it up on Google later.”

Post the rules.

Set up rules so that all the students know what inquiry really means in math. The rules I use are:
1. Until you decide differently, everyone is wrong. Even the teacher and textbook.
2. Every question is a great question.
These two rules build confidence. Not in getting the right answer, but in deciding what it means to be a right answer. If a kid gets to decide when the answer is right, they will ask more questions. Inquiry!

Be wrong – often.

Modeling this “wrongness” makes kids comfortable with it. The more comfortable they are with being wrong, the more likely they are to engage in inquiry.

You can be wrong by not knowing something or actually doing a problem wrong (doing your arithmetic wrong, for instance).

If you are normally perfect, fake it. Mess up. Do it for the kids.

Destroy the back of the book.

I’m not sure you can get away with this without being fired.

If you don’t mind getting fired from your teaching job, or if you homeschool, get the kids to rip out the back of the book – you know, the part with all the answers in it. And don’t let them talk you into letting them “check their answers” on the calculator. That’s just as damaging.

The more they get to decide if their own answer is right, the more they will ask. The more inquiry will happen!

Will you create an Inquiry Zone?

Share your experiences in the comments.

Feature image by Crystl | Flickr.com | CC BY

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January 20, 2012
Inquiry-based Math Instruction
Inquiry-based math instruction is the opposite of performance-based math instruction. And the research shows that inquiry-based math instruction is more effective than performance-based.

But performance is required if you’re teaching anywhere other than a homeschool. So what do you do?

You have to balance the requirement of performance with the need for discovery and inquiry-based learning. Which means you have to integrate discovery and inquiry-based elements into your math teaching.

You can do this formally or informally. You can say it out loud, or just do it. And which method you choose will depend on how much you are supported.

Set aside time for inquiry-based instruction.

Bring inquiry-based math instruction into your lessons by breaking up class time into “performance-for-tests learning time” and “discovery/inquiry-based learning time.”

You can have specific topics for the discovery learning time or even a “free math time” where there is no specific topic.

Make sure you keep the discovery topics independent from test based/performance-based topics. As much as you’re tempted, don’t connect the two. If the students connect them, acknowledge it briefly and keep moving.

Keeping them separate keeps the “must get the right answer” attitude out of the discovery time. This is very important.

For example, if you’re teaching multiplication this week in class, set aside the discovery time as patterns or geometry. This can be 5-10 minutes at the beginning of each class period or one day of the week devoted to it.

Create a safe discovery/inquiry zone.

If you want to include discovery in the regular curriculum, you have a little bit more of a challenge. Children learn early that performance is required in math classes. So they avoid being creative and asking questions. (See the research paper on that here.)

Which means you have to undo years of creativity-destruction to get them to participate in inquiry based activities. Depending on the students’ ages, you might have to start with introducing really goofy stuff to break them out of their comfort zone.

Let them wear fuzzy red hats and crazy glasses and tell tall math tales for the first few times. They’ll get warmed up to dig into some creative math inquiry. Anything’s easy when you’re wearing fuzzy red hats!

After a while they’ll be used to the safe environment and the inquiry-based math learning will start to flow from them.

Do both.

Ideally, you can have a “fun” time – where the math you have to do is set aside and you let the students dream about crazy math stuff. In addition, all your lessons involve the safe zone.

If you can make it work – do it. You’ll grow confident, adventurous, smart kids – the research supports it!

Will you try? Tell us in the comments.

* Inquiry based math instruction is really the wrong term. Instruction means giving of something – in this case knowledge. It really should be inquiry based math learning. Teachers and parents are inquiry-based facilitators.

Feature image by philcampbell | Flickr.com | CC BY

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January 17, 2012