Tag: rules

7 Rules of Life in Math!
I’m not big on sappy sayings or lists. But when I saw a list of “7 Rules of Life” on Facebook, I couldn’t help but see the 7 Rules of Life in Math in it.

1. Make peace.

Did you have a math teacher laugh at you? Write him a letter and tell him he was a meanie.

Did you have a math teacher say you weren’t good at math? Find her number, give her a call and let her know that she was wrong.

Find a way to make peace with that past event.

You’re not bad at math. You never have been. You just had some teachers that made you feel yucky.

2. Ignore others.

Forget about what others think. Your learning in math is your business.

Don’t worry yourself wondering if you’re learning as fast as someone else. If you’re happy with your learning, that’s good enough.

3. Give it time.

Time helps — a lot.

Learning isn’t something you sit and do today and then have in your brain forever. Often we put things in today and they don’t really make sense until 6 months from now.

And practice over time helps it to gel. So be patient.

4. Don’t judge.

Just as your learning is yours, other people’s learning is theirs. If they don’t get it, avoid launching into the damaging “all you have to do is…” routine. Those words say, “Anyone can do this. It’s easy. And if you can’t, well… you’re an idiot.”

Knock it off.

Everyone learns differently — just because you get it quickly, doesn’t mean you get to be pushy about teaching it to others.

5. Embrace ignorance.

It’s okay to not know the answers. Math is about exploring. Discovering.

If you don’t get the answer today, come back later. Don’t beat yourself up about it.

In spite of what all the textbooks and teachers say, math is not linear. If you don’t get something today, keep rolling. It’s okay to skip it.

When you least expect it, you’ll understand that “missing” concept so much better than if you tried for force yourself into it too soon.

6. Take charge.

No one’s in charge of your learning except you. Really.

If you have to play the grades game, fine. But remember to learn along the way.

Don’t jump through hoops for the sake of jumping.

7. Smile.

The next time you’re smiling, look around. There was math in what you did that made you happy.

Maybe you saved 75% off a great dress. Or gotten to an event on time. Or had more people show up at your party than you expected.

All of those are math. And you’re smiling about it!

So keep smiling and share your thoughts in the comments or on twitter/x.

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December 4, 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
Rules Aren't Complete without the Details!
This is the 7th in the draft purge series where I’m throwing stuff out over a three week period.

Rules often leave out the details.

Don’t drink alcohol and drive a vehicle in public, simultaneously.
Find a common denominator, when adding fractions.
Do it to both sides of the equal sign.
Multiplication comes before addition in arithmetic.
Find a point using slope from another point on the line.

Details!

This article is a part of the 50 Word Friday series. Learn more about this strange, limited writing style here…

Share your thoughts in the comments or on Twitter/X.

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May 25, 2012
We Use Math and Grammar Rules – They Don’t Use Us!
I got engaged in a twitter fight about grammar with Chiew from @aClilToClimb (now @Chiew_Pang). Yes, I’m the math mom, but my college minor is English. And I tend to be a sharpie carrying, sign correcting, grammar vigilante.

I complained that Twitter has the link “Who To Follow” when it should be “Whom To Follow.” Here’s an excerpt from the fight:

The fight raged on.

This guy was so adamant that you could use “who” as the object in a sentence (clearly wrong), and just wouldn’t let it go. After quite a few tweets I got curious. “What’s this guy’s deal? All he has to do is pull out the Little Brown Handbook and read it in plain black and white.”

So I went and looked at his site. Holy cow! He’s a grammar blogger!

I couldn’t find his “About” page, but from what I could gather in his fervor in our twitter fight, he’s trying to do for grammar what I’m trying to do for math. Demystify, take away the “have to” rules, and make it accessible, acceptable and appreciated by everyone.

We make the rules!

The rules of grammar, like the rules of math, are created by humans and used by humans. They are changeable.

Of course the difference is that, in grammar, if you deviate slightly from the rules that others follow, you’ll most likely be understood. In math, you really have to define how you’re using things before you begin to work.

For instance, if I wanted to have a conversation with someone about a new way of adding fractions I was inventing, I could totally do it. As long as I started the conversation with, “Here’s how we are going to talk about adding fractions for the next hour…”

Make it your own!

Teaching math and teaching grammar are two of the fundamental things we do for our children. And neither should be hard, creepy or frustrating. They should be a normal, natural flow of who we are as people.

Another great math mom says, “Make math your own, to make your own math.” I’d bet Chiew would say something similar for grammar.

And for this, I respect him. </fight>

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October 22, 2011
How to Teach a Weird Math Rule: Negative Times a positive Is a Negative
Thanks to Molly for this question she left in the comments, “Why is a negative times a positive, a negative?”

“Sign – One Way” by Andrew Schmidt

It’s common to hear a child say, “They created this rule just to make me mad.”

And on the heels of that usually comes a frustrated teacher’s comment of, “No, this has a purpose.”

When then faced with, “Okay… so what’s the purpose?” a teacher or parent might become more frustrated. It’s not always clear the purpose of things like the rules for multiplying differently signed numbers.

It may also be that the grown-up secretly believes that this was all created just to make us mad. After all, when the last time you had to multiply a negative number times a positive number in the real world?

I, personally, can’t ever remember a time when that case has come up outside of a math class or tutoring session.

Then why create the rules at all?

The truth is that many math rules are created because we need a rule to continue working – something to agree on among peers working on the same project. We need everyone on the same page.

This agreement somehow gets filtered down to the kiddos as “this is the absolute way it is – do it because we said.”

So it very much looks like we created rules to make them mad.

Good deduction, kids.

How do they pick the rules?

“Street Chess” by Petr Kratochvil

Some math rules are created arbitrarily just so we have something (anything) to agree to. Like the rules of a game. The order of operations is one such situation.

There is no natural reason why we’ve chosen to do multiplication and division before we do addition and subtraction. No more so than the people in the US have decided to drive on one side of the road whereas the people in England, Australia and the Bahamas drive on the other.

We’ve agreed to it.

It keeps us from crashing.

Sometimes, we agree to a rule because it is “less bad” than any of the other possible rules we can think of. The result of any number raised to the zero power is one of these. 3⁰ feels like it should result in either zero or 3. But if you mess with all the other rules (in particular the one about subtracting exponents here $\frac{3^7}{3^7}$ ) you’ll see that 3⁰ really needs to be 1. If it were anything else, it would mess up the rule of $\frac{\text{anything}}{\text{anything}}=1$ .

How do we teach crazy math rules?

Why is a negative times a positive equal to a negative? Is it because it messes other things up or is it an arbitrary rule? Instead of explaining the reasoning to a child, allow them discover it.

Have a “King for a Day” day where the students get to rewrite a particular math rule. Allow them to sit as a class or family and decide on the rules for multiplying signs numbers.

Give them plenty of time to experiment and see if the new rule messes anything up. (If your administrators or math curriculum specialists fret about you allowing students this time, note to them that the students are behaving like real mathematicians. They are inventing a concept or rule and testing it out to see what happens.)

If the students discover that the new rule has dire consequences when applied to the rest of our number system, they then see the reason for the rule. And they’ve learned through experience and solidified the rule in their minds!

If the students discover that there are no consequences of the new rule, they can then determine that the rule was created arbitrarily and agreed upon for convenience. It is a rule for rules’ sake.

You can discuss with them how things would be different if they kept the new rule and everyone else in the world followed the old rule. Again experience and discussion will solidify the “real” rule.

So the next time you’re faced with “why?” regarding a math rule, give it a shot. Let the children be the rulers of their own math world!

Will it work? Did it work? Share your thoughts in the comments!

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June 29, 2011