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# Tag Archives: Math Boot Camp

## Is there one right way to harvest all of these tulips?

Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?

Now look at this addition problem:

## Is there a “correct” method to solve this problem?

Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?

If you have never had formal or informal instruction about teaching math you might be thinking “‘Yes Jenny! You are asking crazy questions!  Just start from the right!”

That’s what I used to think over ten years ago before I first started learning about teaching math from a Constructivist point of view. Ten years ago I would have taught children to draw a bunch of lines and junk and crank through the traditional algorithm. Yes, they could learn to do that. NO WAY would they ever be able to solve a problem like this quickly and accurately in their head.

It took me almost ten years as an adult to unlock my brain from “the right to left method”.

## But kids can learn multiple methods with high accuracy in just a few years, if they have a good teacher who holds off on teaching traditional algorithms until the students actually understands math.

Here is what that type of teaching might look like. If this is new to you, hold onto your seat and prepare for the crazy.

Notice that the problem is written horizontally instead of vertically. If you want your kid to be good at mental math then you have to present problems to them horizontally at least as often as you present them vertically. If you think that the best way to solve problems is by stacking them vertically, then that is your first problem! Maybe the best way is to stack the problem vertically, or maybe not. Strong mathematical thinkers could do the problem either way.

## But if horizontal is hanging you up, let’s go vertical:

I’ve seen this method called the “Sum All Totals” way and I think that’s pretty cool. Kids who learn this method really understand that the “4” is really 4,000. That “3” is really 300. etc.

# Now let’s go mental:

Start at the left, look to the right, reassess your answer, and keep moving.

## If this is new to you, you might need to stare at that last picture a really long time.

Remember how I told you it took me about ten years before I learned to unhook my brain from borrowing and carrying and get good at other methods?

It’s super easy to teach a swimmer how to climb into a rowboat. It’s super hard to teach a non-swimmer how to climb out of the rowboat and learn to swim.

No mom would send a non-swimmer into the ocean on a rowboat and say “Look! My kid is water safe!” But lots of people mistakenly think that children who can crank out algorithms “know math”. Maybe they do, maybe they don’t.

I’d like to close with a comment Crimson Wife left on my blog earlier this week that illustrates a lot of what I just said. She’s in the enviable position right now of teaching her super swimmer son how to climb on the rowboat. I’m guessing it’s not going to take Rusty 10 years to learn, like it did me!

Crimson Wife says:

The funny thing is that I’m currently fighting with my almost 7 y.o. to NOT use mental math because he’s working through a section in his Singapore math book where they are having the student practice the traditional algorithm. I finally had to pull a worksheet from my older child’s pre-algebra program where the task was to add three 5 digit numbers. The numbers were so big that my DS couldn’t just use the mental tricks but had to use pencil & paper.

# Let’s get started!

Quick question:  What is 120 really Do you know?  Can your child explain it to you?

Can they make that 120 friendlier?

I think that 100 + 20 is a lot friendlier than 120. It will be easier to take 38 away from 100, than it would have been to take it away from 120.

Since I don’t really need that 20 right now, I’m going to stick it on my forehead.

I’m holding that 20 in my brain and I’m going to come back to it later.

Sweet!  Now I can just deal with taking 38 away from 100.  That’s way easier.

100-38 on an abacus is super easy.  Don’t have an abacus?  Try a blank hundreds chart.

I like the Abacus because with enough practice kids start to visualize what 100 really is and know answers intuitively.

Ooops!  Is there still a number on my forehead?  I better deal with that 20 now.  62 + 20 = 82  I’m using adding (which I’m really good at) to help me do subtraction.

That means that 120 – 38 = 82!

# Square numbers are super easy.

Do you think I’m nuts?  “Square numbers?  Don’t you have to know about multiplication and square roots and…Eeeek!”

# I bet your four-year-old could tell you which number is square.

## But look! 9 makes a square. It’s a square number!

If we were to keep building (which would require a lot of crackers) then we would see something like this.

The next square number is going to be 16.

Children who are learning about multiplication can also learn the corresponding equations that go with each square number.

1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16  et cetera

So do you believe me now?

# Square numbers are super fun!

(Don’t you wish you learned math this way?)

# Today is all about “Food for Thought”.

## Let’s do an experiment.

Pretend you are at the grocery store.

You have \$9.50 in your wallet and you forgot your credit card. You want to buy a watermelon which costs \$4.25 and a gallon of milk which costs \$2.99. Will you have enough money?

There are lots of ways you might solve that problem in your head.

Maybe you looked at those prices and thought “2.99 is almost \$3. So… \$4 + \$3 = \$7. Then add in the quarter and you get \$7.25. But take away the penny from the \$2.00/\$3.00 conversion, and my final total is \$7.24.  So yes, I have enough money.”

But can you still go to Starbucks afterwards? How much money will you have left over?

Now you might be thinking “\$9.50 – \$7.24 = about \$2.25. I can afford a cup of coffee, but not a mocha.”

## What you just did was real life math.

I bet your accuracy was fantastic.

## But now let’s do another experiment.

Pretend you are in middle school. You are crammed into one of those super uncomfortable chairs with the attached desks. The teacher is some old guy up front wearing a weird tie. There is a vague smell of tuna-melt wafting through the room from the cafeteria next door.

You are taking a really important test. NO MISTAKES ALLOWED! Here’s the problem:

950 – (425+299) = ?

a) 475

b) 226

c) 329

d) 225

## Now what are you going to do?

If you are like most people my age or older, you might have reached for a paper and pencil. Probably you stacked those numbers up and started borrowing and carrying. It might even be possible that your accuracy went down.

One of my favorite books about math is called The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs) by Keith Devlin. In the final chapters of the book, Dr. Devlin shares research about this phenomenon of grocery store math vs. school math.

In real life people form their own strategies for solving problems and tend to be pretty accurate in their calculations. In school though, those same people can be hit-and-miss as they attempt to crank out traditional algorithms.

## Maybe you are better at math than you thought.

Give yourself permission to let go of the notion that there is one right way to solve a problem.

Give your children permission to explore and discover strategies that make sense to them.

## Then imagine the possibilities…

If you can already do grocery store math in your head with kick-awesome accuracy, what do you think might have happened to your own math ability if you had been encouraged to follow that type of problem solving as a young child? Would you be doing algebra in your head? Would calculus be fun?

When a teacher forces a child to do something over and over again that doesn’t make any sense to them, how is that helping?

# In my ideal world, “Drill and Kill” would be illegal.

The real art in teaching math to children comes from asking them questions about their own thinking and then listening. “How would you do this? What makes sense to you?”

It’s really hard to do that in the classroom, especially if you are responsible for 30 kids.

But the next time you are at the grocery store with your own son or daughter, try asking them if you have enough money to buy ice cream. Then listen to what they have to say…

# I’m your coach Jenny and I like to think about numbers.

No really, tell that to your kids. Clearly express to them that you are their coach and that you like math (whether that’s true or not).

# Let’s start by warming up!

What’s wrong with this picture?

A third grader who draws all of those lines and junk on a simple problem like 1,000-344 = is telling you a lot. They are showing you that they are clinging to a traditional algorithm instead of using their brain.

# We need to teach our kids to think.

There are LOTS of better ways to solve this problem. Today we are looking at one possible method.

I’m using number cards from my Right Start kit, but you could just use paper and pencil.

Notice that I’m laying out the problem in a horizontal fashion. This encourages children to let go of their algorithm life-raft and start using their brain instead.

Let’s start by thinking about the number 344. What do I need to do to 344 to make it a friendly number?

No wait! I’m going to make this even easier. I’m just going to think about the 44. What do I need to do to 44 to make it a friendly number?

I know. I could add 6 to it and get 50. 50 is a friendly number.

That means that 44 + 56 = 100. 100 is a really friendly number.

That makes me think that 344 + 56 must equal 400.

And you know what? I know that 600 + 400 = 1,000.

That means that 654 + 344 = 1,000. I’m using adding (which I’m really good at) to help me solve a big subtraction problem.

What do you know? I can do that problem in my head!!!

## The real art in teaching math comes from asking questions.

How would you solve this problem? Do you have a way that you like better?  Feel free to leave a comment and tell us about your stratgey.  Or, you can just mock me for having numbers on my forehead.  Whatever…

Math Boot Camp will be back in session tomorrow!