Category: Math Education

Categories
Math Education Math for Parents Math for Teachers

Summer Session: What your rising first grader should know

Math for Grownups blog readers tend to fall into two camps: grownups who are not parents and really hate math (or think they’re not good at it), and parents who are worried that they’re going to pass along their math anxiety to their kids. And so I thought I’d spend a little bit of time addressing some of the concerns of these parents.

Earlier this week, my friend and fellow freelancer, Debbie Abrams Kaplan forwarded the summary of a new bit of research on kids and math.  Debbie is the author of two great blogs: Jersey Kids and Frisco Kids, and she figured that I might find some blog fodder from this study.

Boy did I!  A couple of things jumped out at me:

  1. No one has ever studied how the basic math skills of first graders affect their later understanding of math throughout elementary school.  (Compare that with the many studies of early reading skills, and this fact will blow your mind, too.)
  2. There are three basic skills that will help first graders become good fifth-grade math students.

I’m going to tell you those skills a little later, but first I want to introduce the concept of numeracy.  Quite simply, numeracy is the ability to work with and understand numbers.  When children are young, numeracy includes the ability to count, recognize the symbols that we use for numbers (which is akin to learning the alphabet), and even do some very simple operations (like 1 + 1 = 2).  For high school students, numeracy includes more complex problem solving skills and properties of real numbers.Among math educators, there are big debates about how we can better teach numeracy.  I guess this is like the debates about phonics vs. context support methods in reading education.  But now that this study is out, it’s clear parents can help lay a firm foundation for our kids’ later success in math. According to this study, published by a team of University of Missouri psychologists, rising first graders should understand:

  1. Numbers — I’m going to take this to mean whole numbers, since most first graders aren’t very familiar with fractions or decimals.
  2. The quantities that these numbers represent — In other words, kids should be able to match a number with that same number of objects (five fingers, two cats, etc.)
  3. Low-level arithmetic — And I’m guessing researchers mean things like adding and subtracting numbers that are smaller than 10 (excepting problems with negative answers).

If you’re like most parents, this is probably a duh moment.  What’s so hard about recognizing whole numbers or understanding what five objects are?  But I don’t think many parents spend much time emphasizing these ideas — at least not in the way that we commit to reading to our children every night.So here are a few ways that you can help instill numeracy in your pre- or elementary-school aged children.

  1. Count things.  Count everything — like the stairs that your climbing or the cars that pass your house or blocks as you take them out of the box or those adorable little toes!
  2. Have your child count things.  You can do this in really simple ways.  Ask him to get you five spoons so you can set the table.  When she wants some goldfish, tell her she can have 10 (and watch her count them).  When you’re planning his birthday party, have him tell you which 10 friends he wants to invite. (Write them down for him, so he has something visual to count.)
  3. Notice numbers.  When she’s really tiny, ask her to say the numbers that are on your mailbox or on a license plate.  Older kids can name multi-digit numbers, like 157 or 81.  (And if you want to really be precise and prep your kid for school, don’t say things like “one hundred and fifty-seven.  In math, “and” represents a decimal point, which is something most elementary school teachers will really drive home.)
  4. Teach your child to count backwards.  This can be a great way for kids to start understanding subtraction.  If you know you have 10 steps in your staircase, count backwards as you go down the stairs.  Then count frontwards as you go up!
  5. Start adding and subtracting.  Give your child 5 raisins and show her how to “count up” to 7 by adding 2 raisins to the pile.  Then as your child eats the raisins one by one, “count down” to find out how many are left.

You don’t need to make a big deal about math.  And for goodness sakes, skip the worksheets, flashcards and even video games — unless your kid really loves them.  Integrate these basic skills into your daily life, and you’ll see your child’s understanding grow.  (And you probably won’t feel so stressed out about it all!)What kinds of things do you do with your young elementary-age kids?  Any teachers out there want to share their thoughts with the class?  Post in the comments section.

Categories
Math Education Math for Parents Math for Teachers

Is Math a Foreign Language?

When I was in college, majoring in math education, I learned that math is the language of science.  In fact, we called it the Queen of the Sciences.  (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!)  And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science.  [pullquote]We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar. — Rick Ackerly[/pullquote]

In some ways, everyday math is also the language of science.  Home cooks use ratios to ensure that their roux thickens a gumbo just right.  With proportions, gardeners can fertilize their vegetable beds without burning the leaves from their pepper plants.  And a cyclist might employ a bit of math to find her rate or the distance she’s biked.

But I think too often we adults get caught up in the nitty gritty of basic math and lose the big picture.  This is when many of us start to worry about doing things exactly right–and when math feels more like a foreign language, rather than a useful tool.

Earlier this week, I read a blog post from Rick Ackerly, who writes The Genius in Children, a blog about the “delights, mysteries and challenges of educating our children.”  In Why Mathematics is a Foreign Language in America and What to Do about It, he writes:

Why do Americans do so badly in mathematics? Because mathematics is a foreign language in America. The vast majority of children grow up in a number-poor environment. We’ve forgotten that the language of mathematics is founded in curiosity.  We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar.  Being curious together can be a really special part of the relationship in families.

And I couldn’t agree more.  For all of you parents and teachers out there: how many questions do your kids ask in one day?  10? 20? 100? 1,000?  As Ackerly points out, especially younger children are insatiably curious.  They want to know why the sky is blue and what makes our feet stink and how come that ladybug is on top of the other ladybug.

These Stevendotted ladybugs are not wrestling. Photo credit: Andr Karwath

A full 90% of the time, we can’t answer their questions. Or maybe we just don’t want to yet.  (“That ladybug is giving the other one a ride.”)  With Google‘s help, we can find lots of answers.  But how often are we asked a math-related question–by a kid or a grownup–and freeze?

For whatever reason, many people are afraid to be curious about math.  Or they’ve had that curiosity beaten out of them.  I think that’s because don’t want to be wrong.  As fellow writer, Jennifer Lawler said to me the other day:

It’s funny because when I make a mistake in writing—a typo, etc.—I let myself off the hook (“Happens to everyone! Next time I’ll remember to pay more attention.”) But if I misadd a row of numbers I’m all “OMG, I’m such an idiot, and everyone knows I’m such an idiot, I can’t believe they gave me a college degree, and why do I even try without my calculator?”

The same goes for answering our kids’–or our own–calls of curiosity.

So what if we decided not to shut down those questions?  What if it was okay to make some mistakes?  What if we told our kids or ourselves, “I don’t know–let’s find out!”  This could be a really scary prospect for some of us, but I invite you to try.

What’s keeping you from being curious about everyday math? What do you you think you can do to change that?  Or do you think it doesn’t matter one way or the other?  Share your ideas in in a comment.

Categories
Math Education Math for Parents Math for Teachers

Math for first graders

Want to know what really burns me up?  Telling a kid he’s not good at math.  Know what’s just as bad?  Telling a mom that her kid isn’t good at math.

This morning, I was early for my fitness boot camp class.  (Sadly, I don’t get to work with Robert the personal trainer.)  I chatted with a couple of the women who, like me, show up every morning at 6:45 for an hour of torture.  Of course, I had to share that I got advance copies of my book, Math for Grownups, yesterday.  Per usual, the conversation turned to the absolutely ridiculous and completely frustrating notion that people are either good at math and science or they’re good at language arts.

Now, for the record, I wholeheartedly disagree with that line of thinking. (Can you tell?) Keep reading to find out why.

One mom said that her son’s first grade class was good at reading but not math.  How did she know this?  The teacher told her.  There are so many unbelievably wrong things about this situation, and thinking about it makes me want to scream:

  1. They’re first graders! How can six year olds be bad at math?  They might be missing some basic concepts, like counting up to add or the difference between a triangle and a square. But remember, nobody is born bad at math.
  2. It’s the teacher’s job to make sure kids understand basic math concepts.  Blaming the students is a cop out.
  3. Telling parents that an entire group of kids is bad at math is a self-fulfilling prophecy.  Already, parents (and other grownups) believe that math ability is like being tall or having blue eyes–you either have it or you don’t.  This teacher may have unwittingly reinforced this idea, by making such a silly generalization.
  4. If she told the parents this, what message is she sending the kids?  If you’ve been a parent, you know that there are a trillion different messages that we send to our kids every day, without even knowing it.  I would bet my last dollar that this teacher is somehow relaying to her students that math is just not their thing.

First graders who think they’re not good at math, grow up to be middle schoolers who think algebra is beyond them. These middle schoolers of course awkwardly morph into teenagers who are convinced that they won’t need (and can’t do) geometry, trig, advanced algebra, probability, statistics and calculus. And then of course, these acne-prone, love-sick adolescents become the smart, successful adults who tell me every day that they desperately need my book, because they can’t balance their checkbooks to save their souls.

But really, I’m not blaming this one teacher.  I promise.  She’s just the beginning of a long line of teachers and other grownups who buy the lies about math: that only people with “math brains” can comprehend the Pythagorean Theorem and no one uses math in everyday life anyway.

So, what’s the solution?  The issue is not the students.  The issue is that we somehow believe that there is only one way to teach math.  Of course that’s not true.  Teachers and parents have to figure out how our kids think and approach math in a way that makes sense to them.  And we have to quit labeling ourselves and our kids.

All you parents out there, I’d be forever grateful if you’d do just one of these things:

  1. If a teacher says your kid is bad at math–or worse, declares an entire class bad at math–please challenge him or her.  There are only a few people in the world who have real issues with processing mathematical information, and I’m betting your kid isn’t one of them.
  2. Stop telling people that you, yourself, are bad at math.  Next time your dinner companion asks, “Can you help me figure out the tip?” bite your tongue.  If you truly can’t find 15% of $24.68, pretend you didn’t hear or fake it.  But please avoid saying the all-too-common, “I’m so bad at math!”
  3. If you can’t help your kid with his homework, don’t declare: “I just don’t have the math gene!”  Here’s the reality:  You may not remember how solve a proportion, but that’s because you probably haven’t seen one for at least 15 years.  If you were asked to diagram a sentence and couldn’t do it, would you say that you’re no good at speaking English?  Of course not.
  4. Replace your generalizations about math ability with messages like these: “I don’t remember how to do that.  Let’s figure it out.” or “I remember doing these kinds of problems in school, and they gave me trouble.  But I’m sure we can figure it out together.”

And just a quick footnote/disclaimer: I am the biggest advocate of schools and teachers that you will ever meet.  Having been a public school teacher and been raised in a family of teachers, I’ve seen first-hand what our educators face on a daily basis.  I just wish I didn’t hear stories like the one I heard this morning.

I’m going to gingerly climb off of my soapbox now.  (My glutes are killing me after that workout!)  But I ask you to share your thoughts on these generalizations about math ability and math education.  What messages have you or your kids received?  What do you think about them?  How do you think we can counter them?  And for all you teachers out there: how do you send the message to your students that they are good at math?

I’ve decided to start a regular feature about math education, called Summer School.  In it, I’ll discuss some ways that parents can send the right messages about math.  We don’t need another generation of grownups who think they can’t do math!  🙂

Categories
Math Education Math for Parents Math for Teachers

Mixing in Math: Teacher Cooks Up Lesson in the Kitchen

So this apparently is big news in Myrtle Beach.  A middle school math teacher actually took her kids out of the classroom to teach them math.  In the school cafeteria, the students converted decimals to percents and found surface area and volume — as they were cooking up some healthy eats.

Photo courtesy of Jessica Masulli

Ya’ll, seriously.  This is what how we use math as grownups.

(Okay, so the surface area and volume is a bit of a stretch.)

If you think doing math is about chalkboards and protractors, you’re flat out wrong.  (Besides schools use dry erase boards these days.)

Math is about getting your hands dirty, sketching a picture on a scrap piece of paper, doing some quick calculations on the iPhone.  Most of all, math is about solving real problems — not those silly things that have something to do with trains in Omaha — and coming to these solutions in creative and sensible ways.  (There. I said it: creative and sensible.)

Look, I like what this teacher is doing.  And so do her students:

“You learn it better because you enjoy doing it,” said Maya Bougebrayel, who made a vegetable chicken stir fry with teammates Allison Klein and Carlisa Singleton. The girls, all 13, agreed that the project put a creative spin on learning and made it easier for those who are visual learners.

But if it wasn’t such a novel idea, wouldn’t grownups be better at math?  Feel free to chime in in the comments section.