Math for Grownups
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In Math for Parents

Film Friday: When will I ever use this stuff?

It’s the perennial question from students of all ages: “When will I use this stuff?” So when tutor, Ryan faced this query (probably for the upteenth time), he took to the streets to find the answer.  What he found is in the video below:

And of course I have some thoughts — for teachers and students.

It is absolutely true that series (that’s what the funny looking E — an uppercase sigma — means in this problem) are not the stuff of ordinary folks in non-science fields.  But they’re not as difficult as they seem.  It’s the notation that’s confusing.

Skip this part, if you don’t really want to do any algebra today.

A series is just the sum of a sequence (or list) of numbers.  That’s it.  Nothing more, nothing less.  So when you have

sum{n=1}{7}{3n-1}

you’re simply saying, “Find the sum of the first 7 values of 3n-1, where the first value of n is 1.” In other words: 2 + 5 + 8 + 11 + 14 + 17 + 20 = 77.

Now back to my opinions.

Okay, so I don’t need to know what a series is in order to visit the grocery store or get a good deal on a car or even figure out how much I earned this year over last year.  But here’s what I wish some of those folks who were interviewed for this video had been able to say:

“That funny-looking E is a Greek letter, right?”

“Doesn’t this have to do with adding things together?”

“Hey, I dated a girl from {Sigma}{Sigma}{Sigma} once!”

And second, this tutor did pick a humdinger of a problem to focus on.  Series (and their brothers, sequences) are not the main focus of any mathematics course.  But honestly, they wouldn’t be taught if they weren’t useful somewhere.  And boy-howdy are they useful!

So, here are a few ways that real people do use series in their real jobs (courtesy of Algebra Lab and Montana State University:

1.  Architecture:  “An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?”

2.  Business: “A company is offering a job with a salary of $30,000 for the first year and a 5% raise each year after that. If that 5% raise continues every year, find the amount of money you would earn in a 40-year career.”

3. Investment Analysis: “A person invests $800 at the beginning of each year in a superannuation fund.  Compound interest is paid at 10% per annum on the investment. The first $800 was invested at the beginning of 1988 and the last is to be invested at the beginning 2017. Calculate the total amount at the beginning of 2018.”

4. Physics: “The nucleii of a radioactive isotope decay randomly. What is the total number of nucleii after a given period of time?”

And this brings me to some additional news of the week.  Sol Garfunkel (Consortium for Mathematics and Its Applications) and David Mumford (emeritus professor of mathematics at Brown) made a bit of a splash on Wednesday, with an editorial in the New York Times: How to Fix Our Math Education.

Their proposal is that we teach tons of math that applies to everyday life — and focus on those applications. (Yay!) And we ditch “highly conceptual” math for folks who won’t need it for their jobs. (Boo!)

Hopefully, you’ve already identified the problem: How do we know if a kid won’t decide to go into physics or engineering or high school math education? Hell, how do we even attempt to lure them into these fields, if they don’t see the math at all?  (And by the way, physics, engineering and applied mathematics were recently identified as the top-paying degrees in the U.S.)

Look, I empathize with the student who isn’t interested in what any of the Greek letters mean in math class.  And I think it’s true that most folks won’t use these skills at all after high school.  (It is worth mentioning that everyone depends on series in their daily lives–they just don’t see the math.) But my response to the kid who asks, “What’s this good for?” is to tell him where it can be applied.

And if he says he won’t be going into any of those fields, I would say, “Suck it up, cupcake, because you’re too darned young to know for sure.”

Please share your thoughts in the comments section.  Do you agree that these concepts should be taught in high school, even though most kids won’t use them in their everyday lives? How do you think we should encourage more students to go into science, technology, engineering and math (STEM) fields? 

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In Math for Parents

Math Secret #2: You Were Born This Way (take 2)

Photo courtesy of woodleywonderworks.

All summer long, we’ve seen some pretty amazing research on math ability and education.  We’ve been told that understanding geometric concepts may be innate and that elementary-aged students with a good sense of numeracy do better in math by the 5th grade.  And yesterday news of another study hit the internet.

According to the headlines, we were born either good or bad at math.  At least that’s how this study is being interpreted by bloggers and news outlets.  Except that’s not necessarily what the study concludes.

This makes me mad.  Really mad.  I have not read the full study, but nothing in the abstract–or even the stories and blog posts about this study–suggests that people are born with or without math ability.  Instead, it seems that the cheeky headlines were just too good to pass up.

Here’s what the study author, post-doctoral student Melissa Libertus, does say:

The relationship between ‘number sense’ and math ability is important and intriguing because we believe that ‘number sense’ is universal, whereas math ability has been thought to be highly dependent on culture and language and takes many years to learn… Many questions remain and there is much we still have to learn about this.

And here’s the nitty gritty on the study itself.  A group of 200 children, with an average age of 4 years old, was given a number sense test. (You can take the exact same test here).  These children were then asked to perform a variety of age-appropriate math tasks, including counting, reading numbers and computations.  The results make a lot of sense: children who performed well on the number sense test did better on the math tests.[pullquote]No one says that we’re born good or bad at reading.  We’re all expected to learn to read–and read well. So why do we say that about math?[/pullquote]

But the results seem to be misrepresented by media and others.  These kids were selected precisely because they haven’t had any formal math education.  They’re preschoolers.  So, according to many news reports, kids are either born with number sense or get it from formal education.

Rubbish.

If you had a child in the last 10 or 15 years–or know someone who has–you are probably familiar with the big, big push for early literacy. Parents are encouraged to read to their kids, even when they’re babies, which research has shown helps the children develop age-appropriate literacy skills. In fact, kids who have had access to pre-reading experiences as infants, toddlers and preschoolers do much better with reading in elementary school.  (This is one of the tenets of Head Start programs around the country.)

No one says that we’re born good or bad at reading.  We’re all expected to learn to read–and read well. So why do we say that about math?

Just like the researcher, I think this study raises more questions.  And here’s the really big one: What can parents do to boost their kids’ numeracy before formal education begins? (I actually wrote about this earlier this week.)

I still maintain that we are born with an innate understanding of math–just like we’re born knowing something about language.  But without stimulating this understanding, kids can fall behind their peers or at least not reach their full potential.  We read to little children so that they can learn to read on their own.  And we should be doing something similar with kids so that they can do math.

A friend and fellow math blogger, Bon Crowder has launched an amazing program she’s calling Count 10, Read 10. It’s a simple idea: Parents should spend 10 minutes each day reading to their young kids and 10 minutes doing some sort of math with them.  But nobody is saying flash cards, worksheets or chalkboards are necessary.  The trick is to sneak the math into everyday activities, which can be as simple as counting the steps your new walker takes.

So here’s what I think happened with the news reports of this study: reporters, editors and bloggers simply tapped into their own misconceptions about math–and even their own math anxiety–and distorted the message.  For many people, it’s a “fact” that some people are just naturally bad at math.  I hope you’ll help me challenge that notion.

Meanwhile, be careful what you read.

P.S. A great math educator, David Wees has also chimed in on this topic, and shares–more eloquently–some of the same concerns I have.  Read it!

So what do you think? Are people born good or bad at math? Can parents help develop numeracy in their children?  How?  Share your ideas in the comments section.

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In Home

Food for Thought: 5 Ways Hurried Moms Can Make Math Easy

Photo courtesy of sabianmaggie

Boy, do I remember those early days of parenting my daughter. I was working full time, coddling a strong-willed toddler, trying to serve balanced meals, selecting great books to read to her and trying to keep my house and yard clean enough that my neighbors wouldn’t call Child Protective Services on me.

Adding one more thing to the list would have made my head blow off of my shoulders.

And yet, today, we are being asked to do that one more thing: introduce numeracy to our little Janes and Johns. In other words, math.

Want some tips on how parents can develop numeracy in their little kids–and keep their own heads on their shoulders, right where they belong? Read the rest of this post at Words To Eat By, where I guest posted today.

By the way, would you like me to guest post at your blog?  Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest.  I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow.  Get the details here.

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In Math Education

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.

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In Math Education

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!  🙂

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