Category: Math for Teachers

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Ode to Special Numbers

There are numbers, and there are special numbers. Okay, so just like children, all numbers are special. But a few of these numbers have qualities that make them stand out from all of the rest. Some of them you’ll recognize right away, because they’re used in everyday math. Others may be completely new to you — or at least you haven’t thought about them for years!

Let’s take a look.

Zero
It may look pretty ordinary, but 0 is one of the most important numbers in the entire system. It’s called the additive identity, because when you add 0 to any number, you get that number back. As a digit, it is used as a placeholder in the decimal system. Without 0, 4.32 equals 4.032, which would really shakes things up!

It may seem strange, but zero is an even number. That’s because it is evenly divisible by 2 (0 ÷ 2 = 0). But dividing any number by 0 is undefined; you can’t do it! Zero is neither negative nor positive, and it’s neither prime nor composite. When you raise 0 to any number (square, cube, etc.), you get 0.

One
Another ordinary number, 1 is called the multiplicative identity. In other words, when you multiply any number by 1, you get that number. As a result, 1 is it’s own square, cube, etc. It’s often called the unity, and it’s the first odd number in the natural numbers. Like 0, it is neither prime nor composite.

i
Remember the rule that says you can’t take the square root of a negative number. Well, this is where i comes in. In fact, i is the square root of -1. It’s known as the imaginary number, but believe me, it’s very real. (Okay, it’s not real in the sense that it’s not part of the real number system.) That means that the square root of -25 is ±5i. The square of i is 1.

Imaginary numbers aren’t used in everyday math, but they’re a big deal in electromagnitism, fluid dynamics and quantum physics.

Φ 
Phi is another number that you might not be very familiar with, but many mathematicians would say that it’s the most beautiful of all numbers. That’s because it represents the Golden Ratio. Two numbers are in the golden ratio if the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity. Whew! That complicated definition boils down to the irrational number 1.6180339…

The golden ratio is found in art, architecture, music and even finance. The proportions of the Parthenon are said to mirror the Golden Ratio or Φ, and Salvador Dali’s The Sacrament of the of the Last Supper employs Φ. Stradivari used the Golden Ratio to place the f-holes in his violins. And it seems that the financial markets mimic the Golden Ratio.

Nature abounds with the Golden Ratio. If you divide the number of male bees by the number of female bees in a hive, you’ll get 1.6180330… Measure of the distance from your shoulder to your finger tips and the distance from your elbow to your finger tips. Divide the longer measurement by the shorter, and — yep, you guessed it — you’ll get Φ.

e
Like i and Φ you may not be very familiar with the number e. Quite simply, e is the base of the natural logarithm. It is equal to the irrational number 2.71828…

Computer geeks love e. When Google went public, the company’s goal was to raise $2,718,281,828 or e billion dollars to the nearest dollar. In further homage to the special number, the company put up a mysterious billboard designed to attract potential employees, who were also enamored with e.

π
Of course no list of special numbers would be complete without π or pi, which is equivalent to 3.1415926… But do you know where π comes from and why it’s so important? The number is the ratio of the circumference of a circle to its diameter. In other words, if you divide the circumference of any circle by its diameter, you’ll get π. Cool huh? Pi helps us find the area and circumference of a circle. It’s also useful in trigonometry.

More importantly, π has it’s own day: March 14 (or 3/14), when eating pie is encouraged, as well as celebrating the most famous constant in all of mathematics.

Do you have any additions to this list? Share your ideas in the comments section.

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Math Tricks: Good or bad?

When I do interviews or speak to groups about math, one of the things I worry about is that people will expect me to do math tricks. And I worry about this for good reason. I can’t multiply two three-digit numbers in my head. I don’t know π to the 100th decimal place. Heck, I can’t always remember what 9 x 8 is!

There are plenty of folks out there who have these abilities, and god bless ’em. It’s not my schtick. In fact, while I think these tricks are pretty nifty, I’m not so keen on people learning them, at the expense of gaining a deeper understanding of the math behind them. This goes for kids and adults.

This is what I write about in one my first posts as the math expert for MSN.com’s site for parents, Mom’s Homeroom. Over the next several months, I’ll write articles and develop activities designed to give parents the tools they need to help their kids succeed in math. (Other experts address reading, social skills, homework and study habits and parental involvement.) One of my first posts, 5 Cool Math Tricks You Didn’t Know, looks at some neat shortcuts for basic math facts — like multiplying any number by 11 or finding out if a number is divisible by 3.

The twist is that I show readers why these tricks work. But this is a step that most folks skip altogether. My friend, Felice Shore, who is an assistant professor and co-assistant chair of Towson University’s math department, explains why it’s critical to master the math behind the magic.

“The important mathematics [in third and fourth grade] is still about building understanding of relationships between numbers — the very reasons behind math facts. Once you show them the trick, it’ll most likely just shut down their thinking.”

That goes for grownups, too. If you’re brushing up on some basic math skills, don’t just memorize facts or use nifty tricks. When you take a little time to look beyond a quick answer, you will likely learn a great deal more. And as we all know, this can extend to other applications and concepts.

Math is often described as a set of building blocks stacked on one another — the foundation must be there to move into more complex concepts and more difficult applications.

But it’s also a web. What you learn about multiplication applies to division, which applies to factors and multiples, which applies to fractions. Sometimes, a concept that passes you by can be better understood later on when the idea shows up again. In other words, you might just learn your 12s times tables,when you’re applying measurement conversions (12″ = 1′). Tricks just might keep you from deeper understanding.

So whether you’re trying to get good at math on the fly or helping your child remember that 9 x 8 = 72, be careful with the tricks. They just might keep you or your child from learning much bigger concepts.

Do you depend on math tricks? If you’re a teacher, what do you think of students using math tricks?

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Ten Things Students Wish Math Teachers Knew

Two weeks ago, I posted Five Things Math Teachers Wish Parents Knew. Now it’s the teachers’ turn to be on the hot seat. I asked a handful of the middle and high school students that I knew to chime in with some advice or helpful feedback for math teachers. And this is what they came up with:

Make the math relatable.

These kids get it — you honestly like pure mathematics and the State Board of Education has dictated that you cover x amount of material in y period of time. (See what I did there?) But when all students are doing is solving algebraic equations with no connection to the real world, the stuff won’t stick — and eyelids will shut.

Do more “interactive stuff instead of book work.”

Get rid of boring worksheets. Spend a few days applying the material to larger projects. Have the students design carnival games based on probability. Or track March Madness results. Or use special right triangles to find the length of a shadow and compare it to an actual shadow.

Ensure that everyone is ready to move on — before moving on.

Again, these students know that you have some constraints. And I’m willing to bet that most students understand that the class doesn’t revolve around them. (Okay, maybe many students, rather than most.) But if a good portion of the class isn’t following, there’s no point in barreling through to the next concept. I’ll add this: some students won’t tell you that they’re not ready to move forward. Teachers have to get creative in assessing readiness.

Don’t call on the same students all the time.

Everyone knows who the mathy kids are. Don’t let them dominate the discussion. A few days ago, a parent told me that her daughter’s school is really clamping down on “blurters” — kids who get the answers quickly and blurt them out. These blurters can suck all of the life out of a classroom, especially when the majority of students need a little more time and a lot more confidence. And it’s a good lesson for anyone to learn: keep your mouth shut and sit on your hands once and a while.

Don’t refuse to call on a student who usually has the answer.

This one’s personal. In middle school, my daughter was told to stop raising her hand all of the time — and not in a nice, encouraging way. She was crushed by this harsh order. Everyone deserves a chance to participate, at least part of the time. And besides, there are different methods for encouraging participation that don’t require teachers to single out and call on individual students. Learn these methods and use them.

Skip the timed tests.

They freak students out and can bring down a grade in a heartbeat. Fact is, faster isn’t smarter. Speed tests don’t allow different approaches to problems. Besides, what’s more important: automatic recall of the times tables or really understanding where these facts come from? (Please say the latter. Please say the latter.)

Grade as much as possible.

Give students a chance to bring up their grades with graded homework assignments. And give them feedback on their understanding as often as you can. It’s not enough for a student to know that the answer is wrong. Detailed feedback on why is critical for deeper understanding. Kids know this.

Recognize that not all kids learn in the same way.

Remember, the definition of insanity is doing the same thing over and over and expecting different results. If students don’t understand the concept, try explaining it in a different way. Or ask the kids to come up with their own ideas. Discovery is a great tool, and it’s often very engaging.

Stop talking down to students.

Yep, students really said this. And I could wallpaper my bathroom with the number of emails I’ve received from adults who felt shamed by a math teacher. Every adult that a kid meets has the power to make a positive difference in that kid’s life. Belittling, shaming and talking down to kids will have the opposite effect.

And I’ll add #10:

Don’t ever, ever tell students that they’re bad at math.

Want to insure that a kid will never try at math again? Want to smash his confidence? Want to send a lasting message that she won’t be able to balance her checkbook or become an engineer or help her kid with math homework? This is a one-way ticket to that bleek future, and it can happen in a split second with an offhand remark. Remember what it was like to be a student and follow the Golden Rule.

Do you have suggestions for math teachers? Share them (nicely) in the comments section. I’d also love to hear from students and former students who had great experiences with their math teachers. Are you a math teacher? Feel free to offer your feedback, too!

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Journey from Math Loser to Math User

Today, I’ve asked Siobhan Green to share her math story with everyone. As the CEO Sonjara, Inc., a woman-owned technology firm, she is a huge proponent of increasing women and men’s math skills worldwide. But she hasn’t always felt confident in her math skills.  As she told me, “I think my story is not that unusual in how many of us, especially girls, too easily believe that math is hard and only for super smart math geek types.” Amen!

I was considered a smart kid. I learned to read early, knew my numbers and letters before age 3, entered first grade early and did well in school. However, when I got to third grade, I and my teachers started noticing a discrepancy between my math scores and the rest of my school work. I would regularly get poor grades on timed math tests — two- and three-digit addition and subtraction problems —  which predominated our math education. I easily mastered the concepts presented, but when given a timed test, I would run out of time and/or make a lot of odd mistakes.

This pattern continued in elementary school. The result was that I was either yelled at by teachers for being lazy or intentionally not focusing on my math work, or the teachers just assumed I was “bad at math.” I vividly remember one teacher saying “Yeah, girls are better at verbal skills, boys at mathematical/spacial ones. Just stick to what you are good at.”

Things got better in seventh grade when we moved to pre-algebra. I was excellent at pre-algebra and routinely got As and Bs on tests. But I also managed to make the teacher mad when a group of students was interviewed by a local paper and I made a disparaging comment about him (I had no idea what I was doing). As a result, he recommended that I NOT move into Algebra as my grades would warrant but rather into pre-algebra/algebra, for kids who struggled. No one — not my guidance counselor, nor my parents, nor even me — remarked on this fact, as we all had agreed by that point that I was “bad at math.”

This decision had huge implications. Math is tracked; students take algebra, then geometry, then algebra II and then trig, and only then can you take calculus. By not allowing me to go into algebra in eighth grade, I would not take calculus in high school — something that excluded me for many science (especially computer science) learning opportunities.

The rest of my educational history with math was similar – I excelled in algebra (go figure), did fine in algebra II and trig and did surprisingly well in geometry, but my heart wasn’t in it. I also took some basic computer programing courses — BASIC and Pascal. I enjoyed these but never associated them with math, and the overwhelmingly geeky-boy atmosphere of the computer lab turned me off to more experimentation in these fields. By the time computer science camps started becoming popular in high school (in the mid/late 80s), many programs expected that students would be in advanced math classes.

My college degree was in international affairs, which required two years of economics. I was NOT good at economics, and because I didn’t know calculus, and my antipathy for anything involving numbers, was a big part of it. I excelled in the social sciences and went onto a career in international development.

However, over the years of my career, I noticed that I was good at technology — I was the person in the office who figured out the printers, who set up macros and templates in Word, and who taught herself basic HTML. I was also a whiz with developing databases and excel spreadsheets and was often the person who tracked expenses and invoices. I became more and more interested in using technology for international development; I did my masters’ dissertation on the Internet in Africa in 1997. Falling in love with a software developer didn’t hurt, either.

It was actually through my husband (the math/computer science major and total math geek) that I realized I am NOT bad at math. I am in fact pretty darn good at it, and a lot of the tasks I enjoyed “count” as math!

Andy recognized that I have a mild learning disability — dyscalculia. I transpose numbers, have a hard time retaining numbers in my head, don’t memorize numbers well (I still don’t know my 7 and 8 times tables by heart — and by now, I will never memorize them), and often misstate numbers when going from listening to writing. (Trying to capture a number left on a voicemail is torture for me.) And this is true after years of learning coping skills! He was the one who said “Your calculation mistakes are not normal. And they have NOTHING to do with your math abilities.”

See, remember those timed tests? Thinking back, I would think one number and write down another one. Now, I always take a second to double check, but in a timed situation at age 8, I would panic and just move on to the next one. Many of the mistakes I made in the early years were down to calculation errors. When the math was based in patterns (like algebra) or depended on calculators, I did much better. But by that time, my math ability had become a self-fulfilling prophecy. The research is clear about the impact of low expectations on ability; I never pushed myself and accepted lower scores as evidence of my innate lack of talent.

I didn’t realize that my strong abilities in building relational databases, especially to track quantitative data, counts as math! I absolutely love building databases, especially related to financial management. Those spreadsheets I use to track finances?  They speak to me and tell me a story in numbers. I had no idea that my ability to create and read those numerical pictures of my firm also counted as math.

Andy also taught me how to program, and while I will never be a full blown developer (mainly because I don’t have time to gain in-depth programming experience), he found that I grasped the key pattern processes quite easily. This skill has been invaluable in my role as business process analyst for web application development. It helps me translate between user needs and programming architecture, which helps with figuring out edge cases and pricing.

Today, my job as CEO of a web application company involves a lot of math. For example:

* Pricing work, especially figuring out hourly rates for specific roles/individuals based on salary, benefits, and overhead plus profit. It is very easy to “win” enough work for bankruptcy (win the work but price it so low you don’t cover your costs). We are always repeating the joke “yeah, we lose $1 per widget sold but we will make it up in volume.” (The explanation is at the bottom.)

* Overseeing projected and actual utilization of my staff. If our rates are based on this person being at 80% billable, and they are regularly at 75% billable, that 5% difference will eat into my profit.

* Understanding the difference between the profit and loss statement, the balance sheet, and a cashflow statement. This is omething that every business owner must understand in order to figure out how the business is doing. You can have huge paper profits but still be in serious trouble if you cannot make payroll, or you could be cash rich but slowly going under because your easy access to credit is masking the fact you are spending more than you are earning.

* Making decisions about how to spend money. What investment will make a bigger impact? For example, should I hire another person or pay down a loan? Should we purchase this new computer now on credit or wait until the next check comes in?

Oh, and here’s the explanation of the above joke:  “Yeah, we lose $1 per widget sold but we will make it up in volume.” Assuming that your costs do not scale (decrease per widget based on volume), if you sell 100 widgets, you have now lost $100. And if you sell 1,000,000 widgets, you have now lost $1,000,000. It is astonishing the number of business people I meet who do not get this concept. Usually, they are not in business for long.

Can you identify with Siobhan’s story? Share yours below. 

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The Math of Poetry (Yep, there’s a connection)

anyone lived in a pretty how town
(with up so floating many bells down)
spring summer autumn winter
he sang his didn't he danced his did

So goes my very favorite poem, written by e.e. cummings. In my senior year of high school, I wrote a term paper explicating the verse, and I fell in love. At the same time, I was taking two math classes, and somehow the process of solving a system of equations was similar to understanding cummings’ strange syntax and playful turns of traditional poetic forms.

April is not only Math Awareness Month but also National Poetry Month. In a facebook conversation with another writer, I found myself offering to show the connections between math and poetry — a task that is surprisingly simple but (if similar articles and blog posts are any indicators) could be very contentious. I like a challenge and a good intellectual fight, so here goes:

Symbols

I’ve long asserted here that mathematics is a language that describes the physical world. Without mathematics, we cannot describe physics. And mathematical models allow us to predict the future or see the invisible. Math also depends heavily on symbols — variables, Greek letters and characters that represent operations like addition and division.

Clearly, symbolism is the very basis of poetry. When Robert Frost writes, “Two roads diverged in a yellow wood, / And sorry I could not travel both” he doesn’t mean that he is literally sorry that he cannot literally travel two literal roads. Nope. The yellow wood represents the later years of the poet’s life when he’s considering the choices (roads) he could have made (taken). (For sure, there are many versions of this interpretation.)

The same is true for the symbolism in math. When you graph a curve that represents the steady increase of your take-home pay over several years, the curve is a symbol of your financial (and perhaps professional) success. But you can interpret or apply the curve in a variety of different ways, and the curve doesn’t tell the entire story.

[laurabooks]

Patterns

You can’t deny the patterns found in mathematics. All you need to do is list multiplication facts for a certain number, and a structure will jump off the page or computer screen. (Eventually.) Then there are a variety of sequences and series, like Fibonacci’s Sequence (1, 1, 2, 3, 5, 8, 13, …) or a geometric series (like 1 + 2 + 4 + 8 + …).

The patterns in poetry are often found in meter and rhyming schemes. So the first line of Shakespeare’s Sonnet 73 is in iambic pentameter: “That time of year thou mayst in me behold.” We know this because it features five two-syllable feet that are expressed as non-stress, stress. (In other words: “That time of year thou mayst in me behold.”) Along with iambic, traditional poetry may follow trochaic, spondaic, anapestic or dactylic meters — but there are endless more styles. Cummings’ “anyone lived in a pretty how town” is generally considered to be a ballad, which, when you know the key that unlocks the poem’s meaning, makes perfect sense.

Symmetry

The idea that two halves are symmetric is not mandatory in mathematics or poetry, but oftentimes it takes center stage. In math, we have symmetric shapes, like circles or isosceles triangles. Symmetry is also critical in solving equations, as you must do the same thing to both sides of the equation.

And in poetry, symmetry is often found in the ways that verses and stanzas are structured. “The Road Not Taken” features four stanzas with five verses each.

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

Then took the other, as just as fair,
And having perhaps the better claim
Because it was grassy and wanted wear,
Though as for that the passing there
Had worn them really about the same,

And both that morning equally lay
In leaves no step had trodden black.
Oh, I marked the first for another day!
Yet knowing how way leads on to way
I doubted if I should ever come back.

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I,
I took the one less traveled by,
And that has made all the difference.

Many mathematicians and poets have pointed out even more similarities (some that, in my opinion, suck the life and art out of both math and poetry), but these are some basic ideas. I’ll leave you with what Einstein said on the matter: “Pure mathematics is, in its way, the poetry of logical ideas.” To which I say: math and poetry are designed to give the illogical some kind of logical shape.

There are some really interesting everyday life math examples in my books. Visit this page and buy the book today!

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Formulas: Or is this going to be on the test?

Quick! What’s the formula for finding the circumference of a circle? Do you remember the Pythagorean Theorem? What about the distance formula?

If you’re around my age and not a math geek, chances are the answers are “I don’t know,” “No,” and “Are you kidding me?”

When you were in school, memorizing formulas was required. But as a grownup, that’s not necessary. In fact, you can find all sorts of shortcuts that make formulas unnecessary. Here are two examples:

1. Last week, during spring break, I offered to teach my daughter and four of her friends how to make circle skirts. We bought material, set up three sewing machines and two ironing boards and got to work. I found a really wonderful (and easy) tutorial at Made, which employs a great shortcut for cutting out a circle: fold the fabric into fourths and then trace one-fourth of a circle, which will be the waist. After that, measure the length of the skirt (plus hem allowances) and trace another one-fourth circle.

We needed the radius of the smaller circle, but really all we had was the circumference of that circle — the measure around the waist. Dana at Made has a quick and easy process for this: divide the waist measurement by 6.28. Ta-da! The radius!

But why does this work? Because the circumference of a circle is C = 2πr. 2πr is approximately 6.28r. That means that you can divide the circumference by 6.28 to get the radius. Neat, huh?

2. Yesterday, I was the guest on the 1:00 hour of Midday with Dan Rodricks, Baltimore’s public radio station’s noon call-in program. Dan asked listeners to find the surface area of a cylinder with a radius of 6 and height of 8. A caller reminded me that there is a formula for this: SA = 2 π r2 + 2 π r h. But lordy, I didn’t remember that!  Instead, I found the area of each base — both circles — and the area of the rest of the cylinder (using the circumference of the base times the height of the cylinder). I added these and got the same answer.

So what’s the point? You don’t need to remember a formula. If you can break the problem down into smaller parts, do that. If it’s easier to remember to just divide or multiply by something, go for it. Unless you’re taking middle school math or have to teach a math course, the ins and outs of the formulas are not critical. What you need to be able to do is use the concepts you understand to solve the problem. Sometimes that means remember the formula, sometimes that means finding a sneaky way around your bad memory.

Don’t forget to enter the Math for Grownups facebook contest! Just visit the page to find out today’s clue (and Monday’s and Tuesday’s). Then post where you’ve noticed this math concept in your everyday life. Good luck!

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Parlez-Vous Mathematics? Math as a foreign language

In redesigning my blog, I’ve read a lot of the posts I’ve written over the last year. In fact, take a look at this math: On average, I’ve written 13 blog posts each month or 164 posts (counting this one) since last May. And so I decided to repost this one, in honor of Math Awareness Month, which addresses the language of math.

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.

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.

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

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.

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.

Our first Math Treasure Hunt winner is Marcia Kempf Slosser! Congratulations Marcia, you’ve won a copy of Math for Grownups (or if you already have a copy, I’ll send you a gift card). Want to enter? All you need to do is find an example of the daily clue, which is announced on the Math for Grownups Facebook page each day. 

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Five Things Math Teachers Wish Parents Knew

Parents: when it’s time for math homework, do you suddenly have something else to do? When it’s parent-teacher conference time, do you first tell the teacher that you’re no good at math yourself?

First off, you’re not alone. It’s the number one thing I hear from parents: “I don’t know how to help my kid with math!” So I asked one of my favorite math teachers, Tiffany Choice. As an elementary and middle school teacher, Ms. Choice is a math education expert. And because of that, we instantly connected. Oh, she was also my daughter’s fourth grade teacher.

I asked Ms. Choice to share her best advice for parents. Want to help your kid succeed at math? Here’s how.

Just because you struggled in math class doesn’t mean your kid will.

Don’t pass on your dislike or acceptance of not being “good at math.” Always highlight the importance of math. If you cannot provide math homework support, find someone who can. Even if your kid has to call an uncle across country to try help clarify a problem, it goes a long way.

Math is best understood when applied to the real world.

Show your kids how you use dollars and coins at the store. Encourage understanding when they use birthday money to buy things. Discourage them from throwing the wad of money on the counter without understanding what they are doing. Explain to your child what you are doing when balancing that checkbook, measuring a wall or following a recipe. You are your child’s first teacher.

How you were taught to do something in math may or may not be the best way.

Education is swiftly changing to keep up with technology and each generation. Be open to many new ways of learning math concepts. Ask your child’s teacher to show you how a concept is being presented. I’ve had parents stop in during math instruction or for an after school conference.

Math isn’t learned right after the first lesson.

Parents should emphasize and allot time for practice — just like we encourage practicing the piano, ballet, reading, soccer, or French.

Realize the importance of and reinforce math vocabulary.

Math isn’t just numbers, it’s words too. Talk about what 20% off really means when they’re asking for that new toy. Use the words “total,” “difference,” and even “mixed number.” Believe it or not, truly knowing what those math words mean helps in the long run. I hate to mention standardized tests, but it’s something that’s here to stay (at least for now). More and more, math tests are transforming into reading tests.  Most of the questions are word problems. Certain understanding of math vocabulary can and will help your child avoid the sneaky test-makers tricks.

I’ll add one more thing: Encourage your child to explain their reasoning behind the math they’re doing — whether you’re helping with homework or asking him to divy up candy pieces at a play date. One of the biggest things that kids are being asked to do is write about math. (In my daughter’s school, these are called BCRs or Brief Constructed Response and ECR or Extended Constructed Response.) The kids who already verbalize their understanding of math will have an easier time with these tasks.

Do you have advice for parents? Whether you’re a teacher, parent or innocent bystander share your ideas in the comments section. Have a question? Share that, too!

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Welcome to Math Awareness Month! Share your math story

Oh, math! How I love thee.

Not.

I like math. I even appreciate math. But I can’t say that I love it. Sometimes I get a little thrill in seeing math around me. Mostly, I just feel comfortable with the math I use everyday and get anxious when I see something I haven’t used in years (like differential equations). Anyone else?

Math is a tool. And just like a hammer or a vacuum cleaner, it probably doesn’t evoke deep emotion in many of us. Still, being aware of math makes sense. Math is everywhere but you don’t have to love it.

To start the month, I thought I’d ask each of you to share your math stories. We all have some sort of feeling about math, whether it’s a deep-seated fear or passion or even indifference. How did you get to that place? What experiences did you have that influenced your feelings and thoughts about math?

You can read my math story here. (Check it out. You might be surprised!) And please share your story in the comments section. I’d love to know how each of you feel about math and what got you there. (Sad and happy stories are welcome!)

Also, don’t forget to enter this week’s Math Treasure Hunt contest on facebook. Each week, you’ll have a chance to win a copy of my book or another cool prize. Get all of the contest details here.

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Math Awareness Month: Have you hugged your math lately?

Get it? (Photo courtesy of jin.thai)

April is a big deal here at Math for Grownups. Not only do we have new digs — how do you like the redesign? — but it’s Math Awareness Month.

I saw that. You rolled your eyes. Some of you may have even groaned a little. Don’t worry — I’m not about to go all geeky on you. (Okay, maybe just a little, but it won’t be scary.) I have just one goal for Math Awareness Month: to prove that math is indeed everywhere.

So yeah, you know this already. But what do you really notice? Time to turn on your spy eyes, because you could win a prize.

Starting Monday, April 2, I’ll be giving away a copy of Math for Grownups each and every week. (Already have a copy? You could win something else.) At the end of the month, I’ll choose one more winner from all of the entries. How can you win? Join the Math Treasure Hunt on the Math for Grownups Facebook page.

Here are all of the Math Treasure Hunt details.

But wait! There’s more! This month you’ll meet new people and learn about some really cool applications of math — all designed to help you see for yourself the role that math plays in our everyday lives. We’re going to take a break from Math at Work Monday (but it’ll be back in May!). Instead you’ll hear some folks’ math stories (and hopefully share your own), get advice from real, live math teachers (for yourself and your kids), and get the scoop on some new ways that math is making our lives easier and better (like assessing liver damage after an acetaminophen overdoses).

Want to join in? Be sure to check out the Math for Grownups Facebook page, follow me on Twitter(@mathforgrownups) and get a notice in your inbox each time a new post appears. (To do that, just fill out the little form on the right). Whether you like math or not, Math Awareness Month is for you.

Oh, and be sure to drop me a line or comment about the new blog design. I’m really excited to make things easier to find and posts easier to read.

Happy Math Awareness Month!

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Political Reporting: The “math” of delegate votes

Photo courtesy of paulinaclemente

It’s been a weird primary season. Like an exciting Preakness race, the remaining Republican candidates are still going strong, and in some ways, the candidacy is way, way up in the air. Unlike previous primaries, we’re no closer to a Republican candidate than when we started this whole thing.

And now the political pundits and reporters are touting “delegate math,” with headlines like “It’s math vs. momentum as Romney, Santorum fight on” (Baltimore Sun) and “Romney’s Delegate Math Still Adds Up” (Wall Street Journal). See, when an election gets or stays tight, estimations won’t work any longer — especially as folks wonder when one of the candidates is going to drop out. It’s important to pull out the calculators or actually look up how many Republican delegates are in play in Illinois (69, if you’re actually curious).

But in all of my reading and listening, I haven’t gotten a good break-down of the delegate math that people keep talking about. I want to know which states Romney has to win in order to clinch the nomination. I want to know which states Santorum has to win to present a credible threat. In other words, how hard would it be for Santorum to pull out a win? What about Gingrich or Paul?

Fact is, math can help clarify these complex ideas — or not.

DISCLAIMER 1: This is as good a point as any to tell you that this is not a political blog. In my rough analysis, which will not be precise, I am not making any statements about whom I want to win the primary. I am not registered with either party, and my political beliefs (which I’ll keep to myself here) don’t play into this post. Of course, those who disagree with my numbers will probably think otherwise, as they are free to do.

DISCLAIMER 2: This post was written on Tuesday, March 20, before the Illinois primary, so those results are not included here — nor, for that matter, are any results in subsequent primaries.

DISCLAIMER 3: I am not a seasoned political journalist, and I’ve done the best I can with a mini crash course on Republican delegates. I’ve fact checked myself as best I can, but to be sure, these counts vary from source to source. If you think you have better numbers, by all means let me know in the comments section. (Just remember rule No. 1: be nice.)

Anywho…

I’ve done some research on this in the hopes I could break this code and give to you straight — while demonstrating that math is indeed useful in reporting, despite the countless journalism majors who have difficulty with liberal arts math. (That’s a joke, ya’ll. Don’t get mad.)

In the process, I discovered the reasons that these projections are impossible: 1) not all delegates have to vote the way their primaries go, 2) some states have winner-takes-all primaries, where the winner of the primary gets all of the delegates, but 3) other states have proportional primaries, where each candidate gets a proportion of the delegates based on the vote.

But there still must be a way for math to help me (and others) understand where we’re headed — even if it’s just a rough sketch — right? Let’s take a look.

There are 2,286 Republican delegates, and in order to win the nomination, a candidate must earn 1,144 delegate votes.  Here’s what the candidates have right now (according to The Green Papers, a website that makes it its business to track these delegate counts):

Romney: 407 (soft*) + 515 (hard*) = 922

Santorum: 170 (soft*) + 239 (hard*) = 409

Gingrich: 133 (soft*) + 157 (hard*) = 290

Paul: 26 (soft*) + 78 (hard*) = 104

*hard delegates are allocated votes and come super-delegate votes, while the soft delegates represent proportional votes, where the primary has been held and the proportional votes are estimated but not confirmed, or are uncertain super-delegate votes

So how many more delegates must each candidate earn before they can clinch the nomination (assuming that all of the soft delegate counts will become hard delegate counts)?

Romney: 1,144 – 922 = 222 delegates

Santorum: 1,144 – 409 = 735 delegates

Gingrich: 1,144 – 290 = 834 delegates

Paul: 1,144 – 104 = 1,040 delegates

See, to me these numbers tell a much clearer picture, but some additional comparisons would help. For example, what percent of the winning delegates does each candidate have, according to these numbers?

Romney: 922 ÷ 1,144 = 81%

Santorum: 409 ÷ 1,144 = 36%

Gingrich: 290 ÷ 1,144 = 25%

Paul: 104 ÷ 1,144 = 9%

(Notice, this doesn’t mean that Romney has earned 81% of the delegate votes. It means he’s earned 81% of the delegate votes he needs to come on top at the convention. And of course by earned, I mean these delegates have been identified as likely (or definitely, depending on the state) voting for Romney at the convention.)

For weeks, we’ve heard that Romney and Santorum are running neck-in-neck. But when you look at those percentages, well, they paint a different picture. Still there’s another number that I think would really help: the percentage of remaining delegates that each candidate must win.

Let’s assume (and this is a big assumption) that there are 1,725 delegates still up for grabs and (another big assumption) that all of the soft delegate counts will become hard delegate counts, just as they are noted here.  Then the candidates would need to win these percentages of the remaining votes in order to secure the nomination.

Romney: 222 ÷ 1,725 = 13%

Santorum: 735 ÷ 1,725 = 43%

Gingrich: 834 ÷ 1,725 = 48%

Paul: 1,040 ÷ 1,725 = 60%

There’s a huge difference between 13% and 43%. I’m not saying that it can’t be done. But with these numbers, this doesn’t look like a close race any longer.

I’m not saying that these are the be-all, end-all numbers that should be used to describe the Republican primary. But I am saying that math can help us understand where the candidates stand. And we absolutely should not depend on the candidates themselves to give us this analysis. Instead, journalists should be spending time with a pencil, paper and calculator (or a spreadsheet) — and some reliable sources — to figure these things out for their readers.

Any thoughts on how the math has been used in reporting this political race? Share them in the comments section.

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Using Math to Predict Hurricanes

Okay, I’ll admit it. I don’t typically watch television news. (Sorry Tony!) But when bad weather comes along,  seeing those weather maps is often exactly what I’m looking for.

I lived in a hurricane prone area for 15 years, weathering (eh-hem) many a storm and getting through some close misses. When you see that many big storms, you get used to the terminology (like storm surge) and develop a false confidence in your own ability to predict what’s coming.

But as you know, a gut feeling isn’t enough. In fact, meteorologists use a complex system of previous data and what they know about how these storms act to make predictions. What they’re saying, though, is that there is a chance something will happen. And what is that based on? Probability and statistics.