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In Math for Grownups

Decoding Geeky T-Shirts, Episode 1

We’ve all seen them. Mathy t-shirts, mugs and social media graphics that offer a fun phrase for those who can decode the message. But have these ever made you feel a little, well, not so mathy? Me too.So let’s unlock the mysteries of these inside jokes.

I’ve gathered a few of the most common t-shirts featuring math symbols. One by one, I’ll interpret them for you. Of course if you have any ideas to share, feel free. And if you disagree with my analysis, by all means, let me know!

Here’s to feeling much smarter.

Math is fun!

We’ll start with a doozy and break it down bit by bit.

M = M One of the shortcuts that these t-shirts take is simply inserting letters as variables. Or you could make an argument that the M in this example stands for mass.

This one took me a few moments to figure out. It’s based on the Pythagorean Theorem — solving for a. Here’s a quick rundown:

This is the Ideal Gas Law, which I know nothing about. But there’s some algebra to get from the law itself to this representation.

H = H Seems to me that this is simply the variable H, which could stand for just about anything. (If you have another suggestion, let me know in the comments section.)

I love this one! You may remember that you cannot take the square root of a negative number. And then you may remember that there is a very special number for the square root of -1. That number is the imaginary number — or i. It’s crazy to think that we can have imaginary numbers, but there you have it. It was important enough to create a whole new system of numbers so that we could deal with the square root of -1. (And yet, we still can’t divide by zero!)

If you were a Greek during college or remember a little bit of your Algebra II class, you’ll remember that this symbol is the Greek letter sigma. It’s used to denote summations — not the legal kind; the math kind. When you want to find the sum of a set of numbers, you can indicate it by using the letter sigma.

The last clue is a little bit of a fudge, I think. First the f and parentheses. In math-speak this represents a function, and you probably remember seeing it written like this: f(x). In this form, it means a function in terms of x. But — and here comes the not-so-accurate part, in my opinion — u raised to the nthpower is not something you would see in function notation. And u raised to the nth power doesn’t really translate to –un.

And that’s how you get “math is fun” from all of those symbols. Not too bad, eh? Next time, we’ll have some pie!

In Current Events

Common Core Common Sense: Myths About the Standards, Part 1

In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the first in that series, which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #1: Common Core is a Curriculum

This is perhaps the most pervasive misunderstanding. In fact, the Common Core Standards are simply that: standards. In education-speak, this means they are statements of what students should know, upon completing a course or grade. Common Core does something a bit more than other sets of standards, giving a clear expectation of the depth of this understanding. Compare these fifth-grade math standards, one from Virginia’s Standards of Learning (SOL) and it’s corresponding objective from Common Core:

SOL: The student will describe the relationship found in a number pattern and express the relationship.
Common Core: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

The Common Core Standard isn’t just longer — it expresses much more depth. Students begin to pay attention to the relationships between numerical expressions, algebraic expressions and graphing. The goal is for students to know that these number patterns can be shown in a variety of different ways. And that’s a pretty big deal when students get into more complex algebra.

But here’s the thing: How students are taught is left completely to school districts and/or states. Some select ready-made curriculum, like Everyday Mathematics. Others opt to develop their own curriculum, which is exactly what my daughter’s middle school did.

Certainly, curriculum development companies have leapt on the opportunity to create new lessons, textbooks, activities and online components that correspond with Common Core. That’s capitalism at work in our country. (And it’s fed my bottom line quite well over the last three years. I’ve turned away more work this summer than I was able to accept.) There is nothing in the Common Core that dictates which curriculum must adopt, however. Localities still have control over that decision and process.

This is not to say that the Common Core hasn’t forced some pretty major changes in how mathematics is taught. Under these standards, students are encouraged to discover mathematical concepts, rather than be told how math works or should be understood. For traditionalists this could be a bad change. Yet, I believe that a discovery-based approach helps students conceptualize mathematics, which gives them a much better chance at developing strong numeracy than those who learn merely by rote. More on that in a later myth.

But regardless of what you think of the standards themselves, it’s important to know that they are merely a guideline for teachers and schools. Just like state educational standards — and each state has them — Common Core is merely outlining what the students should know, once they’ve mastered the material. Now how states and districts choose to measure students’ understanding of the standards is a different story — and a completely separate discussion of the standards themselves.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it!

In Algebra

Finding the Funny in Algebra

So the person who inspired this series on Algebra is my dear friend Michele “Wojo” Wojciechowski – a very funny writer and stand-up comic. In her honor, I thought I’d wrap things up with a post looking at the humorous side of algebra.

When something makes us uncomfortable, we make fun of it. I mean, why not, right? As a first-year teacher, I remember giving a geometry test, on which I asked students to define space. One student wrote: “The final frontier.” And I have to admit that I laughed.

So, whether or not I’ve convinced you that algebra is a useful, everyday skill, at least join me in a little laughter today. And be sure to come back next week, when we start celebrating National Math Awareness Month. (The excitement never ends, does it?)

These next two are great for math teachers, as they demonstrate very common errors that students make.

You have to be a Harry Potter geek to get the next one:

Happy weekend, everyone! Use some algebra and make the world a better place.

Got any math jokes? Feel free to share them in the comments section.

In Algebra

Building Formulas: Spreadsheets, algebra and guest lists

The classic answer to the question, “When am I going to use algebra?” is spreadsheets. Now I will admit straight up — I am a spreadsheet junkie. I’ll build one for just about anything, from menu planning to blog schedules to tracking which clients have sent me 1099s. And I know for a fact that this attraction to spreadsheets is not normal. I promise, I will not try to convince you that spreadsheets are the be-all-end-all (though I think they are) or that using a spreadsheet will make your life easier (though it could).

But there’s no denying one important thing: algebra is extremely useful in spreadsheets. And that’s because the power of a spreadsheet is in its ability to crunch numbers for you.

In fact, algebra teachers are using spreadsheets to help students better understand algebra and its real-world uses. Want to see how data is related? Use a spreadsheet to create a line of best fit. Want to find an average quickly? Spreadsheet. Want to know how many children and adults you’ve invited to your wedding? Open up Excel or Numbers or OpenOffice Spreadsheets.

(Yes, we’re back to the wedding. It’s consuming my life right now, so you get to play, too.)

When it came time for me to create the guest list for my wedding — undeniably the most painful part of this entire experience — I naturally reached for good-old Excel. Once I had everyone entered into a spreadsheet, I was able to create a variety of formulas that have helped me manage certain tasks. Here’s an example.

Our reception venue, which also provides the catering, offers a much lower rate for children. They’re getting chicken tenders, rather than the fancy-schmancy meal, so that’s only fair. But there are a lot of kids on our list, and I needed to get a rough estimate of what we would pay. This way, I could make really good decisions about who we could and could not invite. (Told you, this part was really painful.)

Each family, couple or person was listed in one row of the spreadsheet. In two of the columns for each row, I included the number of adults and kids who were invited.

Ann Laing	2		2
Melissa Zach	2	4	6
Drew Laing	2		2
Graham Laing	2		2

So you can see that my sister, Melissa, has 4 children under 16 years old, while my mother and two brothers don’t have any. But each of their families has 2 adults. The column all the way to the right is the total people in their families who are invited. In fact, I used a very simple formula to find the last column: =SUM(B2:C2). This means, “Take the sum of the values in columns B2 through C2.” The formula allows me to make changes to the values in columns B2 through C2 and automatically update the last column.

But that’s not really where the algebra comes in. At the bottom of my spreadsheet, I use the SUM formula to total the number of kids and the number of adults. Then I use those values to find the cost of the reception food, using a formula I built. Here’s how that worked.

Let’s say I’ve invited 15 kids and 100 adults. I’ve let my spreadsheet automatically find those totals in cells B101 and C101. And let’s say that the cost per adult is $50 and the cost per child is $25. Algebra will help me create a formula based on the cells where this data is found.

=((B101*50)+(C101*25))

Looks ugly, right? Well, that’s because the spreadsheet needs some extra formatting to recognize the formula. But there’s a simpler way to show this:

y = 50a + 25k

In other words the total cost for the food (y) is equal to 50 times the number of adults (a) plus 25 times the number of kids (k). Algebra at work in the real world of wedding planning.

My job today is not to explain the algebra to you step by step. But I did want to demonstrate one really useful — and somewhat common — way that a regular person uses algebra in their regular life. (Okay, so maybe I’m not regular, but hopefully you get my drift.)

Do you use spreadsheets? What formulas have been useful to you in your spreadsheets? Did you think of that as algebra? Why or why not? Share your thoughts in the comments section.

In Algebra

Say “I Do” to Algebra: Using math to plan a wedding

There must be a special circle of hell for those of us planning our weddings and receptions. I know this first-hand, because I’m planning my own nuptials for this summer, and I’m about to pull my hair out. (No wait! If I do that, I’ll ruin my opportunity for the perfect up-do!)

Weddings are magical events, filled with joy and love. They’re also damned expensive. Crazy costly. The average wedding in my neck of the woods costs about $25,000. Sure, couples can opt for a family BBQ or a quiet ceremony in a public park. But when you’ve waited as long as I have — I’m 45 years old — there’s no backyard large enough for everyone who wants to be there.

And that’s the variable that matters in wedding planning — the number of guests. The smaller the guest list, the smaller the budget. When the guest list grows, you can expect to shell out a lot more. That’s because the biggest cost of a wedding is the reception — unless you’ve got your heart set on the latest gown to walk the runway in Paris.

If you’re like me, there’s some flexibility in this list. Children or no children? Cousins or just immediate family? What about college friends you haven’t seen in years or office mates? All of these decisions have a direct affect on your bottom line. And this is where the algebra comes in.

Many reception venues follow a simple formula: a flat rental fee, plus a per-person rate. If the number of guests is the variable, you can easily set up an equation to help you settle on the number of people you can afford to attend the reception. Here’s an example.

Let’s say that the venue you’re considering has a flat rental fee of $3,000. In addition, there’s a $75 per person rate to cover food and drinks. (Of course, this rate depends on the menu chosen, plus other add ons, like upgraded linens, top-shelf liquors, etc.) Basically, you need to multiply the per-person rate by the number of people invited and then add the flat fee. In other words:

In this equation, y is the total cost of the reception venue, and x is the number of guests. Break it down, if you’re confused: The total cost of the reception venue is $75 times the number of guests, plus $3,000.

But why take the time to write an equation? Well, this allows you to play with the number of guests or your total budget. For example, if you know you want to invite between 150 and 200 people, you can come up with a range for your budget:

In this scenario, you can expect to pay between $14,250 and $18,000, depending on your final number.

More likely, you know your budget and want to find out the maximum number of people who can attend the wedding. For example, if your budget for the reception venue is $15,000, how many people can you invite?

With a budget of $15,000, you’ve got a guest list of 160 people.

The beauty of creating an equation to help in this problem is that you can play around with the numbers. Once you have the equation, you can try different things, without thinking too hard. And if you’re comparing the costs of several venues or several packages at one venue, you can create several — very similar — equations, one for each option.

I get it. Most brides and grooms aren’t going to take this step. Who wants to do math when planning one of the most magical days of their lives? But this is a clear example of how algebra can reduce the stress of planning a wedding — and possibly save you some cash.

So what do you think? Have I convinced you that algebra can be useful? Share your thoughts in the comments section. And how have you saved money in planning your wedding? Did math help at all? Dig deep and be honest!

In Algebra

It’s Not Tomato Season Yet, But You Still Need Algebra

So I’ve been harping on the fact that math is flexible. And I’ve also said more than once that we do the math that we need to do. (No one here is suggesting that calculus computations are necessary for everyday life.) In fact, because of those first two facts, we often don’t need to write down literal equations at all – we might not even know we’re using a formula.

Here’s an example: Let’s say you need to build a fence around your tomato plants. If you know that the bed is 4 feet by 2 feet, how much fencing do you need? (Yes, I’m ready for spring and summer and fresh veggies. Will this cold weather ever end??)

This is a perimeter problem. Some of you might write down the formula for perimeter of a rectangle: P = 2l + 2w. But I’d be willing to bet that most of us simply add: 4 + 2 + 4 + 2 = 12 feet. No formula needed, right?

But what if we turn the problem on its head? Let say you have 12 feet of fencing, and you’re building a tomato plant bed that must be no longer than 4 feet. How wide can the bed be?

Again, there are tons and tons of ways to approach this problem. One is with literal equations. What do you know about the information you have? The perimeter and the length. What are you solving for? The width.

P = 2l + 2w

The object of the game is to solve the formula for w, in terms of P and l. (Stay with me here. I promise this is easier than that previous sentence made it sound.) To do that, you need to get w by itself on one side of the equation. This is where the algebra comes in.

The most important rule about solving algebraic equations is this: Whatever you do to one side of the equation, you must do to the other. Period. End of Sentence. Amen. Shalom. To do that, you need to undo the operations. It’s like taking something apart. Here’s how it works:

Don’t panic! This is not as messy as it looks. All you need to do now is substitute what you already know, use the order of operations to simplify, and you’ll have w.

So the width of the tomato bed must be 2 feet. My point is not that you must always solve a problem like this one in this way. Nuh-uh. My point is that there’s algebra behind this problem – no matter how you solve it. And whether you like it or not.

How would you have solved this perimeter problem? See if you can spot the algebra in your approach. And share in the comments section.

I am so pleased to be Meagan Francis‘s guest this month on The Kitchen Hour, her 45-minute podcast for parents on the go. We talk about math anxiety, math education and how to encourage our kids to embrace math — while overcoming our own fears. Listen and/or download the podcast at The Kitchen Hour.

In Algebra

Using Algebra – Literally

Parks and Recreation, the Amy Poeler-driven mocumentary on NBC about a small-town parks department, features a tightly wound character, Chris Traeger, whose favorite word is literally – as in: “Biking for charity is literally one of my interests on Facebook.” It’s funny because it makes us grammar fanatics crazy. Literally is literally one of the most misused and/or overused words in the U.S.

I had never seen the word applied to mathematics until recently. No kidding! That’s when I learned about literal equations. I mean, I already knew about them; I just didn’t know what they were called. And yes, you know about them too. They’re one of the ways that we use algebra in our everyday lives – without even knowing it.

Literal equations are equations with more than one variable. Ta-da! See, you knew about them, too. Here are some examples, in case you’re not convinced:

Look at all of those variables. Each equation has more than one, which means that each of the above is a literal equation. That’s it. Easy.

Now, the algebra of literal equations is much, much easier than most mathematics, especially if the equation is simple, like the distance formula. (Don’t panic. This is not one of those train-leaving-Pasadena questions.) The algebra is in identifying the variables, substituting into the equation and then solving.

Let’s say that you’re an avid cyclist. In fact, you’ve got all the cool accouterments, like a gel-padded seat, clip-on pedals and a speedometer. You average about 16 miles per hour on flat roads, and you love trying out new routes, just riding where your bike takes you. But it’s critical that you know the half-way mark for most of your routes – otherwise, you won’t have enough steam to get back home.

That’s where the distance formula can come in. If you know your speed (or rate, r) and the time you’ve been out, you can find the distance. This way, you know when to turn around and head back to enjoy those endorphins.

One gorgeous Saturday morning in March, you head out on an unfamiliar route, cruising at about 16 miles per hour. Checking your watch, you find that you’ve been on your bike for half an hour. How far have you traveled? You can actually do this math in your head – just multiply 16 by 0.5. How do I know this? With the literal equation d = rt.

See? You just used a literal equation. And you did it on your bike. As Chris Traeger would say, “You are literally the most impressive cyclist I know.”

How have you used literal equations recently? Want to share in the comments section? Feel free. Also, feel free to challenge my thesis that algebra is an important part of a solid middle and high school education. I can take it. Really.

In Algebra

Coloring Inside the Lines: How algebra helps

Math is black-and-white, with right-or-wrong answers. It’s hard to color outside the lines in math.

While I often argue with this point, there is some truth to it. Just like grammar, chemistry and baking, math is a pretty precise subject matter. Sure, there are many different ways to add 24 and 37 in your head, but fact is, you can’t just decided that the answer is –19, right?

Rules make math work. And algebra helps us write down these rules. Now, we don’t necessarily need to think of math rules in this way, but believe me, when teaching and writing about math, it sure does help. And there are some real-world situations when an equation can really help make math easier.

Let’s consider the process for multiplying fractions. Do you remember what it is? Take a look at this problem, and see if you can figure it out:

Of course there are several ways to describe what is happening above, right? You can do it in plain English:

To multiply two fractions, multiply the numerators and multiply the denominators.

Or, you can write this using algebra. This is not as hard as you might think! First, assign a variable to each of the unique numbers on the left side of the equation:

a = first numerator

b = first denominator

c = second numerator

d = second denominator

Then substitute those variables for the numbers themselves:

Now, perform the rule that was described in plain English above: multiply the numerators and multiply the denominators.

How about that! Lickity split, we made like mathematicians and created a rule described algebraically. How hard was that really?

Now you can use this rule to multiply any fractions of any kind. I don’t care if they’re elementary fractions made up of just numbers or if they’re fancy-schmancy algebraic functions that have — gasp! — variables in them. You don’t even have to think of the a, b, c or d. Instead, think of those variables as place holders. (Hint: this is where your mind can be really flexible, even though the rule is not.)

Because you know this rule, you can solve this problem (even with the x and the y). Just multiply the numerators and then multiply the denominators.

Because of the rule for multiplying fractions — which includes the variables a, b, c and d — you can see how to multiply any fractions. That’s where the algebra comes in handy.

Now, I know exactly what you’re thinking. When will I ever need to solve a problem like the one above. And here’s my honest answer: for most of you, never. Really and truly. I won’t lie.

However, there are times when creating a rule for a specific real-word problem is very useful. That’s when we might create an equation. Stay tuned, when we’ll talk wedding receptions, guest lists, the price per person and rental fees.

So what do you think of algebra and math rules? Did this example help you understand how algebra is important in developing and stating these rules? Do you disagree with me about why this is important? I can take it — so please do share your thoughts in the comments section.

In Algebra

Numbers and Letters Together: What is algebra?

A Math for Grownups follower asked me earlier this week to define algebra, and I thought that was an excellent place to start this month-long discussion. I think that most people might be surprised by what is generally found under the algebra tent. The basic definition is pretty broad:

Algebra is a branch of mathematics that uses letters and other symbols to represent numbers and quantities in formulas and equations. This system is based on a given set of axioms.

What does this mean? Well, it’s basically the step beyond arithmetic, where we only deal with numbers. Algebra allows us the flexibility of an unknown — the variable — so that we can make broader statements about situations.

Look at it this way: 8 + 3 is always 11. Always. But 8 + x depends on the value of x. This means we can pretty much substitute whatever we want for x. See? Flexibility. (Of course 8 + x has no meaning without some kind of context. But we’ll get to that later in the month.)

Algebra allows us to discover and create rules. These rules might be formulas or equations that describe a particular situation. Because of algebra, we know that the circumference of a circle is 2πr, where π is the number 3.14… and r is the radius of that circle.

Now, let’s take this definition one step further. What is the circumference of a circle with radius 1?

C = 2πr = 2π(1) = 2π

But what about the circumference of a circle with radius 2?

C = 2πr = 2π(2) = 4π

If you look closely at this, you can draw a conclusion: The larger the radius of a circle, the larger its circumference. When the radius is 1, the circumference is 2π; when the radius is twice as long, the circumference is twice as big.

This points to a critical aspect of algebra: relationships.

Algebra is a branch of mathematics that deals with general statements about the relationships between values, using numbers and variables to describe them.

The formula for the circumference of a circle is a description of the relationship between the circumference and the radius of any circle. When the radius changes, so does the circumference. When the circumference changes, so does the radius. (π is a constant, even though it is technically a Greek letter. Whenever you see π, you know you’re dealing with the number 3.14…)

So that’s it. Algebra is nothing more than a way to describe the relationships between values (numbers, measurements, etc.). In the example of circumference, we’re dealing with two branches of math. The geometry describes why the circumference is twice π times the radius. The algebra is how we describe that relationship in the form of a formula.

Without algebra, we really don’t have ways to describe many things about our lives — from geometry formulas to finding compound interest on a loan. We can fumble around and come to a conclusion, but in the end, algebra can make this process much simpler.

What do you think about these definitions of algebra? Does thinking about algebra in these ways make it a little less threatening? If so, how? Share your ideas in the comments section!

In Math Education

Pre-Algebra on Facebook: How Mark Zuckerberg helped a frustrated parent

Wednesday on Facebook, I had the most amazing experience. Suffering from an all-day migraine, I had spent the afternoon bored out of my mind, obsessively checking Facebook while the television droned in the background. At one point, this status update from my friend Alyson appeared in my feed:

ALGEBRAAAAAAAAAAAAAAAAAAA!!! (Shaking fist angrily in air at math gods)

I was Batman and here was the bat signal. How could I help?

The first response was from someone I didn’t know and very typical: “Outside of college, you don’t really need it, right?” I rolled my eyes inwardly and thought about why Alyson might need to solve an algebra problem. Then I remembered her incredibly bright son, who is completely enamored with computers. I mean in love with the machines. I’d bet my last dollar that the boy will find himself programming or engineering or something in STEM as an adult. In other words, he would need algebra.

I posted a few questions to see how I could help, and eventually Alyson posted the original equation to solve:

Whew! It is a doozy, right? Alyson had one very specific question: how to handle the last term of the equation: . I told her the simple answer — that it was the same thing as . Still a teacher at heart, I wanted to see what she could do with that information. Was it enough to help her solve the problem?

Meanwhile lots of other people were chiming in, and Alyson was expressing lots of feelings:

And just so everyone knows, I suck at fractions. Always have, always will. When I took SAT and ACT and whatever else, I literally turned all fractions into decimals because I can never remember how to add, subtract, divide, multiply, etc. fractions.
I’m close to crying…I still don’t understand what you’re saying. He worked the whole thing out at got what my online algebra check thing says is a wrong answer, and I’m trying to work it out so I can figure out how to get the RIGHT answer and I really do think I’m going to cry…
Frustration cry. Because I didn’t think I’d ever use math. And I was wrong. For the record. Sorry, Mrs. Blankenship.

This is a super smart lady. She edits college-level courses of all kinds, and she’s had a successful freelance writing career for many years. And I can completely identify with her frustration. I’d been struggling with Venn diagrams and conditional statements all day. No wonder I had a migrane.

But then something really amazing happened. Really amazing. A mutual facebook friend and writer, Jody (owner of Charlotte on the Cheap) tagged us both in her status update:

Do I have it right? Do I?

She had attached this photo:

At 6:15 on a Wednesday evening, she had not only worked out a challenging pre-algebra problem but also taken the time to scan it and post on Facebook. She was so excited. And, yes, she had gotten the correct answer.

She had also done it differently than I did. But that’s not even the best part. Alyson saw Jody’s process and looked carefully — very carefully. She posted this:

I worked through it on my own twice using your strategy, which ended up making a lot of sense to me once I talked it out a few times. So now I can explain it to [my son] and actually have a clue what I’m talking about. THANK YOU.

Within an hour, another of Alyson’s friends had posted one more way to do the problem. It was a smorgasbord of solutions!

But here’s the very best part: with all of these threads, there were very few people chiming in to say that they were too dumb to help or “who cares?” In fact, I saw many more people posting things like this:

This I can do. Proof reading for grammar errors…….not so much!
I will be glad to do some algebra when the time comes.
I love math, call me, text me pictures!!!! I will PM you my number.
Why WHY WHY are you having an algebra party without ME?! I love me some equations!

It wasn’t a complete love-fest, but it was worlds different than I’m used to seeing. The tenor of the discussion was supportive and positive, rather than defeated. Sure, there’s was lots of frustration. And I’m betting that there were lots of people reading the threads and thinking, “Good god, I’m going to be in BIG trouble when my kid takes algebra.” But what played out in the end was a good experience — not just getting the right answer but learning different ways to approach the problem.

I originally became a math teacher because I was convinced of two things: math is important and anyone can do math. For years, I’ve felt pretty alone in those two estimations — especially after leaving the classroom. Yet, here was a community of people who were working from the same premise, encouraging Alyson and excitedly trying out the problem themselves.

I can’t think of a better way to end Back-to-School month at Math for Grownups. If you parents can express this enthusiasm — along with your frustration, if you have any — you’ll be doing your kids a big favor. It’s the pushing through and looking for ways to understand things differently that makes a difference. Imagine how much more empowered and confident our kids will feel if they get the message that math is important and that they can do it.

What positive messages about math have you seen lately? Have you found ways to be more encouraging about math with your own kids? Share your thoughts in the comments section.

In Math Education

Algebra: Is It Too Hard for Students?

Earlier this week, Andrew Hacker, a political science professor at Queens College, City University of New York, opined in an essay for the New York Times that high schools should stop teaching higher Algebra concepts — because kids don’t get it.

I’m sure Mr. Hacker isn’t alone in his frustration with the failure rates of students in these courses. (Trust me, math teachers are pulling their hair out, too.) Yes, math is hard. And it’s also the underpinning of our physical world. By pretending it doesn’t matter or that our future engineers, teachers, nurses, bakers and car mechanics don’t need it one eensy-teensy bit, we risk the dumbing down of our culture. And our students risk losing out on the highest-paying careers and opportunities.

The problem isn’t the math — as Mr. Hacker eventually mentions, though obliquely. It’s how the math is taught. We need to get a handle on why students feel so lost and confused. And here are just two reasons for this.

1. Kids don’t know what they want to be when they grow up — especially girls who end up in math or science fields.

When I was in seventh grade, I thought I was a horrible math student. I was beaten down and frustrated. I felt stupid and turned around. Unlike my peers, I took pre-algebra in eighth grade, effectively determining the math courses I would take throughout high school. (I wasn’t able to take Calculus before graduating.)

And that was a fine thing for me to do. Turns out I wasn’t stupid or bad at math. I just had a poor understanding of what it meant to be good at math. I had really talented math teachers throughout high school. I was inspired and challenged and encouraged. By the time I was a senior, it was too late to take Calculus, so instead I doubled up with two math courses that year.

After graduation, I enrolled in a terrific state school and became a math major. Four years later, I graduated with a degree in math education and a certification to teach high school. And now, 22 years later, my job revolves around convincing people that math is not the enemy.

What if I had been told that algebra didn’t matter? What if I had been shepherded into a more basic math course or track? Because higher level math courses were expected of me — and because I had excellent math teachers — I found my way to a career that I love. Even better, I feel like I make a difference.

How many other engineers, scientists, teachers, statisticians and more have had similar experiences? How many of us are doing what we thought we wanted to do when we were 12 years old? Why close the door to discovering where our talents are? To me, that’s not what education is all about.

Look, I can’t say this enough: I was an ordinary girl with an ordinary brain. I can do math because I convinced myself that it was important enough to take on the challenge. I was no different than most students out there today. We grownups need to figure out ways to hook our kids into math topics. I’m living proof that this works.

2. Higher algebra concepts describe how our world works.

How does a curveball trick the batter? How much money can you expect to have in your investment account after three years? What is compound interest?

Students need to better understand the math in their own worlds. We do them a grave disservice when we give them problem after problem that merely asks them to practice solving for x. The variable matters when the problem is applied to something important — a mortgage, a grocery bill, the weather, a challenging soccer play.

We can’t pretend that everyone depends on higher-level mathematics in their everyday lives. But neither can we pretend that these concepts are immaterial. Knowing some basics about algebra is critical to being able to manage our money or really get into a sports game.

For example, when the kicker attempts a field goal in an American football game, he is depending on conic sections — specifically parabolas. Does he need to solve an equation that determines the best place for his toes to meet the ball in order to score? Nope. But is it important for him to know that the path of the ball will be a curve, and that the lowest points will be at the points where he makes contact with the ball and where the ball hits the ground.

That’s upper-level algebra at work. If you were to put the path of the football on a graph, making the ground the x-axis, those two points are where the curve crosses or meets that axis.

What’s so hard about that?

Look, we need to adjust the ways we teach math and assess math teachers. I agree that math test scores aren’t the be all, end all. I agree that most high school students won’t be expected to use the quadratic formula outside of their alma mater. (Though algebra sure is useful with spreadsheets!) And I agree that asking teachers to merely teach the concepts — without appealing to students’ understanding of how these concepts apply to their everyday lives — is draining the life out of education.

And really, how much of the rest of our educational system is directly useful? Do I need to spout out the 13 causes of the Civil War or balance a chemical equation or recite MacBeth’s monologue? (“Tomorrow, and tomorrow, and tomorrow, Creeps in this petty pace from day to day…”) I can say with no hesitation: Nope! But learning those facts helped inform my understanding of the world. Algebra is no different.

What do you think about the New York Times piece? Do you agree that we should drop algebra as a required course? In your opinion, what could schools do differently to help students understand or apply algebra better?

In Math for Parents

Allergic to Algebra? Use these resources

One of the complaints I’ve heard about Math for Grownupsis that it only covers basic math. And I’m not apologetic about that. The whole point of the book is to make basic math a little less mysterious and a little more practical.

But there may be times when you need an Algebra II refresher or review of basic calculus facts. If we don’t use this stuff we lose it.

Throughout the years, I’ve discovered a few really wonderful websites that offer just this kind of assistance. From explaining basic math in theoretic terms (which may be necessary to help our kids with their middle school math homework) to reviewing more complex math topics, these sites are really wonderful. When you need a little more than the basics, I recommend taking a look.

The Math Forum @ Drexel University

This site offers a wide variety of resources for parents, teachers and students. But the part I love the most is Ask Dr Math. Hundreds of college professors answer math-related questions from students, teachers and parents around the world. These responses are archived in a searchable database. Plus there are broad categories to browse, like Formulas and Middle School.

Purplemath

This site is devoted to algebra–from absolute value to solving systems of linear equations. Students (and parents) can skim lessons for quick answers or read them carefully for more in-depth review of the topics. You can also post a question in the forums and receive a thoughtful response that invites you to think critically or refers you back to the lessons themselves. (There are no quick answers here!)

Mathwords

Have you forgotten what a Cartesian plane is? Are you wracking your brain trying to remember why the y-intercept is a big deal? Mathwords offers definitions for thousands of math terms. There are no examples or explanations here, but sometimes knowing a definition is enough to jog the old synapses. Right?

Do you have any favorite math resources? Share them in the comments section!