Math for Grownups

Author: Math Expert

Math at Work Monday: Stephen the Realtor

When we moved to Baltimore almost seven years ago, my family and I found amazing friends in our next-door neighbor Stephen Sattler and his partner Neil. So, it is really no surprise that Stephen has now found his calling as a Realtor, working primarily with relocation. Here’s how Stephen uses math in his work.

Can you explain what you do for a living?

Basically, I help my clients find shelter–which includes the buying, renting, selling, and ferreting out of places to live, after listening and then understanding what they’re trying to tell me.

When do you use basic math in your job?

The whole idea of proration is key to the real estate industry. At the settlement table, the property’s monthly taxes, utilities, interest, and other financial considerations must be equitably split between both buyer and seller, as of that date. The same thing holds true if you’re renting a house, especially if you’re beginning your term in the middle of a month. Leases typically call for a yearly total of rent due, which means you just multiply the monthly rent by twelve. But calculating the first month’s rent can be tricky if you don’t know how to calculate the daily rate. It sounds complicated, but all you have to do is divide the yearly rent by 365. Then you can multiply that by the days left in the month.

Stephen Sattler

Do you use any technology to help with this math?

I do have a fancy real estate calculator that helps with the more complex things like finding a monthly amortization amount at a given interest rate over a set period of time, but for the most part I hand-calculate the math I tend to use from day to day.

How do you think math helps you do your job better?

I wouldn’t really have a job unless I could apply math at its most basic levels: settlement costs are a typically a set percentage of the sales price, prorated bills are due as of the date the property is transferred, and my income is always a percentage of the total sales price–which can change at each and every transaction. I feel like I’m always taking quick, armchair calculations to figure out where things generally stand at the end of any given week.

How comfortable with math do you feel?

I was one of those students in school who tended to excel more in the creative arts–writing, languages, history, and the like. I have horrible memories of feeling I was the last person in math or science class to even generally grasp the problem being discussed, from algebra to geometry to even basic chemistry. I don’t think I ever quite figured out how to balance a chemistry equation!

I turned 50 this year, which meant I could finally let go of what hasn’t worked for me in the past. With GMATs and all the other truly stressful mathematical events I’ve had in my life, I was convinced that my brain just wasn’t wired the right way, or that I even had some sort of math disability. Put me in a job I absolutely love, however, and help me see how math can help my clients find and then settle into the home of their dreams, and I’m astonished at how mathematically competent I now feel!

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I took everything mathematical a good properly-educated, college-bound boy was supposed to take, but my God was it absolute torture. There were so many rules to understand and follow, and you couldn’t really reason or write your way out of a problem–like you could in an essay question in, say, English class–unless you knew how to manipulate the underlying mathematical formulae (which of course my feeble brain could barely even understand let alone memorize and apply). It also didn’t help that all the math teachers at my school seemed to double as coaches for various sports teams in their after-school lives, and using the same motivational threats they used on the field (Yo– what the &*^%$ were you #@!) thinking!) didn’t quite have the same result in the classroom with those of us who were not quite as macho about math.

Did you have to learn new skills in order to do the math you use in your job?

Actually, successfully using math as much as I do now in my everyday job has finally helped me feel I’m not the complete and utter dolt I always thought I was when it came to dealing with figures.

Do you have questions for Stephen about the math of real estate? Please ask them in the comments section. He can responded there or I’ll write another post addressing more complex issues.

May 14, 2012
The Real Cost of Car Ownership

Earlier this week, we took a look at one of the big personal finance decisions out there–buying a car. But the price of the vehicle alone isn’t the only consideration. Unlike a blender or sofa, your shiny new mode of transportation will tap your budget year round. But by how much?

Generally speaking, car ownership involves four additional costs: fuel, maintenance, insurance and taxes. (Some states and municipalities don’t have a property tax on vehicles, so you might be off the hook for that last one.) Problem is, these costs aren’t like your mortgage or cable bill. They can be hard to predict and aren’t due at the same time each month.

So how can you plan for these? Well, just like any other irregular or unexpected costs, it’s a good idea to put something away each month for car expenses. The trick is figuring out how much you’ll need. Let’s start by estimating the annual costs for each of these items.

Fill ‘er up

With gas prices rising and falling like the barometric pressure on a spring day, budgeting for fuel sure ain’t easy. But you can get a rough idea of what to expect, and then tweak that amount as the year goes on.

You’ll need to consider several variables for this one: the miles you travel in a given year, your vehicle’s miles per gallon, and the cost of gas where you live. This is going to be an estimate, of course. Unless you’ve got a wicked crystal ball, you won’t be able to predict any of this for sure–but you can get close.

If you’ve been keeping records of your miles traveled, you can take a look at the previous year to predict this number. Of course if you’re like me, those records don’t exist. So figure out a rough estimate based on your commute (if you have one), annual trips and even carpool. You should add on for errands and other around-town trips. For reference, the U.S. Department of Transportation estimates that on average, Americans drive 13,476 miles per year.

Now calculate the amount of gas you will likely consume. Let’s say your car gets 32 miles per gallon, and you expect to drive 14,500 miles this year. To find out how many gallons of gas you’ll use, divide:

14,500 ÷ 32 = 453.125 gallons

And the last part is simple: multiply this number by the cost of gas per gallon. In my area, we’re averaging about $3.85 per gallon, so for the sake of this example, let’s use that number.

453.125 • 3.85 = 1,744.53

The annual cost of gas for this fictional vehicle is estimated at $1,744.53.

Maintenance and Repairs

While maintenance can be pretty predictable, repairs are something that you can’t foresee–just like you didn’t see that light pole behind you in the Giant parking lot. But you can budget for these.

Again, if you keep good maintenance records, you can review these to see what you have paid in past years. Your mechanic may have these on file, as well. Remember, most maintenance is based on the number of miles driven, so if you add a long commute, you can expect these costs to rise. The kind of car you drive also matters. And of course, older cars will likely require more maintenance and repair.

If you haven’t tracked these expenses, you will probably have to make a good guess. Ask your dealer or mechanic about this. Or start with $2,000 per year and see what you have left over in December.

Whatever you do, don’t forget your Emergency Fund. This is where you’re big, unexpected repair costs will come from, like an accident that isn’t covered by insurance.

Speaking of Insurance

If you’re driving in the good old U. S. of A. and you don’t have “Farm Vehicle” stamped on the bumper of your truck, you will need to pay insurance. Again, this is a cost that depends on several variables, including your age, your driving record, and much more. But once you choose your insurance policy, that number will be set in stone, as long as you keep your driving record squeaky clean.

The Tax Man

Some states (and some municipalities) require personal property taxes on vehicles. Problem is, these payments are not usually monthly. Sometimes they are only charged annually, and in some places, residents pay these taxes quarterly.

To budget for taxes, take a look at what you paid last year. Or look up a property tax calculator for your state.

Month by Month

Let’s say you’ve found all of these annual costs. Now it’s time break them down, so that you can put away some cash each month.

Fuel = $1,744.53 per year

Maintenance = $2,000 per year

Insurance = $1,566 per year

Taxes = $2,867 per year

First add these to find your total annual costs:

1,744.53 + 2,000 + 1,566 + 2,867 = $8,177.53

Now divide this total by 12 to get your estimated monthly costs.

8,177.53 ÷ 12 = $681.46

So, based on this fictional numbers, socking away $682.46 for car expenses should cover the annual cost of owning and maintaining this fictional car. (Your milage may vary.)

Do you have any tricks for covering these unpredictable costs? Share your ideas or questions in the comment section.

May 11, 2012
Dealership or Want Ads: Deciding between a new or used car

When you’re looking at your personal finances, the big expenses stand out. That means purchasing a car is a huge consideration, and deciding between new and used can make your mind turn to mush. Do dealer and automaker incentives–like free financing or cash back–make a big difference? Sometimes yes, sometimes no.

Today, I’m bringing you an excerpt from my book, Math for Grownups. Use this math, and you can make an educated vehicular purchase, speedy quick.

Used cars are generally less expensive than new ones, unless you’re deciding between a pre-owned Hummer and a brand new Hyundai, of course.

But how do dealer and automaker incentives stack up to buying used?

Check it out!

Roxanne is trying to decide between two cars. Her local dealership has a current model priced at $25,000, including tax. But online she saw the same car—pre-owned—for $15,000. The used car is in excellent condition and certified. Plus, the warranty transfers, so price is her only real consideration.

The dealership is offering free financing. And the automaker has a $2,000 cash-back program. That means she’ll pay exactly $23,000 for the car and no interest at all.

But to finance the used car, she’ll have to get a loan. To compare the prices, she’ll need to find out how much she’ll pay in all for the used car. That means she needs to know what interest on a loan will cost.

In order to calculate that, she’ll need to know the principal (the amount she is borrowing and the basis of the interest calculation). That means the principal is $15,000. She’ll also need to know the interest rate. Her bank is offering a 6% interest rate on car loans, for a period of 4 years. The interest is compounded annually, so once a year, the interest rate is calculated and added to the loan amount. Thus compounding interest means that in every year for the term of the loan, except the first year, Roxanne is paying interest on the interest she paid the year before (and the year before that . . . and you get the idea).

Roxanne can use an online calculator, or she can turn to a really simple formula:

A = P(1 + r)ⁿ

Okay, breathe. It only looks hard. It’s not difficult at all if you remember the order of operations—that is, what you do first, then second, and so on.

First, do anything inside the parentheses. Next, take care of exponents—those are the little numbers at the right top of another number. They tell how often to multiply the bigger number by itself. (Thus 4²means 4 4, and 16⁵ means 16 16 16 16 16.) Then multiply or divide. And finally, add or subtract. In other words, Please Excuse My Dear Aunt Sally, or PEMDAS:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Ready to apply this formula? With PEMDAS, you can do it!

A is the total amount she’ll owe

P is the principal

r is the interest rate per compounding period

n is the number of compounding periods

Roxanne’s principal (or the amount she’s borrowing) is $15,000, so P = $15,000. Her interest compounds yearly, so her rate is 6%. To make it easier to multiply, she can convert that percent to a decimal: r = 6% = 0.06. And because the compounding period is annual, and the length of the loan is 4 years, n = 4.

A = $15,000(1 + 0.06)⁴

First add the numbers inside the parentheses.

A = $15,000(1.06)⁴

Now calculate the exponent. Remember, 1.06⁴ = 1.06 • 1.06 • 1.06 • 1.06.

A = $15,000(1.26)

Last step! Just multiply.

A = $18,900

So, Roxanne would pay $18,900 total if she finances the purchase of the used car.

That’s a heck of lot less than the $23,000 she’d pay for the new car. And she hasn’t even figured in her down payment yet.

Why does that change anything? Because after making a down payment, she would be paying interest on less principal (remember, that’s the amount she’ll be borrowing). How would a $1,500 down payment affect her decision?

For the used car, she’d finance $13,500 instead of $15,000.

A = $13,500(1 + 0.06)⁴

A = $13,500 • 1.26

A = $17,010

So the total she’ll pay for the used car is $17,010.

And for the new car? She just needs to subtract her down payment from the adjusted price: $23,000 – $1,500, or $21,500.

Judged on the basis of price alone, the new car doesn’t seem so minty fresh.

Do you have questions about using this formula? What about questions about buying cars and fitting the payments into your monthly budget? (On Friday, I’ll talk about the year-round cost of owning a car, a consideration that is critical at the buying stage. And later this month, we’ll take a closer look at compound interest.)

May 9, 2012
Math at Work Monday: Jameel the financial organizer

Welcome back to Math at Work Monday! (We took time off from this regular feature, so that we could spend more time celebrating Math Appreciation Month.) If you’re new here, each Monday I post an interview with someone about how they use math in their jobs. I’ve interviewed Maryland’s Commissioner of Health, one of my former students who is a glass blower and my sister who is a speech therapist.

Because we’re focusing on personal finance this month, I thought it would be a great idea to reintroduce you to Jameel Webb-Davis, a financial organizer and budget counselor who helps people get realistic about their finances.

Can you explain what you do for a living?

I help people get their finances organized. Sometimes that involves actual bookkeeping work – going into people’s offices, balancing their checkbook, organizing their mail, entering stuff into a computer, generating checks for them to sign, and then making little spreadsheets for them to look at telling them when they’re going to run out of money. This brings a bit of money which provides time for me to be a budget counselor.

The Budget Counseling is much more fun. That’s where I sit with people one-on-one, have them tell me how often they get paid, how much they make, and what their bills are, amount due and due dates. I plug everything into a spreadsheet (it takes about 30 minutes) and then I counsel them around whatever money issues they may have. Some people are struggling and don’t know how to pay their bills, but most are making good money and don’t understand why it disappears on them. Most sessions turn into therapy sessions rather than a discussion about making or saving money.

People with a lot of money are just as bad, if not worse, at managing their money as people with a little money. In fact the amount of money and education you have has nothing to do with how well you manage your day-to-day money life. It just takes arithmetic and subtraction, but many people find this hard to believe.

When do you use basic math in your job?

I use it every day. Addition and subtraction. Easy stuff, but people run from it screaming. The spreadsheet I designed looks basically like a checkbook register (see it here). I use it for my own personal finances. I plug in how much money a person has today. Then I list all the times the person will have to spend money in the future (date, reason, amount). Then I list all the times the person is expecting money in the future (date and amount). Then I sort the list by date. I’ve basically created a checkbook balance for the future. This way they can know exactly how much extra money they have or when they’re going to run out of money.

Read the rest of the post here. If you have questions, feel free to ask them here or in the original post. I’ll see them in both places, and I’ll be sure to let Jameel know.

May 7, 2012
Saving for a Rainy Day (or for Singin’ in the Rain)

If you run your own business — like I do — your personal and professional expenses will overlap. So I understood exactly what commenter, Emma, was getting at when she posted this on Wednesday:

My question is like this: what are some things I can do to keep saving when I know I have large expenses that come up a lot? I’m am actor, and I’ve had several big trips for auditions and jobs the past few months that have taken a lot of money all at once to get me to where I needed to go, staying over in a hotel, food on the road, that kind of thing. And I get home and it’s like…. oh. Guess my savings for that pay period is kind of shot.

Here’s the short answer: You have to budget for these expenses, even though they’re not regular. The costs of traveling to auditions and jobs is what I would call overhead. But whether these are business or personal expenses, the issue is the same: You’ve got to budget for them.

The same is true for anyone facing irregular or unexpected costs. Many financial advisors suggest something called an Emergency Fund (EF). Whether this fund is used for home repairs, unexpected medical costs, to replace a totalled car or to travel to The Poughkeepskie Playhouse to star in a revival of 42nd Street, the mission is the same — have enough cash on hand to cover unforeseen expenses.

You also must budget for savings. Even if it’s only $50 each month, make sure that this money is going into a savings account before other expenses are paid for. I like to say that I’m paying myself first. After a while, you won’t even know that it’s gone. You might even be able to set up an automatic transfer, which is a great way to keep you honest.

Why do you need savings? Well, the answer is obvious. If you literally follow the old stage adage and do break your leg, you could be out of commission for a while — no auditions + no gigs = empty bank account. In fact, it’s now recommended that you have six months to a year of living expenses in your bank account for this very reason. So, if you’re spending $3,500 each month, you’ll need $21,000 to $42,000 in the bank to take care of these emergencies. That’s a lot of cash!

If that amount feels out of reach, set some goals — 10% by the end of the year, for example. Doing a few calculations can help you break things up into manageable pieces.

And here’s the other thing: you can squirrel away cash for lots of different reasons, including travel. You could decide to split your savings deposit, putting 70% in an emergency fund and 30% in an auditions/jobs account. So, if you have $100 for savings each month, that would mean $70 in savings and $30 in a travel account. This will give you some cushion, if a really cool opportunity comes up that you haven’t budgeted for.

So how do you budget for travel to auditions and jobs (or create an emergency fund)? My suggestion is to take a look at what you’ve spent in the past. Add up all of your audition expenses for the last three months and divide by three. (Or over the last year and divide by 12 or whatever numbers you have on hand.) Then take a good critical look at that number. Does it realistically represent what you normally spend on auditions and jobs? Did you go on more or fewer than usual? Did you have to fly farther or stay in an expensive city? Adjust this number based on the answers to those questions.

Now you have a good idea of what you can expect to spend each month on traveling to auditions or gigs. More than likely, this won’t be an exact number. If you spend less, put the extra in an auditions/jobs account. If you spend more, take it from that account. (And if you don’t have enough saved up yet, you might need to make other adjustments to your budget — like eating Ramen noodles for a while.)

Here’s one more step you can take. Your business is like mine. It’s feast or famine — you never know exactly how much you’ll be bringing in each month. So estimating a percent that you can use for travel expenses can help you stay on track. There are several ways to do this, and here’s one idea:

1. Find your average monthly expenses for traveling to auditions and jobs. (This is what you did above.)

2. Find your average monthly other expenses. (This will include rent, groceries, utilities, education costs, and yes, savings.)

3. Add the two together to get your total average monthly expenses. (Another way to think of this is your total income.)

4. Divide the travel expenses by the total. That will be your audition expenses rate.

So let’s say that your average monthly audition expenses are $2,000 and your other monthly expenses are averaged at $4,500. That means the average of your total monthly expenses (or total income) is $6,500. To find the audition expenses rate, divide:

2,000 ÷ 6,500 = 0.31 or 31%

So, on average, 31% of your monthly expenses should go to traveling for auditions and jobs. Even if your monthly expenses go up or down, you can keep this percent in mind for setting your audition expenses budget. If you’re making less money, you can trim your travel expenses. If you’re making more money, you can up that part of your budget.

Hope that helps, Emma!

Do you have different advice for Emma? If so feel free to share (nicely) in the comments section. How do you think this process would work for your unexpected expenses? If you have a personal finance question, don’t hesitate to ask!

May 4, 2012
Saving Lives with Math

Math Appreciation Month has finally come to a close. And I thought I would end with some math that could save your life. This is serious — and I think really interesting — stuff.

If you’re seen a recent “best college degrees” list, you probably wondered two things: Why the heck is Applied Mathematics on the list, and what is it? First off, applied mathematics is not about crunching numbers. Instead, these folks use higher level mathematics — from abstract algebra to differential equations to statistics — to solve a myriad of problems in a myriad of industries. And that, my friends, is why it’s on the list. In industries like energy, cell phone technology and medicine, math modeling and statistical analysis have been applied to solve really big problems.

Math modeling is one branch of this field that has become a very big deal. Let’s say a city planner wants to know how many snow plows to buy so that the city isn’t paralyzed by a winter storm. Modeling this problem using mathematics is one way to address this problem. The way I look at it, math modeling helps us understand things we can’t see — because they’re part of situations that haven’t occurred or are too far away or are too tiny and hidden.

That too tiny and hidden part that is what math modelers are honing in on with medicine. In this field — sometimes called bioinformatics or computational biology — mathematicians help medical professionals address problems that are under the skin. Here are two examples:

Fighting Cancer: Researchers at University of Miami (UM) and University of Heidelberg in Germany have created a math model that will help oncologists predict how a tumor will grow, and even if and how it will metastasize. There have been other math models that look at tumors, but this one is different. Instead of looking at each cell or all of the cells has a big group, this model creates a kind of patchwork quilt of areas of the tumor to examine. As a result, the doctor can create a tailored plan for treating the disease that is very specific for each patient. The promise is that with specialized (rather than generalized) treatment plans will offer patients a better chance at survival.

Treating Acetaminophen Overdoses: When a patient comes into the emergency room having overdosed on acetaminophen, the ER staff is faced with a really complex decision. Often these patients are hallucinating, unconscious or comatose. And since it’s relatively easy to overdose on the drug (it takes only five times the daily safe dosage, and acetaminophen is in many different over-the-counter and prescription medications), it’s sometimes impossible to determine when and how much of the drug was ingested. There is an antidote, but at a certain point, the doctor needs to skip that step and put the patient on the liver transplant list immediately. The trick is accurately identifying that point. University of Utah mathematician, Fred Adler, developed a set of differential equations that can better pinpoint the critical information needed to make these decisions.

In both of these cases, the math is pretty darned complicated, depending on a branch of calculus called differential equations. This approach is a step up from statistical analysis, which compares patient data to data collected from other patients. In other words, it assumes that tumors grow in the same way in all patients — which we know isn’t true. These dynamical math approaches allow doctors to offer treatments that are customized for each patient, based only on the information collected from the patient.

And the best part is that the doctors don’t have to know the math. If future studies bear out these new discoveries, a simple app can be designed for smart phones or tablets, allowing physicians to make diagnoses and treatment plans bedside.

I suspect these applications will continue to grow, as the medical community turns to mathematicians for insight into what we can’t see. That’s great news, because these advances can save lives.

I hope you’ve enjoyed what we’ve put together here for Math Appreciation Month. If you have questions, please ask them below. I’m always open to ides for future blog posts, so please share them!

April 30, 2012
Math at an Indian Restaurant

I’m late posting today for good reason. I’ve been in New York City since Wednesday, attending the American Society for Journalists and Authors conference. And it’s been a blast! I rode up on the bus with hilarious humor writer, Michele Wojciechowski. I’ve met folks I’ve blogged for (including Debbie Koenig at Parents Need to Eat, Too) and folks who have been featured in Math at Work Monday (like career coach, Kiki Weingarten (and her sister Rachel Weingarten).

I’ve also attended workshops on creating video (look for that soon!) and being fearless in writing (with super mom blogger Jen Singer). Tomorrow, I’ll be moderating a panel called One Plus One Equals Cash: Math for Writers. Yep, I’m bringing the math message to my fellow freelance and book writers.

This little introvert is going to be exhausted by the time I get back to Baltimore on Sunday night. But I’ll also have a ton of inspiration — exactly the kick in the pants I need for the kind of isolated work I do.

Of course conferences mean dinners out with lots of people at one table. And in New York, this almost always means splitting the check ourselves, maybe even after a glass of wine or two! It’s a daunting prospect even for a former math teacher. So here’s a quick look at how you can do it, easily and without worry.

Dividing the Restaurant Check
1. Decide if you’re going to split everything evenly or if people want to pay only for what they purchased. Last night, I ate Indian with a group of friends. We chose to have a variety of dishes and share them family style. At the end of the dinner, we simply split everything seven ways.

2. Add the tip before you divvy things up. The server should receive 15% to 20% for good service on the entire bill. If you figure the tip after the division, you could end up tipping less than the server deserves. And — trust me on this — it makes the math easier.

(Remember how to find the tip? Take 10% of total bill by moving the decimal point one place to the left. For 20%, double that amount. For 15%, take half of that amount and add it to the 10%.)

3. Round. Unless you’re Mr. or Ms. Picky-Pants (and honestly, no one wants to eat dinner with someone like this), rounding is going to be close enough. But here’s the thing. You must round up. Otherwise, you could leave too small a tip or find out you don’t have enough money to cover the whole bill.

This rounding thing goes for both splitting options — dividing the check evenly or adding up each person’s total. But how should you round? Well, that depends on you and your comfort with the mental math. You can round to the nearest dollar (which is usually my preference) or to the nearest 50 cents. Use your best judgement — but pay attention to how your choice may affect others’ totals and the server.

4. Another option is to estimate. Last night our total bill was $156 with the tip. We had seven people, and I immediately noticed something wonderful — $156 is pretty close to $140. Why does that matter? Well, it’s because 7 x 20 = 140. (Okay, so actually I noticed that 7 x 2 = 14, but it’s basically the same math fact.) This meant that each of us would owe something close to $20.

Clearly we each owed more than $20, right? (156 is greater than 140.) So, I estimated that it would be pretty close to $23. Because I was thrilled to figure this out, I pulled out my iPhone and checked. Turns out $156 ÷ 7 = $22.29. My estimation pretty darned good!

5. And of course another option is to use a calculator. I am here to tell you that there is no shame in this! Look at it this way: you have lots of things on your mind, and that glass of wine probably isn’t going to help you do mental math. You’re a grownup, and your fourth-grade teacher isn’t looking over your shoulder telling you that calculators are bad. Use the tools that work for you.

6. Finally, when everyone has contributed, add it all up to make sure there’s enough to cover the bill. Several of us remember last year’s cocktail party when people left early but didn’t leave enough money to cover their drinks. That left the rest of us stuck with more than we expected to pay. Checking your answer is a great way to avoid these costly mistakes and tarnishing your good name!

Of course there are many other ways to approach these everyday — or every conference — problems. You just need to pick the one that works for your special brain. Remember, just because you do it differently doesn’t mean you’re wrong.

But I do encourage you to look at the relationships between numbers — even when you’re using a calculator. You might pick up a few neat tricks. And if you’re my age, it can’t hurt to exercise those brain cells a little.

How do you split the check at a restaurant? Have you ever said, “I’ll treat!” to avoid the math? Share your tricks here and feel free to ask questions, too.

April 27, 2012
Ten Things Parents Wish Math Teachers Knew

We’ve gotten advice from math teachers to parents and from students to math teachers. But parents can also play a big role in how their kids learn math and succeed in school. So, I’ve decided to given them a chance to share their feedback with math teachers. (Besides, when I went looking for students to give me advice, parents just couldn’t help themselves!)

I’ve been on both sides of this equation, so I have lots of empathy for teachers and parents. Neither of you have easy jobs! In case it’s not clear, I wholeheartedly believe that most teachers are in the classroom because they love kids and want to make a positive difference in their lives. But we’re all human, and teachers can always strive to be better at their craft.

Here goes:

Help a parent out.

The language of math is different than it was when most of us learned it the first time. (For example, in subtraction many of us “borrowed.” Our kids “regroup.”) A cheat sheet or a website with information would go a long way in helping parents help their kids with understanding the concepts.

This goes double (or triple) for discovery-based math curriculum, like Investigations or Everyday Mathematics. These programs often don’t rely on the algorithms that many of us are used to using. To be fair, the curricula have parent components, but if the school or teacher doesn’t use them, parents are often left in the dark.

Know the kids.

Parents do understand that there are a lot of big stressors on teachers. Teachers are often told to do things that they wouldn’t choose to do (like teach to a test). They have large classes and short periods of time with the kids. But parents still expect teachers to know each child well. Teachers should know which kids have trouble with memorization and which ones struggle with understanding difficult concepts.

Give parents a homework estimate.

How long should students be working on an assignment? An hour? 15 minutes? Two hours? Kids work at different speeds, and parents need to know when we should be encourage our kids to pick up the pace or investigate whether our children are moving slowly because they don’t understand the concepts. And while we’re on the topic of homework, parents told me that there was no point in sending home 50 of the exact same problems. One parent said: “Hours of pointless busywork make kids hate math.”

Mean what you say and say what you mean.

This doesn’t have anything to do with classroom management, though this is good advice here, too. Parents told me about very poorly worded questions that confused their kids. “My [child with Aspergers] is very literal,” said one mom. “This sometimes means he actually answers the question correctly but not the way the teacher intended. More than once I have had to ‘correct’ his homework and say, ‘Yeah, I know what you put is accurate, but that is not what the teacher meant by the question.’” One parent suggested having someone who is not an educator look at your materials to be sure that the questions are clear.

Update your materials.

Don’t pull old worksheets from old curricula that doesn’t apply to current pedagogy. And by all means, make sure that what you’re sending home with kids is what they’re learning about in class. It’s really frustrating for parents and kids to see homework that is not jibing with classwork.

Review tests and graded assignments.

Students need to understand where they made their mistakes and why. Parents need to know where students’ gaps in understanding are. Reviewing tests also reinforces the important idea that tests are a means for assessing understanding, not a big, red stop sign for learning. But don’t let students check each other’s work. “It’s demoralizing,” said one parent.

Don’t confuse computational errors with conceptual misunderstanding.

When a student makes a common addition error, that doesn’t mean she doesn’t understand the concepts behind the problems.

Introduce relevant and meaningful application (word) problems.

At the beginning of this school year, my sixth-grade daughter vented about a word problem she was given for homework: Carlos eats 25 carrots at dinner, and his brother eats 47 carrots. How many carrots did they eat in all? “Who eats 47 carrots?” she wanted to know!

If you don’t know what’s relevant to your kids, ask them. Or watch a television program they may like or talk to parents or search the internet. Along with word problems, parents want financial literacy introduced early and often. These problems can be included in a variety of places within traditional curricula.

When a child isn’t succeeding, ask why.

Sometimes this is because of misbehavior, but sometimes misbehavior occurs when a child is bored or confused or just feels unconnected to the class. Some kids give up easily. And others have undiagnosed–or unaddressed–learning disabilities. Get the parents involved as quickly (and often) as possible.

Don’t write our kids off.

Some kids struggle and some kids understand the concepts right away. Parents want teachers to stick with their kid, no matter what. Parents can tell when teachers have decided that a kid isn’t worth their effort. That’s heartbreaking to parents–and students.

Not all parents want or can be intimately involved in their kids’ math education, but I think it’s fair to give each parent a chance. Just as it’s fair for parents to give teachers the benefit of the doubt.

Parents, do you have any additional advice for teachers? Teachers, do you want to respond to any of these ideas? Let’s get a good conversation going!

April 25, 2012
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.

April 23, 2012
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?

April 20, 2012
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!

April 18, 2012
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.

April 16, 2012