Photo courtesy of Riebart

It’s been a long while since I’ve posted a new Math at Work Monday interview. But this feature remains one of the most popular here at Math for Grownups. Perhaps that’s because teachers and parents like to prove to their kids, “See, you will use this stuff one day!” And I imagine that others stumble upon it while looking for career advice. At any rate, it’s been an eye-opening experience for me, too. And here are a few lessons learned.

People don’t know they’re doing math

I’ve intentionally  focused on careers that are not traditionally STEM related — from a textile designer to an FBI profiler to a children’s book author. And almost everyone says the same thing: “I don’t use much math in my work.” Then they follow up with a revelation – they do more math than they think!

People do the math they want to do

This makes a lot of sense. Why go into a career that requires skills you don’t have? Those folks who really dislike calculus are most likely not going to become physicists. Folks who hate statistics avoid careers in research. And people who have a disdain for geometry aren’t likely to become carpenters or architects. At the same time, when someone feels drawn to a career, they’re willing to whatever it takes to be successful. That often includes a little bit of math.

People do a lot of mental math

While most folks I interview say that they check their work with a calculator or good old back-of-the-envelope calculations, a fair amount of math is being done in their heads. This may be as simple as using fractions to mix the perfect hair color to deconstructing formulas so that the math can be done in the field, say on a fish hatchery.

People also depend on technology

When it comes to money, especially, or critical situations, like healthcare, a computer, spreadsheet or calculator is often a necessary tool. But often these require a clear understanding of the math going on. It’s not enough to give someone some software. These folks must know how the math works in order to use their technological tools.

People often don’t have a good relationship with math

This is kind of sad to me, but it’s been very true: I rarely meet someone in a non-STEM field who says that they really understood math in school and now feel really confident in their skills. Yet, all of the folks I interview for Math at Work Monday do use math. That says to me that their issues with math are often in their head – and probably not really their fault. The reality is that our educational system and other adults often fail us in this regard. It’s not about making math fun. It’s about making math useful.

I’d like to keep Math at Work Monday going, but I need your help. Do you know someone who would be interested in being interviewed? Think of basic fields: home improvement, medicine, the arts, law, public service and more. Does your partner use math in his work? What about your next door neighbor or your sister? The answer is yes, and I’d like to interview them. Shoot me a line at llaing [at] comcast [dot] net, and I’ll reach out to them.

What have you learned from the Math at Work series? Have you been surprised by anything? Share your thoughts in the comments section.

P.S. I wanted to explain why I was so silent last week. Because of the horrific events in the U.S., I felt it would be trite to post about Math Awareness. Clearly our national attention was needed elsewhere, and so aside from a Boston-related post, I made the decision not to post. My thoughts continue to be with everyone in Boston and West, Texas.

At the finish line of the 2013 Boston Marathon. Photo courtesy of Aaron “tango” Tang.

We can all agree that the horrific events at Monday’s Boston Marathon sent a chill down our country’s collective spine. The two bombs that exploded have made us afraid and sad and hopeless. One message that seemed to ease many’s pain and fear was from Mr. Rogers, who once said:

When I was a boy and I would see scary things in the news, my mother would say to me, ‘Look for the helpers. You will always find people who are helping.’ – Fred Rogers

This is an amazing idea in the midst of the mayhem and terror that followed the explosions. There were dozens and dozens and dozens of people who ran toward the bomb sites, because that’s what they do – help those in need.

In the days that have followed, the FBI and others have been investigating the explosions, gathering information that will likely lead to an arrest and hopefully a conviction. Our natural question in these situations is, “Why?” Catching the person or people who did this will help us find that answer.

It shouldn’t surprise you to know that these investigators will depend on mathematics to help them solve this crime. From measuring the trajectory of the shrapnel to piecing together a timeline of events, math is a critical component in investigation.

A while back, I had the pleasure of interviewing Mary Ellen O’Toole, a former FBI profiler and author of Dangerous Instincts: How Gut Feelings Betray Us. She answered my questions about how she used math as a profiler. And I’m betting that this holds true for the investigation in Boston, as well.

Math at Work Monday: Mary Ellen the FBI profiler

Can you explain what you do for a living?

For half of my career, I worked in Quantico, at the FBI’s Behavioral Analysis Unit, the very unit that is the focus of the television show Criminal Minds. While there I tracked down, studied, and interviewed some of the world’s most infamous criminals, and I analyzed their crime scenes, too. These criminals included Gary Ridgeway (the Green River Killer), Ted Kaczynski (the Unabomber) and Derrick Todd Lee (the serial killer of Baton Rouge.) I worked everything from white-collar crime to work place and school violence to kidnappings to serial murder.

Since my retirement in 2009, I’ve worked as a consultant to law enforcement, corporate security, administrators, and many other professionals. I also teach at the Smithsonian, FBI Academy and many other locations.

When do you use basic math in your job?

As I and other profilers worked to solve a crime, we used every type of math from basic addition to geometry and pattern analysis to statistics and probability to reasoning and logic.

Read the rest of the interview.

If you’d like to share your wishes for the victims of the Boston Marathon bombing, please feel free to do so in the comments section. 

One promise of Common Core? A greater emphasis on critical thinking. Photo courtesy of Andrew Horne

Not all of us are parents or teachers, but I’ve long asserted that education is a “public good,” something that each and every one of us should be very, very concerned with. When kids don’t graduate or graduate with poor critical thinking skills, a lack of curiosity of the world around them or a dearth of basic math, reading and writing abilities, everyone suffers. And in a world where STEM-based employers are recruiting and paying more, we owe it to the next generation to do better.

(This is not to say that our educational system doesn’t have some absolutely enormous issues in other areas. Perhaps the biggest problems our schools face are not academic at all. I believe that if our country took a good, hard look at poverty, violence and teacher care, we’d make huge strides in the right direction. But this post is about academics.)

Enter the Common Core Standards. For decades, each state has developed and cultivated its own standards – or objectives required by each basic course, from history to language arts to biology. But over the last 20 years, a movement has grown to standardize these objectives across the country. With this umbrella of standards, what little Johnny is learning in Arkansas will be similar to what little Patrice is learning in Maine.

Right now, the Common Core Standards only cover English (language arts) and math. They’ve been adopted by 45 states. (Alaska, Nebraska, Texas and Virginia haven’t adopted them at all, and Minnesota adopted only the English language arts standards.) Standards for other subjects are in the works, including science and social studies.

For the last six months, I’ve been writing and editing curricula designed to meet the Common Core Standards for mathematics. I’ve gotten a pretty good feel for what they are, and I have to say that I like them for the most part. Here are some general thoughts I have:

Students will learn certain concepts earlier. I haven’t spent much time with the elementary level standards, but at least in middle and high school, various mathematical topics will be introduced earlier in the standards. For example, exponential functions (an equation with x as an exponent, like with exponential decay or compound interest) is covered in Algebra I, rather than Algebra II. 

The result is two-fold. As the standards are rolled out, some students will be left behind. In other words, kids who started school without Common Core may have a hard time catching up or bridging the gap. Second, students will have the opportunity to learn more mathematics throughout their high school career. The idea is to better prepare them for STEM in college and careers.

The emphasis is on critical thinking. This part, I love, love, love. For example: geometry proofs are back! And rather than compartmentalizing the various branches of mathematics, students will make connections between them. I just wrote a lesson that looks at how the graphs, equations and tables for various functions – linear, quadratic and exponential – are alike and dissimilar. Previously, students may never have seen these functions together in the same unit, much less the same lesson.

This means that assessments will change. Students will be asked to explain their answers or verbalize the concepts. Expect to see much more writing and discussion in math class.

Applications, applications  applications. Math is no longer done for math’s sake. And this couldn’t be better news. As I’ve said here many times before, math is pointless until it’s applied. Students should get this first-hand with Common Core, which outlines very specific applications for various concepts.

The idea here is to demonstrate that the math they’re learning is useful. The result? Hopefully more students will choose to enter STEM careers or major in these fields in college.

Students learn in different ways. Modeling plays a big role in the new standards, which means that students can approach the math in a variety of ways – from visualizing the concepts to using manipulatives like algebra tiles to working out equations in more traditional ways to graphing. This way, students can enter the material from a variety of different doors. And that can translate to greater success.

Sure, there is a lot to be concerned about (most especially the gap that we expect to see in student performance), but from my perspective the Common Core Math Standards are a step in the right direction. It’s important to know that these do not form a federal curriculum; the states are still responsible for choosing curricula that meet these standards, and education resource companies are scrambling to meet these meets. (That means I’m very, very busy these days!) It’s also important to know that chucking old ideas and implementing new ones puts a huge burden on already over-taxed schools and school systems. Finally, there is no doubt that this initiative was driven by the textbook companies, which means we’re still beholden to politics and capitalism.

But in looking at the standards alone, I think Common Core is excellent. If we can implement the standards well and keep them in place for a while, I think our kids will benefit.

What do you think of Common Core? Share your thoughts in the comment section.

This is my father in the summer of 2006.

Math shares its awareness month with another mission that is very near and dear to my heart: It is also Organ Donor Awareness Month. When I found that out earlier this week, I thought I’d indulge myself a bit and spend a post looking at the math of organ donation.

When I was in middle school, my father learned that he had a very strange autoimmune disorder. His immune system was attacking his liver. In fact, his liver looked like that of a raging alcoholic, which he wasn’t. After months and months of testing and treatments (some pretty ugly), his doctors were finally able to get things under control. But they told us one thing that stuck with me forever: “This isn’t a terminal disease, but it is chronic. As a result, he won’t live as long as he would have if he was healthy.”

To this day, we have absolutely no clue why my father’s immune system turned on him. When I was a toddler, he had surgery to remove part of his thyroid, because it was so overactive. As he aged, he developed other autoimmune disorders, including vitiligo, which caused his skin to lose pigment. But he kept on keeping on.

About seven years ago, his doctors discovered liver cancer. This was a specific kind of cancer, related to his liver disease. They could remove it, but the writing was on the wall: his liver was on its last legs.

So they put him on the liver transplant list. He stopped travelling more than a couple of hours from his hospital. He got poked and prodded. And he waited. And waited.

I’m not sure how many people were on the list at the time. Today, there are nearly 17,000 people waiting for liver donations. Each of these individuals are scored, based on the severity of their liver damage. In 2006, when my father was on the list, the median national waiting time was 321 days. I wasn’t able to find out how many people die before receiving a liver transplant, but it’s estimated that 6,500 people die each year while waiting for a heart, kidney or liver.

After eight months or so of waiting, my family and his doctors got worried. The tumors were coming back and multiplying. He needed a transplant soon. And so I made a decision that changed my life forever. I would donate my liver to him.

The liver is the only organ (besides the skin) that grows back. And a live-donor liver was a great option for someone like my dad. I flew through the medical testing with flying colors.

At about 5:00 a.m. on October 1, 2007, I was wheeled into an operating room at Virginia Commonwealth University Medical Center. They prepped me first, and then brought my father in for the transplant. The entire surgery took at least 8 hours, during which they took one full lobe of my liver and transplanted it into my father. Something like two hours of that time was devoted only to stitching up the large lambda-shaped incision that cut through my abdomen.

After two days of recovery, my father was off the ventilator, and I was walking down the hospital corridors on my own to visit him. Within another two weeks, an MRI showed that my liver had already grown back to about 95% of its original size. (I’m not kidding!) In that time, I had lost around 20 pounds, from not being able to eat for about a week and from the energy my body spent regrowing an organ.

I’m so sad to say that this story does not have a happy ending. I’m perfectly healthy. And my transplanted liver was doing great inside my dad. But no one knew that my father had pulmonary fibrosis. It must have been at the very, very early stages of his disease when he was tested and tested and tested prior to the transplant surgery. The doctors suspect that the progression of the disease was sped up considerably due to massive amounts of oxygen that were pumped into his lungs during surgery and while he was in intensive care.

Had he not had this complication, I have no doubt that he would be living today. He died on November 6, 2007; his liver was still going strong.

My point is not to share a very sad story. My point is to share with everyone some small mathematical facts about organ donation:

1. Each day, about 18 people die, while waiting for a kidney, liver or heart. (That’s 6,500* people per year divided by 365 days.)

2. Right now there are approximately 117,729 people waiting for a kidney, liver or heart. Each year, 4,000 more people join this list.

3. Becoming an organ donor doesn’t have to be as dramatic as my experience was. Most donated organs are from a deceased donor. It takes a split second for you to indicate on your driver’s license that you want to be an organ donor. Or you can sign up at OrganDonor.gov.

4. And happily, most people do not have my father’s experience. As of May 2009, 73.8% of those who had received a transplanted liver were still alive, five years after their surgery. Here are the percentages for others: 69.3% of kidney recipients, 74.9% of heart recipients and 54.4% of lung recipients.

5. It’s not just the big organs that matter. Organs and tissues from a single deceased donor can help up to 50 people. (Yes, 50!) On average 79 people each day receive a donor organ or tissue.

In fact, my father was so convinced of the value of organ donation that even after much of his body failed him, my father was able to donate his eyes, skin and tissue. It is an amazing thought that I and he were able to join together to do this.

So if you haven’t taken the time to indicate that you’d like to donate your organs after death, please do so now. I don’t regret for a moment my gift to my father. At the same time, had there been more deceased donors, it wouldn’t have been necessary.

Talk to your family about organ donation. Get some good information. And at the very least, make an intentional decision one way or the other.

*Earlier, I had a typo here. This number has been corrected.

Photo courtesy of Justin See

Most folks readily tell me that they don’t do any math in a day. Not a stitch. So maybe they don’t sit down and solve for x or graph a quadratic equation or use the Pythagorean Theorem. But we all do math every day. And I decided to prove it.

It was last Tuesday — a pretty regular day.

April 2, 2013

6:00 a.m.: Review to-do list, estimating the time that each item would take. Count up the number of hours estimated to be sure not to exceed eight hours, while leaving time for lunch and exercise.

7:00 a.m.: Track all Weight Watchers points that I expect to use for the day, by planning what I’ll have to eat for breakfast, lunch, dinner and snacks. Allow the online program to add everything up, but pay close attention that my breakfast and lunch are around 6 points each and that I’m using less than 8 points from my weekly extra points.

10:00 a.m.: Review invoicing for first quarter. Within bookkeeping program, look at the data in a variety of ways: bar graphs, showing income for each month, and tables showing the income for each client. Compare income to goals and adjust expectations where necessary.

11:00 a.m.: Set budget for new book postcard, using designer’s estimates. Compare costs of a fewer number of cards to the costs of a much larger run. Table the decision to think about things.

12:00 a.m.: Attend weekly Weight Watchers meeting, and learn that I lost 0.4 pounds last week. Spend meeting mentally calculating how that could have happened, given the fact that I didn’t stay within my allotted daily points for a few days. Remember that balancing the equation of caloric intake and output, with variables like water retention, is way too complex for mental math. Decide to just feel fortunate and proud.

1:00 – 3:30 p.m.: Outline online lesson about linear, quadratic and exponential functions. (Yes, this is where I and the rest of the world differs! But I wanted you to know that this curriculum doesn’t appear out of thin air.)

4:00 p.m.: Meet with potential photographer for our wedding. Count backwards from the start of the wedding to estimate the time necessary and the cost of a second photographer. Mentally calculate how much over our budget we’d go if we hired this photographer. (Everything goes over budget, I’ve found.)

6:30 p.m.: Meet a friend for drinks at a local restaurant. Scan menu for lowish-calorie drink, decide that since a cosmo is the same points as a glass of wine, why not have the pink drink in the fancy glass?

7:30 p.m.: Get the check. Find the tip by taking 10% of the bill and doubling it. Then split the check evenly since we got the same drink and shared an appetizer.

11:30 p.m.: Daughter can’t sleep. Mentally add up the number of hours of sleep we can each expect to get if she would just fall asleep right now. Finally she dozes off.

And there you have it — my math day. As you can see, the math was tucked into various nooks and crannies. If I hadn’t been paying attention, I wouldn’t have even noticed it. And most of it had nothing to do with the way I learned to do math at school.

So what about you? Here’s my challenge: Just for today, jot down when you’ve used math. Then share what you learned about yourself in the comments section. Did you find that you used math more than you thought? Did you discover that you’re using a kind of math that you never, ever expected? I want to know!

Photo courtesy of Kevin Utting.

One of the questions I get most often from parents is this: How can I help my kids from being anxious about math like I am? And for a math nerd like me, the answer is pretty simple. I’m unnaturally aware of the math around me. Because of my background and experience — and maybe even the way my brain is wired to see patterns in damned near everything — I can weave math into just about any situation I come across.

(Go ahead, try me. Post a situation in the comments section, and I’ll bring the math. It’s a game I used to play with my daughter, until she got really tired of losing.)

But for most parents, this level of math awareness is just not as simple to access. This is where Laura Bilodeau Overdeck comes in. With degrees in astrophysics and public policy, Overdeck is probably a little like me — finding math in everything and pointing it out to her kids at every turn. But she didn’t just keep this to herself. Nope, she launched Bedtime Math, a really simple idea designed to help parents inject a little math in their kids’ everyday lives.

Each day, she and her crackerjack team send out an email to subscribers (it’s free!) that offers three math questions — one for Wee Ones, one for Little Kids and one for Big Kids — that are centered on a little story or current event. Yesterday, the theme was tongue twisters. On Wednesday, it was hopping.

During Math Awareness Month, Overdeck and her team have introduced a series of mini, math videos. And these things are funny. The first is about ninja training — what kid (or parent) wouldn’t want to find out what happens? Check it out below:

I can’t tell you how much I love Bedtime Math. If you have little kids, give it a shot. You’ll probably learn something too — and you might even raise your awareness of the math around yourself.

Are you a Bedtime Math subscriber already? How do you use it with your kids? What do your kids think about it? Share in the comments section.

Get it? (Photo courtesy of jin.thai)

Lots of people make one of two incorrect assumptions about me. I’m a writer, so they initially assume that I don’t have a good relationship with math. And when they find out that I have a degree in math, they assume that I love to sit down and solve trigonometry problems all day long.

Sure, I like math. I’ve said it a hundred times – math is a useful tool. I feel comfortable using math to figure out problems that I have, like how much fabric I need to order to recover my couch or the number of calories in a 3/4 serving of granola. (Yes, I actually do that second thing on a regular basis.) But I’ve never been head-over-heels in love with math.

What do I really love? A good story. And so for the third year, I’m inviting you to share your math story. Telling others how you came to love, like or hate math is an interesting process. I’ve learned that education – and particularly teachers – make a huge difference in how people feel about math. Get a great teacher, and you have a much better chance of at least coming out of the class appreciating math. But a burned out, cynical or, worse, mean teacher can destroy any positive feelings a student might be cultivating about math.

Why share your story now? Well, April is Math Awareness Month, which is not about appreciating math. Nope. The goal of this month is to simply encourage people to notice the math around them. (Which is also my personal goal with this blog and my book.) The first step can be telling the story that helped form your impressions of math. Is there something blocking your understanding or appreciation? Could be.

Before you share your story, you may want to read some others’. Start with mine, and then check out how math almost ruined Lisa Tabachnick Hotta‘s life and how Siobhan Green learned to use math, despite an early bad experience.

Then tell your story in the comments section. Do you like math, hate it, don’t care one way or the other? Does math make your hands sweat? Why do you think you have these feelings about math? Do you have a sad story — giving up and giving in? Or did you triumph? Whatever your personal experience, I want to hear from you. And if you’d like more space, feel free to contact me about a special guest post.

So what are you waiting for? Share your story today.

P.S. The official theme for this year’s Mathematics Awareness Month is sustainability. That’s a wonderful topic, but I think for many of us, it’s a little esoteric. So I’m going to pull back and focus on some more mundane topics this month. However, math educators should check out the Math Awareness Month website for ideas on how to relate this theme to the classroom. There are some really cool resources there.

Granular Cell Tumor (Photo courtesy of euthman)

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!

Photo courtesy of fung.leo

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.

Photo courtesy of alkruse24

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:

1. 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.

2. 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 classrooms 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.

3. 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.”

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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!