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Math at Work Monday: Tiffany the 6th grade teacher

I know what you’re thinking. “It’s so obvious how a 6th grade teacher would use math! She’s teaching fractions and division and percents!”

There’s always a lot more to teaching than the rest of us may think. And that’s why I asked Tiffany Choice to answer today’s Math at Work Monday questions.  Ms. Choice was my daughter’s 4th grade teacher, and she’s the best elementary math teacher I’ve ever met.  She truly made the math fun, and she really got into her lessons.  I know this for sure, because I had the pleasure of subbing for Ms. Choice while she was on maternity leave.  Let me tell you, those kids loved her — and so do I!

Last year, Ms. Choice moved to Fairfax County, Virginia.  She’s getting ready to start teaching 6th grade there.  In honor of what was supposed to be our first day of school — until Hurricane Irene changed our plans! — here’s how she uses math in her classroom.

Can you explain what you do for a living? I teach state-mandated curriculum to students. My job also includes communicating to parents progress and/or concerns, appropriately assessing my students, and analyzing data to drive my instruction and lessons.

When do you use basic math in your job?  I use math all the time — mostly basic addition, subtraction, multiplication and division. When I plan lessons, I need to appropriately plan for activities that will last a certain length of time. Then, when I am teaching the lessons, I am watching the clock and using timers to keep my lessons moving or calculating elapsed time.

I also use math to grade assignments and calculate grades. I break a student’s grade into 4 categories; participation, homework, classwork, test/projects. Each category has a different weight. Participation and homework are each 10 percent, while classwork and test/projects are each 40 percent. Then for each grading period, I average grades and take the appropriate percentage to get the overall grade.

I also use math to analyze data and drive my instruction. After quarter assessments or chapter tests are given, I look for trends. Which questions did the majority of students get incorrect? If I notice out of 60 students only 30% of them got a certain question correct this says to me that most of them (42 to be exact) got the question wrong. I need to figure out why and go back.

I will also use math to group my students for games and activities. When I originally plan for them I always assume all students will be present. However, with absences and such I have to use last-minute division to regroup them.  I move desks around into different groups periodically during the year, and that requires division as well.[pullquote]It’s completely normal to feel anxious or nervous about math. But a great teacher at any level (primary to college) will help you “get it.”  Just don’t give up.[/pullquote]

When I plan for field trips, I have to calculate the total cost for each student depending on the fees involved. Then, I have to count large amounts money that has been collected to account for the correct amounts.

Do you use any technology (like calculators or computers) to help with this math?  At my first teaching job, I had a computer program that calculated grades for me, but when I left and went to a new district I didn’t have that software, so I did grades all by hand using a calculator.

How do you think math helps you do your job better? The whole point of my job is to get students to learn and become great thinkers. I wouldn’t be able to find or focus on areas of weakness if I wasn’t able to properly analyze data and comprehend what it really means to me.

What kind of math did you take in high school?  Did you like it or feel like you were good at it? I only took algebra and geometry in high school. I was terrible at math in high school and didn’t enjoy it or “get it” until college. I started in a community college and I had to take two developmental math classes before I could take what was required. It was during those developmental courses I finally “got it” and began to actually enjoy it. Everything finally made sense.

It’s completely normal to feel anxious or nervous about math. But a great teacher at any level (primary to college) will help you “get it.”  Just don’t give up.

Did you have to learn new skills in order to do this math? The math I use to do my job is math that is taught up to the middle school level. I didn’t have to learn anything special.

Thanks so much, Ms. Choice!  (I don’t think I can ever call her Tiffany!)  If you have questions for Ms. Choice, just ask them in the comments section.  She has agreed to come back to Math for Grownups to talk a bit about how parents can work with their kids’ math teachers, so stay tuned for more advice from her.  

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In Math for Parents

Film Friday: When will I ever use this stuff?

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

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

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

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

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

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

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

Now back to my opinions.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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In Math at Work Monday

Math at Work Monday, Ursula the glass artist

Ursula Marcum

Ursula Marcum practices an amazing art form called kiln-formed glass, which she can explain better than I.  Her pieces are layered and rich, unlike any other glass I’ve ever seen.  Like most artists, Ursula does quite of bit of basic math in her work, and she shares the details here.

What do you do for your living?

I’m an artist who works in kiln-formed glass. Rather than blowing glass, which people may be familiar with, I cut up and compose individual pieces of glass, then I fire it all in a specialized kiln to get the result I’m after. Each piece may take several firings. I then sell the completed works at art fairs and to shops as well as a show at galleries. I also teach kiln-formed glass classes at Vitrum Studio, which specializes in this medium.

When do you use basic math in your job?

Because I’m self-employed, and therefore wear many hats, I use math ALL the time, for all kinds of reasons. Most of the time it’s basic computation, but I work with fractions quite often because of all of the measurings I have to do. For example, if I’m making a glass patter, I need to measure all the pieces of glass so that they fit together and, ultimately, fit into a ceramic mold that guides the glass into a particular shape. Or, I need to center a piece of hardware that’s going to go on the back of a hanging panel.

Sometimes, though, I need to refer to specific formulas. Let’s say I’m doing a sculptural piece. When I put the glass in the kiln, at a certain point the heat will turn the glass from a solid into a liquid and, if I’ve made the correct calculations, it will fill a void that is in a plaster mold. I need to figure out the volume of the void so that I know how much glass, by weight, to use. This is one of several formulas that I have in a notebook which I refer to again and again.

Do you use any technology (like calculators or computers) to help with this math?

I use both calculators and computers to help me because I know that when used correctly they are accurate! In order to do something like the volume formula that I spoke of earlier, I will first use a calculator to convert the numbers to the metric system. It makes it so much easier. I also use the computer to help me keep track of things like inventory and finances. It’s much faster than using a pencil and paper, though I use those tools, too.

drawer #4 from Marcum’s collections series

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

Accuracy is very important, and a piece of artwork looks professional because of the details. If my corners aren’t square, or my hardware is off-center, or I don’t have enough glass to completely fill the mold, that is sloppy work. If I can’t keep the financial books in order, or I don’t know what inventory I have on hand, I will be out of business pretty quickly.

How comfortable with math do you feel?

The work that I do help me to become comfortable with math. I am the sole proprietor, so if I don’t do it, there isn’t anyone else to take up the slack! Practice, practice, practice made it feel less scary. Eventually, I got to the point where I had enough confidence to feel comfortable with the math I was doing, as well as believe that I could figure out something new that came my way.

Bird Feathers

What kind of math did you take in high school?

I really, really struggled with math in school once I got past basic arithmetic. The exception was geometry, which I aced. In hindsight, I understand that I did well in this class because I was (and still am) a strong visual learner. Because there were shapes that I could draw and relate to, geometry made sense to me in a way that algebra never did. I got through trigonometry with the help of a very, very patient teacher who stayed after school two days a week to tutor me. It was so frustrating for me though – and I’m sure it was for her, too! At the time I thought, “Well, I’ll just get through this and then I’ll NEVER use math again.” Admittedly, it was a bit short-sighted. Not only does my job require math, but LIFE also requires math.

Did you have to learn new skills in order to do this math?

Mostly, I had to learn to confront my fear of math. I had been taught all of the skills that I needed for my work, I just didn’t believe that I knew how to use them. But I loved working with the glass, and I had the desire to make my work to the best of my ability, and that meant that I had to brush up on those dusty old math skills.

If math makes you nervous, see if you can apply it to something you love. It’s a great motivator!

Do you have questions for Ursula?  Visit her on her Facebook page. 

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In Math at Work Monday

Math at Work Monday: Marie Grace the children’s knitwear designer

A pattern snippet from one of Marie Grace’s original designs.

If you don’t knit, a knitwear pattern probably looks like a random selection of letters and numbers.  But that special code actually reveals beautiful creations–sweaters, hats, booties and blankets.  Marie Grace Smith is the founder ofMarie Grace Designs, and she lives these patterns.  You might be surprised to learn how much math is involved in developing these patterns.  Marie Grace was!

“If I had known how much math I would need to do to make a living playing with yarn I would have become a painter or something. Just kidding. Sort of.”

What does a children’s knitwear designer do? I design and write patterns for hand-knitting. I have my own pattern line and have had patterns published in various knitting magazines.

When do you use basic math in your job?  I use math for almost every aspect of what I do. It takes a lot of math to get from an idea and a ball of yarn to a written pattern somebody else can follow to make a finished sweater (or hat, or blanket, etc…)

The first thing I have to do to work up a new design is figure out the stitch and row gauges–or the number of stitches and rows in an inch of knitting with the yarn I’ve chosen for the design. To do this, I knit a square and then measure it, dividing the width measurement by the number of stitches across and the length by the number of knit rows. This gives me the number of stitches per inch (stitch gauge) and the number of rows per inch (row gauge). Every measurement after this–chest width, sweater length, sleeve circumference–all must be converted from standard inch measurements to stitch and row gauge. That means lots of math. Additional things like fancy stitch patterns, button and buttonhole placement, and shaping for armholes and necklines mean even more math.

Maggie Knit Blouse, one of Marie Grace’s designs

Once I’ve worked out all the counts and directions for my sample sweater I also need to figure all those same counts and measurements for various other sizes of the same design… sometimes as many as 8 sizes total. That way when you buy one of my knitting patterns you can knit sizes 2, 6 or 10 and have all the accurate directions and counts needed for the final product to turn out just like my original design sample. I also include how much yarn you’ll need for any given size which means–you guessed it–even more math.

Along with all the design stuff, I also have all the same responsibilities as any other business owner as far as figuring my incoming and outgoing funds, expenses, and taxes. More math!

Do you use any technology to help with this math?  Spreadsheets! Lots and lots of spreadsheets. I’m sort of a spreadsheet junkie. Most of the math I use is basic math, but its very repetitive so spreadsheets save lots of time and cut down on mistakes. It would take a ridiculous amount of time and effort to work up a new design from beginning to end if I didn’t have tools like spreadsheets.

How do you think math helps you do your job better? I couldn’t do my job with any sort of accuracy without math.

How comfortable with math do you feel?  I’m relatively comfortable with day-to-day math but I wouldn’t say I’m good at it. I have to stop and think things through one step at a time and I often scribble things down on paper even for simple calculations, just to be sure I’m on the right track. I’m much more comfortable with the math I do for work, simply because its so repetitive. Its sort of like doing multiplication drills on a regular basis.

Marie Grace Smith

What kind of math did you take in high school?  I went through Algebra, Geometry, Trigonometry, and Calculus by the time I was out of high school. I didn’t like math, and I don’t think I was naturally good at it. But I can figure things out given time and scrap paper. I think that’s how I managed through all the math in school.

Did you have to learn new skills in order to do this math?  The math I do for designing is all pretty much basic math (addition, subtraction, multiplication, and division), along with some algebra and percentages. It’s all stuff we all learn in school.

Do you have questions for Marie Grace?  Ask them in the comments section, and I’ll be sure that she sees them.

I’m still on my virtual book tour, visiting a variety of interesting spots all over the blogosphere!  Due to a technical glitch, my scheduled podcast at Out of the Storm News is postponed to next week, but you can catch up on last week’s travels at these links:

CollegeSurfing Insider: Why Math is a Must for Any Career

Frisco Kids: Q&A: Math for Grownups by Laura Laing

Flynn Media: When It Comes to Math, Parents Should Chill

Credit.com: A Simple Approach to Your Debt and Finances

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In Math at Work Monday

Math at Work Monday: Nikki the hair stylist

If you’re even the least bit vain, like I am, you know that finding a talented hair stylist is worth its weight in gold.  Like many other careers, that talent is part science and part art, as Nikki Verdecchia of NV Salon Collective in Baltimore can attest.  Nikki is an award-winning stylist who opened her own salon a few years ago.  Now, along with figuring the ratios for a custom color, she also does a lot of business math.  

Meet Nikki!

For Honfest, Nikki gives a young girl a traditional Baltimore beehive.

What kinds of things do you do each day at work?  I am a hair stylist and salon owner.  My job as a hair stylist on a daily basis is to make people look and feel their best.  As a salon owner I have to make sure that the business is running smoothly and that there is more money coming into the bank than there is going out.

When do you use basic math in your job?  As a salon owner I use simple addition and subtraction to make sure the salon’s income supports the checks I write each month.  I also need math for payroll.  For this I use percentages since our stylists are paid a commission, or a percentage of the money they bring into the salon.

As a hair stylist, I use fractions to mix custom color formulas for our clients.  In order to make each formula special, we mix color tones together in 2 ounce formulations to create unique looks.  For instance, I may use 1 oz of dark golden blonde, 1/2 oz of dark neutral blonde, and 1/2 oz of light golden blonde to create a warm, buttery blonde for a client.

Nikki is also a makeup artist and works closely with Baltimore’s most notable burlesque duo, Trixie Little and the Evil Hate Monkey

Do you use any technology to help with this math?  As a business owner, all of those tasks are done using computers and calculators so that I have records of everything I do.  Since I am often dealing with large numbers, it makes my job easier to use technology.  As a stylist I am a creative person first and foremost, and the computations I do to mix color are done with mental math.

How do you think math helps you do your job better?  I would never get the paychecks right or be able to create beautiful color without math!  It keeps me consistent.

How comfortable with math do you feel?  I have always been comfortable using math to create hair color.  When I opened my business and had to start using math more often I was very uncomfortable and sure that I wouldn’t be able to do it well.  I have surprised myself that I am much better at it than I ever thought I was.  Technology definitely makes it so much easier!

What kind of math did you take in high school?  I took algebra, geometry and calculus in high school.  My grades in those classes were dramatically lower than language-based classes that I took.   I never liked math before, but every time I balance my check book to the penny at the end of the month I get this secret thrill that I have managed to overcome a fear I had and learn how to perform a new task that I never thought I could do well.

Did you have to learn new skills in order to do this math? Most of the math I do every day is so simple that I’m sure I learned it in grade school.

Questions for Nikki?  Please post them below, and I’ll make sure she sees them.

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In Math at Work Monday

Math at Work Monday: Martha the cafe owner

Boheme Cafe in downtown Baltimore

My friend Martha Lucius owns and manages Boheme Cafe in downtown Baltimore.  She has also catered my book launch before, and so I thought it would be great to introduce you to her — and to the math that she does.  

What is involved in owning and running a cafe?  My job is diverse; I wear many hats.  I make sure that customers can be served the food on the menu (a matrix of salads and items for the pastry case), which also means ensuring that staff follows the recipes (read: math) every time. I also make sure our catering clients get trays of food and that they receive their bill.  And my job includes marketing, artwork, and simple mechanics!

When do you use basic math in your job?  I make conversions every day: pounds to ounces or vice versa.  My entire business profile is on QuickBooks, so often I can ask the program to do the math for me, but simple percentages, and regularly noting where daily numbers are, helps me know how healthy the business is. (Healthy and profitable are actually related subjects.)

Do you use any technology to help with this math?  We do use calculators and computers; they confirm the math that we do in our heads.  Sometimes we talk about food costs, which refers to how much we are paying for any one product.

How do you think math helps you do your job better?  I must do the math on my job or I would be out of business.  Without math, I would not necessarily know if there is money in the bank to do anything.

How comfortable with math do you feel?   I am comfortable with the math I use at work, and at home.  My daughter takes algebra, which I like, but I wish she wouldn’t rush me… it takes me a while to understand the topic they are discussing.

What kind of math did you take in high school?  I took high school algebra, geometry, and trigonometry, and I was comfortable with it.  As time has passed, I have come to love getting the correct answers!

Did you have to learn new skills in order to do this math? No, most of the math I do is just a reintroduction to math I already knew. I just have to reach back there and see what I did know–get back to the page in the proverbial textbook.

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In Math at Work Monday

Math at Work Monday: Ron the web designer

Ron Doyle

Ron S. Doyle is both a web designer and a freelance writer.  In fact, he’s found a particular niche in developing web sites for other freelance writers.  He’s also got a wicked sense of humor and uses math in his work.

Can you explain what you do for a living?

The highfaluting answer: I help clients build or restructure their online presence through web development and design, business analysis, project management, strategic brand management, consultation and training.

The mundane answer: I make websites!

When do you use basic math in your job?

I use proportions, algebra and basic geometric concepts at work every day. Most of what I’m doing involves simple addition, counting pixels. For example, if a website’s main container is 960 pixels wide, I have to make sure that all the margins, padding, borders and boxes inside add up.

The Health*Conscious*Travel homepage above  is 960 pixels wide, but here’s what I see:

2px border + 21px padding + 1px border + 555px feature box + 1px border + 21px padding + 1px border +

334px subscribe box +1px border + 21px padding + 2px border = 960 pixels wide!

This basic addition turns into algebra when a client comes to me and says “I have this 300 pixel wide advertisement that must go here” or
“I want to embed this YouTube video there.” Then all the other elements become variables—and I change them to make everything balance with the ad or video.

It gets even more complicated when I start adding things like drop shadows or glowing edges to an object, which have a specific radius from the edge. A 3px drop shadow spreads 1.5 px past the edge of the object, etc.

Certain objects, like videos, also must appear in specific proportions, e.g., 16:9. For example, if I know I must fit a high-definition video into a space that’s 500 pixels wide, I know that the video will be a little more than 281 pixels tall.

16/9  =  500/x

16x  =  4,500

x  =  281.25

I also use proportions for my favorite design element: The Golden Ratio, 1: 1.618. It’s a proportion that naturally occurs in nature and is used widely in design and architecture. I agree with the ancient Greeks that it’s a beautiful shape and I try, whenever possible, to use it in my designs. Sometimes, it’s a fun little secret for me. For example, Ann Logue’s website doesn’t seem to have many boxes or rectangles at all:

But there are actually seven golden rectangles coded into the layout:

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I use paper to draw initial designs, a calculator to figure out proportions and design software like Adobe Creative Suite to help with measurements and placement of objects before I write any code. I suppose I could do it all while I’m writing the code, but I like to keep costs low for my clients—and I like going outside from time to time.

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

Math doesn’t just help me do my job better, it makes it possible.

How comfortable with math do you feel? 

None of this math feels uncomfortable to me. All web designers use math, whether they realize it or not, but some have a natural ability to see things like the golden proportion without picking up a calculator. I don’t know if I have that innate aesthetic skill—so the numbers make me feel more confident in my design decisions.

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

I didn’t develop a relationship with math until the seventh grade. That year, I had a great algebra teacher; things just clicked and I’ve loved mathematics ever since. I took Geometry, Algebra II, Trigonometry, PreCalculus and AP Calculus in high school. I always felt confident in math class, except Calculus; my teacher struggled teaching the subject and I had a bad case of graduation fever.

As a psychology major in college, I didn’t love research but I enjoyed the statistical part of the work (and I took Calculus for Engineers even though it wasn’t required). Before I started my current business, I was a high school teacher. Trigonometry was one of my favorite subjects to teach.

Did you have to learn new skills in order to do this math? Or was it something that you could pick up using the skills you learned in school?

School definitely helped me feel confident with math, but I learned the skills I use today from building things with my father when I was younger. I spent a lot of my childhood with a tape measure with my father rattling off fractions at me—I understood 5/8 and 3/4 and 9/16 on a visual level long before I learned them in school.

Everything else I learned from Donald Duck in Mathemagic Land:

Do you have questions for Ron?  If so, ask them in the comments section below.

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Math at Work Monday: Graham the fish hatchery technician

Graham Laing is my brother, and I don’t think he’d be offended by my telling you that some of us in the family were a little worried that he might not amount to anything.  But that’s another story for another day.  Today, he’s a fish hatchery technician, which basically means he raises trout — “from eggs to eating size,” he says.  That means he moves truckloads of live fish from pond to pond (and raceway and stream) according to their size, and he treats them for parasites and other oogie things.  He also does a lot of weed whacking and mushroom hunting.  

You might not think that a guy who works outside all day long would use math, but Graham does.  And I think his approach is pretty unique.  As you read through this, see if you can figure out what he’s not doing.  I’ll share my thoughts at the end.

Graham wrestles a snapping turtle. Yes, this is part of his job (but I don’t think the turtle does math).

When do you use basic math in your job?

I use basic math every day. When we load the trucks in the morning, we’re told to load a certain amount of pounds of fish per tank on the truck. Since we can’t load all of the fish at one time, we’re handed a net of fish that usually weighs between 40 and 50 pounds. We have to keep track, in our heads, of how many pounds we have in each tank until it is loaded.

I also use basic math when we treat fish for parasites, using either salt or formalin. Salt baths depend on volume, so I find the volume of the tank in cubic feet and then multiply that by the number of gallons in a cubic foot–to get the total number of gallons to be treated. Then I have to multiply that by the number of pounds in a gallon of water to find the total number of pounds of water to be treated. Since we usually do a 5% salt bath, we find the number of pounds in 5% of the volume and weigh the salt.  Finally, we can mix the salt in the water.

When treating with formalin, we have to calculate a gallons-per-minute flow rate. We find this by counting the number of seconds it takes to fill a gallon and then divide that number into 60.  (There are 60 seconds in a minute.)  So if it takes 10 seconds to fill a gallon, the flow rate is 6 gallons per minute.  Since the treatment runs for an hour, I multiply by 60 and then multiply that number by 0.0036, which is the number of grams of formalin needed per gallon. Finally, I multiply by the parts-per-million needed for the treatment, which depends on the water temperature.

Do you use any technology to help with this math?  

I use calculators for sampling and for calculating the treatments. If we’re doing a lot of samples at one time, we plug the numbers into an excel spreadsheet that has the formulas we need. Calculators reduce error. One blown sample due to error could cause us to underestimate the number of fish in a raceway. Or it could cause us to underfeed a raceway, resulting in a large size-variation of the fish.

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

Graham is also a master at finding little critters like this toad. Click on the picture to see it up close. (Photo courtesy of Mary Bruce Clemons)

My whole job revolves around math.  Without math, the fish would die or become infected with parisites. We would not know how many fish we have on the farm, and we wouldn’t know if we were reaching our stocking goal set forth by the state.

How comfortable with math do you feel?  Does this math feel different to you?

I feel very comfortable with math and have since I was a very small child. When I got this job, I had all the skills I needed — it just took a little remembering to become adept at using them.

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

I took algebra, geometry, and trig.  I was forced to take trig, so I didn’t do so well in it. I slept through trig everyday and was still able to make 40s and 50s on the tests just by intuition.

Trust me.  If you met Graham you wouldn’t know he’s a math geek.  He doesn’t give a whit about calculus or abstract algebra or fractals.  He’s just really good at mental math.  

Here’s the interesting thing about Graham’s process: All of the math he describes above can be represented by formulas.  And when Graham uses a spreadsheet for the math, he has to use the formulas.  BUT when he uses math in the field, he unpacks each formula into a set of steps.  (First multiply, then divide, then multiply, etc.)  He doesn’t have to memorize a formula to do the work.  Instead, he thinks about the process, and he’s attached meaning to each step (“divide by 60 because there are 60 seconds in a minute”), so he doesn’t forget to do something.  This is the foundation of mental math — breaking up complicated problems into doable steps.

I’m betting many of you do the same thing.  Want to share that process in the comment section?  I sure hope you will!

And if you have questions for Graham — whether they’re about huge snapping turtles, tiny toads or wildlife management in general — post them, and I’ll be sure to get Graham to answer them.  (I am his big sister, so I can boss him around — a little bit.)

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Math at Work Monday: Andy the robot guy

Because of the 4th of July holiday here in the states — and because this is so darned cool! — I’m veering a little from the normal Math at Work Monday topic.  We’re going to get a little geeky today with Andy Testa, a simulations and analysis engineer for NASA.

Andy Testa, simulation and analysis engineer

Okay, I don’t even know what a simulations and analysis engineer is, but yeah, Andy uses lots of math in his job–but not the way you think.  He operates a robotic arm for the Space Shuttle, which will enjoy its last launch later this month.

So get your geek on, and enjoy a little independence from any math fear or anxiety you may have.  Andy has a cool job that’s worth reading about!

Can you explain what you do for a living?

I work at NASA’s Johnson Space Center as a support engineer for the Space Shuttle’s robot arm, known as the Remote Manipulator System or Canadarm. I’m responsible for running computer simulations of the arm performing new tasks or moving new payloads and am also an expert on the arm’s control software running on the Shuttle’s computers. [pullquote]It isn’t efficient to do advanced math all the time. The hard stuff is built in to the simulators and special software that we develop one time. The day-to-day work is much more basic.[/pullquote] The simulations are usually to make sure that planned operations won’t stress the arm beyond what it’s designed to handle, which is surprisingly easy to do. I do troubleshooting when something doesn’t work right during a mission, whether that’s a software glitch, a mechanical failure, or an unplanned procedure that has to be simulated. Much of the time I’m working on backup plans for how to complete a mission if any number of potential failures happen.

When do you use basic math in your job?

When I describe my job to most people they respond with “I could never do that!” They imagine that I do a lot of advanced math, but the reality is that it isn’t efficient to do advanced math all the time. The hard stuff is built in to the simulators and special software that we develop one time. The day-to-day work is much more basic.

So, I use basic math every day. When working with robots like the Shuttle arm you’re constantly having to think about two things: the position of the tip of the arm in space, and the angles of all of the joints.  These are related by geometry and trigonometry. I spend a lot of time working out geometry problems relating to the payloads that the arm moves. Each payload, like satellites or a piece of the Space Station, has to have a lot of numbers generated to allow the robot’s computer software to move them correctly. I need to calculate where the arm attaches itself, where the mass is centered, where the docking ports are located, and the direction the arm should move in when the astronauts move the controllers. Trigonometry is also used quite heavily, since I spend a lot of time worrying about angles and rotations, whether for each individual joint on the arm, or coordinated rotations of the payload as a whole.

Do you use any technology to help with this math?

That’s the robotic arm. (Photo courtesy of NASA)

Yes, we use computers constantly to help with the math, especially when we have to calculate trigonometry problems. Many of the problems I work on are similar enough that I can make a template for them in a spreadsheet, and use that over again with new payloads. For example, I frequently have to calculate a specific set of rotations to define how the arm attaches to payloads. By doing the calculations once and storing them in a spreadsheet, I can use it again just by inputting the unique geometry of each new payload. It saves a huge amount of time and effort, and lets me send all of the calculations to other people by sharing the files.

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

Not just better; without math my job would not be possible. Everything about spaceflight, including the Shuttle robot arm, is completely dictated by math. Knowing math not only allows me to continue to solve the problems we know about right now, but it also gives me the tools I need to figure out how to solve new problems.

How comfortable with math do you feel?

I feel quite comfortable with the level of math I use on a daily basis. I will frequently use similar math at home for hobbies or entertainment, for example, finding out exactly how much bigger a new widescreen TV is than my old tube TV.

What kind of math did you take in high school?

I took mostly standard college prep math classes in geometry and algebra. I didn’t take calculus until college. I was relatively good at math in high school, but I didn’t really understand it well until after a few years of practice in college.

Did you have to learn new skills in order to do this math?

Much of the math I use daily could be easily taught to someone with good high school math skills. Using the geometry and trigonometry to build descriptions of payload and robot motion is a skill that was developed more in college physics classes, though. That doesn’t mean it’s harder, just that it’s a specialized way of using the basic math that is being taught in high school. But the meat of what I do, hand calculating angles, areas, and sines and cosines, are straight out of basic high school math.

Thanks so much for playing, Andy!  Readers, if you have questions, please feel free to post them in the comments section.

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In Math Education

Is Math a Foreign Language?

When I was in college, majoring in math education, I learned that math is the language of science.  In fact, we called it the Queen of the Sciences.  (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!)  And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science.  [pullquote]We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar. — Rick Ackerly[/pullquote]

In some ways, everyday math is also the language of science.  Home cooks use ratios to ensure that their roux thickens a gumbo just right.  With proportions, gardeners can fertilize their vegetable beds without burning the leaves from their pepper plants.  And a cyclist might employ a bit of math to find her rate or the distance she’s biked.

But I think too often we adults get caught up in the nitty gritty of basic math and lose the big picture.  This is when many of us start to worry about doing things exactly right–and when math feels more like a foreign language, rather than a useful tool.

Earlier this week, I read a blog post from Rick Ackerly, who writes The Genius in Children, a blog about the “delights, mysteries and challenges of educating our children.”  In Why Mathematics is a Foreign Language in America and What to Do about It, he writes:

Why do Americans do so badly in mathematics? Because mathematics is a foreign language in America. The vast majority of children grow up in a number-poor environment. We’ve forgotten that the language of mathematics is founded in curiosity.  We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar.  Being curious together can be a really special part of the relationship in families.

And I couldn’t agree more.  For all of you parents and teachers out there: how many questions do your kids ask in one day?  10? 20? 100? 1,000?  As Ackerly points out, especially younger children are insatiably curious.  They want to know why the sky is blue and what makes our feet stink and how come that ladybug is on top of the other ladybug.

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

A full 90% of the time, we can’t answer their questions. Or maybe we just don’t want to yet.  (“That ladybug is giving the other one a ride.”)  With Google‘s help, we can find lots of answers.  But how often are we asked a math-related question–by a kid or a grownup–and freeze?

For whatever reason, many people are afraid to be curious about math.  Or they’ve had that curiosity beaten out of them.  I think that’s because don’t want to be wrong.  As fellow writer, Jennifer Lawler said to me the other day:

It’s funny because when I make a mistake in writing—a typo, etc.—I let myself off the hook (“Happens to everyone! Next time I’ll remember to pay more attention.”) But if I misadd a row of numbers I’m all “OMG, I’m such an idiot, and everyone knows I’m such an idiot, I can’t believe they gave me a college degree, and why do I even try without my calculator?”

The same goes for answering our kids’–or our own–calls of curiosity.

So what if we decided not to shut down those questions?  What if it was okay to make some mistakes?  What if we told our kids or ourselves, “I don’t know–let’s find out!”  This could be a really scary prospect for some of us, but I invite you to try.

What’s keeping you from being curious about everyday math? What do you you think you can do to change that?  Or do you think it doesn’t matter one way or the other?  Share your ideas in in a comment.

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In Math at Work Monday

Math at Work Monday: Beth the registered nurse

Elizabeth Hanes, RN

Beth Hanes is a registered nurse in a plastic surgery center.  She takes care of patients before, during and after their surgeries.  Here’s how she uses math everyday.

What kind of math do you use in your job?

I use basic math for a lot of things, but probably the most important calculations are the ones related to medication use. Sometimes I dilute medication before giving it. For example, Promethazine needs to be diluted before it’s given in an IV. Using a 10mL syringe, I draw up 1mL of Promethazine and then add 9mL of normal saline (0.9% sodium chloride) to create a 10% Promethazine solution.

I also use basic math to determine, based on body weight, how much medication to administer. Medications are generally given on a milligram per kilogram basis. So, I convert a person’s weight in pounds to weight in kilograms (divide pounds by 2.2 to obtain kilograms), then I multiply this number of kilograms by the number of milligrams per kilogram to get the correct dosage. For example, Lidocaine might be ordered as 1mg/kg. A 220-pound patient weighs 100kg, so the correct dosage is be 100mg of Lidocaine.

How do you do your calculations?

I do use calculators because they’re typically faster, but I think it’s important to know how to do math by hand. I usually don’t have a calculator on hand in the operating room! Also, it’s critically important for me to have basic formulas memorized (such as how to convert pounds to kilograms). Without that knowledge, having a calculator or not is irrelevant.

Why is math important for your job?

Math skills help me ensure patient safety. There was a highly publicized case a few years ago in which actor Dennis Quaid’s infant twins were administered a very high dose of Heparin. This error occurred for many reasons, but one key factor was doing the math involved. This is a classic case of calculating dosage based on weight, and obviously errors were made in that calculation. In nursing, if you misplace a decimal point, you can kill someone.

When it comes to math in nursing, I think the main thing is to be very careful about calculations, double-check them, and then have someone else double-check them. No matter how good you may be at math, anyone can misplace a decimal point when calculating on-the-fly. It’s much better to take the extra seconds to have someone review your calculations and keep patients safe than to have any sense of ego about your math ability and endanger a patient.

What kind of math did you take in high school?

I had a rather sketchy math education, because my parents moved around a lot, and I only made it through Algebra II. On the other hand, advanced math was not yet common at the high school level when I was that age. Calculus, for example, was a college course. I did not feel I was good at math in high school. However, this “low math esteem” led me to focus on practicing real-world math skills.

These days, I am fairly comfortable with math, in general, though I frequently have to think through conversion problems, which are common in nursing. I find I often want to divide when I should multiply, for instance, so I have to be careful about that! Once I have a formula memorized, however, I feel very comfortable substituting variables with real values and arriving at the correct answer.

If you have questions for Beth, ask them in the comments section.  Oh, and today, June 20, is her birthday!  So take minute to wish her a happy day!

Read other Math at Work Monday entries in the archive.  And if you or someone you know wants to be interviewed for this regular, Monday feature, let me know.

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In Math Education

Math for first graders

Want to know what really burns me up?  Telling a kid he’s not good at math.  Know what’s just as bad?  Telling a mom that her kid isn’t good at math.

This morning, I was early for my fitness boot camp class.  (Sadly, I don’t get to work with Robert the personal trainer.)  I chatted with a couple of the women who, like me, show up every morning at 6:45 for an hour of torture.  Of course, I had to share that I got advance copies of my book, Math for Grownups, yesterday.  Per usual, the conversation turned to the absolutely ridiculous and completely frustrating notion that people are either good at math and science or they’re good at language arts.

Now, for the record, I wholeheartedly disagree with that line of thinking. (Can you tell?) Keep reading to find out why.

One mom said that her son’s first grade class was good at reading but not math.  How did she know this?  The teacher told her.  There are so many unbelievably wrong things about this situation, and thinking about it makes me want to scream:

  1. They’re first graders! How can six year olds be bad at math?  They might be missing some basic concepts, like counting up to add or the difference between a triangle and a square. But remember, nobody is born bad at math.
  2. It’s the teacher’s job to make sure kids understand basic math concepts.  Blaming the students is a cop out.
  3. Telling parents that an entire group of kids is bad at math is a self-fulfilling prophecy.  Already, parents (and other grownups) believe that math ability is like being tall or having blue eyes–you either have it or you don’t.  This teacher may have unwittingly reinforced this idea, by making such a silly generalization.
  4. If she told the parents this, what message is she sending the kids?  If you’ve been a parent, you know that there are a trillion different messages that we send to our kids every day, without even knowing it.  I would bet my last dollar that this teacher is somehow relaying to her students that math is just not their thing.

First graders who think they’re not good at math, grow up to be middle schoolers who think algebra is beyond them. These middle schoolers of course awkwardly morph into teenagers who are convinced that they won’t need (and can’t do) geometry, trig, advanced algebra, probability, statistics and calculus. And then of course, these acne-prone, love-sick adolescents become the smart, successful adults who tell me every day that they desperately need my book, because they can’t balance their checkbooks to save their souls.

But really, I’m not blaming this one teacher.  I promise.  She’s just the beginning of a long line of teachers and other grownups who buy the lies about math: that only people with “math brains” can comprehend the Pythagorean Theorem and no one uses math in everyday life anyway.

So, what’s the solution?  The issue is not the students.  The issue is that we somehow believe that there is only one way to teach math.  Of course that’s not true.  Teachers and parents have to figure out how our kids think and approach math in a way that makes sense to them.  And we have to quit labeling ourselves and our kids.

All you parents out there, I’d be forever grateful if you’d do just one of these things:

  1. If a teacher says your kid is bad at math–or worse, declares an entire class bad at math–please challenge him or her.  There are only a few people in the world who have real issues with processing mathematical information, and I’m betting your kid isn’t one of them.
  2. Stop telling people that you, yourself, are bad at math.  Next time your dinner companion asks, “Can you help me figure out the tip?” bite your tongue.  If you truly can’t find 15% of $24.68, pretend you didn’t hear or fake it.  But please avoid saying the all-too-common, “I’m so bad at math!”
  3. If you can’t help your kid with his homework, don’t declare: “I just don’t have the math gene!”  Here’s the reality:  You may not remember how solve a proportion, but that’s because you probably haven’t seen one for at least 15 years.  If you were asked to diagram a sentence and couldn’t do it, would you say that you’re no good at speaking English?  Of course not.
  4. Replace your generalizations about math ability with messages like these: “I don’t remember how to do that.  Let’s figure it out.” or “I remember doing these kinds of problems in school, and they gave me trouble.  But I’m sure we can figure it out together.”

And just a quick footnote/disclaimer: I am the biggest advocate of schools and teachers that you will ever meet.  Having been a public school teacher and been raised in a family of teachers, I’ve seen first-hand what our educators face on a daily basis.  I just wish I didn’t hear stories like the one I heard this morning.

I’m going to gingerly climb off of my soapbox now.  (My glutes are killing me after that workout!)  But I ask you to share your thoughts on these generalizations about math ability and math education.  What messages have you or your kids received?  What do you think about them?  How do you think we can counter them?  And for all you teachers out there: how do you send the message to your students that they are good at math?

I’ve decided to start a regular feature about math education, called Summer School.  In it, I’ll discuss some ways that parents can send the right messages about math.  We don’t need another generation of grownups who think they can’t do math!  🙂

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