Math for Grownups

Category: Math for Grownups

  • Math at Work Monday: Beth the nurse

    Math at Work Monday: Beth the nurse

    When I was really young, I wanted to be a nurse. Those who know me now are probably laughing. It’s not that I’m squeamish about blood, but I absolutely cannot handle any other, um, bodily fluids. Ick. Thank goodness for people like Beth Hanes, who have made a career of caring for others who are sick or undergoing surgery. [Editors note: Since this interview appeared a year ago, Beth has decided to freelance write full time.Now that I can identify with!]

    Beth Hanes is a registered nurse in a plastic surgery center.  She takes care of patients before, during and after their surgeries.  And, of course, 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 actorDennis 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. 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.

  • X to the Power of Huh? Or, How Math Anxiety Almost Ruined My Life

    X to the Power of Huh? Or, How Math Anxiety Almost Ruined My Life

    I’m betting that many of you dear readers will identify with today’s guest post from Lisa Tabachnick Hotta. Math anxiety may still dog some of us, but it doesn’t have to ruin our lives. Read my guest post on her blog here.

    “Miss Tabachnick,” exclaimed my grade 8 math teacher.  “Please come up to the board and demonstrate how you obtained the answer to that equation; I’m sure the entire class will benefit from your explanation.”

    Sweat trickled its way from my brow to my toes. Show the class? Now? At the chalk board? Somehow I must’ve squeaked out the answer because I did graduate – from grade 8, then from high school and ultimately obtained two university degrees. (My majors, of course, had absolutely nothing to do with math!)

    Anxiety in all its sweaty glory – shaky hands, racing pulse, nausea – is pretty much the story of my life when it comes to math. Of course I’m rarely at a chalk (or smart) board deciphering mathematical problems these days as a writer, community volunteer and parent. But, you will often find me deep in “grownup” math conundrums.  Here are but a few examples:

    • Recently I was out for dinner with the girls and we were splitting the check. “Anne, you’re the accountant, you can figure out what we all owe,” I half-joked to one member of our group. She wasn’t amused. (Maybe it’s like the doctor who’s always getting asked for health tips at parties?) Her reluctance to assist me meant having to figure out not only what my drink, dinner and dessert cost but also my portion of the tax and tip – not at all easy for someone who’s math challenged!
    • My son who is (miraculously) gifted in math, asked me fairly simple questions in the car as a kind of numbers game: What’s 2 + 2, What’s 4 + 4, What’s 8 + 8, What’s 16 + 16, etc. Now, the first few questions? No problemo. But, as the numbers and queries got larger, I had to think harder to come up with the answers and, yes, that in turn increased my anxiety level.
    • Just today my kids and I were at a medical appointment. The administrator explained that receiving a response from the government to our query could take up to 30 weeks. I laughed along with the other adults who joked about government inefficiencies but, somewhere in my mind, I was still trying to figure out how many months equalled 30 weeks.

    All joking aside, being mathematically challenged has caused me enormous stress. From hiring tutors throughout middle and high school, to being told (by that same grade 8 math teacher) that I’d never amount to anything because my math skills were so poor, to ensuring that I am charging clients appropriate rates on invoices – I’ll be forever haunted by issues around math.

    So, how do I cope as a math-phobic adult? Luckily, I’ve learned to lean on my strengths – writing, communications and art. I also lean on calculators! Have you heard the expression, “fake it ‘til you make it”? I’ve also employed that strategy more than once. And, I’ve found that humor works well – I’ll just admit outright that math isn’t my forte and, while I’d be happy to volunteer as project manager or group leader, appointing me treasurer really isn’t the best idea.

    Lisa Tabachnick Hotta is a professional writer, editor, social media expert and researcher who lives just north of Toronto, Ontario. Lisa specializes on topics related to health, mental health, family, the arts and society. Check out her blog: KidsAndMentalHealth.com.

    What are your childhood memories of math anxiety? How does math anxiety influence your life now? How have you learned to get around it?

  • Math at Work Monday: Labor Day 2012 Edition

    Math at Work Monday: Labor Day 2012 Edition

    It’s been a rough year for the U.S. economy and workforce. No matter what your political stripe, there’s no sugar coating the numbers: unemployment is still high and people around the country are struggling. In honor of Labor Day, we’ll look at the numbers behind this news.

    Once a month, the Bureau of Labor and Statistics releases its employment data, and here are some interesting numbers from July 2012. (August 2012 data will be released on September 7, 2012.) Remember, this is just raw data. The numbers are important, but they can’t really tell the story behind the country’s (or a portion of the population’s) economic and employment situation. People will interpret this information differently, based on their ideologies and personal philosophies. (Politicians will interpret this data based on who they want to attract to the voting booth.)

    155.013 million: The number of people in the workforce (16 years and older).

    47.8: Percent of women in private workforce

    82.6: Percent of women in total production and non-supervisory positions.

    34.5: Average weekly hours worked for all employees.

    33.7: Average weekly hours worked for all production and non-supervisory positions.

    $23.52: The average hourly earnings for all employees.

    $19.77: The average hourly earnings for all employees in production and non-supervisory positions.

    11.472 million: Number of people in the workforce with less than a high school diploma or equivalent.

    37.047 million: Number of people in the workforce with a high school diploma or equivalent.

    37.398 million: Number of people in the workforce with some college or an associates degree.

    47.697 million: Number of people in the workforce with a bachelor’s degree or higher.

    9.616 million: Number of self-employed workers (including agriculture workers).

    8.246 million: Number of people who are working part time (one to 34 hours a week), for economic reasons.

    6.9: Unemployment rate* for all veterans.

    8.9: Unemployment rate for all Gulf War II-era veterans.

    12.4: Unemployment rate for all Gulf War II-Era veterans in the previous month (June 2012).

    8.3: Unemployment rate for all non-veterans (18 years and older).

    18.866 million: Number of people who are working part time (one to 34 hours a week), for other reasons (including childcare problems, school, training or family or personal reasons).

    2.711: Number of people who have been unemployed for less than 5 weeks.

    3.092 million: Number of people who have been unemployed for 5 to 14 weeks.

    6.945 million: Number of people who have been unemployed for more than 15 weeks.

    38.8: Average duration of unemployment in weeks.

    *The unemployment rate is the percentage of the workforce that is unemployed at any given date.

    Based on these numbers, what do you think about the current economy? What kinds of questions do these numbers raise? Are there other numbers that you would like to see? How does this data inform you as a voter? (Don’t worry, we won’t get into big political discussions here. I promise.)

  • Math at Work Monday: Tiffany the math teacher

    Today is the first day of school here, so I decided to repost this Math at Work Monday interview with Tiffany Choice, a middle school math teacher in Fairfax, Virginia. You might be a little surprised by how she uses math in her work!

    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.  

  • Common Core Common Sense: Myths About the Standards, Part 4

    Common Core Common Sense: Myths About the Standards, Part 4

    In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the fourth in that series (read Myth 1, Myth 2 and Myth 3), which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

    Myth #4: The Standards Require More Testing

    Perhaps the most controversial aspect of the U.S. education system is standardized testing. And for good reason. There are a myriad of problems with these tests–from their links to private companies to their use as teacher evaluation tools.

    While I’ve said from the start that it’s not fair to judge the Common Core Standards based on their implementation in individual states, it’s also not fair to pretend that the standards and testing don’t go hand in hand. States aren’t abandoning standardized testing any time soon, so don’t hold your breath.

    But what we do know for certain that the adoption of Common Core Standards does not mean more testing–in the long run. In fact, there is no testing requirement inherent in the adoption of Common Core. None!

    However, as states move from previous standards to Common Core, there will be some changes in testing. First, student may take two sets of standardized tests–at first. In these situations, one test is the one aligned with the state’s previous standards. And students may take practice tests, based on the Common Core Standards. Usually this translates to more testing during one school year, with only one test score used for student placement or teacher and school evaluations.

    Because the Common Core Standards focus on critical thinking, Common Core-aligned tests will probably look a little different than the all-multiple choice tests that we’re all used to. Students are required to show their work and may even be asked to explain how they came to their answers. Here’s a two-part example, which corresponds with the third grade math standards:

    A. Fill in the blanks below to make a number sentence that represents the drawing:
    ________ x ________ = ________
    B. Put the dots below into five equally sized groups and write an equation that represents the drawing.

    •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  

    Answers:
    A. 4 x 6 = 24 or 6 x 4 = 24 or 8 x 3 = 24 or 3 x 8 = 24, etc.
    B.   •  •  •      •  •  •      •  •  •      •  •  •      •  •  •      •  •  • 
    3 x 5 = 15 or 5 x 3 = 15 or 15 ÷ 3 = 5 or 15 ÷ 5 = 3

    There’s something going in the above problems that’s difficult (or impossible) to measure with multiple choice questions. First, students are asked to draw as a way of problem solving. Second, there are multiple correct answers.

    (Psst. Want to test your third grade or fifth grade math skills? Take one of the Math for Grownups math quizzes. No one has to know your score. Promise!)

    So while Common Core does not eliminate testing or prevent test results from being used inappropriately, if the tests are well constructed–and dang, that’s a big if–students have a much better opportunity to demonstrate critical thinking and the open-ended nature of mathematics. That’s not more testing, that’s better testing.

    Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it! And if you missed Myth #1, Myth #2 or Myth #3, you can find the here, here and here.

  • Math at Work Monday: Samantha the Freelance Designer

    Math at Work Monday: Samantha the Freelance Designer

    I had the pleasure of speaking with Samantha Volz who has the pleasure of working from her very own home every day. That is one of the benefits of being a freelance designer. In addition to graphic design, this artist also does photography. It seems she is creatively blessed with talent.  I was curious about how she uses math in her work. Let’s take a look at what she had to say:

    Can you explain what you do for a living?

    I’ve been working as a freelance designer since 2001.  I design marketing/advertising material for companies. In addition, I also design websites and other support files for social media applications. I am a photographer, painter, and artist as well.

    When do you use basic math in your job?

    I have to use specifications to set up design files. Set up bleed, trim and safe zones so that when the file gets to the printer, it is set up correctly and prints correctly. For instance, if I have a print sheet that is 8.5 by 11 inches for a trifold brochure, I need to divide the paper by three and adjust 1/8th of the 3 panel. Depending on how the trifold folds, I will need to adjust the panels 1/16th of an inch if a panel folds in. Then, on the layout in the software I have to consider set up for a printing press or digital printing if my graphics bleed to the edge I have to add at least 1/8th to 1/4th of an inch of graphics that extends past the actual final layout for being trimmed down to allow for machine error. So my final file that is handed over to the print vendor is 8.5 x11 with bleed 1/8th bleed on all sides. Total graphic coverage is 8.75 x 11.25 trimmed down to 8.5 x 11 and scored for folds indicated on the set up with 3 panels roughly 3.66 ” wide, again depends on the fold design chosen for that tri-fold brochure how it will read, flow and open up to reveal the information being provided.

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

    Yes, I use a calculator a lot.

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

    I could not do my job without it. It is how everything flows from the client to me, the designer, and then to the printer until it is produced as an end product.

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

    I am comfortable with normal addition, subtraction, division, multiplication, and fractions. Nothing too complicated.

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

    I took honors math classes.

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

    Yes, what I use now I learned in high school.

    Who knew that the creative type still need to know their basic calculations and fractions?  Seems like everywhere you go, even in your home, math is sure to follow. I hope you enjoyed learning a little more about Samantha. Let me know if you have any further questions for her. 

    Photo Credit: 55Laney69 via Compfight cc

  • Math at Work Monday: Leah the firefighter

    Math at Work Monday: Leah the firefighter

    Leah Davis is tough as nails. She’s been a firefighter in North Carolina for 17 years. These days, she is a Captain EMT — intermediate. I had never really thought about the math required to fight fires, but reading through Leah’s responses, it all makes perfect sense. If your little guy or gal is interested in firefighting as a career, this interview is a must-read!

    Can you explain what you do for a living?

    I am a Captain on a fire engine. This means that I respond to and mitigate emergencies ranging from motor vehicle accidents, fires (all sorts), medical emergencies and rescues. In addition to providing emergency response, I complete preplans of existing businesses; the preplans are walk-through inspections that provide information about a building’s layout and any hazards that might be associated with the business. As a member of the fire service, I am responsible for participating and providing training in all aspects of the job.

    When do you use basic math in your job?

    Within the fire service, there are many opportunities to use math. The first one that comes to mind is calculating pump pressure to determine the PSI (pounds per square inch) on the end of a nozzle.  Basic math skills, like addition, subtraction, multiplication, and division, are necessary. A basic understanding of hydraulics and a good understanding of formula usage is vital.

    In order to calculate the amount of nozzle pressure is necessary, the engineer must find the friction loss of hose distance, along with appliances and elevation. Only then can the pump be set up properly. Engine pressure is the sum of the nozzle pressure plus the friction loss plus any elevation or devices. Based on the engine pressure formula EP = NP + FL, if we need a nozzle pressure of 100 psi to flow 100 GPM then the engine pressure needs to be greater then 100 psi.

    When determining how much water will be required for any given structure that is 100 percent involved in a fire, the fire engineer must calculate the area and divide by 3. This gives the gallons per minute required to extinguishing the fire.

    Math is also used when providing medical care. The division is used in calculating the correct dosage of medications to administer. Many medications are calculated milligrams per kilograms or mg/kg.

    Do you use any technology to help with this math?

    I use a calculator when finding the fire flow or GPM needed on the preplans.

    Technology is not usually used on the fire ground when calculating the engine pressure. The engineer needs to be well trained and able to calculate the engine pressure in their heads.

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

    Having a math competency provides me with additional problem-solving skills. The fire service is about problem-solving.

    [laurabooks]

    How comfortable with math do you feel?

    Although I am not a math whiz by any means, I do feel relatively comfortable with math most of the time. The math that is used within the fire service–like the area of a structure, GPM needed, nozzle pressure, medication dosage–helps ensure the safety of firefighters and others.

    What kind of math did you take in high school?

    I did not take much math in high school because I did not like it and did not feel successful. However, in college, I was required to take remedial math courses and then was able to move on to taking more advanced classes, including calculus. I graduated from college with a good understanding of math and problem-solving. I also found that I enjoyed the problem-solving aspect of math.  Too bad I didn’t pay more attention when I was in high school.

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

    I was comfortable with my math skills when I entered the fire service.

    Do you, or your child, have math questions like the ones in this firefighting story? If so, buy the book that will help you with the math here. As for summer-slide activities, why not take your child to a fire station for a tour? While you’re there, ask about the math required on the job.

  • Math at Work Monday: Charlie the baseball writer

    Math at Work Monday: Charlie the baseball writer

    Anyone who knows anything about baseball knows that math plays a pretty big role. From how the pitcher releases the ball to the many stats that help rank the best players, the game depends on numbers. No one knows this better than Charlie Vascellaro. He’s been a freelance baseball (and travel) writer for 20 years. Here’s how he uses math in his work.

    Can you explain what you do for a living?

    I write baseball and travel feature stories for magazines, newspapers and web sites. A lot of my baseball writings are historical retrospective pieces that include statistical analysis and comparisons. In a recent story on this year’s National Baseball Hall of Fame inductee, Barry Larkin, I compared his batting statistics to those of other shortstops enshrined in the Hall of Fame. I also write spring training preview stories on major league baseball teams that rely heavily on statistical information used to explain each teams relative strengths and weaknesses and how they compare to other teams. I use this information to measure each teams’ relative prospects for the upcoming seasons. Last spring I wrote a feature story on current players chances of being elected to the Hall of Fame based on statistics produced so far and projections for the future (see excerpts below).

    Jered Weaver, 29, had what could be described as a breakout season in 2011, reaching a career best with 18 victories and a 2.41 ERA. In six seasons, Weaver has compiled an 82-47 record, for a very Hall-of-Fame-like .632 winning percentage with a 3.31 ERA.  The 300-victory-pitcher is fast becoming an endangered species, and consequently, not a necessary prerequisite for the Hall, but Weaver would still have to maintain his current pace, and actually improve upon it a bit, to merit consideration for Cooperstown; a 20-win season or two would certainly improve his chances. 

                Of the current White Sox players, slugging first baseman/DH Paul Konerko compares favorably with Hall of Famer Orlando Cepeda in similarity of scores posted on Baseball-Reference.com, and although he has not quite reached 400 home runs, (he’s currently at 396) he probably will this year. Konerko’s numbers are also similar to what Reggie Jackson’s were at the same age, and his .282 batting average is 20 points higher than Jackson’s .262 career mark. Jackson hit 39 home runs at age 36 and 99 home runs in his last 5 years on the field. Konerko hit 31 last year at age 35, and will probably end up pretty close to Jackson’s 563. In today’s age of inflated offense, Konerko’s eventual career statistics might be on the cusp of Hall-of-Fame-worthiness, but I like his chances. 

    When do you use basic math in your job?

    Oftentimes while I am writing a baseball story I will consult the www.baseballreference.com website to research statistical material. Sometimes I might have to tally up home-run and runs-batted-in totals and divide them by the number of years to decipher the average numbers per year.  I do a lot of multiplication and division to figure percentages. For example, a player’s batting average can be figured by dividing the number of hits by the number of at bats. Three hits out of 10 at-bats is 3 ÷ 10 or .300.

    Earned run average (ERA) is a measure of a pitcher’s relative effectiveness and is often referenced when writing about pitchers. Earned run average is the number of earned runs scored against a pitcher, divided by the number of innings pitched multiplied by nine (the number of innings in a regulation game). Earned runs are scored without the assistance of a fielding errors. ERA is represented with a number followed by a decimal and two percentage points explaining how many runs a pitcher gives up in an average nine-inning game. Here’s an example: In 1985, Dwight Gooden of the New York Mets gave up 47 earned runs in 276 and 2/3 innings pitched for a National League leading ERA of 1.53, a number which has not been reached by any starting pitcher since Gooden accomplished the feat. Prior to Gooden’s stellar season, no pitcher had recorded an ERA as low as Gooden’s 1985 figure since Bob Gibson of the St. Louis Cardinals in 1968. (His ERA was 1.12.)

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

    I use the calculator on my computer, which I can move around on top of the statistical information, so that both are visible to me at the same time.

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

    Math and baseball are inseparable. Mathematical measurements are employed to explain batters’ and pitchers’ relative success and failure. Individual and team statistics are used by writers to explain what has transpired during the course of a baseball game, a baseball season and a baseball career.

    How comfortable with math do you feel?

    I was not very proficient at math in high school or college. In fact I struggled with high school algebra which is as far as I have advanced in mathematical skills and could probably not solve an algebraic equation today. I would like to strengthen my math skills.

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

    Thankfully, I have been figuring batting averages and earned run averages since I first became a baseball fan. Fortunately I can still get by in my baseball writing with the rudimentary math skills that I have. However, statistical analysis in baseball has become much more complicated and there are certain statistical formulas that I do not understand.

    Read a few of Charlie’s stories:

    The Real Indians of Baseball

    The Living Spirits of Sports Legends

    The King and I: Remembering and Writing about Dave Kingman

    Do you have questions for Charlie? Ask them in the comments section, and I’ll let him know they’re here. Do you remember learning math through baseball when you were a kid? Share your stories below.

  • Math at Work Monday: Ethan the game designer

    Math at Work Monday: Ethan the game designer

    Aaaaand we’re back with weekly editions of Math at Work Monday! This month, we’ll have lots of great interviews with folks who are in the kinds of jobs that kids say they want. This way, parents can tell their kids with confidence: “Yes, you will need math.”

    First up is Ethan Ham, who is a game designer and professor. Games he’s worked on include Sanctum and The Sims Online. In fact, he’s such an expert, he’s written the book on game design: The Building Blocks of Game Design (Routledge, May 2013). As you might imagine, game design is chock full of math — the kind of math that most folks don’t do regularly. Take a look.

    Can you explain what you do for a living? 

    A game designer is the person who plans out the rules for a game, whether it is a board game or a computer game. A game programmer is the person who takes the game design and implements it on a computer. I did both of these jobs professionally for about 6 years. While I still work on the occasional game project, these days I spend most of my time teaching game design (at the City College of New York, CUNY) and writing about it.

    When do you use basic math in your job?  

    The main math I use as a game designer include probability and algorithms.

    Any game that involves chance (such as the chance that a sword swing in World of Warcraft will hit) requires probability. It’s an odd branch of math and something that our intuition is often wrong about. When I teach game design, I always introduce probability by asking my students what are the odds that rolling two six-sided dice will result in at least one die coming up as a “6.” In the past 8 years I have never had a student guess the correct answer (11/36).

    (Editor’s Note: Ethan developed this dice simulator to help game designers quickly deal with probabilities. It’s very cool!)

    An algorithm is a like recipe for making a calculation. A lot of computer game design involves coming up with game mechanics in the form of algorithms.

    As a programmer, I largely use algebra, geometry and trigonometry. I don’t use calculus much, but would probably use it more often if I did games that involve modeling physics. Recently I used logarithms in some computer code that shifts the pitch of a sound.

    Beyond math, logic and problem-solving skills are incredibly important to game programming.

    Do you use any technology to help with this math?  

    Aside from the obvious need of computers to program the games, I often find myself searching the web to refresh my memory of how to calculate, for example, how to find the change in position based on an object’s vector.

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

    It’s critical—I couldn’t do my job without it.

    How comfortable with math do you feel?  

    I’m comfortable figuring things out that I don’t initially understand (a characteristic of most programmers). So even though I don’t always have the math I need in my head, I can track it down.

    What kind of math did you take in high school?  

    Geometry, trigonometry, one semester of Advanced Placement calculus. I was reasonably good at it, but not the best in my class (except for probability).

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

    Most of the math I learned in school, but I often need to re-learn it in order to put it to use.

    Do you (or your kids) have questions for Ethan? Ask them in the comments section, and I’ll be sure to let him know to come back and respond. But first, print out this quirky — and challenging — connect-the-dots picture that Ethan created. After reading the instructions on page 2, see if you (or your kid) can figure it out!

  • Algebra: Is It Too Hard for Students?

    Algebra: Is It Too Hard for Students?

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

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

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

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

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

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

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

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

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

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

    2. Higher algebra concepts describe how our world works.

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

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

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

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

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

    What’s so hard about that?

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

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

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

  • Comparison Shopping: Get the best vacation deal

    Comparison Shopping: Get the best vacation deal

    t’s summer. It’s hot. I’m busy with 9 million things. And so today, I bring you an excerpt from my book, Math for Grownups. If you’re wondering how to figure out the best vacation deal for you, read through this example. A little bit of planning–and math!–can help you relax, while you’re saving some cash.

    Going on vacation means packing, finding someone to take care of Fido, and taking some time off from work. It also means charging some pretty hefty items on your credit card.

    The finances of vacationing can boggle the mind. And even with online trip planners and the ability to comparison-shop with the click of a mouse, planning a vacation can make you ready for another one.

    Red and Emily are ready for their second honeymoon. After 25 years of marriage, two kids, and the stress of everyday life, they deserve it. So Red is going to surprise Emily on their anniversary with a 1-week getaway to Aruba.

    For 5 years, he’s been secretly putting away a little cash here and there. He’s got $7,500 saved up, and that’s just enough to whisk his bride away for some R & R. (That’s romance and rest.) Red has even arranged for Emily to take some time off from work.
    But first he’s got to figure out how he can spend his vacation nest egg. After Emily goes to sleep, he cruises trip-planning websites looking for the best deal. And he’s very quickly overwhelmed.

    There are all-inclusive packages, non-inclusive packages, romance packages, and adventure packages. Some include the cost of flights and drinks and meals. Others offer some combination of these features.

    It’s going to be a long night.

    Within an hour or so, Red has some options scribbled down on a piece of paper. He has chosen their destination—a secluded resort with 5-star dining, access to a private beach, a spa, and great online reviews. Now it’s on to the pricing. There are a number of options:

    Because two of his options don’t include airfare, Red prices out some flights. He finds out that he can get two round-trip tickets for about $925. Not bad!

    If he chooses a non-inclusive option, he’ll need to pay for meals, drinks, and activities. And that requires more research. Red wonders whether there is a good way to estimate these.

    He considers meals first. The resort includes a free breakfast, so he won’t need to include that in his calculations. But unless they’re going with the all-inclusive option, they will have to buy lunches and dinners. Red does some more research and comes up with the following numbers:

    Average lunch → $25/person
    Average dinner → $60/person
    Average lunch → $25/person
    Average dinner → $60/person

    And because there are two of them, and they’ll be there for 7 full days:

    Lunches: $50 per day for 7 days = $350
    Dinners: $120 per day for 7 days = $840

    It looks like the cost of meals will be $350 + $850, or $1,190.

    He and Emily aren’t big drinkers, so that’s pretty simple to figure out. Assuming that the cost of drinks is pretty high, he guesses $25 a day for two fancy cocktails, and if they have a nice bottle of wine with dinner each night, that’ll run them about $200 for the week.

    ($25 • 7) + $200 = $375

    Now, Red thinks about activities. A day on a sailboat and some snorkeling sounds great ($450). Then he’d like to book a few spa treatments for Emily ($500).

    $450 + $500 = $950

    Because all of the prices so far have included tax, Red doesn’t no need to do any math for that. But he will need to tip the baggage carriers, taxi drivers, servers, and spa staff. Red takes a shot in the dark, and guesses $350 for all gratuities. (That could be too much, but it’s probably not going to be too little.)

    This is a ton of information, and Red’s legal pad looks like a football coach’s playbook. He’d better get organized if he wants to book this trip and get some sleep. Red decides to make a list.

    Package

    All-inclusive = $7,225

    Romance package: $6,150 (package) + $925 (air) =  $7,075

    Hotel + Travel: $4,340 (hotel/air) + $1,915 (meals/drinks/tips) + $950 (activities) =       $7,205

    A la carte: $3,450 (hotel) + $925 (air) + $1,915 (meals, etc.) + $950 (activities) =  $7,240

    Now Red can really consider his options.

    The most expensive choice is à la carte, but all of the totals are pretty darned close. If he goes by price alone, the clear winner is the Hotel + Travel package. But that requires him to handle everything on his own—and honestly, he’s ready for bed.

    On the other hand, the Romance package is only $70 more. And right now, that extra bit of cash seems worth it. Red pulls out his credit card and books their flights and vacation packages. Then he snuggles up next to Emily and savors his little surprise!

    How have you found the best travel deals? Share your ideas in the comments section.

  • Savings Tips from an International Traveler

    Savings Tips from an International Traveler

    I’m no big world traveler. So when faced with the prospect of filling an entire month with travel-related blog posts, I reached out to more experienced folks. Fellow freelance writer, Beth Hughes offered to write this post, detailing how she’s able to hop the globe on a limited budget. While there’s not a lot of hard math here, she does share a really smart estimation tip that helps her keep cash in her wallet–for her next trip. And you can definitely see how a little bit of planning and observation adds up to big savings. So, welcome Beth!

    When I travel, I usually head to pricey places like Japan, Hong Kong and Hawaii. Yet I’ve figured out how to make these trips without breaking the bank, even when the dollar is weak. The key is planning, observing, and a little mental trickery.

    Before you go

    Use a travel agent. Because I usually travel with a friend, my agent, Julie Sturgeon of Curing Cold Feet, creates custom group packages for us. Savings on our last 10-day jaunt to Hawaii were about $20 each, or a tank of gas. Some years, she saves us twice that.   Savings: $20-$40

    Decide how connected you must be. Free WiFi is not ubiquitous. Select a hotel with free WiFi so you can stay in touch via email and Skype if you have a smartphone or other device.  Savings: up to $20 per day

    Make sure you select a hotel that equips the rooms with an electric kettle and a refrigerator. Pack food for your arrival if you’re getting in late–small cans of pop-top tuna, packs of instant oatmeal, a little jar of peanut butter and some crackers. Pack coffee or tea, and any equipment for preparing it. Savings: about $10 per day

    Research the fees your bank’s ATM network, what it charges for ATM withdrawals and what service fee it tacks onto credit card purchases outside the United States. Your goal is to reduce the fee burden by withdrawing enough cash from an affiliated ATM to cover anticipated expenses for five or six days. You get a better exchange rate than you do at a moneychanger. In Tokyo recently, the airport moneychanger offered ¥71 for each US$1 while an affiliated bank’s ATM gave me ¥78. Stash the extra cash in your hotel room safe. Avoid using your credit card for a cash advance. The interest rates are punishing. Savings: up to $25

    Upon Arrival

    Buy a SIM card with the least expensive international call and data plan that you can top off online using a credit card. (In Japan, tourists must rent SIM cards.) The SIM card will be valid for as long as six months. You will probably leave money behind but compared with international roaming charges, it’s less than a pittance. Savings: up to $50

    After a good night’s sleep,  start saving by making breakfast in your room. While this is a traveler’s tip as old as the Appian Way I figure it saved us about $200 each on a recent Tokyo stay.

    Here’s how: Our budget hotel offered a daily breakfast buffet for ¥1,900 per person, or a whopping $208 per person if we had indulged for all nine mornings of our stay. So we traveled with a pound of ground coffee, which cost US$12, filters, a drip cone and our own tall, insulated travel mugs. That gave us each two cups of good coffee each morning with plenty left over for a boost if we returned in the afternoon before setting out on the night shift. We stocked up on individual yogurts, which averaged ¥100 each, spent about the same amount on fresh fruit and bought a pint of milk for coffee.

    Our breakfast total per person for nine days: about ¥2,000, or $25. We’re not big breakfast eaters but if we could have added in bags of granola (¥298 per) or boxes of cereal (¥350- ¥500) and still saved. Savings: $200

    Our trick for lunch in an expensive city is “Follow the office ladies!” They gravitate to good, cheap food. In Bangkok, I ended up in a utility company cafeteria that welcomed anybody who could find it, just by trailing office workers. On weekends, follow the middle-aged ladies traveling in pairs for a meal out with good chat on the side. Rarely did lunch in Tokyo cost more than $10 or $12. Wherever we ended up, and it was never a food court, we would order one of the lunch specials, always and everywhere the cheap date of meals. By making lunch the main meal of the day, we were then free to indulge ourselves with happy hours or splash out with a dainty dinner at a big-name joint. Savings: $200

    Mind Trick

    Now for my mind game, and yes, I am dim enough to trick myself by rounding down when making mental currency conversions. (Editor’s note: I don’t think this is dim at all–but a pretty darned smart use of estimations!)

    Here’s how it worked on a trip to Hong Kong, where the exchange rate has been stable for the past 10 years: US$1 converting in a narrow range to HK$7.8 to HK$7.6.

    Rather than deal with decimals, I divided a price in HK dollars by US$7. This made everything from menu selections to a pink leather wallet that caught my eye seem more expensive than they were. So much for splurging in a notorious paradise for food and fashion.

    I also set a daily budget. If I came in under, I didn’t automatically roll the money over to the next day. I put it in a separate pocket in my wallet. Then, when a local friend suggested a Michelin-starred restaurant for lunch, I ponied up from my secret stash.

    Even with that magnificent meal, I returned home with US$279 of my budgeted travel kitty unspent. That’s a whisker less than half the cost of a ticket from the West Coast to Hawaii, and about one quarter the price of my next trans-Pacific flight. I’m thinking late November, early December before the holiday rush when the fares spike.

    Do you have questions for master traveler Beth Hughes? If so, please ask in the comments section. And share your own cash-saving tips for travel!