Categories
Math Anxiety Math for Grownups Math for Parents Math for Teachers Math for Writers

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?

Categories
Math Education Math for Parents Math for Teachers

September: Back to School

Got your sharpened No. 2 pencils? Graph paper? Protractors? It is definitely back-to-school time. Whether your little genius attends public or private school or learns at home with you, as a parent you can look forward to afternoons at the kitchen table talking about multiplication tables, coordinate geometry and trigonometry.

Maybe this thought scares you a little. Maybe you are worried that you won’t be able to help your kid when she’s confused. Maybe you hate the way she’s taught math. Those are all great reasons to focus on math education this month. Throughout September, I’ll bring you posts that help boost your confidence and even understand the math your kid is doing. I’ll have guest posts about math anxiety— a huge problem for lots of kids (and adults) — and I’ll continue bringing you Math at Work Mondayinterviews, from people with cool jobs that your kids want to have.

Have questions that you want to see addressed this month? Ask them in the comments section or send us an email. I’ll track down the answers, so that you can feel good about the math your kid is learning and your role in that process.

To start off, let’s revisit some of the most popular Math for Grownups posts of all time. In this short series, I asked teachers, parents and kids what they wanted from each other when it comes to math education. And boy howdy, did they tell me! See if you recognize yourself in any of these lists.

Five Things Math Teachers Wish Parents Knew

Ten Things Students Wish Math Teachers Knew

Ten Things Parents Wish Math Teachers Knew

So what are you waiting for? Ask your questions in the comments section. Let’s get back to school!

Categories
Math Education Math for Parents Math for Teachers

Four Sneaky (And Fun) Math Resources

For most of us, summer has wound down and school is either in session or just around the corner. The time for preventing summer brain drain is over. But you can continue to reinforce math skills with your kids (and even yourself!) no matter what time of year it is. Here are some really neat games, puzzles and books that help:

Rush Hour

As the video below shows, this game looks like it’s for little kids — but it’s not! I became obsessed with Rush Hour a few years ago, and I periodically bring it out to give myself a challenge. Additional cards can be purchased in expansion packages. Kids (and parents) can play alone or challenge one another to see who can get out of the traffic jam quickest! (Ages 8 years old and up, $19.99, ThinkFun)

https://www.youtube.com/watch?v=-0RpbCZANto

Sudoku

If you’ve ever done one of these puzzles, you know that Sudoku doesn’t have much to do with everyday math. But they do reinforce pattern-identification skills, which is critical for basic math skills. These puzzles aren’t limited to numbers, either. For little kids (Kindergarten through first grade), try picture-based Sudoku. Or use a number Sudoku to help your child remember or learn his numbers.

Connect the Dots

For really little kids, this perennial favorite is a great way to reinforce counting numbers. But these puzzles aren’t just for tiny brains. Look for options that count by 2s or 10s or even consecutive prime numbers. Check out Monkeying Around for much more challenging designs.

Set Game

This is an oldie, but a goodie. The idea is to identify a “set” of three cards (from an array of 12 cards), based on four characteristics: color, shape, shading and number. It takes a while to get hang of this, but once players see the similarities and differences in the cards, the game can get really fast. Check out other games made by SET Enterprises. (Ages 8 years old and up, $12.99, SET Enterprises)

https://www.youtube.com/watch?v=bMhJmrJVP4Q

Books by Greg Tang  (Bonus suggestion, which wasn’t a bonus until a kind commenter pointed out that I didn’t count accurately. Oy.)

Featuring an intuitive approach to learning and understanding math, Greg Tang‘s books aren’t contrived stories that have a math lesson. Each page is chock full of problem-solving skills that encourage kids to discover new connections in math. New York Times Bestseller, Grapes of Math centers around a series of math riddles that delve deep into kids understandings of grouping and creative addition processes. His website was just amped up with cool online games, too.

Do you have a favorite game or book that sneaks in some math? Share it in the comments section!

Categories
Math at Work Monday Math Education Math for Parents Math for Teachers

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.  

Categories
Math Education Math for Grownups Math for Parents Math for Teachers Math for Writers

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 1Myth 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 herehere and here.

Categories
Math at Work Monday Math for Grownups Math for Parents Math for Teachers

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

Categories
Math Education Math for Parents Math for Teachers

Let the Boys of Summer Review Math with Your Kid

The first professional baseball game I attended was at Tiger Park. I don’t remember who Detroit was playing that night, but I do remember the score card and tiny golf pencil I was given. I wasn’t (and still am not) a baseball fan, but I did love keeping track of the runs and outs on my score card.

That was also my introduction to the role that math plays in baseball. On Monday, Charlie Vascellaroexplained this in his Math at Work Monday interview. Between a player’s batting average and games back, this math helps fans (and team managers and sports writers) understand how well players and teams are performing.

If your kid is a baseball nut, this could be just the thing that can help keep skills sharp over the summer months. Instead of simply reading about these stats, how about teaching your kids to actually calculate them? Here’s how:

Batting Average

First up, ask your kid to tell you what he thinks a batting average is. What kind of math does he think will be involved?

Yep, he ought to notice the word “average.” Kids learn to find an average — or mean — in elementary school. A child in fourth grade or older should be able to tell you that the process involves three things: counting, adding and dividing.

A batting average is easy to find:

number of hits ÷ number of official at-bats

In other words, you’ll divide the total number of hits by the total number of times the player has (officially) been at bat. The answer is rounded to the nearest thousandth (or three places to the right of the decimal point. Easy peasy, right? Try it out.

In the last seven days, Mike Trout of the Los Angeles Angels had 23 at bats and 6 hits. What’s his batting average?

6 ÷ 23 = .261

Follow up questions: What does the batting average mean? If someone has a low batting average, what can you say about his skills as a hitter? What does a high batting average mean? What happens to a player’s batting average, if over the season he gets more hits in each game? Could a player’s batting average be zero? Why or why not? Could a player have a batting average if he didn’t have any at-bats? Why or why not?

Skills reviewed: division, decimals, rounding

Earned Runs Average (ERA)

In case you didn’t know — and I didn’t — an earned run is when a pitcher allows a batter to score. The earned runs average is the average number of times a pitcher allows runs in a game. Here’s the formula:

(number of earned runs • 9) ÷ number of innings pitched

Again, we’re dealing with an average, so it’s important to know that division is going to be involved. And if you look at that formula, you might notice another important concept: the order of operations. We’ve had quite a lively discussion about the order of operations or PEMDAS on the Math for Grownups facebook page.* In September, I’m going to demonstrate another way to remember what order is necessary for these operations. But for now, let’s just stick with Please Excuse My Dear Aunt Sally or Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Since the multiplication is in parentheses, do that operation first. Then divide. (Okay, so really you don’t need the parentheses at all, but it’s easier to write these problem online using them.)

Here’s an example:

In the last seven days, Jordan Zimmermann of the Washington Nationals has had 2 earned runs and pitched 11.7 innings. What is his ERA?

(2 • 9) ÷ 11.7 = 1.54

Follow up questions: What does a big ERA indicate? What about a small ERA? Can you explain why? If you did the division before the multiplication, would you get the same answer? Why or why not? Could the average ever be zero? Can a pitcher have an average if he didn’t pitch a single inning? Why or why not?

Skills required: order of operations, multiplication, division

There are many other baseball stats that require math, like baserunning average, fielding percentage, slugging percentage and games back.  In addition, you can take a look at a player’s stats over time and see how they’ve improved or declined. And of course, it’s interesting to compare the stats between players. If you’re unsure of the math, just google the terms!

What are some other ways to use sports for math review? Share your experiences in the comments section.

*Have you liked Math for Grownups on facebook yet? If not, what’s stopping you?

Categories
Math Education Math for Parents Math for Teachers

5 Ways Pinterest Can Help Stop the Summer Slide

I joined Pinterest last spring. I knew it was dangerous. The internet is like Alice’s rabbit hole for me — once I go down it, it’s near impossible to get back out. But I’ve found that I love using Pinterest. It inspires me and helps me stay organized. (One little click, and I’ve filed away an idea for later!) And because I’m a very visual thinker, I find that organizing my online life with Pinterest is much easier than using traditional bookmarks.

I’m also a hopeless DIYer (hopeless in that I can’t stop trying these projects!), so my boards are filled with recipes, home projects and sewing ideas. And — you saw this coming — all of these require some math. I noticed that any one of these projects could be useful to a parent trying to stop the summer (math) slide, and I started collecting ideas.

You can view my Stop the Summer (Math) Slide board here. (If you’re not following me on Pinterest, what’s stopping you?) Take my ideas to create a board of your own. Then add to it. I’ve outlined a few of my absolute favorites below. Please share yours in the comments section!

1. Make a circle skirt.

This was actually a Spring Break project that, thanks to MADE, I did with my daughter and some of her friends this spring. I’m particularly tickled with how MADE describes the math behind drawing the circle. (Suggestions: Unless you’re a very experienced sewer, avoid slippery fabrics. And if you have a serger, boy-howdy is that helpful!)

2. Find your fuel economy.

Your child can help you track your car’s miles per gallon. This site shows you how (and includes some other nifty tools). But really all you need to do is divide the number of miles traveled by the number of gallons used. (Remember: per means to divide.)

3. Build a tomato trellis.

I featured this project on my blog in June, but it’s well worth mentioning again. The beauty of this idea is that it brings in some higher-level math, like the Pythagorean Theorem and right angles. (But don’t worry, it’s not hard math.)

4. Paint a room.

Last year, my daughter wanted to repaint her room. I said fine, on two conditions. She had to figure out how much paint was required, and she had to help (a lot). This site shows, step-by-step, how to calculate the paint needed.

5. Use coupons.

In this economy, everyone needs to save some cash. Coupons are a great way to reinforce math skills, like estimation and basic operations.

I’ll continue to add to this board, so check back from time to time and see what’s there. If you create something similar, please share it on the Math for Grownups facebook page or here in the comments section. I’d love to write another post later about what you guys have come up with!

What are your favorite projects to do with kids? How is math involved? Share your ideas in the comments section.

Categories
Math Education Math for Parents Math for Teachers

Roll with It: Get Sneaky with Math

I’ve written about this in a hundred different places, but it’s worth saying again: Parents know how to get their kids interested in reading. But in general, they don’t have a clue about math.

If you had a child in the last 10 years in the United States, you probably heard somewhere along the way how important it is to read to said child every single day. I started reading to my daughter when she was only a couple of months old, partly to establish a bedtime routine (for the both of us) and partly because I wanted her to fall in love with books at a very young age. Reading with our children helps reinforce the parent-child bond and is a super-duper easy way to spark neurons that lead to mega brain development.

And did I mention that reading to our kids is easy? And can be a lot of fun? (How many of us read Harry Potter aloud every night for a few years?)

Sneaking in some math is a little more of a challenge for most parents. But I promise, it can be as easy — and is abso-tootin’-lootly as important as reading to our kids. Not only does math help our kids understand the world around them, but reinforcing the concepts kids learn at school helps counteract the summer slide or brain drain.

But for a parent who isn’t so confident in his or her math skills, this prospect could be quite daunting. Or downright confounding. I could give you a list of ways to sneak in some math on a hot, summer day. But let’s see if you can come up with some ideas on your own. It all starts with a few questions:

1. Think about your day from start to finish. Mentally go through it bit by bit, and see if you can come up with five ways you used math. How do you use math in your everyday life?

2. Now, take one of those examples and consider the math. What process did you follow to solve the problem?

3. Examine that process even closer. What math did you use in the process? 

4. And finally think like your kid (not any kid, but your kid). How could you make your experience meaningful to your child? How would you explain the math that you did?

Try this out for a few days. Write things down if you want or keep it all in your noggin. In other words, start noticing where, when, how and why you’re doing the math that you need to function in your everyday life. Think simple, not complex. Are you estimating how long it will take to get to work? Are you reading a clock to find out how late you are to your meeting? Are you figuring out how many pounds of beef you need to buy for the cookout? Are you thinking about how much you’ll spend on your vacation?

Unless your child is itty-bitty, you can probably boil these things down to a level that he or she will understand. And now all you need to do is talk about these things.

My favorite approach is to think aloud.

“Boy, I’m late! I’m supposed to be at the office by 9:00, and it’s already 8:45. Let’s see, how late am I going to be if I leave in five minutes?”

“Do you think it will take me less time to roll down this hill than you? Let’s find out!”

My second approach is to ask my kid to help me. I usually claim being way too busy to handle everything on my own.

“Could you do me a quick favor? I need to know how many hotdogs and buns I should buy for the cookout. We’re having 10 people over. The hotdogs come 8 to a package and the buns come 10 to a package. Could you figure it out for me, while I make the rest of my grocery list?”

And lastly, I talk about math — just any old math.

“I just noticed the other day that I never can remember what 6 times 7 is. So I figured out that if I multiply 5 and 7 and then add 7, I get the answer. Cool, huh?”

I swear these things work with my kid. I’m not kidding. We talk about how we do math and we solve problems together. Sure, she still experiences some brain drain in the summer months, but I think all 12 year olds have a secret hole in their heads that allows far too much knowledge to fall out when they’re not in school. (And sometimes when they are in school.)

So tell me what you think. What daily math do you do in a day? How can you repackage that math so that your kid can practice a little in the summer? Try it, and then share your experience in the comments section. Or just do some brainstorming. You come up with a math situation, and I’ll offer some suggestions for sneaking it in to time with your kids.

P.S. If you haven’t seen Bedtime Math yet, check it out right now. Each day, three problems are posted — one for each of three age-groups — that addresses the math in a news item or a historical event. You could easily pose these questions to your kids. Ta-da! Work done for you!

Categories
Math Education Math for Grownups Math for Parents Math for Teachers

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?

Categories
Math Education Math for Parents Math for Teachers

Back to School: Back to Math

I remember the first week of my fifth grade year. I had a math worksheet for homework, and I was completely stumped.

“I don’t remember how to do this stuff, Mom.”

“What do you mean?” she said. “It’s just long division!”

Yep, in three blissful months of summer vacation, I had completely forgotten to long divide. My mother, a teacher herself, was shocked. Brain drain can sneak up on even the pros.

Being ready for school is much more than having a new backpack, plenty of No. 2 pencils and a healthy breakfast. Studies show that during the lazy months of summer, all kids suffer from “brain drain” or the loss of learning. In fact, students lose (on average) 2.6 months of mathematical competency in June, July and August. Wow!

I promise: I will not tell any parents that they should be teaching math over the summer. I’m not big on academically based summer camps (unless kids desperately need remediation or love these kinds of activities). I hate the idea of kids being subjected to flash cards or worksheets when they could be playing at the pool or reading a great book.

But I do believe — whole heartedly — that parents can help slow the loss of mathematic comprehension with some really simple and even fun activities.

And that’s what August is about here at Math for Grownups. We’ll focus on parenting, primarily, but I’m guessing that even non-parents can gain some additional understanding from some of the activities I’ll suggest. (No one should feel left out!) I’ll also hit on a variety of grades and ages — from toddlers to college students. And I hope to bring you some Math at Work Monday interviews that will inspire even the most reluctant math student.

But first, I want to know: What are your questions? What kinds of activities are you looking for? What topics are you having trouble helping your kids with? You ask ’em, and I’ll answer ’em — or at least point you in the right direction (perhaps to my posts at MSN.com’s Mom’s Homeroom).

So let’s start easing back into the school mindset — so September is not a shock to anyone’s system!

I want to hear from you! Ask your questions in the comments section or email me

Categories
Math for Parents Math for Teachers Personal Finance

Back-to-School Shopping: Applying the order of operations

Last week, we had some fun with the order of operations at the Math for Grownups facebook page.* Turns out remembering the order that you should multiply, add, etc. in a math problem is a tough thing for adults to remember. Imagine how kids feel! But this is a really simply thing that you can apply to your everyday life — all the while, reminding your kid how it goes.

First off, here’s the problem that we considered on facebook last week:2 • 3 + 2 • 5 – 2 = ?The answer choices were 38 and 14.I would say that the responses split pretty evenly. Lots of folks chose the incorrect answer first and then realized their mistakes.

So what’s the correct answer? 14. Why? Because of the order of operations. A lot of us learned the order of operations — or the set of rules that establishes the order we add, subtract, multiply, divide, etc. — with a simple mnemonic:Please Excuse My Dear Aunt SallyORParentheses, Exponents, Multiplication, Division, Addition, SubtractionORPEMDAS

(Before going further, I must acknowledge that there are some problems with this approach. First off, it doesn’t really matter if you add before your subtract or multiply before you divide. Those operations can be done in either order with no problem. Second, many teachers are approaching this differently, a topic that I’ll explore in September.)

If you do the operations in the wrong order — add before you multiply, for example — you’ll get the wrong answer. And that’s how people got 38, instead of 14. They simply did the math from left to right, without regard to the operations.CORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?6 + 10 – 2 = ?16 – 2 = 14INCORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?8 • 5 – 2 = ?40 – 2 = 38

All of this is well and good, but what does it have to do with the real world? How often are you faced with finding an answer to a problem like the one above? And that’s exactly what one reader asked me. So I promised to explain things using a real-world problem.

Thing is, you do these kinds of problems all day long, without even thinking of the order of operations. And that’s because you’re not writing out equations to solve problems. You’re simply using good old common sense.

Let’s say you’re going back-to-school shopping with your child. He’s chosen a pair of pants that are $15 and five uniform shirts that cost $12 each. But the pants are $5 off. What’s the total (without tax)?

You probably won’t write an equation out for this, right? (I wouldn’t.) Instead, you’d probably just do the math in your head or scribble some of the calculations on a scrap piece of paper or use your calculator. So here goes:

First the shirts: there are five of them at $12 each. That’s a total of $60, because 5 • 12 is 60.

Now for the pants: all you need to do here is subtract: 15 – 5 = 10. The pants total $10.

Finally, add the cost of the pants and the cost of the shirts: $10 + $60 = $70.

The above should have been super easy for most of us. And — surprise! surprise! — it used the order of operations. Here’s how:15 – 5 + 5 • 12 = ?The order of operations says you must multiply before you can add:

15 – 5 + 60 = ?

Then you can add and subtract:

10 + 60 = 70

There are other ways to set up this equation. In fact, I would use parentheses, simply because I want to keep the pants’ and shirts’ calculations separate in my mind:

(15 – 5) + (5 • 10) = ?

The result is the same, because the process follows the order of operations — do what’s inside the parentheses first and then add.

UPDATE: A reader asked if I’d also show how this problem can be done wrong. So here goes! When you do the operations in the wrong order, you won’t get $70.15 – 5 + 5 • 12 = ?10 + 5 • 12 = ?

15 • 12 = 180

That’s more than twice as much as the actual total!

Try this with your kid. You can make it more complex by figuring out the tax. And there are lots of different settings in which this works — from shopping to figuring the tip in a restaurant and then splitting the tab to dividing up plants in the garden.  Just about any complex math problem that involves different operations requires PEMDAS. And that’s something all kids need to know about.

When have you used PEMDAS in your everyday life? Did this example spark some ideas? Think about the math that you did yesterday — or today — and share your examples in the comments section.

*Have you liked the Math for Grownups facebook page yet? What’s stopping you? We’re having great conversations about the math in our everyday lives. And I ask questions of my dear readers. Come answer them!