Category: Math Education

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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.

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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?

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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.

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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!

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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?

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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. 

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Ten Things Parents Wish Math Teachers Knew

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

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

Here goes:

Help a parent out.

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

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

Know the kids.

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

Give parents a homework estimate.

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

Mean what you say and say what you mean.

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

Update your materials.

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

Review tests and graded assignments.

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

Don’t confuse computational errors with conceptual misunderstanding.

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

Introduce relevant and meaningful application (word) problems.

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

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

When a child isn’t succeeding, ask why.

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

Don’t write our kids off.

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

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

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

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Math Tricks: Good or bad?

When I do interviews or speak to groups about math, one of the things I worry about is that people will expect me to do math tricks. And I worry about this for good reason. I can’t multiply two three-digit numbers in my head. I don’t know π to the 100th decimal place. Heck, I can’t always remember what 9 x 8 is!

There are plenty of folks out there who have these abilities, and god bless ’em. It’s not my schtick. In fact, while I think these tricks are pretty nifty, I’m not so keen on people learning them, at the expense of gaining a deeper understanding of the math behind them. This goes for kids and adults.

This is what I write about in one my first posts as the math expert for MSN.com’s site for parents, Mom’s Homeroom. Over the next several months, I’ll write articles and develop activities designed to give parents the tools they need to help their kids succeed in math. (Other experts address reading, social skills, homework and study habits and parental involvement.) One of my first posts, 5 Cool Math Tricks You Didn’t Know, looks at some neat shortcuts for basic math facts — like multiplying any number by 11 or finding out if a number is divisible by 3.

The twist is that I show readers why these tricks work. But this is a step that most folks skip altogether. My friend, Felice Shore, who is an assistant professor and co-assistant chair of Towson University’s math department, explains why it’s critical to master the math behind the magic.

“The important mathematics [in third and fourth grade] is still about building understanding of relationships between numbers — the very reasons behind math facts. Once you show them the trick, it’ll most likely just shut down their thinking.”

That goes for grownups, too. If you’re brushing up on some basic math skills, don’t just memorize facts or use nifty tricks. When you take a little time to look beyond a quick answer, you will likely learn a great deal more. And as we all know, this can extend to other applications and concepts.

Math is often described as a set of building blocks stacked on one another — the foundation must be there to move into more complex concepts and more difficult applications.

But it’s also a web. What you learn about multiplication applies to division, which applies to factors and multiples, which applies to fractions. Sometimes, a concept that passes you by can be better understood later on when the idea shows up again. In other words, you might just learn your 12s times tables,when you’re applying measurement conversions (12″ = 1′). Tricks just might keep you from deeper understanding.

So whether you’re trying to get good at math on the fly or helping your child remember that 9 x 8 = 72, be careful with the tricks. They just might keep you or your child from learning much bigger concepts.

Do you depend on math tricks? If you’re a teacher, what do you think of students using math tricks?

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Ten Things Students Wish Math Teachers Knew

Two weeks ago, I posted Five Things Math Teachers Wish Parents Knew. Now it’s the teachers’ turn to be on the hot seat. I asked a handful of the middle and high school students that I knew to chime in with some advice or helpful feedback for math teachers. And this is what they came up with:

Make the math relatable.

These kids get it — you honestly like pure mathematics and the State Board of Education has dictated that you cover x amount of material in y period of time. (See what I did there?) But when all students are doing is solving algebraic equations with no connection to the real world, the stuff won’t stick — and eyelids will shut.

Do more “interactive stuff instead of book work.”

Get rid of boring worksheets. Spend a few days applying the material to larger projects. Have the students design carnival games based on probability. Or track March Madness results. Or use special right triangles to find the length of a shadow and compare it to an actual shadow.

Ensure that everyone is ready to move on — before moving on.

Again, these students know that you have some constraints. And I’m willing to bet that most students understand that the class doesn’t revolve around them. (Okay, maybe many students, rather than most.) But if a good portion of the class isn’t following, there’s no point in barreling through to the next concept. I’ll add this: some students won’t tell you that they’re not ready to move forward. Teachers have to get creative in assessing readiness.

Don’t call on the same students all the time.

Everyone knows who the mathy kids are. Don’t let them dominate the discussion. A few days ago, a parent told me that her daughter’s school is really clamping down on “blurters” — kids who get the answers quickly and blurt them out. These blurters can suck all of the life out of a classroom, especially when the majority of students need a little more time and a lot more confidence. And it’s a good lesson for anyone to learn: keep your mouth shut and sit on your hands once and a while.

Don’t refuse to call on a student who usually has the answer.

This one’s personal. In middle school, my daughter was told to stop raising her hand all of the time — and not in a nice, encouraging way. She was crushed by this harsh order. Everyone deserves a chance to participate, at least part of the time. And besides, there are different methods for encouraging participation that don’t require teachers to single out and call on individual students. Learn these methods and use them.

Skip the timed tests.

They freak students out and can bring down a grade in a heartbeat. Fact is, faster isn’t smarter. Speed tests don’t allow different approaches to problems. Besides, what’s more important: automatic recall of the times tables or really understanding where these facts come from? (Please say the latter. Please say the latter.)

Grade as much as possible.

Give students a chance to bring up their grades with graded homework assignments. And give them feedback on their understanding as often as you can. It’s not enough for a student to know that the answer is wrong. Detailed feedback on why is critical for deeper understanding. Kids know this.

Recognize that not all kids learn in the same way.

Remember, the definition of insanity is doing the same thing over and over and expecting different results. If students don’t understand the concept, try explaining it in a different way. Or ask the kids to come up with their own ideas. Discovery is a great tool, and it’s often very engaging.

Stop talking down to students.

Yep, students really said this. And I could wallpaper my bathroom with the number of emails I’ve received from adults who felt shamed by a math teacher. Every adult that a kid meets has the power to make a positive difference in that kid’s life. Belittling, shaming and talking down to kids will have the opposite effect.

And I’ll add #10:

Don’t ever, ever tell students that they’re bad at math.

Want to insure that a kid will never try at math again? Want to smash his confidence? Want to send a lasting message that she won’t be able to balance her checkbook or become an engineer or help her kid with math homework? This is a one-way ticket to that bleek future, and it can happen in a split second with an offhand remark. Remember what it was like to be a student and follow the Golden Rule.

Do you have suggestions for math teachers? Share them (nicely) in the comments section. I’d also love to hear from students and former students who had great experiences with their math teachers. Are you a math teacher? Feel free to offer your feedback, too!

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Journey from Math Loser to Math User

Today, I’ve asked Siobhan Green to share her math story with everyone. As the CEO Sonjara, Inc., a woman-owned technology firm, she is a huge proponent of increasing women and men’s math skills worldwide. But she hasn’t always felt confident in her math skills.  As she told me, “I think my story is not that unusual in how many of us, especially girls, too easily believe that math is hard and only for super smart math geek types.” Amen!

I was considered a smart kid. I learned to read early, knew my numbers and letters before age 3, entered first grade early and did well in school. However, when I got to third grade, I and my teachers started noticing a discrepancy between my math scores and the rest of my school work. I would regularly get poor grades on timed math tests — two- and three-digit addition and subtraction problems —  which predominated our math education. I easily mastered the concepts presented, but when given a timed test, I would run out of time and/or make a lot of odd mistakes.

This pattern continued in elementary school. The result was that I was either yelled at by teachers for being lazy or intentionally not focusing on my math work, or the teachers just assumed I was “bad at math.” I vividly remember one teacher saying “Yeah, girls are better at verbal skills, boys at mathematical/spacial ones. Just stick to what you are good at.”

Things got better in seventh grade when we moved to pre-algebra. I was excellent at pre-algebra and routinely got As and Bs on tests. But I also managed to make the teacher mad when a group of students was interviewed by a local paper and I made a disparaging comment about him (I had no idea what I was doing). As a result, he recommended that I NOT move into Algebra as my grades would warrant but rather into pre-algebra/algebra, for kids who struggled. No one — not my guidance counselor, nor my parents, nor even me — remarked on this fact, as we all had agreed by that point that I was “bad at math.”

This decision had huge implications. Math is tracked; students take algebra, then geometry, then algebra II and then trig, and only then can you take calculus. By not allowing me to go into algebra in eighth grade, I would not take calculus in high school — something that excluded me for many science (especially computer science) learning opportunities.

The rest of my educational history with math was similar – I excelled in algebra (go figure), did fine in algebra II and trig and did surprisingly well in geometry, but my heart wasn’t in it. I also took some basic computer programing courses — BASIC and Pascal. I enjoyed these but never associated them with math, and the overwhelmingly geeky-boy atmosphere of the computer lab turned me off to more experimentation in these fields. By the time computer science camps started becoming popular in high school (in the mid/late 80s), many programs expected that students would be in advanced math classes.

My college degree was in international affairs, which required two years of economics. I was NOT good at economics, and because I didn’t know calculus, and my antipathy for anything involving numbers, was a big part of it. I excelled in the social sciences and went onto a career in international development.

However, over the years of my career, I noticed that I was good at technology — I was the person in the office who figured out the printers, who set up macros and templates in Word, and who taught herself basic HTML. I was also a whiz with developing databases and excel spreadsheets and was often the person who tracked expenses and invoices. I became more and more interested in using technology for international development; I did my masters’ dissertation on the Internet in Africa in 1997. Falling in love with a software developer didn’t hurt, either.

It was actually through my husband (the math/computer science major and total math geek) that I realized I am NOT bad at math. I am in fact pretty darn good at it, and a lot of the tasks I enjoyed “count” as math!

Andy recognized that I have a mild learning disability — dyscalculia. I transpose numbers, have a hard time retaining numbers in my head, don’t memorize numbers well (I still don’t know my 7 and 8 times tables by heart — and by now, I will never memorize them), and often misstate numbers when going from listening to writing. (Trying to capture a number left on a voicemail is torture for me.) And this is true after years of learning coping skills! He was the one who said “Your calculation mistakes are not normal. And they have NOTHING to do with your math abilities.”

See, remember those timed tests? Thinking back, I would think one number and write down another one. Now, I always take a second to double check, but in a timed situation at age 8, I would panic and just move on to the next one. Many of the mistakes I made in the early years were down to calculation errors. When the math was based in patterns (like algebra) or depended on calculators, I did much better. But by that time, my math ability had become a self-fulfilling prophecy. The research is clear about the impact of low expectations on ability; I never pushed myself and accepted lower scores as evidence of my innate lack of talent.

I didn’t realize that my strong abilities in building relational databases, especially to track quantitative data, counts as math! I absolutely love building databases, especially related to financial management. Those spreadsheets I use to track finances?  They speak to me and tell me a story in numbers. I had no idea that my ability to create and read those numerical pictures of my firm also counted as math.

Andy also taught me how to program, and while I will never be a full blown developer (mainly because I don’t have time to gain in-depth programming experience), he found that I grasped the key pattern processes quite easily. This skill has been invaluable in my role as business process analyst for web application development. It helps me translate between user needs and programming architecture, which helps with figuring out edge cases and pricing.

Today, my job as CEO of a web application company involves a lot of math. For example:

* Pricing work, especially figuring out hourly rates for specific roles/individuals based on salary, benefits, and overhead plus profit. It is very easy to “win” enough work for bankruptcy (win the work but price it so low you don’t cover your costs). We are always repeating the joke “yeah, we lose $1 per widget sold but we will make it up in volume.” (The explanation is at the bottom.)

* Overseeing projected and actual utilization of my staff. If our rates are based on this person being at 80% billable, and they are regularly at 75% billable, that 5% difference will eat into my profit.

* Understanding the difference between the profit and loss statement, the balance sheet, and a cashflow statement. This is omething that every business owner must understand in order to figure out how the business is doing. You can have huge paper profits but still be in serious trouble if you cannot make payroll, or you could be cash rich but slowly going under because your easy access to credit is masking the fact you are spending more than you are earning.

* Making decisions about how to spend money. What investment will make a bigger impact? For example, should I hire another person or pay down a loan? Should we purchase this new computer now on credit or wait until the next check comes in?

Oh, and here’s the explanation of the above joke:  “Yeah, we lose $1 per widget sold but we will make it up in volume.” Assuming that your costs do not scale (decrease per widget based on volume), if you sell 100 widgets, you have now lost $100. And if you sell 1,000,000 widgets, you have now lost $1,000,000. It is astonishing the number of business people I meet who do not get this concept. Usually, they are not in business for long.

Can you identify with Siobhan’s story? Share yours below. 

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Parlez-Vous Mathematics? Math as a foreign language

In redesigning my blog, I’ve read a lot of the posts I’ve written over the last year. In fact, take a look at this math: On average, I’ve written 13 blog posts each month or 164 posts (counting this one) since last May. And so I decided to repost this one, in honor of Math Awareness Month, which addresses the language of math.

When I was in college, majoring in math education, I learned that math is the language of science.  In fact, we called it the Queen of the Sciences.  (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!)  And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science.

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

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

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

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

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

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

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

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

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

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

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

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

Our first Math Treasure Hunt winner is Marcia Kempf Slosser! Congratulations Marcia, you’ve won a copy of Math for Grownups (or if you already have a copy, I’ll send you a gift card). Want to enter? All you need to do is find an example of the daily clue, which is announced on the Math for Grownups Facebook page each day. 

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Five Things Math Teachers Wish Parents Knew

Parents: when it’s time for math homework, do you suddenly have something else to do? When it’s parent-teacher conference time, do you first tell the teacher that you’re no good at math yourself?

First off, you’re not alone. It’s the number one thing I hear from parents: “I don’t know how to help my kid with math!” So I asked one of my favorite math teachers, Tiffany Choice. As an elementary and middle school teacher, Ms. Choice is a math education expert. And because of that, we instantly connected. Oh, she was also my daughter’s fourth grade teacher.

I asked Ms. Choice to share her best advice for parents. Want to help your kid succeed at math? Here’s how.

Just because you struggled in math class doesn’t mean your kid will.

Don’t pass on your dislike or acceptance of not being “good at math.” Always highlight the importance of math. If you cannot provide math homework support, find someone who can. Even if your kid has to call an uncle across country to try help clarify a problem, it goes a long way.

Math is best understood when applied to the real world.

Show your kids how you use dollars and coins at the store. Encourage understanding when they use birthday money to buy things. Discourage them from throwing the wad of money on the counter without understanding what they are doing. Explain to your child what you are doing when balancing that checkbook, measuring a wall or following a recipe. You are your child’s first teacher.

How you were taught to do something in math may or may not be the best way.

Education is swiftly changing to keep up with technology and each generation. Be open to many new ways of learning math concepts. Ask your child’s teacher to show you how a concept is being presented. I’ve had parents stop in during math instruction or for an after school conference.

Math isn’t learned right after the first lesson.

Parents should emphasize and allot time for practice — just like we encourage practicing the piano, ballet, reading, soccer, or French.

Realize the importance of and reinforce math vocabulary.

Math isn’t just numbers, it’s words too. Talk about what 20% off really means when they’re asking for that new toy. Use the words “total,” “difference,” and even “mixed number.” Believe it or not, truly knowing what those math words mean helps in the long run. I hate to mention standardized tests, but it’s something that’s here to stay (at least for now). More and more, math tests are transforming into reading tests.  Most of the questions are word problems. Certain understanding of math vocabulary can and will help your child avoid the sneaky test-makers tricks.

I’ll add one more thing: Encourage your child to explain their reasoning behind the math they’re doing — whether you’re helping with homework or asking him to divy up candy pieces at a play date. One of the biggest things that kids are being asked to do is write about math. (In my daughter’s school, these are called BCRs or Brief Constructed Response and ECR or Extended Constructed Response.) The kids who already verbalize their understanding of math will have an easier time with these tasks.

Do you have advice for parents? Whether you’re a teacher, parent or innocent bystander share your ideas in the comments section. Have a question? Share that, too!