Category: Math Education

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Getting Aware of Common Core Standards

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Sharing Awareness with Kids: Bedtime Math

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

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

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

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

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

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

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

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Math Awareness Month: What’s Your Story?

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

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

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

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

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

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

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

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

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Pre-Algebra on Facebook: How Mark Zuckerberg helped a frustrated parent

Wednesday on Facebook, I had the most amazing experience. Suffering from an all-day migraine, I had spent the afternoon bored out of my mind, obsessively checking Facebook while the television droned in the background. At one point, this status update from my friend Alyson appeared in my feed:

ALGEBRAAAAAAAAAAAAAAAAAAA!!! (Shaking fist angrily in air at math gods)

I was Batman and here was the bat signal. How could I help?

The first response was from someone I didn’t know and very typical: “Outside of college, you don’t really need it, right?” I rolled my eyes inwardly and thought about why Alyson might need to solve an algebra problem. Then I remembered her incredibly bright son, who is completely enamored with computers. I mean in love with the machines. I’d bet my last dollar that the boy will find himself programming or engineering or something in STEM as an adult. In other words, he would need algebra.

I posted a few questions to see how I could help, and eventually Alyson posted the original equation to solve:

algebra fractions equation
fraction algebra
fraction algebra

Whew! It is a doozy, right? Alyson had one very specific question: how to handle the last term of the equation: . I told her the simple answer — that it was the same thing as . Still a teacher at heart, I wanted to see what she could do with that information. Was it enough to help her solve the problem?

Meanwhile lots of other people were chiming in, and Alyson was expressing lots of feelings:

And just so everyone knows, I suck at fractions. Always have, always will. When I took SAT and ACT and whatever else, I literally turned all fractions into decimals because I can never remember how to add, subtract, divide, multiply, etc. fractions.

I’m close to crying…I still don’t understand what you’re saying. He worked the whole thing out at got what my online algebra check thing says is a wrong answer, and I’m trying to work it out so I can figure out how to get the RIGHT answer and I really do think I’m going to cry…

Frustration cry. Because I didn’t think I’d ever use math. And I was wrong. For the record. Sorry, Mrs. Blankenship.

This is a super smart lady. She edits college-level courses of all kinds, and she’s had a successful freelance writing career for many years. And I can completely identify with her frustration. I’d been struggling with Venn diagrams and conditional statements all day. No wonder I had a migrane.

But then something really amazing happened. Really amazing. A mutual facebook friend and writer, Jody (owner of Charlotte on the Cheap) tagged us both in her status update:

Do I have it right? Do I?

She had attached this photo:

At 6:15 on a Wednesday evening, she had not only worked out a challenging pre-algebra problem but also taken the time to scan it and post on Facebook. She was so excited. And, yes, she had gotten the correct answer.

She had also done it differently than I did. But that’s not even the best part. Alyson saw Jody’s process and looked carefully — very carefully. She posted this:

I worked through it on my own twice using your strategy, which ended up making a lot of sense to me once I talked it out a few times. So now I can explain it to [my son] and actually have a clue what I’m talking about. THANK YOU.

Within an hour, another of Alyson’s friends had posted one more way to do the problem. It was a smorgasbord of solutions!

But here’s the very best part: with all of these threads, there were very few people chiming in to say that they were too dumb to help or “who cares?” In fact, I saw many more people posting things like this:

This I can do. Proof reading for grammar errors…….not so much!

I will be glad to do some algebra when the time comes.

 I love math, call me, text me pictures!!!! I will PM you my number.

Why WHY WHY are you having an algebra party without ME?! I love me some equations!

It wasn’t a complete love-fest, but it was worlds different than I’m used to seeing. The tenor of the discussion was supportive and positive, rather than defeated. Sure, there’s was lots of frustration. And I’m betting that there were lots of people reading the threads and thinking, “Good god, I’m going to be in BIG trouble when my kid takes algebra.” But what played out in the end was a good experience — not just getting the right answer but learning different ways to approach the problem.

I originally became a math teacher because I was convinced of two things: math is important and anyone can do math. For years, I’ve felt pretty alone in those two estimations — especially after leaving the classroom. Yet, here was a community of people who were working from the same premise, encouraging Alyson and excitedly trying out the problem themselves.

I can’t think of a better way to end Back-to-School month at Math for Grownups. If you parents can express this enthusiasm — along with your frustration, if you have any — you’ll be doing your kids a big favor. It’s the pushing through and looking for ways to understand things differently that makes a difference. Imagine how much more empowered and confident our kids will feel if they get the message that math is important and that they can do it.

What positive messages about math have you seen lately? Have you found ways to be more encouraging about math with your own kids? Share your thoughts in the comments section.

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Forget the Ping Pong — Let’s Do Some Math

Today’s guest post is from Laura Overdeck, the ingenious creator of Bedtime Math. Don’t know what that is? Keep reading. And then go sign up for their daily email. You won’t regret it!

As kids go back to school, it’s natural for parents to look at their bright-eyed offspring and wonder what they’ll go on to do in life. Chances are they’re hoping their kids will major in something substantial in college to lay the foundation for a great career. Unfortunately, that isn’t what we see happening: According to the National Center for Education Statistics, today more U.S. undergraduates are majoring in “leisure and recreation studies” than in all physical sciences combined (chemistry, physics, astronomy…you get the idea). And there are more than twice as many majoring in leisure studies as in math.

Why does this happen? Why is our next generation running scared from the subjects that involve math? Can we make math the fun leisure activity that kids flock to do?

The problem is that our culture doesn’t view math the way we view reading. Everyone knows to read to children from a young age, and most educated parents do. By the time kids get to kindergarten, even if they can’t read yet, they probably have a warm, cozy feeling about books. To them, reading is a leisure activity, an activity you do for fun when you have free time. Math, by contrast, doesn’t get the same warm, fuzzy introduction as the bedtime story. While there are plenty of magnetic number sets and 1-10 counting puzzles, for most families math at home stops as soon as the children reach toddlerdom. As a result, for a lot of kids their first real experience with math happens in school, with all the associations of homework, drilling and tests. That’s not going to make it feel like leisure. It feels like a chore.

It’s no wonder, then, that kids start off on the wrong foot with their relationship with math.

Kids should view math as fondly as they think about storybooks. While your child plugs away at the usually dry math material from school, it’s good to counter that with fun math at home as an antidote. By the way, that doesn’t mean forced, contrived set-ups where your child can see right through to your intentions. Luckily, there are plenty of fun activities ripe with “stealth” math that may be part of your day already:

  • Baking: Doubling recipes requires multiplying; cutting in half requires dividing; measuring 1/4-cups or 1/4-tsps uses fractions. Any time you bake, you’re quantifying ratios to make magic in the oven. Toddlers can participate by counting out chocolate chips, and of course eating them as a bonus.
  • Building: Anything that involves measuring gets kids counting, adding, and multiplying. Lego and other building toys revolve around numbers, too. And we all see how kids can entertain themselves with a bunch of cardboard boxes, especially if told they’re off limits. Cutting up pieces to assemble a fort all revolves around measurement.
  • Planning: For example, setting up party favors. They’re all sold in different quantities: 10 in one pack, 24 in another, 18 in a third. If there are 16 kids coming over, how many packs of each do you need, and what’s left over? Even putting out breakfast or dinner takes some planning and counting.
  • Sports and exercise: Kids love stopwatches, and watching the seconds tick off gives kids great exposure to counting. Distances and heights require measurement, and even counting jumping jacks, baseball swings, or the kicks to get a soccer ball to the end of a field, can involve numbers.

All of these activities contain a ton of math as a natural part of the process, and this list is just a start. When kids get absorbed in a favorite activity, they don’t even notice they’re learning, just like when they read a bedtime story.

To that point, math can become a part of bedtime as well. Six months ago I founded Bedtime Math, a free website that offers a fun nightly math problem every night – about electric eels, chocolate chips, zip lines into the neighbor’s pool.  Again, the idea is to take kids’ absolute favorite topics and sneak some math in there. After just six months we have over 20,000 people following us through the daily email, the website or Facebook, and parents have written that their previously math-resistant children now ask for Bedtime Math at night, thanks to this new spin on numbers.

Again, it’s all about catching kids while they still think numbers are fun, and building on that mindset. By making math a fun part of favorite natural routines, kids will think of numbers as recreation instead of compulsory drudgery. When they enter school with that new world view, they will have an entirely different, incredibly positive experience with math at school. And with that foundation, maybe they won’t have to sink to majoring in leisure studies when they grow up.  They’ll major in math instead – for fun.

Laura, you’re singing my song! The beauty of Bedtime Math is that it offers three levels of difficulty. Parents don’t have to try to figure out what they should expect their toddler to do or how difficult the math should be for their 2nd grader. And I guarantee — GUARANTEE! — that if you give this a try, you’ll find yourself injecting math all over the darned place.

So what do you think about these sneaky math ideas? Are you ready to throw away the worksheets and flash cards? Have you figured out some easy ways to encourage your kids to do math — without their even knowing it? Share your ideas in the comments section.

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More Sneaky Math for Kids: Guest post from Erin Flynn Jay

When you’re balancing work and home and all sorts of other responsibilities, it can be downright overwhelming to consider doing everyday math with them, so they can perform well in school. That’s why I invited author Erin Flynn Jay to guest post on this very topic. Her recently published book,  Mastering the Mommy Track, tackles many of the questions all of us working parents have, and today she addresses math.

How do your kids do with their math homework? Is it a struggle to get them to concentrate, or do they have a good handle on calculations?

I grew up watching my mother tutor grammar school kids in math at our home. She was also a substitute math teacher at our local schools when I was in grammar school and high school. Because I am not a math whiz, I asked for her viewpoint on this blog post (she read this and offered a critique).

Kids need examples, which will allow them to understand numbers better.

— Beginning when they are toddlers, help them count their snack food like Cheerios or Goldfish from one to ten. It’s wise to get them counting at the earliest age possible.

— When you take your kids grocery shopping, explain to them what your purchases cost. If they are learning how to add numbers in school, ask them for a total. You could ask them, “Okay we have this corn which is $2, chicken for $8 and lemonade for $2. How much money do I need? What is 2 plus 8 plus 2?”

— Give your kids a weekly or monthly allowance depending on your budget. Take them to the pizza place or movie theater and ask them to pay for their purchase themselves. This way, they can understand the value of a dollar or 50 cents more easily. They can get change back and will get a better grasp of what their favorite items actually cost.

— Finally, teach them how to measure their TV shows in 30 minute intervals. For example, you could say, “Alright, you can watch your show for 15 minutes before bedtime.” When the time is up, let them know 15 minutes has passed and it’s time to pack it in.

One final suggestion is to check with your local librarian or bookstore–get recommendations for age appropriate math books. Read them one math book per night.

When your kids sit down to do their math homework, they will perform better if you have introduced basic math concepts at the preschool age. Repetition will reap results.

Erin Flynn Jay is a writer and publicity expert, with articles appearing in a diverse list of publications, including careerbuilder.com, MSN Careers and Wealth Managers. Order her book Mastering the Mommy Track at Amazon.com or barnesandnoble.com. 

Here at Math for Grownups, you’ve gotten a lot of ideas on how to sneak math into your kids’ everyday lives — from reading time to when you’re on the road. What suggestions have you tried? How have they worked out? I’d love to hear about your successes (and yes, failures)! 

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The Problems with PEMDAS (and a solution)

If you’re on Facebook, you’ve probably seen one of a variety of graphics like the one above.

The idea is to solve the problem and then post your answer. From what I’ve observed, about half of the respondents get the answer correct, while the other half comes to the wrong answer. The root of this problem? The order of operations.

Unlike reading English, arithmetic is not performed from left to right. There is a particular order in which the addition, subtraction, multiplication, and division (not to mention parentheses and exponents) must be done. And for most of us old-timers, that order is represented by the acronym PEMDAS (or its variations).

P – parentheses
E – exponents
M – multiplication
D – division
A – addition
S – subtraction

I learned the mnemonic “Please Excuse My Dear Aunt Sally” to help me remember the order of operations.

The idea is simple: to solve an arithmetic problem (or simplify an algebraic expression), you address any operations inside parentheses (or brackets) first. Then exponents, then multiplication and/or division and finally addition and/or subtraction.


But there really are a lot of problems with this process. First off, because multiplication and division are inverses (they undo one another), it’s perfectly legal to divide before you multiply. The same thing goes for addition and subtraction. That means that PEMDAS, PEDMSA, and PEMDSA are also acceptable acronyms. (Not so black and white anymore, eh?)

Second, there are times when parentheses are implied. Take a look:

If you’re taking PEMDAS literally, you might be tempted to divide 6 by 3 and then 2 by 1 before adding.

Problem is, there are parentheses implied, simply because the problem includes the addition in the numerator (top) and denominator (bottom) of the fraction. The correct way to solve this problem is this:

So in the end, PEMDAS may cause more confusion. Of course, as long-time Math for Grownups readers should know, there is more than one way to skin a math problem. Okay, okay. That doesn’t mean there is more than one order of operations. BUT really smart math educators have come up with a new way of teaching the order of operations. It’s called the Boss Triangle or the hierarchy-of-operations triangle. (Boss triangle is so much more catchy!)

The idea is simple: exponents (powers) are the boss of multiplication, division, addition, and subtraction. Multiplication and division are the bosses of addition and subtraction. The boss always goes first. But since multiplication and division are grouped (as are addition and subtraction), those operations have equal power. So either of the pair can go first.

So what about parentheses (or brackets)? Take a close look at what is represented in the triangle. If you noticed that it’s only operations, give yourself a gold star. Parentheses are not operations, but they are containers for operations. Take a look at the following:

Do you really have to do what’s in the parentheses first? Or will you get the same answer if you find 3 x 2 first? The parentheses aren’t really about the order. They’re about grouping. You don’t want to find 4 + 3, in this case, because 4 is part of the grouping (7 – 1 x 4).  (Don’t believe me? Try doing the operations in this problem in a different order. Because of where the parentheses are placed, you’re bound to get the correct answer more than once.)

And there you have it — the Boss Triangle and a new way to think of the order of operations. There are many different reasons this new process may be easier for some children. Here are just a few:

1. Visually inclined students have a tool that suits their learning style.

2. Students begin to associate what I call the “couple operations” and what real math teachers call “inverse operations”: multiplication and division and addition and subtraction. This helps considerably when students begin adding and subtracting integers (positive and negative numbers) later on.

3. Pointing out that couple operations (x and ÷, + and -) have equal power allows students much more flexibility in computing complex calculations and simplifying algebraic expressions.

Even better, knowing about the Boss Triangle can help parents better understand their own child’s math assignments — especially if they’re not depending on PEMDAS.

So what do you think? Does the Boss Triangle make sense to you? Or do you prefer PEMDAS? What to learn to solve these and other problems, buy the book that will help grown-ups like you with these and other math problems here.

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Math Homework: 5 important ways to help your kid

By 8:30 on Tuesday night, I was ready to go home and curl up with a good book. But there I was, crammed into a windowless computer lab with 25 other exhausted parents, listening to the new math teacher describe how math instruction would work this year.

He described how the Common Core standards will change math education and showed off the fancy online curriculum that our school is lucky to have. Then he asked for questions — and the parents pounced. Poor guy.

See, this fellow is exactly what students need. He’s tough; he’s smart; and he thoroughly understands a critical element of mathematics education: Kids have got to take risks that might not lead to a solution. Just like Sir Isaac Newton and Albert Einstein and Ada Byron Lovelace (yes, she’s Lord Byron’s daughter and the founder of scientific computing) went down long and winding roads to their discoveries, our kids must do the same.

But the parents were having none of that. The homework that Mr. T is sending home each night is really challenging. Really challenging. My daughter was complaining and crying and slamming doors because of it. And I know we weren’t alone in our little nightly soap opera.

As the parents got more frustrated and asked more and more questions about grading and building confidence and avoiding stress, I realized that they were missing the whole point. As parents, it’s not our job to shelter our kids from struggle and frustration. I was having a really hard time resisting the urge to step up to the front of the room and do some damage control.

So I figured I should take this opportunity to share my ideas here. Fact is, Common Core may mean that your child is more frustrated. But there are ways to cope.

1. Get proactive

What do the Common Core objectives say? Well, they’re no big secret. Check out this grade-by-grade list. I want you to notice something really, really important: the list of concepts your child is expected to grasp by the end of the year is pretty darned short. At the same time, these ideas are pretty robust. The objectives cover less material and fewer facts, but they do so more deeply.

Armed with some information about Common Core, you will be better able to set the parameters around what your child is learning at home. If solving for x is not on that list, don’t expect your child to do it. But if ratios are, it could be helpful for you to brush up on those concepts. (See Wednesday’s post for help on this.) But not so you can walk your child through a process. (Keep reading for more info on that.)

2. Meet the teacher

And at this meeting, don’t get hung up on grades and tests. Ask her what her teaching philosophy is. Ask what she wants you to do to help support your child’s learning. It is very possible that you’re making assumptions about your role. Depending on your child’s age, you might need to offer a great deal of help. Or you might need to back off. Your child’s teacher can tell you for sure.

If your child has math anxiety, this is a great time to share that with the teacher. Sometimes even the best teachers inadvertently send messages to their kids that unnecessarily ups the anxiety. (Some struggle is good; too much can shut down the pathways of critical thinking.) Offering the teacher a little background in your kids’ previous math experiences can be really useful.

3. Trust

This is probably the hardest step, but unless you have really good reason not to, you must trust your child’s teacher. Seriously. In my observation, many parents think they understand everything about teaching, simply because they were once students.* That approach undermines teachers’ authority and ignores their education and expertise. It’s actually pretty insulting in some ways. Just because you can flush a toilet doesn’t mean you are a plumber. The same goes for teaching.

Teachers are not just experts in their field of study (math, Spanish, English, science); they’re experts in pedagogy, which is the practice of teaching. And pedagogy is much more mysterious than trigonometry or set theory.  It’s where the science and art of teaching collide. The way in which topics are introduced and explored in the classroom is a careful dance. Sadly, some of this can be undone at home, during the homework wars.

Unless you believe your child’s teacher is downright incompetent, you’ve got to trust that she knows what she’s doing. Chances are, there’s very good reason she sent home those challenging problems.

*This goes for homeschooling parents, too. Anyone who has been successful with homeschooling will tell you that there’s a lot to learn about pedagogy — from the developmentally appropriate times to introduce certain concepts to proven ways to encourage exploration and discovery.

4. Stop spoonfeeding

Especially when kids enter middle school, we parents need to back off — big time. Yes, we want them to succeed. But what may be even more important is this lesson: failure is a part of learning.

I don’t mean that you should be okay with a failing grade or ignore his bellowing, “I DON’T UNDERSTAND!!’ But at some point (very soon!), you must stop checking his assignments or walking him through each and every problem. You also need to endure his frustration. When children make mistakes, they can learn from them. When they struggle, they learn they can overcome adversity.When you swoop in to rescue your child from struggle and frustration, you are actually depriving him of these important lessons. (If you want your kid to live in your basement, rent-free, after graduation, ignore the above.)

Check with your child’s teacher about the grading process for homework. Will he be expected to get the answers right? Or is the teacher merely expecting an honest effort? If effort is the main theme (and I hope it is!), quit trying to explain to your child how to do the work. Instead, offer support and encouragement. If you believe your child can succeed, he’ll believe it too.

5. Get curious

One of the best ways to get involved with your child’s education is to ask questions. Kids are rarely given an opportunity to verbalize what they understand about math. Curiosity is a is a huge gift you can give your kids. But in case you’re stuck, try keeping these questions in your back pocket for stressful times:

— What do you know about the problem? (Encourages your child to think critically about the information included in the problem.)

— What are you being asked to do? (Prompts the child to identify the question in the problem.)

— If your math teacher were here, what would she say? (Demonstrates an alliance between yourself and the teacher, and gives you information about her expectations.)

— What ideas do you have for solving the problem? (Helps students identify problem-solving techniques, like making a list, guess-and-check, drawing a picture, etc.)

Read through the above questions again. What do you notice about them? Yep, not a one of them has anything to do with getting the answer. Not a single one. And that’s because it’s not your job to find the answer. Your job is to help your child move towards an answer, not solve the problem for him.And with questions like these, you’re helping your child see math as a process, not merely a solution.

This is hard work. Even with my background in math education, I’m struggling with homework histrionics. It is no fun to come home from a long day at work, only to be pulled into an emotional tangle over math. But I will guarantee this: If you’re working with a good teacher and you practice the steps above, your child will learn to feel very confident in his math skills. And he’ll be a much better grownup for it.

What do you think about this advice? Which of these steps are you already practicing? Which do you think are challenging to implement? Are there any that you think are downright wrong? Share your feedback in the comments below. And if you have further questions, ask them!

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5 Math Resources for Confused Parents

So your kid needs some help with her math homework. Do you understand what she’s doing? Chances are, it’s not so cut and dry these days — and not because you don’t remember your middle school math lessons. Two things are going on in math ed: 1) concepts and processes are being taught differently, and 2) kids are getting more complex lessons earlier on.

All of this may leave you feeling completely helpless.

Luckily, there are some great resources out there that are there just to help you. Here are my top five.

Your child’s teacher

This is a really obvious idea, but not everyone thinks of it right away. Or maybe, like a lot of parents, you feel intimidated by the teacher or you don’t know how to ask for help. There are exceptions to the rule, but most teachers are eager to speak with parents, not only about their kids’ progress but about the best ways to help their child succeed. Find out how he or she prefers to communicate — email, phone or in person. Then use that resource as much as you possibly can.

Online textbook resources

Do you know what curriculum your child is using in math class? If not, find out, because today publishers are putting a wide-range of resources online — just for parents. This is especially true for discovery-based math programs, like Everyday Math and Investigations. The publishers of these programs know that they’re challenging for parents to grasp (since we learned very different ways of doing the math), so they’ve included very strong parent components.

math.com

This really simple website offers quick reviews of basic math ideas. Forgotten what a GCF is? You can find out here. Don’t remember how to solve for x in a proportion? This is a great place to start. Math.com also includes lists of formulas and some basic online tools, like a scientific calculator.

Purplemath

Focused entirely on algebra, purplemath is where you can find help with solving quadratic equationsor graphing linear equalities. Each concept includes a detailed lesson that walks you through the process and examples. Believe me, it’s been an invaluable tool for my addled brain!

The Math Forum

Ask Dr. Math has been around since 1992, so the site has amassed a wealth of questions from math students and answers from real-live math professors. Because it is generally focused on pedagogy (the concepts behind teaching mathematics) and higher-level math, it may seem a bit overwhelming. But if you search the archive, it is likely someone has asked the very question you have. You can also submit your own questions. But don’t expect an immediate response. This site is not designed for quick, individual feedback.

So there you have it, my top five resources for parents with math questions. Got any others to share? If so please include them in the comments section. Sometimes we need all the help we can get!

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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!

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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!

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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.