It’s gift-giving season for most of us. In honor of the winter holidays, I’ve pulled together a little list of ideas for your math geek. Or perhaps you want to encourage someone to step a little deeper into the math pool. I’ve got ideas for those folks, too. Enjoy!
Since launching this website in 2011, Math at Work Monday has been an extremely popular feature.Teachers let me know that they love sharing insight from these interviews with their students. (What better way to answer the question, “When am I ever going to use this stuff?”) Other grownups have told me that the interviews help them identify when they’re using math in their everyday lives.
Over the years, I’ve interviewed a variety of different people — from an astronaut to a fish hatchery technician to a glass artist. All jobs are terrific fits — because as we all know, Everyone Does Math.
(Did you catch my Everyone Does Math video? Check it out!)
In fact, the series has been so successful, I’m launching a special printed option for teachers and homeschoolers, including unique student-directed questions. I’ll start with one set of my favorite interviews, which can be downloaded as printable worksheets for use in the classroom or at home. Stay tuned for the details, coming in two weeks!
Now I need your help! I’m looking for new people to interview in the next month. If you or someone you know is up for it, let me know. You can email me at laura@mathforgrownups.com (include their names and email addresses). If you’ve been around for a while, you know that the process is simple. My wonderful assistant, Kelly emails a list of questions — yes, everyone gets the same questions! — you respond to the questions and email them back to Kelly. That’s all. Painless.
So what kind of folks am I looking for? You name it!
But you can probably come up with even more great ideas. If you have suggestions (but don’t have someone to recommend), go ahead and post them in the comments section.
I’m so proud of the Math at Work Monday series, and I thank you for making it so popular and for making it possible. I look forward to receiving your recommendations. Remember, email me with potential interviewee’s names and email addresses at laura@mathforgrownups.com.
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Think you don’t need math? Think again! Math is everywhere, and much of the time you might not even realize that you’re doing it.
If you remember wondering when you’d ever use math as a grownup, click on my next Math Manifesto video above.
And don’t miss out on other videos, including: Everyone Has a Math Gene.
More videos are coming, so please subscribe to my YouTube channel: mathforgrownups. Also, I hope you’ll share this video on Twitter, using #idomath and post it on your Facebook page. Share the Math for Grownups love!
As always, I’d love to hear what you think. Ask your questions or share your feedback in the comments section. After watching the video, are you convinced — as I am — that you do math every day? Why or why not?
When I read Richard Preston’s The Hot Zone in the mid-1990s, I was terrified. This was the first I had heard of a scary new disease called ebola. I was working for an AIDS Service Organization at the time, so I understood — better than most — how blood-borne infectious diseases are contracted. Still, the images of how the victims of this virus die are still with me. Horrifying.
But I’m not at all afraid of ebola today. Not one little bit. Why? Math.
It’s difficult for ebola to spread. Really difficult. Like HIV, the ebola virus only lives in bodily fluids, including blood, saliva, mucus, vomit, semen, breast milk, sweat, tears, feces and urine. (HIV is only transmitted through four bodily fluids: semen, vaginal fluids, breast milk and blood.) Transmission can occur when infected bodily fluids come into contact with a person’s eyes, mouth or nose, or an open wound or abrasion.
Compare this to measles, which is transmitted through the air. The measles virus lives in the mucus lining of the nose. A sneeze or cough can release virus-infected droplets into the air. Breathe in the air with little measles droplets, and unless you’ve been vaccinated, it’s very likely you’ll see a tell-tale rash in a few days.
Since measles is highly contagious for four days before symptoms appear, a person can transmit the virus without even knowing he has it himself. According to the CDC, measles is so contagious that if one person has it, it will spread to 90 percent of the people who come in contact with that person (if they are not already immune, thanks to the vaccine).
The way a virus is transmitted helps determine how contagious the disease is. And the big deal here is something called R0 or “reproduction number” (also called “r-naught”). R0 is the number of people that one infected person will likely infect during an outbreak.
Those of us of a certain age might remember a shampoo commercial that illustrates this perfectly.
Like Fabrerge Organics shampoo, ebola’s R0 is 2. When one person contracts ebola, it is likely that two others will become infected. Yes, those numbers add up — and they have in parts of Africa.
Now take a look at measles, with an R0 of 18. When one person gets measles, it’s likely that 18 people around him do too. Then each of those 18 people spread the virus to 18 more people. In one generation of this infection, 18 x 18 (324) have contracted measles. That’s compared to only 2 x 2 (4) people who will likely contract ebola in one generation of the infection. In fact, measles is still one of the leading causes of death in children around the world. According to the WHO:
Measles is still common in many developing countries – particularly in parts of Africa and Asia. More than 20 million people are affected by measles each year. The overwhelming majority (more than 95%) of measles deaths occur in countries with low per capita incomes and weak health infrastructures.
But measles is not a major threat in the U.S., and we all know why — the measles vaccine. Ebola has no vaccine, but a relatively strong health care system in our country and its very low R0 makes ebola a low threat, compared to other viruses, like HIV and certain strains of influenza.
The scary thing about ebola is not how quickly it spreads but how basic medical care can keep it from spreading. We have that basic care here in the U.S. Large swaths of Africa do not.
And along with a low R0, the ebola virus has a relatively short infectious period — about a week. On the other hand, HIV is infectious for years and years — many of those years while the infected person has no symptoms or does not even test positive on an HIV test. The relationship between time and infection matters, too.
For example, the National Institutes of Health (NIH) reports that each year, about 5,000 people under the age of 21 die in alcohol-related incidents, including car crashes, falls, burns, homicides, suicides and alcohol poisoning.
According to the Federal Reserve, Americans held $229.4 billion in consumer credit (outstanding household debt, including credit cards and loans) in July 2014.
The global sea level is rising at alarming rates, according to the National Oceanic and Atmospheric Administration (NOAA). Before 1900, these levels remained constant. Since 1900, the levels have risen 0.04 to 0.1 inches per year. But beginning in 1992, that rate climbed to 0.12 inches per year. This translates to much greater likelihood of flooding in coastal areas (including the neighborhood where I lived for 10 years).
And we should be concerned about ebola in Africa, mainly because we can do something about the higher rates of ebola infection and deaths there.
But ebola in the United States? Really, this shouldn’t be a worry for you. Let the math ease your mind.
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This world is spinning fast, and a lot of things are changing. Today’s interview is with Kelly Case ofTime on Hand Services. She is a virtual assistant or VA — in fact, she’s my VA! Without Kelly, this blog would be empty most of the time. She also lays out my newsletter and does lots of research for me.
I have my own business that provides administrative services to other companies. These companies vary in size and may be located anywhere in the world. Thanks to the internet, there is less and less need for your assistant to be in the physical office with you. My clients enjoy the freedom of having a virtual assistant. They don’t have to provide office space, computer equipment, or benefits. They decide how many hours they want me to work for them each month and then assign tasks to me at their convenience. These tasks vary widely. I do bookkeeping, email management, calendar management, blog management, proofreading, data entry, travel planning, transcription, customer service, email marketing, website design, and more.
I use math just about every day, for my own virtual assistance business as well as for the businesses of my clients. I use math when doing invoicing, payroll, travel planning, and bookkeeping. For instance, when reconciling credit card or checking accounts, I must use math to make sure the credits and debits match the bank statement. When invoicing, I use math to make sure I’m charging their clients or mine the right amounts or percentages. A customer of my client may agree to make three monthly payments to the client for a certain product. I split the payment into thirds and charge at the appropriate time.
Yes, I use the calculator function on my computer whenever I need to calculate long lists of numbers to prevent human error. I usually do it twice to be sure I come up with the same answer each time. I also use Microsoft Excel to keep track of credits and expenses for my clients’ check registers. Quickbooks is used often for the bookkeeping aspect as well.
I’m not sure that it helps me do it better, but it enables me to do my job. I wouldn’t be able to invoice, do payroll, or keep books without the use of math. Numbers are an integral part of our daily lives and work places. And, where there are numbers, there is math.
I am extremely comfortable with math. The type of math I use in my job is very elementary and basic for me.
I enjoy math very much. In high school, I got As in math and was asked by friends to do their homework assignments for them. In fact, I enjoy it so much I took math as one of my college electives because I knew it would be an easy A for me.
No, I didn’t need to learn any new math skills per se. I just had to learn the different programs that I use to do the math, like Quickbooks or an online payroll service.
More and more writers, like me, are hiring virtual assistants. This allows us to focus on our writing, and for me, it means having a detail person on my team. Have a question for Kelly or interested in learning more about her services? Check her out at www.timeonhandservices.com. Wondering how you can use a virtual assistant in your business? Ask in the comments section.
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As a math major in college, I was required to take a computer programming class. In retrospect, the reasoning made perfect sense: successful programming follows a natural logic, very much the same way math does. But at the time, I was resentful, and a little scared.
Sure enough, I was lost by week two. I enlisted in some tutoring from a dear friend in my section. And she demonstrated to me a completely different way of structuring the code. Her process made much more sense than the methods taught by our instructor, so I adopted it. Three days later, I sat in shock, as the prof announced that some of our assignments looked suspiciously similar.
Let me be clear: I had not copied my friend’s coding. I had identified with her way of thinking and modeled my code after her approach. But it was such out-of-the-box thinking, I understood why the prof thought we were cheating. And sadly, instead of talking to him about it, I simply reverted back to his methods. Yeah, I didn’t get much out of that class.
My friend demonstrated some amazing creativity in her approach to coding. She did this in all of her math classes as well — for which she was greatly rewarded. I learned from her that thinking creatively is critical for succeeding in math of any kind. And I mean any kind — from proving Fermat’s Last Theorem to finding out how many gallons of Symphony in Blue you need to paint your living room.
Too often, math is described in black-and-white terms. There’s a right and a wrong answer. There’s a step-by-step process to follow. If you think of math this way, it’s no wonder. Most of us were taught that math is about a right answer.
But those teachers were wrong. Sure, the right answer is important, but just like those inspirational posters say, it’s all about the journey. How you get to your answer is just as important as the right answer.
And that’s where creativity comes in. Because we all access this information in different ways. Some of us are visual. Some of us need time to think. Some of us like to talk things out. Those of us with true numeracy use creative methods for solving ordinary problems. Take 23 x 6, for example.
Most of the world would stack these numbers up, multiply 6 by 3 and then 6 by 2, add (remembering to align the numbers properly) and get 138. But there are many other ways. I like this one:
23 x 6 = (20 + 3) x 6
= (20 x 6) + (3 x 6)
= 120 + 18
= 138
With that method, I can do the problem in my head!
But you don’t need to solve the problem that way. Come up with your own process. Be bold! Set off on your own! Be creative!
So in answer to the question, Is math creative? YES! You’ve just got to access your own out of the box thinking.
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Do you agree that math is creative? Why or why not? What examples of creativity (or lack thereof) can you share?
These days I’m devouring just about any writing I can find that features the cross section between neurology, sociology and psychology. Daniel Pink’s Drive completely changed my mind and confirmed my suspicions about how motivation actually works. And now The Organized Mind by behavioral neurologist Daniel Levitin has helped me better understand how the brain helps us organize our time, thoughts and things — and how our brains can get in the way.
It’s a big book. And parts of it are very dense, including sections that explain the anatomy of the brain and almost an entire chapter devoted to the probabilities of medical outcomes. But the rest of the book is quite narrative, with funny and relatable examples. This science and geek loved it all.
For me, the takeaways were in productivity and learning. It’s not fair to boil it all down to two categories, but I will. At the same time, I’ll point out how all of this relates to math, with a few quotes from Levitin‘s book.
Turns out the brain is perfectly designed for identifying similarities and differences.
In the last few years, we’ve learned that the formation and maintenance of categories have their roots in known biological processes in the brain. … Theoretically, you should be able to represent uniquely in your brain every known particle in the universe, and have excess capacity left over to organize those particles into finite categories. Your brain is just the tool for the information age.
Where’s the math in that? Everywhere. It could be argued that math is the study of categories. Start with our number system. Positive numbers that are not fractions and decimals fall in the category of whole numbers. Add negative numbers to that group, and you’ve got integers. (And so on.) Or you can group numbers as prime and not prime or even and odd. Graphs of equations can be lines or curves — and some curves are parabolas, while others are circles. See where I’m going with this?
This is all good news. Because the brain is so excellent at forming and maintaining categories, your brain was made for math.
But how can we make sure we remember all of these categories?
The last two decades of research on the science of learning have shown conclusively that we remember things better, and longer, if we discover them ourselves rather than being told them explicitly.
This idea has huge implications for math education. For the most part, approaches to teaching math fall in one of two categories (see what I did there?): telling and discovering. Most of us who grew up in the 70s and 80s learned math through the “telling” method. The teacher gave a lecture, demonstrating how to perform a skill, and asking students to practice the steps shown in the lesson. Discovery turns this process on its head, giving students the opportunity to figure things out on their own, even finding new ways to solve problems. When they can discover ideas on their own, students have a much better shot at remembering what they’ve learned.
Of course discovery is messy and difficult, which brings us to ways that our brain gets in the way.
This idea from Levitin blew my mind. Apparently it’s a proven fact that people don’t manage frustration well. It’s why we procrastinate, and that feeling of frustration is rooted in our brains.
The low tolerance for frustration has neural underpinnings. Our limbic system and the parts of the brain that are seeking immediate rewards come into conflict with our prefrontal cortex, which all too well understand the consequences of falling behind. Both regions run on dopamine, but the dopamine has different actions in each. Dopamine in the prefrontal cortex causes us to focus and stay on task; dopamine in the limbic system, along with the brain’s own edogenous opiods, causes us to feel pleasure.
Then we play into this automatic system with two “faulty beliefs: first, that life should be easy and second, that our self-worth is dependent on our success.” So, when the going gets tough, we quit — shoot for an easier option.
Unfortunately, this is just something we need to fight against. And Levitin has some great strategies to offer. At the same time, I felt very validated in my instinct to choose low-hanging fruit, rather than reaching for loftier goals. That also goes for the math student who is immediately frustrated by assignments he can’t understand, and the grownup who always lets someone else split the restaurant tab.
For years I’ve struggled with my inability to internalize the concepts of probability, so I was really relieved to learn that my brain is wired this way.
Cognitive science has taught us that relying on our gut or intuition often leads to bad decisions, particularly in cases where statistical information is available. Our guts and our brains didn’t evolve to deal with probabilistic thinking.
No wonder I have to work so hard to understand the probability I’ll suffer from a medication’s side effects or even the chance I’ll win in Roulette. Unlike categorizing, my brain isn’t set up to have an intuition about probability. (This isn’t to say that others can’t find calculate probabilities quickly, of course.)
Of course much depends on our understanding of probability, including life-and-death situations, like choosing the right medical treatment. It’s important to think about these things in a clear and focused way. That’s one reason Levitin spends so many pages on something called FourFold tables. (More on those in a later post.)
I encourage you to pick up a copy of The Organized Mind. (No, you can’t borrow mine; I’ve been referring to it over and over since I finished reading!) It’s a great look at how we can maximize the things our brains do well and work against the tricks our brains play on us — to be better organized and productive, while learning and using math.
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Have you read Daniel Levitin’s book? If so, what did you think? Share your comments and questions.
I’ve hit the age when many of my friends and colleagues are managing the realities of having aging parents. Luckily, I’m not there yet — my mom is still very active, both physically and mentally. But many of us in our 40s or 50s are probably at least thinking about how we might manage our parent(s) affairs if/when they are unable to handle things on their own.
My friend and fellow writer, Beth, faced this problem last year, when she, her husband and her mother moved to another state. Beth’s mother needed a little more supervision, and so Beth and her husband arranged for her to live with them. That brought up some emotional and practical questions, which Beth shared in an online writing’s group that we both belong to. She gave me permission to share them here:
Mom lived independently until we combined households. She wants to pay us a monthly fee that covers “room and board.” The question is: How to figure a fair and reasonable amount.
It’s been a long time since [my husband] and I had a roommate. In those days, we simply divided the big stuff by three (rent, utilities, cable), and each person was responsible for his/her own food. That doesn’t seem fair in the current situation for a variety of reasons (not the least of which we’re talking about my MOM, not some friend).
I feel I’m making this unnecessarily complicated. Can anyone help me sort this out? I bring it up because Mom talks about it constantly. She seems to feel the amount she’s paying is too low, and I keep putting the brakes on changing the dollar figure until we have better data about our expenses.
Naturally, I think math can help us find some simple solutions to emotional problems. So I offered this:
I have a really easy and non-biased way to look at this. Calculate your total household costs — mortgage, utilities, food, etc. Then divide this by three. Each of these is a share.
Next, you can decide how many shares each person should have. For example, your mom may have only a half-share, based on what you think she can afford or how much she eats, etc. Take half of a share, and that’s her monthly rent.
Naturally, I like taking a mathematical approach, because it can help reduce the emotions. And if any of the variables go up or down — utilities, for example — you can adjust the rent really easily.
And that seemed to do the trick for Beth. In fact, she took things even farther, considering fair market value, as suggested by another group member:
Here’s how we solved the problem in the end:
1. I drew up Mom’s current monthly budget.
2. I drew up a list of household expenses that apply to her (including the mortgage payment). I didn’t include things like pet expenses or [my husband’s] fuel for commuting, obviously, because those are our sole expenses.
3. I used Laura’s methodology to divvy up the total household expenses into three full shares. Then I calculated partial shares: 3/4, 2/3, and 1/2.
4. I used [another member’s] data about the fair market value of a studio apartment in [my county] for comparison purposes.
5. Then I sat down with Mom and first explained her current budget. Next, I went over the household expenses.
6. I told her about the fair market value of a studio apartment and explained how that related to our attempt to determine what was a fair amount for her to pay us each month.
7. I showed her the share information.
8. I showed her how each share amount would affect her net income. Even at a “full share,” she still retains about 45% of her net income for “mad money,” and that’s without touching any investments. (I didn’t point that out to her, in terms of trying to steer her. I think what I wrote kind of reads that way. I just used a calculator to show her what each share amount would leave her, in terms of disposable income.)
9. I had written all these figures down on paper, so I stepped away to giver her time to peruse the numbers for awhile and consider what SHE wanted to do.
10. After a few minutes, she called me back and said she’d decided to pay a full share. She’s the type of person who likes to “pay her own way,” and she’ll still have plenty of mad money left over. She also was very happy she wouldn’t need to dip into any investments.
It’s important to note that this cut-and-dry approach didn’t erase all of the feelings in Beth’s situation. She was very nervous talking to her mother, and her mother felt responsible for paying a full share. See? Feelings.
Another interesting aspect is how flexible this process can be. With some simple parameters — the value of a full share vs. a half-share, for example — Beth’s family can alter the process depending on where everyone is financially. And if her mother needs more resources or Medicare helps to pay for things, the entire formula can be changed.
Just a bit of math helped Beth gain some perspective and offer her mother tremendous autonomy. The process also set them up to avoid conflict later on. Nice work, math!
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I’m currently reading The Organized Mind, by Daniel Levitin, and I can’t wait to share a review with you when I finish. He offers some really terrific math to help when medical decisions are tough. Four-square decision tables anyone?
What do you think of the process Beth worked out? (I also offer this approach as a way to divvy up the cost of a beach house among several family members.) Have you used math to help you come to a difficult or emotional decision? Do you think this approach would work for a young adult who hasn’t flown the nest? Share your stories in the comment section.
Now that Labor Day is behind us, it’s safe to say that most of country is back at school. In honor of this new beginning, I decided to share three of my most favorite posts for teachers, students and parents.
In this post, I asked veteran middle school teacher, Tiffany Choice, to share her advice for parents on how to help their kids succeed in math class. Her advice is golden, and stupid-easy to follow. In fact, none of her ideas involve learning new math methods. Huzzah!
I polled the high school and middle school students I know to get this great advice for teachers. If you teach math — at any level — do yourself a favor and take these to heart. Students aren’t asking for the moon.
And there’s one more for teachers. Those of you who are parents see both sides of this equation. The homework wars are real, kids are stressed out and parents feel sometimes powerless to help.
If you’re a parent who needs even more support — and who among us doesn’t? — check out these bonus posts, where I outline ways that you can help your child become a master mathematician — or at least leave math class not feeling like a dummy!
And of course, I’m around to answer your questions and give you support. Let’s get this school year off to a great, mathy start!
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Got a question or comment about any of the above resources, share in the comments section!
Nothing says hello to a new neighbor like sending a greeting card or an invitation. And cards can mean so much in times of grief or illness. Those special little messages to pull the heart strings have to come from somewhere, right? Louisa Wimberger, founder of Weehah Greeting Cards and Invitations has built a business around these special messages. From greeting cards to invitations, she makes some of the best cards available.
I design and create greeting cards and invitations. I sell them through my website, at retail shows and festivals, and also wholesale them to stores.
I use math all the time! For example: I use QuickBooks to invoice customers. I have to determine the cost of my supplies and my time in order to come up with a reasonable retail price ($3.95 per card or 10 for $35) and wholesale price ($2.25 per card).
I keep a budget, make purchases with credit cards, and pay that off monthly. On occasion, I hire someone to do mindless or repetitive tasks for me such as packaging cards. I learned that I have to pay someone per piece, and not by the hour!
I have to order cardstock and envelopes almost every week. My cardstock sheets come in 8.5 x 11 or 11 x 17 usually. So, when a customer wants 100 flat cards that measure 4.25 x 5.5 each, how many can I get per sheet? The list goes on.
I use QuickBooks (for invoicing and budget/bookkeeping) and occasionally a calculator (to figure out measurements for things, mostly).
If it weren’t for math, I wouldn’t be able to actually make any money doing what I do!
I haven’t usually liked math in the past, but I have learned to appreciate (and even sometimes enjoy) it in the context of my business.
I think I took Algebra and Geometry but not Calculus. I never, ever felt like I was good at it. I glazed over a lot. I excelled in English, and that came naturally. Math was a push for me almost all the time. (And yet, I did pretty well on the math section of my SATs, oddly enough!)
I did not learn new skills. I more had to learn the theories people have behind how to price things, which doesn’t seem exactly like math to me.
Do you have a question for Louisa? Would you like to check out her cards? You can find out more about her at her website.
It’s been a blast going unraveling five myths about the Common Core here at Math for Grownups. And I’ve gotten a lot of terrific feedback from commenters. In case you missed any of these posts, I thought I’d put them together in one package. Enjoy — and be sure to share your thoughts in the comment sections of each post!
This is perhaps the most pervasive misunderstanding. In fact, the Common Core Standards are simply that: standards. In education-speak, this means they are statements of what students should know, upon completing a course or grade. Common Core does something a bit more than other sets of standards, giving a clear expectation of the depth of this understanding. >>read the rest
While grabbing a latte at the local Starbucks a few weeks ago, I ran into a friend of mine. She was taking a break from teaching cursive to high school students at a nearby private school’s summer program. “Kids don’t learn cursive in elementary school anymore, and so they can’t sign their names,” she explained. “Kids aren’t even required to learn their multiplication tables these days!” >>read the rest
One of the reasons for Common Core is to be sure that when students graduate from high school they are ready for college and/or the job market. And these days that means having some advanced math skills under their belts. But if you read the Common Core course headings, algebra is not mentioned until high school. >>read the rest
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. >>read the rest
First, a definition: fuzzy math is a derogatory term for an educational movement called reform math. Therefore the claim of fuzzy math isn’t so much a myth as an attempt to insult the way that many math teachers and education researchers advocate teaching mathematics to K-12 students. >>read the rest
Know someone who could use an education on what the Common Core standards for math reallysay? Forward them this link. Or tweet about it and post on your Facebook page.
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 last post of that series (read Myth 1, Myth 2, Myth 3 and Myth 4), which began in August. Of course, I’m writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc
First, a definition: fuzzy math is a derogatory term for an educational movement called reform math. Therefore the claim of fuzzy math isn’t so much a myth as an attempt to insult the way that many math teachers and education researchers advocate teaching mathematics to K-12 students.
Second, some history: in 1989, the National Council of Teachers of Mathematics (disclaimer: I was once a member) published a document called Curriculum and Evaluation Standards for School Mathematics, which recommended a newish philosophy of math education. The group followed with Principles and Standards for School Mathematics in 2000. School officials and curriculum companies responded by implementing many of the approaches offered by the NCTM and as a result, the way we teach mathematics began to change. This change is what advocates call reform math and critics often call fuzzy math.
Before the NCTM’s publications, math teachers focused on the math — in particular series of steps (algorithms) designed to get the right answer to a problem or question. With reform math, educators became more focused on how students best learn mathematics. Suddenly, context and nuance and “why?” were at least as important as the answer. And it is true that Common Core Standards for Mathematics are largely based on the NCTM’s publications.
If this is truly fuzzy math, then we don’t have a myth here. (Although, to be fair, there is a legitimate branch of set theory and logic called “fuzzy mathematics.” But somehow, I don’t think Common Core critics using this term have real math in mind.) I include the fuzzy-math criticism as a myth because it suggests that teaching math in a conceptual way is a bad idea.
Throughout this series, I have asserted that the best way for students to understand and remember mathematical concepts is by returning over and over to the concepts behind the applications. Why is 24 such a flexible number? Because it has eight factors: 1, 2, 3, 4, 6, 8, 12 and 24. Students who really get this will have an easier time adding and subtracting fractions, reducing fractions, simplifying algebraic expressions and eventually solving algebraic equations through factoring.
This is numeracy, folks.
Students will not become numerate (think literate but with math) without a solid, conceptual understanding of mathematical ideas and properties. Numeracy does not typically evolve from memorizing multiplication tables or long division or pages and pages of practice problems. (Disclaimer: some kids will certainly become numerate regardless of how they’re being taught, but many, many others won’t.)
Numeracy is a life-long quest concentrated between the ages of five and 18 years old. Grownups can gain numeracy, but isn’t it better for our kids to enter into adulthood with this great understanding?
If Common Core critics want to call this whole philosophy “fuzzy math,” so be it. Just know that the ideas behind reform mathematics are deeply rooted in research about how kids learn math, not some ridiculous idea that was made up in the board rooms of a curriculum development company or smoke-filled political back rooms.
In short, the problems with Common Core math are not found in the standards themselves. Instead, the application and heated discourse are clouding Common Core’s real value and promise.
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, Myth #3, Myth #4, you can find them here, here, here and here.