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Tough Equations: Aging parents and housing

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!

Photo Credit: VinothChandar via Compfight cc

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.

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Math at Work Monday: Becca the Trauma Nurse

When it comes to life and death situations, we want to have confidence in those that are taking care of us. How do they know when to give us medicine, or exactly how much we need? Rebecca Paisley has been a registered nurse for five years and describes her use of practical math in the workplace. 

Can you explain what you do for a living?

I work on an inpatient trauma unit. We take care of the patients once they are seen in the ER. The patients either go to the Intensive Care Unit, the Operating Room or come to our floor. We have a variety of patients – from car wrecks, falls, gun shot wounds, stab wounds, motorcycle wrecks, traumatic brain injuries and some very intense medical surgical patients with complex diagnosis. We care for these patients throughout their stay which can be from 1 day to months. We are constantly on the go, getting patients out of bed, doing procedures at the bedside (extensive dressing changes, chest tube insertions, general patient care), occassionally transfering patients to ICU, if they need a higher level of care. We also admit and discharge patients throughout the day. Needless to say, we are busy!

When do you use basic math in your job?

I use math every single day at work. It’s basic math (simple multiplication, division, addition, subtraction), but I have to use it to take care of my patients. Mainly it’s medication related. For example, you’ve got Tylenol 1000 mg ordered, but the patient needs to use a liquid form (650 mg in 20.3 mL) of the medication, you then have to figure out how many milliliters you need to give the correct dose. Once you do the math a couple of times, you remember the mLs that you need. It’s easy to do it that way with a rountine medication, but sometimes we are doing the math extremely fast in an emergent situation (like a chest tube insertion or code situation). We always double check the medication during these times with a second nurse. Another example is when we give pain medication. Say the patient has diluadid ordered our standard protocol is 0.3 mg to 0.9 mg per dose. Using our judgement, we decide on the dose amount. The medication is stock in 2 mg per 1 mL vial. By using basic division I know that the concentration is 0.2 mg per 0.1 mL. I also use it to figure out the drip rate for IV fluids and antibiotics. Ancef is ordered, it comes in a 50 mL bag, it needs to infuse in 20 minutes. Here is the math in my head: 60 minutes (1 hr) divided by 20 is 3. Multiply 3 by 50 (the mLs needed to infuse) and you get 150 ml/hr. Or if we need to bolus some IV fluids, but the doctor wants them over a certain amount of time. Say 500mL over 4 hours, (500 divided by 4 equals 125, so 125 ml/hr). I also use math to estimate my time spent with my patients in the morning (15-20 mins a patient, totaling 1 hour to 1 hour and 20 minutes ), so I can grab my morning cup of coffee! 🙂  However, this math is not always correct!

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

We have certain medications that are continuous drips, like heparin or insulin. The pharmacy has calculators for these high risk medications for us to use. We just have to plug in the correct numbers, and we get the new dosing rate. The formulas for these calculations are available on our protocols, so if the calculators are unavailble (which rarely happens), we have the formula to use to get the new dosing rate. These calculators are used to reduce human error on these high risk medications. They are extremely important for safe patient care, ONLY as long as the nurse is plugging in the correct values! That’s why there is always a second nurse verification! Some of the medications (like the Tylenol example) will have the milliliters needed for the dose in the order information, but I like to challenge myself, and calculate the dose myself.

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

It makes my patient care more efficient. When I am able to do basic math in my head, I can administer medications faster, especially in an emergent situation where time is everything.

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

I feel pretty comfortable with math, but just basic math. The math I use at work has become “second nature,” so I’m able to use it and not really think about it. More complex calculations require good ‘ole paper and pencil!

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

I took geometry, and trigonometry, and I’m guessing Alegbra. I honestly hated math in school, but was fairly good at it. I never wanted to aspire to take calculus or advanced Algebra.

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

In nursing school, we had a pharmacology class, the whole first portion of it was math. We had to pass a math exam to even continue in the class. Everyone was so stressed out about it. We had to hand calculate drip rates, dosages, and do conversions. This math wasn’t foreign to me, as far as proportions and basic alegbra, but it was definitely stressful! Once we learned the “easy” ways to figure these calculations out, it was all good. I had to learn these new ways of solving these problems, it obviously did not come naturally!

Do you have a question for Becca? Send me your question and I will forward it to her.

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5 Math Pitfalls for Journalists

Whether the story originates from a study or a few well placed numbers would help drive home a salient point, math is as much a part of modern journalism as a catchy lede or the perfect source. But even with great math skills, journalists are in danger of falling into several traps — and unintentionally misleading their readers. Don’t make these mistakes!

Confusing mean and median

In terms of computations, these are really easy ideas. The mean is the the arithmetic or simple average, while median is the middle value in a set of data arranged from least to greatest. But when should you use mean? And when is the median recommended?

The mean is best for data that is really similar or for measurements like grades, weight or height. Because of the way it is calculated, the mean is influenced by outliers — one or two very large or very small values in the data. These outliers skew the mean, misrepresenting the data set.

Using the median eliminates the chance for an outlier to skew the data. That’s because the extremes are left exactly where they should be — at the extremes. For that reason, medians are often used for dollar values, like home prices or salaries.

Drawing conclusions not explicitly stated in a study

We’ve all seen those stories — coffee will kill you one day and save your life the next. These whiplash-inducing moments may not be the fault of bad research. Instead a reporter or editor could be connecting research results to outcomes that are not revealed at all.

Drawing conclusions is tricky business that should be left to the pros (statisticians in this case). So while it may be tempting to connect A to B, it’s a good idea to double check what the study results actually say.

Not going to the original source

These days, we writers get story ideas from a variety of sources: press releases, articles, and even social media. But when it comes to data, there’s a lot that can happen between the research and its dissemination.

It’s critical to go directly to the original source, rather than pull numbers and conclusions from third parties (yes, even university press releases). Read the study. Call the organization or researcher making these claims.

Using bad data

This pitfall is related to the previous one. If the numbers are wrong in the press release, you risk perpetuating the mistake.

However, it’s also important to consider the original source. Highly partisan or idealogical organizations are often not the best sources for reliable data. Train yourself to be extra skeptical, even of sources that are considered trustworthy. The integrity of your story depends on your digging a little deeper.

Reporting skewed chart data

Pictures are pretty. And while they may paint thousands of words, that story could well be a fairy tale.

An important part of interpreting charts is to carefully consider if the data is properly shown. Do the pie pieces add up to more than 100 percent? Does the range shown on the vertical axis of a line graph make the data seem flatter than it actually is? Sometimes these mistakes are made innocently. Other times, misleading charts are intentional. It’s your job to check these charts for inaccuracies.

Journalists don’t need to be mathematicians, but we do need to question numbers, just as we would question sources. And mostly, you don’t need fancy computations or deep statistical knowledge. Instead, use your natural curiosity and skepticism to be sure that your numbers don’t lie.

Photo Credit: kohlmann.sascha via Compfight cc

Do you have other potential pitfalls to add? Share in the comments section. Or ask questions about the ones listed here! And if you want more details about the math of writing, pick up a copy of Math for Writers, the only math book that most writers and journalists need. Also, look for my upcoming Statistics for Writers course, being offered online later this fall.

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Back to School for Teachers, Students and Parents

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.

Five Things Math Teachers Wish Parents Knew

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!

Ten Things Students Wish Math Teachers Knew

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.

Ten Things Parents Wish Math Teachers Knew

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!

Lowering Homework Stress: 5 easy steps for parents

Five Math Resources for Confused Parents

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!

 Photo Credit: loop_oh via Compfight cc

Got a question or comment about any of the above resources, share in the comments section!

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Math at Work Monday: Louisa the Greeting Card Designer

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.

Can you explain what you do for a living?

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.

When do you use basic math in your job?

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.

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

I use QuickBooks (for invoicing and budget/bookkeeping) and occasionally a calculator (to figure out measurements for things, mostly).

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

If it weren’t for math, I wouldn’t be able to actually make any money doing what I do!

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

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.

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

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!)

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

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.

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Common Core Common Sense: The Series

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!

Myth #1: Common Core is a Curriculum

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

Myth #2: The Standards Omit Basic Math Facts

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

Myth #3: The Standards Introduce Algebra Too Late

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

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. >>read the rest

Myth #5: Common Core is Overflowing with Fuzzy Math

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. 

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Common Core Common Sense: Myths About the Standards, Part 5

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

Myth #5: Common Core is Overflowing with Fuzzy Math

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.

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Common Core Common Sense: Myths About the Standards, Part 3

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 third in that series (read Myth 1 and Myth 2), 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 #3: The Standards Introduce Algebra Too Late

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.

Up to this point, the math is referred to by the grade level, not subject(s) covered. So at first glance, this looks suspiciously like there is no mention of algebra in middle school. You have to dig a little deeper to learn that tough algebraic concepts are covered in the middle school standards. In fact, algebra is introduced (in an extremely conceptual way, with no mention of the word algebra) in kindergarten!

The Common Core math standards are divided into domains — or mathematical concepts. Here is the full list:

  • Counting & Cardinality
  • Operations & Algebraic Thinking
  • Number & Operations in Base Ten
  • Number & Operations — Fractions
  • Measurement & Data
  • Geometry
  • Ratios & Proportional Relationships
  • The Number System
  • Expressions & Equations
  • Functions
  • Statistics & Probability

Of this list, you can find algebraic ideas and skills in at least four domains: Operations & Algebraic Thinking, Ratios & Proportional Relationships, Expressions & Equations and Functions. (You can argue that algebra appears in others as well.) In kindergarten, students are introduced to the idea of an equation, like this: 3 + 2 = 5. They also answer questions like this: What number can you add to 9 to get 10? (Algebraically speaking this question is x + 9 = 10, what is x?)

Variables aren’t introduced until much later, in 6th grade, when students are expected to “write, read, and evaluate expressions in which letters stand for numbers.” At this point, students begin to learn the language of algebra, with vocabulary words like coefficient (in the expression 3x, 3 is the coefficient) and term (in the expression 3x – 6, 3x and 6 are terms). Also in 6th grade, they start solving simple equations and inequalities, like 4 + x = 7 and 5x = 15.

In 8th grade, radicals and exponents are introduced, and students learn to solve simple equations with these operations. In addition, they graph lines and put equations into point-slope form and slope-intercept form, and begin solving systems of equations (pairs of equations with two variables). They also make connections between an equation of a line and the graph of a line. Finally, functions are introduced in 8th grade.

All of that happens well before high school, leaving lots of time in high school to delve into polynomials, quadratic equations and conic sections.

But here’s the most important thing: under Common Core, students are given a tremendous amount of context for all of this math, as well as time to develop true numeracy. This can speed along algebraic understanding. For example, students who are fluent with multiples and factors of whole numbers and decimals will have a much easier time learning how to solve equations by factoring. That’s because they will have the foundation of factoring or expanding. They will be able to use the distributive property with ease and focus their attention on the new concepts being presented.

In other words, this slow build develops numeracy.

So don’t let the Common Core headings fool you. Algebraic concepts and skills are meted out throughout the grade levels, allowing students to truly understand foundational concepts and fluently perform basic algebraic skills well before high school begins.

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 or Myth #2, you can find the here and here.

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Common Core Common Sense: Myths About the Standards, Part 2

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 second in that series (read the first here), 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 #2: The Standards Omit Basic Math Facts

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!” 

Well, I know for a fact that multiplication facts are covered in math classes across the country, including those in our fair city. But there’s this idea out there that third-graders are using calculators to find 8 x 2. While I don’t doubt that this has happened on at least one occasion, it’s not a trend in education. And math facts are a part of the Common Core.

The Common Core Standards emphasize critical thinking. And without a foundation in basic facts, students will not be able to apply critical thinking skills to problem solving of any kind.

Sure, there is no Common Core Standard that says students must be able to recite the multiplication tables 1 through 12 by heart. Instead, Common Core focuses on the concept of multiplication — which is pretty darned complex — encouraging teachers to illustrate multiplication with arrays (the picture below is an array), equal-sized groups, and area. The difference boils down to this: We grownups probably memorized that 8 x 2 = 16, while today’s students might figure it out on their own with a drawing like this:

• • • • • • • •

• • • • • • • •

The array above gives context to multiplication. Students can see for themselves that there are two rows of eight dots and 16 dots in all. The simple illustration even offers students a way to discover (or remember) the math fact themselves before memorization naturally occurs. In short, it’s much more meaningful than flash cards.

And while the example above is very visual, the idea behind it is flexible, allowing students with different learning styles to understand multiplication. A more kinetic (tactile) student can arrange 16 pennies in an array. A student with an aural learning style can count the dots out loud — in rows, in columns and in total. And so on.

There are plenty of other math facts included in the Common Core Standards, from the properties of number systems to formulas for area and volume. But I admit, you won’t find anything like, “Students will recite the value of π to the ninth decimal place.”

And this is a great change from more traditional approaches. Because, nothing sucks the life out of learning like memorization. Besides, can you remember the formula for the surface area of a cube? If not, could you figure it out or find it online? In my opinion, we want students to kick ass in the figuring-out option — to know that a cube has six sides that are exactly alike, and that surface area is figured when you add the area of each of the sides. Knowing those little details means that a formula isn’t necessary.

So yeah, Common Core hasn’t eliminated math facts. They’re just not front and center, leaving much more room for critical thinking. And that’s a good thing.

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, you can find it here.

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Math at Work Monday: Tina the Event Coordinator

Business is business, right? When it’s time to have those meetings and conferences, you want everything to run smoothly so you can concentrate on the task at hand.  Tina Speers has been ensuring that happens for four years as a corporate event coordinator.  She is the one making sure the projector runs like it should, and the refreshments are available on time.

Can you explain what you do for a living?

I have been an corporate event coordinator for four years. The majority of my job involves scheduling and planning events. I keep a Google calendar and plan the events and schedule rooms based on the needs of each group.  We also do virtual conferences, which requires IT skills such as basic knowledge of IP based systems.  I also stock our small cafe and make coffee on a daily basis.

When do you use basic math in your job?

Basic math is needed for the cafe.  Each item is 50 cents, or we have all day pricing.  I often need to make change (cafe is operated on an honor system).  I never use a calculator unless large groups pay per person for a certain amount of items.

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

If we need to make copies for our groups they are charged per page copied.  I often use a calculator because of the amount we charge.  A black and white copy is 05 cents and a color copy is 15 cents and we usual make copies in large volumes (at least 20 pages).  I also use basic math to complete the usage and metrics for the event center. We tally our guest totals by month.  I use a calculator for this because the numbers are usually large and uneven.

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

Math helps me do my job better because I am able to move fast when a guest is waiting for change.  I can’t imagine having to  use a calculator every time a guest needs change.

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

I am very comfortable with this math and it does not feel different or unusual in any way.  I mean,  I learned how to count change in first grade!  In general, I do not feel very comfortable with math unless it is very basic.

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

In high school I remember taking algebra, trig, and geometry as well as some sort of review class my senior year. I think it was actually called “Senior Review.”  I have not used any advanced math skills in my job. I took Calc I in college and barely passed.  I also feel I had a lot of bad math teachers especially in my middle school years.

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

I have not used any advanced math skills in my job.

Do you have a question for Tina? An event you need to plan? Send me your question and I will forward it to her.

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3rd Grade Math Quiz

[watupro 2] Photo Credit: jontintinjordan via Compfight cc

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Common Core Common Sense: Myths About the Standards, Part 1

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 first in that series, 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 #1: Common Core is a Curriculum

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. Compare these fifth-grade math standards, one from Virginia’s Standards of Learning (SOL) and it’s corresponding objective from Common Core:

SOL: The student will describe the relationship found in a number pattern and express the relationship.

Common Core: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

The Common Core Standard isn’t just longer — it expresses much more depth. Students begin to pay attention to the relationships between numerical expressions, algebraic expressions and graphing. The goal is for students to know that these number patterns can be shown in a variety of different ways. And that’s a pretty big deal when students get into more complex algebra.

But here’s the thing: How students are taught is left completely to school districts and/or states. Some select ready-made curriculum, like Everyday Mathematics. Others opt to develop their own curriculum, which is exactly what my daughter’s middle school did.

Certainly, curriculum development companies have leapt on the opportunity to create new lessons, textbooks, activities and online components that correspond with Common Core. That’s capitalism at work in our country. (And it’s fed my bottom line quite well over the last three years. I’ve turned away more work this summer than I was able to accept.) There is nothing in the Common Core that dictates which curriculum must adopt, however. Localities still have control over that decision and process.

This is not to say that the Common Core hasn’t forced some pretty major changes in how mathematics is taught. Under these standards, students are encouraged to discover mathematical concepts, rather than be told how math works or should be understood. For traditionalists this could be a bad change. Yet, I believe that a discovery-based approach helps students conceptualize mathematics, which gives them a much better chance at developing strong numeracy than those who learn merely by rote. More on that in a later myth.

But regardless of what you think of the standards themselves, it’s important to know that they are merely a guideline for teachers and schools. Just like state educational standards — and each state has them — Common Core is merely outlining what the students should know, once they’ve mastered the material. Now how states and districts choose to measure students’ understanding of the standards is a different story — and a completely separate discussion of the standards themselves.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it!