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## ALGEBRA

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Properties that are damaged by fire, water, storms, smoke, or mold require the services of a professional.  This is a job for Nate Dawson, Restoration Hero and President of Sterling Restoration.  Read on to see how he uses math to restore damaged properties back to mint condition.

### Can you explain what you do for a living?

Sterling Restoration specializes in emergency repair to real property whether damaged by fire, water, storm, smoke or mold. Sterling Restoration is trusted for high quality and comprehensive cleanup, mitigation, and restoration services for both residential and commercial projects. We are a locally owned company based in Springfield, Ohio serving the Miami Valley and Central Ohio areas. We take pride in knowing that our team of professionals and extensive network of resources have the expertise to return any property to its pre-loss condition as quickly as possible.

### When do you use basic math in your job?

Basic math is used in all aspects of our business including our accounting, estimating and production departments. Our accounting department uses it to calculate payroll, receivables, and payables. Our estimators use math more than anyone in our business. During the estimating process for reconstruction, we use square footage formulas (L x W) for calculating materials used, for example:  subfloor framing, roof framing , insulation, drywall, painting, etc.. We use square yard formulas (L x W/9) for calculating vinyl floors and carpet. Basic algebra formulas are used for calculating rafter lengths based on the rise and run of roof slopes.

One of our most interesting uses of basic math, and one I will focus on going forward is with water mitigation (returning a structure to dry standard). Basically, drying a wet building! Once we determine the affected area we then use a cubic footage formula (L x W x H) along with the extent of saturation to know how much dehumidification is needed. Dehumidifiers are rated based upon how many pints of water they are capable of removing from the air within a specific amount of time (AHAM Rating). Therefore, depending on the type of dehumidification used and it’s rating, we are able to determine the number of dehumidifiers we need to dry a structure within the standards of our industry (S-500 ANSI approved standard). We also use the atmospheric readings to determine whether we are creating the desired conditions required to remove water from affected materials and to determine the effectiveness of our equipment. To do this we use the temperature and relative humidity to determine specific humidity (the weight of moisture p/lbs of air) and dew point (the temperature at which water vapor will begin to condense). The formula we use to determine the number of dehumidifiers needed is as follows:

Step 1 – Determine Cubic feet (CF).

Step 2 – CF/Class Factor(a low grain refrigerant dehu has a class factor of 40 in a class two loss) = # of AHAM pints needed.

Step 3  – AHAM points needed/Dehumidifier rating = number of dehumidifiers needed.

I know! It’s starting to sound a little complicated but it is all basic math.

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

Absolutely! Even though we are in the building trade we are not in the dark ages. We use the most advanced estimating system designed specifically for the insurance restoration (property repair) business. After in-putting the dimensions into a sketch type format, this system automatically calculates all the square footages, cubic footages, and linear footages. The next step is to add a specific line item. For example, when you add drywall to your estimate  it uses a current square foot price to calculate how much to charge for hanging, taping and finishing the drywall in your project. It will also calculate how many sheets of drywall, how many fasteners are needed , how much drywall tape, and how much joint compound is needed. Finally, it will calculate the material sales tax and any state sales tax on the service.

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

I do not feel it’s a matter of doing my job better. I simply could not perform my job without math! As I stated earlier, we use math in every aspect of our business. I do not feel there are too many moments throughout the day that I am not using some form of math.

### What kind of math did you take in high school?

During my high school years I completed algebra and some trigonometry. If I remember correctly, that was all that was offered (yes, I graduated high school 32 years ago). Once leaving high school I furthered my math education in mechanical engineering. In my opinion, the levels of math being taught in high school today are far superior to what was then taught.

### Did you like it/feel like you were good at it?

I feel like there are individuals that have an aptitude for math and those who do not. Math will obviously come easy for those who have this aptitude. I would also say that if you are good at something, the chances of enjoying it are far greater than if you are not good. Having said that, I do not believe I had this aptitude. Therefore, I had to work a little harder than others, and, at best, I was average at math. Guess where I’m going with this…no I did not like it.

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

I had to learn how to use the math skills I had already acquired to accomplish the task at hand. For example, if you have the lengths of two sides and the angle of a triangle, you can calculate the length of the third side. It is crazy how much I use this algebraic formula; however, it took some time and experience to learn how many applications this formula has. Having said that, ninety percent of my daily tasks require math learned in high school.

Are you interested in learning more about restoration? Let me know and I will pass your information along to Nate.

There must be a special circle of hell for those of us planning our weddings and receptions. I know this first-hand, because I’m planning my own nuptials for this summer, and I’m about to pull my hair out. (No wait! If I do that, I’ll ruin my opportunity for the perfect up-do!)

Weddings are magical events, filled with joy and love. They’re also damned expensive. Crazy costly. The average wedding in my neck of the woods costs about \$25,000. Sure, couples can opt for a family BBQ or a quiet ceremony in a public park. But when you’ve waited as long as I have — I’m 45 years old — there’s no backyard large enough for everyone who wants to be there.

And that’s the variable that matters in wedding planning — the number of guests. The smaller the guest list, the smaller the budget. When the guest list grows, you can expect to shell out a lot more. That’s because the biggest cost of a wedding is the reception — unless you’ve got your heart set on the latest gown to walk the runway in Paris.

If you’re like me, there’s some flexibility in this list. Children or no children? Cousins or just immediate family? What about college friends you haven’t seen in years or office mates? All of these decisions have a direct affect on your bottom line. And this is where the algebra comes in.

Many reception venues follow a simple formula: a flat rental fee, plus a per-person rate. If the number of guests is the variable, you can easily set up an equation to help you settle on the number of people you can afford to attend the reception. Here’s an example.

Let’s say that the venue you’re considering has a flat rental fee of \$3,000. In addition, there’s a \$75 per person rate to cover food and drinks. (Of course, this rate depends on the menu chosen, plus other add ons, like upgraded linens, top-shelf liquors, etc.) Basically, you need to multiply the per-person rate by the number of people invited and then add the flat fee. In other words:

In this equation, y is the total cost of the reception venue, and x is the number of guests. Break it down, if you’re confused: The total cost of the reception venue is \$75 times the number of guests, plus \$3,000.

But why take the time to write an equation? Well, this allows you to play with the number of guests or your total budget. For example, if you know you want to invite between 150 and 200 people, you can come up with a range for your budget:

In this scenario, you can expect to pay between \$14,250 and \$18,000, depending on your final number.

More likely, you know your budget and want to find out the maximum number of people who can attend the wedding. For example, if your budget for the reception venue is \$15,000, how many people can you invite?

With a budget of \$15,000, you’ve got a guest list of 160 people.

The beauty of creating an equation to help in this problem is that you can play around with the numbers. Once you have the equation, you can try different things, without thinking too hard. And if you’re comparing the costs of several venues or several packages at one venue, you can create several — very similar — equations, one for each option.

I get it. Most brides and grooms aren’t going to take this step. Who wants to do math when planning one of the most magical days of their lives? But this is a clear example of how algebra can reduce the stress of planning a wedding — and possibly save you some cash.

So what do you think? Have I convinced you that algebra can be useful? Share your thoughts in the comments section. And how have you saved money in planning your wedding? Did math help at all? Dig deep and be honest!

Parks and Recreation, the Amy Poeler-driven mocumentary on NBC about a small-town parks department, features a tightly wound character, Chris Traeger, whose favorite word is literally – as in: “Biking for charity is literally one of my interests on Facebook.” It’s funny because it makes us grammar fanatics crazy. Literally is literally one of the most misused and/or overused words in the U.S.

I had never seen the word applied to mathematics until recently. No kidding! That’s when I learned about literal equations. I mean, I already knew about them; I just didn’t know what they were called. And yes, you know about them too. They’re one of the ways that we use algebra in our everyday lives – without even knowing it.

Literal equations are equations with more than one variable. Ta-da! See, you knew about them, too. Here are some examples, in case you’re not convinced:

Look at all of those variables. Each equation has more than one, which means that each of the above is a literal equation. That’s it. Easy.

Now, the algebra of literal equations is much, much easier than most mathematics, especially if the equation is simple, like the distance formula. (Don’t panic. This is not one of those train-leaving-Pasadena questions.) The algebra is in identifying the variables, substituting into the equation and then solving.

Let’s say that you’re an avid cyclist. In fact, you’ve got all the cool accouterments, like a gel-padded seat, clip-on pedals and a speedometer. You average about 16 miles per hour on flat roads, and you love trying out new routes, just riding where your bike takes you. But it’s critical that you know the half-way mark for most of your routes – otherwise, you won’t have enough steam to get back home.

That’s where the distance formula can come in.  If you know your speed (or rate, r) and the time you’ve been out, you can find the distance. This way, you know when to turn around and head back to enjoy those endorphins.

One gorgeous Saturday morning in March, you head out on an unfamiliar route, cruising at about 16 miles per hour. Checking your watch, you find that you’ve been on your bike for half an hour. How far have you traveled? You can actually do this math in your head – just multiply 16 by 0.5. How do I know this? With the literal equation d = rt.

See? You just used a literal equation. And you did it on your bike. As Chris Traeger would say, “You are literally the most impressive cyclist I know.”

How have you used literal equations recently? Want to share in the comments section? Feel free. Also, feel free to challenge my thesis that algebra is an important part of a solid middle and high school education. I can take it. Really.

Math is black-and-white, with right-or-wrong answers. It’s hard to color outside the lines in math.

While I often argue with this point, there is some truth to it. Just like grammar, chemistry and baking, math is a pretty precise subject matter. Sure, there are many different ways to add 24 and 37 in your head, but fact is, you can’t just decided that the answer is –19, right?

Rules make math work. And algebra helps us write down these rules. Now, we don’t necessarily need to think of math rules in this way, but believe me, when teaching and writing about math, it sure does help. And there are some real-world situations when an equation can  really help make math easier.

Let’s consider the process for multiplying fractions. Do you remember what it is? Take a look at this problem, and see if you can figure it out:

Of course there are several ways to describe what is happening above, right? You can do it in plain English:

To multiply two fractions, multiply the numerators and multiply the denominators.

Or, you can write this using algebra. This is not as hard as you might think! First, assign a variable to each of the unique numbers on the left side of the equation:

a = first numerator

b = first denominator

c = second numerator

d = second denominator

Then substitute those variables for the numbers themselves:

Now, perform the rule that was described in plain English above: multiply the numerators and multiply the denominators.

How about that! Lickity split, we made like mathematicians and created a rule described algebraically. How hard was that really?

Now you can use this rule to multiply any fractions of any kind. I don’t care if they’re elementary fractions made up of just numbers or if they’re fancy-schmancy algebraic functions that have — gasp! — variables in them. You don’t even have to think of the abc or d. Instead, think of those variables as place holders. (Hint: this is where your mind can be really flexible, even though the rule is not.)

Because you know this rule, you can solve this problem (even with the x and the y). Just multiply the numerators and then multiply the denominators.

Because of the rule for multiplying fractions — which includes the variables aband — you can see how to multiply any fractions. That’s where the algebra comes in handy.

Now, I know exactly what you’re thinking. When will I ever need to solve a problem like the one above. And here’s my honest answer: for most of you, never. Really and truly. I won’t lie.

However, there are times when creating a rule for a specific real-word problem is very useful. That’s when we might create an equation. Stay tuned, when we’ll talk wedding receptions, guest lists, the price per person and rental fees.

So what do you think of algebra and math rules? Did this example help you understand how algebra is important in developing and stating these rules? Do you disagree with me about why this is important? I can take it — so please do share your thoughts in the comments section.

Hating on algebra is all the rage these days. From New York Times editorials to cute little Facebook images, it seems that we’re settling into a big assumption: algebra is not useful to the average person. For the most part, this idea is pretty harmless. When I see those Facebook posts, I generally smile to myself and think, “Oh you’re using algebra. You just don’t know it!” (And yes, sometimes I say this out loud. I work alone, and my cats don’t care.)

But of course when there are calls to remove algebra from high school math curriculum, things get pretty serious. If you had driven past me at lunch time one fall day last year, you might have seen me (literally) shaking my fist and shouting at my radio. My local public radio station was airing a talk show featuring some doofus (I think he was a philosophy professor?) who was advocating that we actually stop teaching algebra. Seems it upsets students too much and, heck, we don’t need it anyway.

Want to make me mad? All you have to do is suggest this in a serious way.

So, prompted by all of the online ribbing that I get from people, I’ve decided to take on a challenge. This month, I’ll be writing about exactly how algebra is useful. My goal is to convince anyone who thinks differently that they’re wrong. But I know this is a tough sell. So I’ll settle for a couple of small concessions.

My thought is that I’ll focus on everyday uses for algebra (from spreadsheets to formulas), algebraic thinking (how we can think critically, thanks to algebra) and why I believe algebra is a cornerstone subject for middle and high school students.

Want to challenge my thinking? Go right ahead! Want to offer your own experience? Please do! I’d love to promote a real conversation on this topic. I can always learn something new about how real, live people use the math devoted to finding x.

In the meantime, share your algebra story in the comments section. I’d love to hear from everyone — whether algebra was the first time math clicked for you or you were one of those folks who said forget it, once letters were introduced to your math.

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:

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?

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.

Earlier this week, Andrew Hacker, a political science professor at Queens College, City University of New York, opined in an essay for the New York Times that high schools should stop teaching higher Algebra concepts — because kids don’t get it.

I’m sure Mr. Hacker isn’t alone in his frustration with the failure rates of students in these courses. (Trust me, math teachers are pulling their hair out, too.) Yes, math is hard. And it’s also the underpinning of our physical world. By pretending it doesn’t matter or that our future engineers, teachers, nurses, bakers and car mechanics don’t need it one eensy-teensy bit, we risk the dumbing down of our culture. And our students risk losing out on the highest-paying careers and opportunities.

The problem isn’t the math — as Mr. Hacker eventually mentions, though obliquely. It’s how the math is taught. We need to get a handle on why students feel so lost and confused. And here are just two reasons for this.

1. Kids don’t know what they want to be when they grow up — especially girls who end up in math or science fields.

When I was in seventh grade, I thought I was a horrible math student. I was beaten down and frustrated. I felt stupid and turned around. Unlike my peers, I took pre-algebra in eighth grade, effectively determining the math courses I would take throughout high school. (I wasn’t able to take Calculus before graduating.)

And that was a fine thing for me to do. Turns out I wasn’t stupid or bad at math. I just had a poor understanding of what it meant to be good at math. I had really talented math teachers throughout high school. I was inspired and challenged and encouraged. By the time I was a senior, it was too late to take Calculus, so instead I doubled up with two math courses that year.

After graduation, I enrolled in a terrific state school and became a math major. Four years later, I graduated with a degree in math education and a certification to teach high school. And now, 22 years later, my job revolves around convincing people that math is not the enemy.

What if I had been told that algebra didn’t matter? What if I had been shepherded into a more basic math course or track? Because higher level math courses were expected of me — and because I had excellent math teachers — I found my way to a career that I love. Even better, I feel like I make a difference.

How many other engineers, scientists, teachers, statisticians and more have had similar experiences? How many of us are doing what we thought we wanted to do when we were 12 years old? Why close the door to discovering where our talents are? To me, that’s not what education is all about.

Look, I can’t say this enough: I was an ordinary girl with an ordinary brain. I can do math because I convinced myself that it was important enough to take on the challenge. I was no different than most students out there today. We grownups need to figure out ways to hook our kids into math topics. I’m living proof that this works.

2. Higher algebra concepts describe how our world works.

How does a curveball trick the batter? How much money can you expect to have in your investment account after three years? What is compound interest?

Students need to better understand the math in their own worlds. We do them a grave disservice when we give them problem after problem that merely asks them to practice solving for x. The variable matters when the problem is applied to something important — a mortgage, a grocery bill, the weather, a challenging soccer play.

We can’t pretend that everyone depends on higher-level mathematics in their everyday lives. But neither can we pretend that these concepts are immaterial. Knowing some basics about algebra is critical to being able to manage our money or really get into a sports game.

For example, when the kicker attempts a field goal in an American football game, he is depending on conic sections — specifically parabolas. Does he need to solve an equation that determines the best place for his toes to meet the ball in order to score? Nope. But is it important for him to know that the path of the ball will be a curve, and that the lowest points will be at the points where he makes contact with the ball and where the ball hits the ground.

That’s upper-level algebra at work. If you were to put the path of the football on a graph, making the ground the x-axis, those two points are where the curve crosses or meets that axis.

Look, we need to adjust the ways we teach math and assess math teachers. I agree that math test scores aren’t the be all, end all. I agree that most high school students won’t be expected to use the quadratic formula outside of their alma mater. (Though algebra sure is useful with spreadsheets!) And I agree that asking teachers to merely teach the concepts — without appealing to students’ understanding of how these concepts apply to their everyday lives — is draining the life out of education.

And really, how much of the rest of our educational system is directly useful? Do I need to spout out the 13 causes of the Civil War or balance a chemical equation or recite MacBeth’s monologue? (“Tomorrow, and tomorrow, and tomorrow, Creeps in this petty pace from day to day…”) I can say with no hesitation: Nope! But learning those facts helped inform my understanding of the world. Algebra is no different.

What do you think about the New York Times piece? Do you agree that we should drop algebra as a required course? In your opinion, what could schools do differently to help students understand or apply algebra better?

It’s the No. 1 question asked of math teachers: “When will I ever use this stuff?”

And in terms of upper-level math — conic sections, radicals, differentiation and the quadratic formula — the answer may very well be, “Not much.”  (Unless you’re in one of those jobs with top-paying degrees.)

As I hope you know by now, basic math is ubiquitous.  We encounter percents, fractions, formulas, the order of operations (Please Excuse My Dear Aunt Sally) and geometry pretty regularly.  But algebra?  When was the last time you solved for x?

Algebra describes the relationships between values, and how those values change when we introduce variables.  In short, algebra is based on equations or expressions:

[pmath]3+x[/pmath]

[pmath]x^2+4x-7[/pmath]

[pmath]y=5x+9[/pmath]

(Are your hands sweating or have your eyes glazed over? Hang in there.  I promise this won’t be overwhelming.)

In its simplest form, algebra can be described as the process of solving for a variable.  And you probably did that with random equations for a good portion of your high school math education.

Boring.

Except for word problems, none of the equations had much to do with real life, which is one way that we math educators have sucked all of the life out of math.

But I’m guessing that at least some of you use algebra pretty darned regularly–without even knowing it.  Let me show you how.

As a freelance writer, I’m responsible for maintaining my business records, which for me include expected and actual income, invoices and goals.  I could purchase accounting software for this or hire someone to do the work for me, but to be honest, my business is pretty small.  I have a lot of experience with spreadsheets, and so six years ago, I built one that I still use to track all of my business finances and goals.

Why does this work?  Formulas.  One formula gives me the total of all of my invoices for each month and and another spits out the percent those are of my monthly goal.  I have created formulas that give the percent of my income that is generated from each of my revenue streams.  And because of formulas, I can instantly see how much income has been invoiced but not received.

Meet my good friend, Rebecca.  Like many of us in my neighborhood, Rebecca’s family gets milk delivered once a week by a local dairy.  (I know!  Cool, right?)  But unlike me, she shares her delivery with her next-door neighbor.  And that requires a little bit of math.  Here’s how she explains it:

As you know there are bottle deposits, bottle charges, delivery charges and of course milk (or other product) charges. The charges go to only one credit card. Keeping track of these is a challenge if you don’t want to have to write a check to your neighbor every week – and who wants that? So we have worked out a “kitty” (nice, eh, milk – kitty. ha ha) system where we pay a lump sum to the person whose credit card is being charged. But then we have to know when the kitty is running out.

In other words, each of the families contributes to the kitty, and those funds are used to pay the milk bill on one family’s credit card account.  Rebecca uses a spreadsheet to keep up with how much money is in the kitty at any given time.  When the kitty runs low, she knows to ask her neighbor for a contribution.

Why doesn’t Rebecca ask for the same monthly payment in the kitty?  Well, this is where the algebra comes in.  Not only can we order milk, but also yogurt, meats, eggs and cheese. That means the weekly orders vary.  And — here’s where you can use that English degree — when elements vary, they’re called variables.

Ta-da!  Algebra in real life.  (Gosh, I’m so proud!)

These spreadsheet formulas are so useful that algebra teachers are using them to demonstrate how algebra is indeed useful in everyday situations.

So, when was the last time you used a spreadsheet?  Did you create a formula?  Did you know you were using algebra?  Tell us about it in the comments section.

It’s the perennial question from students of all ages: “When will I use this stuff?” So when tutor, Ryan faced this query (probably for the upteenth time), he took to the streets to find the answer.  What he found is in the video below:

And of course I have some thoughts — for teachers and students.

It is absolutely true that series (that’s what the funny looking E — an uppercase sigma — means in this problem) are not the stuff of ordinary folks in non-science fields.  But they’re not as difficult as they seem.  It’s the notation that’s confusing.

Skip this part, if you don’t really want to do any algebra today.

A series is just the sum of a sequence (or list) of numbers.  That’s it.  Nothing more, nothing less.  So when you have

[pmath]sum{n=1}{7}{3n-1}[/pmath]

you’re simply saying, “Find the sum of the first 7 values of 3n-1, where the first value of n is 1.” In other words: 2 + 5 + 8 + 11 + 14 + 17 + 20 = 77.

Now back to my opinions.

Okay, so I don’t need to know what a series is in order to visit the grocery store or get a good deal on a car or even figure out how much I earned this year over last year.  But here’s what I wish some of those folks who were interviewed for this video had been able to say:

“That funny-looking E is a Greek letter, right?”

“Doesn’t this have to do with adding things together?”

“Hey, I dated a girl from [pmath]{Sigma}{Sigma}{Sigma}[/pmath] once!”

And second, this tutor did pick a humdinger of a problem to focus on.  Series (and their brothers, sequences) are not the main focus of any mathematics course.  But honestly, they wouldn’t be taught if they weren’t useful somewhere.  And boy-howdy are they useful!

So, here are a few ways that real people do use series in their real jobs (courtesy of Algebra Lab and Montana State University:

1.  Architecture:  “An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?”

2.  Business: “A company is offering a job with a salary of \$30,000 for the first year and a 5% raise each year after that. If that 5% raise continues every year, find the amount of money you would earn in a 40-year career.”

3. Investment Analysis: “A person invests \$800 at the beginning of each year in a superannuation fund.  Compound interest is paid at 10% per annum on the investment. The first \$800 was invested at the beginning of 1988 and the last is to be invested at the beginning 2017. Calculate the total amount at the beginning of 2018.”

4. Physics: “The nucleii of a radioactive isotope decay randomly. What is the total number of nucleii after a given period of time?”

And this brings me to some additional news of the week.  Sol Garfunkel (Consortium for Mathematics and Its Applications) and David Mumford (emeritus professor of mathematics at Brown) made a bit of a splash on Wednesday, with an editorial in the New York Times: How to Fix Our Math Education.

Their proposal is that we teach tons of math that applies to everyday life — and focus on those applications. (Yay!) And we ditch “highly conceptual” math for folks who won’t need it for their jobs. (Boo!)

Hopefully, you’ve already identified the problem: How do we know if a kid won’t decide to go into physics or engineering or high school math education? Hell, how do we even attempt to lure them into these fields, if they don’t see the math at all?  (And by the way, physics, engineering and applied mathematics were recently identified as the top-paying degrees in the U.S.)

Look, I empathize with the student who isn’t interested in what any of the Greek letters mean in math class.  And I think it’s true that most folks won’t use these skills at all after high school.  (It is worth mentioning that everyone depends on series in their daily lives–they just don’t see the math.) But my response to the kid who asks, “What’s this good for?” is to tell him where it can be applied.

And if he says he won’t be going into any of those fields, I would say, “Suck it up, cupcake, because you’re too darned young to know for sure.”

Please share your thoughts in the comments section.  Do you agree that these concepts should be taught in high school, even though most kids won’t use them in their everyday lives? How do you think we should encourage more students to go into science, technology, engineering and math (STEM) fields?