When am I Ever Going to Use Algebra in Real Life?!

by Claudia Lee, Secondary Mathematics Teacher

Pushing a greased elephant up a hill – some people think it would be easier to do that than to do algebra.  Why is that?  Maybe they think they don’t have the “math gene.”   You know, the one that allows you to find that ever evasive “x”?  Even the letter x is mysterious.  Think about it.  It’s not the most commonly used letter in the alphabet, and just saying the letter seems to have a negative connotation.   There are those that think they’ll never find x – they think it’s constantly on the move like a fugitive, trying not to be discovered, hiding in dark alleys and behind dumpsters.  But what if we changed our thinking?  What if instead we thought of it as that poor little helpless puppy who just wanted to be discovered?  Wouldn’t you do anything in your power to find it?  

I hear people say, “I can’t do math,” or “I have a mental block when it comes to algebra.” Or better yet, “When am I ever going to use this in real life?”  Well I promise you, when you get abducted by aliens and your only way home is to solve a system of linear equations, you’ll be glad you know how to do it.  OK, I might be exaggerating just a little.  The truth of the matter is, you may not need to know at what time Train A catches up to Train B if it is traveling at twice the speed of Train B but leaves one hour later than Train B, I’ll give you that much.  But you might need to know how to figure out how much material to buy to fence in a yard, or to tile a floor.  Maybe finding out how much solution is needed for the proper ratio of a chemical mixture is something you’ll need for your job.  You might want to know how to calculate earnings on different types of investments, or the probability of a certain event happening.  The list goes on and on.  Here’s the point:  in order to be able to do all of these things, you need to be able to think logically, systematically, and analytically, as well as be able to problem solve.  And guess what?  Algebra teaches you to do that.  Yup, I’m not kidding.  

I’ll prove it to you.  Ready?  Here’s a good one.  

You start with 1 penny on Day 0.  On Day 1, you double it, so you have 2 cents.  On Day 2, you double that, so you now have 4 cents.     Every day, the previous day’s amount is doubled.  Now, let’s say I hire you for only 30 days.  You have the option of one of the following two salary structures.  You could either take $1,000,000 at the end of 30 days OR I start you off with 1 cent before you even start working.  On Day 1, I double that 1 cent, and continue each day according to the algorithm above, for 30 days.  At the end of 30 days you will receive the sum of the 30 day’s earnings.  Which option would you take?  I’ll make it even more interesting…instead of $1 million I’ll make it $5 million.  That’s a lot of money for 30 days of work!  BUT, is it the RIGHT choice???  Let’s look at it more analytically, shall we?

If you start with one cent and double it every day for a week, here is what you would have:

Not very impressive after one week, is it?  I bet that $5 million is looking pretty good right about now, huh?  Well, let’s look at what happens after the second week:

It’s marginally better, but still nowhere near $5 million!!  You are probably thinking who would be foolish enough to choose this option???  Let’s keep going…

Now that’s starting to look a little more promising!  But it’s still so far away from $5 million!  How can this option reach $5 million in 9 days???

Now here’s the kicker…I said in the beginning that at the end of 30 days you would receive the sum of the 30 days’ earnings.  Want to see me really blow your mind??  If you add up all 30 days of earnings, you end up with…wait for it…

$21,474,836.47.  Boom.  Mic drop.

Now, this particular example is probably not going to happen in real life.  I’m fairly confident that a company would go out of business if they offered this salary structure.  But at first you probably thought the $1 million option was pretty good because there was no way that one penny could turn into over $10 million in 30 days.  We approached this very analytically, making a chart so that visually it was easy to understand.  Now, I’m not going to go into the mechanics of the formula and how it works, but suffice it to say, if we hadn’t done this example and I had just given you an equation and said “Here’s a formula for exponential growth”, you might look at me like I have 3 heads.  More importantly, the concept of exponential growth might not make any sense at all to you.  And quite honestly, I wouldn’t blame you.  That might be the equivalent of me saying, “You have 12 pencils and the mail is delivered at 4 pm.  If the dog’s bone is bacon-flavored, how long will it take the dog to bury its bone in the backyard?”  But if we can apply something tangible to it, so that it makes more sense to us, doesn’t that make it easier to understand?  And yes, my friends, this concept of exponential growth is actually algebra, and it’s used in the real world.  Biology, physics, economics, finance, and computer technology all use exponential growth.    

So let’s get rid of this notion of “when am I ever going to use this in real life?” or “I can’t do math.”  It doesn’t fly with me.  You can do it, you just have to do it.  I can’t make it any simpler than that.  You. Can. Do. It.  Is it going to be hard?  Probably.  Will you understand it right away?  Maybe, maybe not.  Will you get discouraged?  Most likely.  Does that mean you shouldn’t try?  Of course not!  I guarantee that even the most notorious mathematicians have made mistakes.  Even they have failed miserably at some things they’ve tried to solve.  But they persevered, and you should too.  Give yourself the chance to be successful – you really have nothing to lose!!    

I implore you to think of algebra not as some course you have to take to get through high school, but rather as a tool that will help you to function in the real world.  Even if a topic doesn’t seem like something you’ll ever use in your life, think of it more as learning how to process information, how to approach a problem systematically, how to determine if a numerical answer makes sense.  I promise you, if you change your viewpoint, you’ll be determined to find that little puppy!

Mindfulness: An Inner Tool for Thriving in School and Life

by Susannah Azzaro, Business Technology Teacher

A few weekends ago, I participated in a workshop entitled Sustainable Compassion for Educators presented by the non-profit, The Courage of Care Coalition.  The mission of Courage of Care, as stated on their web site is “to empower both personal and social transformation by providing deep contemplative training coupled with powerful tools for systemic change. We support individuals, organizations and communities in realizing a more courageous, caring and equitable world.”  ("Courage of Care Coalition")

In the workshop we explored the latest research on the science of care; engaged in mindfulness practices; explored possibilities for creating more inclusive education communities; and affirmed that “the best learning happens when students feel safe, seen, and connected.” ("Courage of Care Coalition")  *

The workshop - particularly the information on mindfulness - inspired me to write this week’s blog post.  Mindfulness is a practice that is radical in its simplicity, and in the realm of Education, it can positively and deeply affect change in the well-being of students, parents, teachers, and administrators.  A regular practice of mindfulness can lay this essential foundation for feeling safe, valued, and connected. 

What is Mindfulness and How Does it Work?  

Jon Kabat-Zinn, Professor of Medicine Emeritus and creator of the Center for Mindfulness in Medicine, HealthCare, and Society at the University of Massachusetts Medical School shares, “Mindfulness is awareness that arises through paying attention, on purpose, in the present moment, non-judgementally.” ("Jon Kabat-Zinn: Defining Mindfulness - Mindful", 2016)

Mindfulness works by calming the part of the brain that wants to react to the constant stream of fickle impulses. By building our capacity to slow down and notice our thoughts and feelings without judgement, we build our ability to make choices that are more in alignment with our highest good.

How Can Something So Simple Help in the Classroom?

Science is proving that stress has a tremendously negative effect on parts of the brain responsible for executive functioning, emotional regulation, and working memory, which are all functions that play a critical role in learning and behavior.  

Kabat-Zinn, in his foreward to Learning to Breathe: A Mindfulness Curriculum for Adolescents by Patricia Broderick, expands on this science:

Through the systematic cultivation of attention, awareness, self-compassion, and kindness toward others…a set of fundamental and highly beneficial life skills are developed…These life skills form the basis for building successful relationships, beginning with oneself.  They can also contribute to optimizing the classroom environment and learning. (Broderick, p. ix)

How Can I Get Started?

While you can practice bringing mindful awareness to any activity, the mindfulness approach I’m referring to in my post today is one in which you pause, close your eyes, slow down your breathing, and pay attention to what you notice.

You don’t need anything but YOU and about 5-15 minutes to start.  If you want to set a timer, you can.  Sit comfortably, close your eyes, slow down your breathing, inhaling and exhaling through your nose (if your nose is obstructed, you can breathe through your mouth).  

Your attention will, inevitably, wander off your breath to any number of topics the mind likes to obsess about. When you notice this has happened, non-judgementally bring your attention back to the feeling of the breath at the tip of your nostrils.  

Just start here.  Try it daily for a while.  Five minutes.  That’s it.  You cannot get this wrong. It takes patience and consistency, but it costs nothing… and the returns are stunning.

What Are Some Effects of Practicing Mindfulness?

• Your Body – By relaxing your body and your breathing, you shift from a sympathetic nervous system response (also known as fight or flight) into a parasympathetic response (also known as rest and digest).  The effects of shifting from sympathetic to parasympathetic response include lowered blood pressure, improved digestion, and better sleep.

• Your Mind – Our minds are like a yard full of untamed puppies.  These puppies are like our thoughts. When you regularly practice mindfulness, you don’t get rid of the puppies, they just calm down, and you become a better caretaker.  Translated: your focus and attention improve, your creativity increases, your capacity for caring and compassion amplifies, and you can make decisions for your life with more integrity.

• Your Inner Self – When you regularly carve out time to pause, relax, and breathe, you become aware of things you never noticed before.  Maybe at first it’s just the sounds and smells around you, but then you start noticing things within you.  You may feel things you have never felt and notice patterns of thought and behavior you never noticed.  This connection with your inner life can help you gain clarity about what’s being reflected back to you in your outer life, which, in turn, can help you make better choices for yourself in any given situation. 

A Word about Resistance

As simple as the technique of mindfulness is, when you begin practicing, you will encounter resistance.  This is normal and expected.  We are creatures of habit, and when we try to incorporate anything new and possibly uncomfortable into our daily lives, we will encounter a push-back from our ego.  What does resistance look like? Boredom, fidgeting, a laundry list of avoidance techniques … the usual culprits. Don’t judge the push-back; just keep showing up and doing the practice anyway.  

An Invitation

I’d like to invite you to give mindfulness a try. Jump in today…right now if you want.
Let me know what your experiences are.  I would love for you to share them here in the comments section. 



It’s a radical thing to get quiet and still, and to be with yourself without judgement; radical, because in our, outward-focused world that doesn’t stop moving, thinking, planning, dissecting, analyzing, talking, and reacting, turning inward has the ability to bring us back into balance, and lay a new foundation for our teaching and learning experiences, our personal lives, our world.

* Check out PDLCS's mission. Part of why we exist is to cultivate this feeling of safety and connectedness with our students and their families.

Works Cited

Broderick, P. C. (2013). Learning to breathe: A mindfulness curriculum for adolescents to cultivate emotion regulation, attention, and performance. Oakland, CA: New Harbinger Publications.

Courage of Care Coalition. (n.d.). Retrieved November 14, 2016, from http://courageofcare.org/

Jon Kabat-Zinn: Defining Mindfulness - Mindful. (2016, January 11). Retrieved November 14, 2016, from http://www.mindful.org/jon-kabat-zinn-defining-mindfulness/