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Think Like a Mathematician – Math is Everywhere!

Why do we have to learn math? A popular question among most students.  Most kids ask this question because they see math as irrelevant.  Something in a textbook that’s not connected to their lives.  We need to reconnect math into students’ lives so they can think like a mathematician!

Here’s a picture of my master bathroom.  No, it didn’t always look like this because it’s been demoed for a remodel.  That’s exciting! But what’s even more exciting is ALL the math that goes into planning and work for the remodel. This remodel has made me think like a mathematician.

This remodel made me think like a mathematician!

How? You might ask? I used a picture of a bathroom I found on Pinterest.  From there I had to decontextualize that bathroom and “mathematize it.”   It’s safe to say that measurement, geometry, number operations, and data all figured into this remodeling plan!

From measuring dimensions, planning a budget, estimating quantities, coordinating patterns to scheduling the work the entire project has required mathematics.

I want students to know that every day we use math to make sense of our world and real-world situations (you know, like those word problems). And when we do, we begin to think like a mathematician!  Mathematicians use math to represent, model and solve real-world problems (and theoretical ones, too!).

Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers. -Shakuntala DeviClick To Tweet

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How Can You Think Like a Mathematician if You Feel Disconnected from Math?

Because our students sometimes feel disconnected from math,  it means they are not thinking like a mathematician.  If our students don’t see that math is used every day, then, of course, they think that math exists only in their textbook at school. They believe that math is only about finding that one right answer to an isolated question that will never come up again in their lives.

The ultimate goal of mathematics is to teach kids to reason.  Mathematics involves different levels of reasoning:  quantitative, additive, multiplicative, proportional and functional reasoning. To reason, you need a problem or situation to solve.  You need a task, something that is connected to a real-life situation.

It's not only the question but the way you try to solve it. -Dr. Maryam Mirzakhani  Click To Tweet

But if students are just working out procedural problems in a textbook, is that really learning math? To reason?  No wonder why students think math is irrelevant. Disclaimer: Of course students need procedural fluency and learn to use algorithms.  But if they don’t see beyond that, they will never learn to think like a mathematician!

You want to know how to rhyme, then learn how to add. It's mathematics. -Mos DefClick To Tweet

And guess what. Students DO use math daily.  They just don’t know that they are or aren’t aware of it.   Just today one of my sons tried to convince me that he didn’t use up all his iPad time (usually 20 minutes) because the 3 videos he watched on YouTube didn’t add up to 20 minutes.

Nice try!  “What about minutes and seconds you used to FIND and choose the videos?” I asked (cue confused look on his face and then light bulb moment).  “Oh, yeah! he responded. Saved by math again!

The Standards for Mathematical Practice are all about “Think Like a Mathematician”

The Standards for Mathematical Practice are the essential attributes of mathematicians. They describe important thinking that goes on when you “do the math.”

In everyday situations, do you not try to make sense of a problem? Do you not try to quantify a situation? Does your brain not look for patterns or a structure? Do you not begin to represent the situation with a model using some kind of math tool? And finally, someone will want to know how you did it, so you’ll have to construct your explanation, answer questions and defend your solution.

Everyone can think like a mathematician.

Bingo! You’re thinking like a mathematician!

  • Deciding how to share that last candy bar? You’re thinking like a mathematician.
  • Deciding which potato chip brand you want to buy based on price and size? You’re thinking like a mathematician.
  • Wondering how you’re going to take a recipe that’s for 4 servings and make it for 10? You’re thinking like a mathematician.

Math happens.  Unlike sh*t, however, it don’t stink!

I've always enjoyed mathematics. It is the most precise and concise way of expressing any idea.-N. R. Narayana MurthyClick To Tweet

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To Think Like a Mathematician also Means Paying Attention to the Real World

So I came up with all these real examples of HOW we use math in our lives every day to solve everyday real-life situations.  I’ve tried to use real examples from daily life to show that we using math every day in lots of different ways.  I think that when you start linking math to everyday real-world situations, students come to understand that math is not just in their textbook.

These everyday situations make us think like a mathematician.

Think Like a Mathematician with Measurement

This is a biggie.  Probably something we use every day without knowing it.  If your students don’t believe you use measurement every day ask them these questions:

  • Did you or someone measure an ingredient for a recipe of your favorite cookies? (capacity)
  • Did someone fill up a gas tank with gas on the way to take you to soccer practice? (capacity)
  • Did someone measure how long your legs were to buy your new pants? (length)
  • Did someone measure how much you weighed at the doctor’s office? (mass)
  • Do your parents make you clean up every inch of your room when some company is coming over? (perimeter and area)

I've always been interested in using mathematics to make the world work better. -Alvin E. RothClick To Tweet

Think Like a Mathematician with Time

Students may not be as hyper-aware of time as most adults are (try getting kids ready for school on time).  But here are some questions to get them thinking of how they manage their time during the day (start times, end times, elapsed time, time to the minute):

  • Do you sit down at a certain time for dinner? (exact time)
  • Do you plan out your recess? Take a certain amount of time to use the restroom, drink water or eat a snack?  (start and end times)
  • When you get home, do your parents only let you play after you’ve completed your homework? (elapsed time)
  • Do your parents limit the amount of time you can spend in the bathroom taking a shower? (start and end times, elapsed time)
  • Do your parents limit the amount of time you can use technology or electronics such as video games and tablets? (elapsed time)
  • Does your sports practice start and end at certain times? (start time, end time)

The mathematics of quantum mechanics very accurately describes how our universe works. -Antony Garrett LisiClick To Tweet

Think Like a Mathematician with Fractions

Students always struggle with fractions because looking at shaded parts of a whole doesn’t compare to real-life examples of when we use fractions.  But there are certainly many real-life examples:

  • What’s the last type of food you shared with a friend? (equal parts)
  • Did your parents limit you to just 30 minutes of television? (parts of a whole)
  • Do you separate your collector cards (Pokemon, baseball, etc) into different groups? (fractions of a group)
  • Did you and your friends try to figure out how to share 2 candy bars between 4 people? (equal shares)
  • Have you ever tried to share a broken up chocolate bar?  Some pieces are smaller and some are bigger.  Did you try to match smaller pieces to a bigger one so when you shared, each of you got the same amount? (equivalent fractions)
  • Sometimes adults get bigger pieces of a slice of cake than kids.  They eat more.  Have you ever compared your piece to the slice your dad or older brother got? (comparing fractions)
  • Who slices the pizza or pies at home so everyone gets the same size piece? (unit fractions)

Mathematics is a place where you can do things which you can't do in the real world. -Marcus du SautoyClick To Tweet

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Think Like a Mathematician with Operations

Operations are probably the easiest domain of math for students to see as there are many real-life examples.  What we need to do is teach them as many strategies as possible when using the 4 operations:

  • You have some coins you’ve been saving.  Now you count your coins to see how much you have. (addition)
  • You baked some brownies with grandma.  You know she’ll want you to share them with your family of 5.  There are 20 brownies, how many brownies will each person get? (division)
  • You’ve been saving that Easter or Halloween candy all year.  You had 35 pieces when you started but now you’re down to 6 pieces.  How many have you eaten? (subtraction)
  • You’re making goodie bags for your birthday party.  You want to put 5 different goodies each into 20 bags.  How many are you going to need of each? (multiplication)

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. -Albert EinsteinClick To Tweet

Think Like a Mathematician with Algebra

It’s more than just an x.  Unknowns are always around us and we have a knack for figuring them out.

  • You need 20 stickers to go to the teacher’s prize box, but you only have 15 right now.  Did you figure out how many more you need? (unknown-addend)
  • The class will help decorate the multipurpose room for the holidays.  Each student will make 4 candy canes for a total of 120 candy canes.  How many students are in the class?  (unknown factor)
  • You’re saving money to buy a new toy.  You’re saving 50 cents every week from your allowance.  How much will you have in 3 months?  (patterns)
  • You have a piggy bank and decide to count how much you have.  You group the coins by value and start counting. (functions)

Of course, even with these real-life examples, students also need to know how people in the workforce (or even mom and dad at home) use math in everyday life.

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. – William Paul ThurstonClick To Tweet

So, who uses math every day?

doctors – lawyers – mechanics – clerks – teachers – librarians – pilots – athletes – engineers – judges – pharmacists – politicians – salespersons – journalists – social media gurus – scientists – ok….let’s just say, EVERYBODY!!!

This professions that require math.

We will always have STEM with us. Some things will drop out of the public eye and will go away, but there will always be science, engineering, and technology. And there will always, always be mathematics. -Katherine JohnsonClick To Tweet

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How do you use math in everyday life? 

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Think Like a Mathematician - Math is Everywhere!
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