Irrational Numbers

"If you think dogs can't count, 

try putting three dog biscuits in your pocket 

and then giving Fido only two of them." 

~ Phil Pastoret ~

A Letter to Students Everywhere

Dear students,

Have you ever heard the expression "first impressions are lasting impressions"?  If not, then allow me to introduce you to the incredibly accurate concept that the first impression you make on a person will remain with him or her, no matter what interactions you have in the future.  For example, if I catch you cheating on the first test you ever take in my presence, I will forever think of you as a cheater.  You may change your ways and become a student of the utmost integrity, and in the back of my mind I'll still forever wonder if you are cheating again.  So, please, think about the person you want to be, and make sure that you act accordingly.  And please, please, please don't cheat.  It won't get you anywhere in life, and it certainly won't get you anywhere in my classroom.

Love,
Miss Math

To err is human.

Two common misunderstandings for some important ideas, and understandings that reflect the overcoming of them (from "Understanding by Design 2nd Edition," page 54-55):

1.  When you multiply two numbers, the answer is bigger.  Multiplication is not repeated addition.  Fractions when multiplied yield a smaller answer, and when divided, a larger answer.  How can that be?  Students often see fractions and decimals as separate number systems; learning to see them as alternative means of representing the "same" qualities is the understanding.

2.  Negative and imaginary numbers are unreal.  Negative and imaginary numbers are no less and no more real than ordinary numbers.  They exist to provide the symmetry and continuity needed for essential arithmetic and algebraic laws.*

* I recently had a discussion with a friend about imaginary numbers, and she expressed her confusion about the purpose of numbers that aren't real.  This is just the tip of the iceberg.  Stay tuned for more info on the importance and purpose of imaginary numbers!

Museum of Mathematics to open in Manhattan next year!

MUSIC NUMBER A museum piece will show the interplay of math and music.

          A recent article in the New York Times, One Math Museum, Many Variables, announced that a new Museum of Mathematics, nicknamed MoMath, will be opening at 11 East 26th Street in Manhattan next year!

SHAPES A Museum of Mathematics exhibit will explain tiling patterns on different shapes.

          According to creator Glen Whitney, the museum’s mission is to shape cultural attitudes and dispel the bad rap that most people give math. “It’s the only field you can go to a cocktail party and talk to people with pride about how lousy you are,” Mr. Whitney said.  Under his vision, MoMath will be one small way to bolster mathematics education in the United States by serving as an intellectual catalyst and teaching resource.

RIDES A traveling exhibit has a tricycle with square wheels.

          “There are all sorts of myths about mathematics out there,” Mr. Whitney says — math is hard, math is boring, math is for boys, math doesn’t matter in real life. “All these are cultural myths that we want to blow apart.” 

A Math Lover's Lament

I was tutoring a student in Algebra at the library the other day (BAD IDEA, just for the record.  If you are going to tutor at a library, make sure you check it out ahead of time so that you know whether or not there are quiet areas in which to work) and there was a woman working with a much younger child at a table nearby.  While my tutee was working quietly on a problem I had given her, I couldn't help but overhear the conversation going on at the next table.  Apparently, the young boy was really enjoying working on math and didn't want to move on to reading.  Now, I completely understand that the tutor had a duty to make sure they accomplished some reading during their time together, but I do NOT agree with the method she used to transition.  She told the young boy, "We have to do some reading now so we don't get a headache from doing all this math."

EXCUSE ME???  What kind of message is that sending to that young and very impressionable boy?  Answer:  Math gives you a headache, math is bad, etc.  Poor math, it's no wonder it gets such a bad rep.  From a very young age, students' minds are filled with false impressions of the subject that I think is so wonderful.  Yes, the tutor needed to transition to reading, but she could have done so in a way that encouraged the child's interest in math.  How about, "I'm so glad that you are enjoying math so much, but reading is fun and important too.  So, why don't we spend some time reading, and then if we have time we can work on some more math at the end?"  Or, "Well, we could spend the rest of our time doing math today as long as we spend our next meeting together reading.  Or we could share our time both days reading and doing math.  What would you like to do?"  Then write a little contract and have the student sign it so that he is held accountable for the choice he has made.  There are so many other options besides, "Math will give you a headache."

Imagine what a difference it would make if everyone, no matter their personal feelings toward math, spoke positively of the subject until students could develop their own opinion about the subject.  Imagine how many more students would end up pursuing careers in science, technology, engineering, and math (STEM).  We need more Americans going into these fields, and first impressions are lasting impressions.  Lets make sure that children's first impressions are positive.

Doodling in Math: Sick Number Games

Imaginary Number

http://nfccomic.com/index.php?comic=205

FOILed Again!

http://nfccomic.com/index.php?comic=228

Math is Beautiful.

A musician interprets the mathematical constant Tau to 126 decimal places:

Suspension of Disbelief

I came across a post on Tumblr that said, "Math is the only place where I hear a person buying 60 watermelons."


According to Wikipedia, the suspension of disbelief "might be used to refer to the willingness of the audience to overlook the limitations of a medium, so that these do not interfere with the acceptance of those premises. These fictional premises may also lend to the engagement of the mind and perhaps proposition of thoughts, ideas, art and theories."  So, if the suspension of disbelief is acceptable in the realm of art, why not math?  Poor math gets such a bad rap.


Fortunately, the tumblr post also came along with a joke:


Q:  "I had 10 chocolate bars.  I ate 9 of them.  What do I have now?"
A:  "Diabetes, maybe?"

The Square Root of 69 is 8 Something, Right?

Yes, Drake.  The square root of 64 is 8 and the square root of 81 is 9, so the square root of 69 is indeed somewhere between 8 and 9.  Thank you for that brilliant lesson in mathematics.

Using Algebra in Everyday Life

The other day, I came across the following image:

I don't agree with the majority of the "lies" on this list, but the one in particular that caught my eye was "you will use algebra after high school."  Now, this is not a new opinion.  The idea that algebra is useless and will never be used after high school is one shared by many students.  I've lost track of how many times, while substitute teaching, I've been asked something along the lines of "Why do we need to learn this?  We're never going to use it again."

The truth is that students need math in almost every occupational field that requires higher education, such as computer science, electronics, engineering, medicine, trade and commerce analysts, science, etc.
Students can check the Math in Careers Database for the math requirements of 291 major occupations.  These jobs together employ 88 percent of the American workforce!  Since most high school students aren't sure what career path they want to follow, they should be encouraged to study algebra and learn all the math that they can so that their career choices won't be limited later in life.  And even if they think they know what they want to do, they could change their mind!

Students still convinced they won't need algebra in the future?  Direct them to the website Algebra in the Real World, which has short movies, lesson guides, and student worksheets that show how algebra is used in real world applications, such as animal conservation, architecture, baseball, farming, roller coasters, solar power, and more!  When you have $360 and you're trying to figure out how many $60 X-Box games you can buy, when you have 64 guests coming to dinner and only 12 plates and need to know how many more to buy, when you're creating a budget, or even just figuring out which size product is the best value while grocery shopping, you are using algebra!

Still not convinced?  In that case, tell students that studying algebra helps develop logical thinking and problem solving skills.  It can increase your intelligence!  So even if you don't use the specific skills you learned in algebra class, your improved thinking skills will help you in all other areas of your life.  How's that for a real world application?

The Adventures of Miss Math: The Journey Begins

I've been considering starting a blog about my substitute teaching experiences for some time now, but something happened in my classroom today that gave me the final push I needed to actually sit down and start writing.  I was giving a high school geometry class their final today, and a student called me over and asked how to find the area of a rectangle.  I was absolutely shocked.  How can someone possibly make it through a GEOMETRY class without ever learning the formula for the area of a rectangle?  As it turns out, his teacher taught him to rely on his "formula sheet" all year, and that particular formula was not on the formula sheet attached to the final.  So that poor student, assuming he did well enough on his final to pass the class, will move on to algebra 2 next year without knowing the area of a rectangle.  And goodness knows how many other gaps there are in his knowledge of math.


Scenarios like this one are simply not acceptable.  By failing to adequately prepare students, teachers are setting them up for failure.  By 2020, only an estimated 50 million Americans will be qualified to fill 123 million highly skilled, highly paid jobs, according to the recent documentary "Waiting for Superman."  


It's time to change students' perceptions of math as the stereotypical least-favorite subject, and encourage them to think of it as a big, fun puzzle that they get to work out.  So won't you join me in celebrating the wonderfulness of math?  Then share it with your children, students, parents, colleagues, friends, and anyone else that cares to listen?  It's time to get everyone excited about math so that students can start enjoying and excelling in the subject that could be the key to their success in the future!