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How Gritty Are You?

What are the causes of success? My college students in my Math Study Skills class have been researching this topic since each one of them desires to be successful at math. We watched a six minute video by Angela Lee Duckworth: The Key to Success? Grit on You Tube.  She relates how she left a top paying job in consulting, to teach math to seventh graders in a New York public school. She soon realized that IQ wasn't the only thing separating her successful students from those who struggled. In the video, she describes her theory of "grit" as a predictor of success.  Below is a summary of what she says.

At first glance, the answer is easy: success is about talent. It’s about being able to do something – hit a baseball, play chess, write a blog – better than most anyone else. But what is talent? How did that person get so good at hitting a baseball or playing chess? For a long time, talent seemed to be about inheritance, about the blessed set of genes that gave rise to some particular skill. Einstein had the physics gene, Beethoven had the symphony gene, and Tiger Woods (at least until his car crash) had the golf swing gene. The outcome, of course, is that you and I can’t become chess grandmasters or composers or golf pros because we don’t have the necessary anatomy. Endless hours of hard work won’t compensate for our biological limitations.

But think about this - Beethoven wasn’t born Beethoven.  He had to work extremely hard to become Beethoven. Talent is about practice. Talent takes effort. Talent requires a good coach. But these answers only raise more questions. What, for instance, allows someone to practice for so long? Why are some people so much better at deliberate practice? If talent is about hard work, then what factors influence how hard we can work?

It is deliberate (conscious, intentional, planned) practice that spells success. In other words, deliberate practice works. People who spend more time in deliberate practice mode perform much better. The bad news is that deliberate practice isn't fun and is consistently rated as the least enjoyable form of self-improvement. Nevertheless, as golfers, musicians, etc. gain experience, they devote increasing amounts of time to deliberate practice, and consistent, deliberate practice is done by grit. Not surprisingly, those with grit are more single-minded about their goals – they tend to get obsessed with certain activities – and also more likely to persist in the face of struggle and failure. Woody Allen famously declared that "Eighty percent of success is showing up." Grit is what allows you to show up again and again

While grit has little or nothing to do with intelligence (as measured by IQ scores), it often explains why an individual is successful. Thomas Edison was right: "Even genius is mostly just perspiration."

Our most important talent is having a talent for working hard, for practicing even when practice isn't fun. It’s about putting in the hours when we’d much rather be watching TV, or drilling ourselves with note cards filled with obscure words instead of getting quizzed by a friend. Success is never easy. That’s why talent requires grit.

Duckworth, A.L., & Gross, J.J. (2014). Self-control and grit: Related but separable
determinants of success. Current Directions in
Psychological Science, 23(5), 319-325

How does your grit compare with others? I had my students take the 12 point survey developed by Duckworth to see how they rated. Some were surprised while others were well aware of their grit level. I even took it!  Want to give it a try or have your students see how gritty they are?  Just click on the word "survey."  When you have completed the survey, fill in the score grid below to find out just how gritty you truly are.

Slope for Vertical and Horizontal Lines

I tutor at the community college where I also teach. Last week, I had two College Algebra students who were having difficulty with slope.  They knew the equation y = mx + b, but were unsure when it came to horizontal or vertical lines. By the way, they were using their graphing calculators which I made them put away. (The book said no calculators.) I feel that if they construct the lines themselves, it puts a visual image into their brain much better than if the calculator does it for them. Sure enough, one of the sections in their math books gave the picture of the line from which they had to write the equation. They were amazed that I could just look at a graph and know the slope, give the equation, etc. When I taught high school math, my students couldn't use a graphing calculator until the middle of this particular chapter as I wanted them to physically draw the lines.

First, for those who have no idea what I am talking about, slope is rise over run.  Rise is how far a line goes up, and run is how far a line goes along.  At the right, the line goes up 3 and has a run 5; therefore, the slope is 3/5.  Rise/Run (Rise divided by Run) gives us the slope of the line.

When a line is horizontal, it has no rise, only a run. So the numerator would be zero (for no rise) and the denominator would be a number such as 5 for the run.  0 ÷ 5 = 0  This is true for any horizontal line.

A vertical line is different.  It has rise, but no run; therefore there would always be a number in the numerator, but always a zero in the denominator.  Since we cannot divide by zero, the slope is considered undefined. (I do use rise over run stating that a horizontal line might have 0/5 which is equal to 0 and that a vertical line might have 3/0 is undefined because we can't divide by zero. Our college algebra book uses O/K for okay and K/O for knock out which I like, but I still think the students need to know why.)

I wanted these two students to have a picture that would help them remember the difference.  I thought of a table for the horizontal line and asked them what would happen if the legs of the table were uneven.  They agreed that the table would have slope.  Therefore, the table would have a slope of zero if the legs were even.

I then went blank.  In other words, by creative juices stopped working, and I could not think of a picture that would help them visualize undefined. Since Teachers Pay Teachers has a forum,, I asked my fellow math teachers if they had any ideas.  Here is what some of them came up with.

The Enlightened Elephant suggested using a ski slope. She talks about skiing down a "cliff", which would not be possible (although some students try to argue that they could ski down a vertical cliff) and so the slope is "undefined" because it doesn't make sense to ski down a cliff.  Skiing on a horizontal line is possible so it's slope is zero,  She also talks about uphill (positive slope) and downhill (negative slope). 

Math on the Mountain likes to explain the concept of steepness of slope as a matter of effort. He tells his students to imagine riding a bike along a sloped line. If they already have some velocity, then a zero slope (horizontal) would take no additional effort. A small slope would require small effort and a greater slope would require much more effort (i.e. the slope/rate is analogous to "effort"). When students consider the amount of effort required to ride a bike up a vertical wall, they can see that it would essentially require an infinite or undefined amount of effort to do so.

Math by Lesley Elisabeth tells her students to use "HOY VUX" (rhymes with 'toy bucks')

             Horizontal - Zero (0) slope - y = ?   
             Vertical - Undefined slope - x = ?

All horizontal lines are =7 or = -3 etc., and all vertical lines are =1 or = 6, etc. Students forget this so the acronym HOY VUX helps them to remember. Once they've mastered the slope concept in Algebra I, for the rest of the school year, for Algebra II (especially equations of asymptotes - a line that continually approaches a given curve but does not meet it at any finite distance) and even in calculus classes for tangent lines, HOY VUX is just faster and more practical. 

Animated Algebra created a video lesson on the Slope Intercept  ($5 on TPT).  She has a boy skateboard down a negative slope, literally right on the graph line. Karen then shows the same boy taking an escalator up on a line that has a positive slope. Later in the lesson, she rotates the line clockwise, each movement with a click, to show the corresponding slope number to link the line to the slope.  She includes lots of other visual cues to help students focus on and pay attention to the concepts.

I did find a video on Pinterest that might help us all. It's called Slope Dude.  My students thought it was corny, but it did help them to remember.

Pi Day Is Epic This Year!

Pi is perhaps most widespread on March 14 which is Pi Day! On Pi Day, nerds, geeks, and mildly interested geometry students alike come together and wear pi-themed clothing, read pi-themed books and watch pi-themed movies, all the while eating pi-themed pie. But Pi Day this Saturday will be even more exceptional because it will be March 14, 2015; that's 3-14-15 or the first five digits of pi! And then add the time of 9:26:53, and it becomes more than attention grabbing.

Pi is an irrational number that approximately equals 3.14. It is the number you get if you divide the circumference of any circle by its diameter, and it's the same for all circles, no matter their size. You can estimate pi for yourself by taking some circular things like the tops of jars or round plates and measuring their diameter and their circumference. Then divide the circumference by the diameter, You should get an answer something like 3.14. It should be the same every time (unless you measured wrong).  In other words, π is the number of times a circle’s diameter will fit around its circumference

Actually, 3.14 is only approximately equal to pi. That's because pi is an irrational number. That means that when you write pi as a decimal it goes on forever and ever, never ending. (It is infinite.) Also, no number pattern ever repeats itself.

Usually in math, we write pi with the Greek letter π, which is the letter "p" in Greek. You pronounce it "pie", like the pie you eat for dessert. It is called pi because π is the first letter of the Greek word "perimetros" or perimeter.  What is interesting is that in the Greek alphabet, π (piwas) is the sixteenth letter; likewise, in the English alphabet, the letter "p" is also the sixteenth letter.

But hold your horses!  The fascination with pi isn't restricted to just mathematicians and scientists. Pi has a special place in popular culture, thanks to its frequency in mathematical formulas and its mysterious nature.  Even T.V. shows, books, and movies can’t help but mention π.

For example, pi gets mentioned in a scene from Twilight, in which vampire-boy Robert Pattinson recites the square root of pi.  In an episode of the Simpsons, two young girls at a school for the gifted play patty-cake and say “Cross my heart and hope to die, here’s the digits that make pi, 3. 1415926535897932384…” 

Yep, whether you like it or not, pi is everywhere. Here are a few more places it has popped up:
  1. The main character in the award-winning novel (and 2012 film) Life of Pi nicknames himself after π
  2. A circular room in the Palais de la Découverte science museum in Paris is called the pi room. The room has 707 digits of pi inscribed on its wall. (The value of pi has now been calculated to more than two trillion digits.)
  3. In an episode of Star Trek: The Original Series, Spock commands an evil computer to compute π to the last digit which it cannot do because, as Spock explains, “The value of pi is a transcendental figure without resolution.”
  4. Pi is the secret code in Alfred Hitchcock’s Torn Curtain and in The Net starring Sandra Bullock.
Here is more arbitrary information related to pi that I found interesting.
  1. If you were to print one billion decimal values of pi in an ordinary font, it would stretch from New York City to Kansas (where I live). 
  2. 3.14 backwards looks like PIE. 
  3. "I prefer pi" is a palindrome. (read the same backwards as forwards)
  4. Albert Einstein was born on Pi Day (March 14) in 1879.
And let's finish this post with a couple of π jokes.

If you divide the circumference of the sun by its diameter, what will you have? Pi in the sky! 

What do you get if you divide the circumference of a jack-o'-lantern by its diameter? Pumpkin pi! 

On Pinterest, I have a board devoted to pi called "Life of Pi."  If you go there, you will find many cartoons, jokes and ideas to use for pi day. And to add to the fun, go to the website entitled “The Pi-Search Page” to find your birthday written with the digits of pi.

By the way, notice my "handle" of Scipi.  The Sci is for science (what my husband teaches) and the pi is for π because I teach math.