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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.

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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
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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.

The Life and Art of Pi

Today I welcome Corinne Jacob as my guest blogger.  She is a fan of Go Figure who contacted me via e-mail, and as a result we began corresponding. Since she spells her first name just like my granddaughter does, we had an immediate connection.

Corinne is a wannabe writer who is convinced that kids learn best when they are having fun. She is constantly on the lookout for new and exciting ways to make learning an enjoyable experience. She loves all things that scream out un-schooling, alternative education and holistic learning.

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Math, after years of being relegated to the role of a heartless monster, has slowly begun to get an image makeover and is getting cooler by the day with fun math games and even days that are dedicated to math concepts like Pi Day, which is celebrated on March 14 of every year.  It is especially significant this year as the date format is 3/14/15 (mm/dd/yy) and at the time 9:26:53, we got the pi (π) sequence – 3.141592653!


Life of Pi

Students will be excited to learn about the mathematical constant Pi, which is represented by the Greek letter π. It is defined as the ‘ratio of the circumference of any circle to the diameter of that circle.’ What is it that sets π apart from the rest? The value does not change even if the size of the circle does. Though it is not a recurring decimal, its decimal form does not end; that is, it is an infinite decimal. Did you know that so far 10 trillion digits have been discovered?

Students will meet π when they start learning to calculate the area and circumference of a circle. It makes an appearance in the formula: A= πr2


Art of Pi

Once students learn about this old stalwart of the math world, they can have fun creating art around π.

Pi Woods

In this activity, students can represent the π sequence with colored Popsicle sticks and decorate it like the woods. Ask your class to take the first 10 numbers of π = 3.141592653. Paint ten sticks in different colors but assign one color for each number. For instance, 3 is blue, 1 is orange, and so on. Students can then glue these sticks in the correct π sequence. Using their thumbs and some green paint, they can create leaves around these sticks. They can also collect small leaves from the garden and glue them around.


Pi number” by J.Gabás Esteban is licensed under CC by 2.0

Pi Poem

Taking the first few digits of π, say 3.1415, students can write a poem in this order:

3 word word word
1 word
4 word word word word
1 word
5 word word word word word

Or they can also rearrange an existing poem or rhyme to fit the π sequence such as:
3 hey diddle diddle
1 the
4 cat and the fiddle
1 the
5 cow jumped over the moon

Pi” by fdecomite is licensed under CC by 2.0

Pi Collage

Students can create a collage with the π numbers. They can take as many as they want; here are 10,000 of them! They can cut them out from magazines, newspapers, drawings and glue them onto construction paper in any order they like to create a colorful collage of π numbers.

These are just a few of the ways in which students will retain this number. And don’t forget to mark your calendar so that you can plan something cool for Pi Day!