My lofty (and somewhat nebulous) goal this year is to teach students to be curious.  This is particularly challenging in a subject that is often presented as “Memorize all of these patterns (formulas) that people figured out hundreds of years ago.  You will need them for a future test or class, but (probably) never again.”  With all of this memorization, what is there to be curious about?  And since that future test and future class are still looming realities, where is the time for curiosity?

Enter Algebra Readiness.  My Algebra Readiness class is designed to be a bridge for students between their middle school math experience and their high school math experience.  My goals are simple.  

1. Understand that math is a creative subject.  

2. Apply Growth Mindset strategies to shift your math experience.

3. Explain foundational math concepts in a variety of ways (i.e. verbally, visually, numerically, etc.)

In an effort to show the inherent creativity in mathematics, I created a unit in which we are exploring patterns 一 lots and lots of patterns.  The first pattern we looked at was the Hailstone Sequence.  The Hailstone Sequence starts with any whole number and follows this pattern: If the number is even, divide it by 2.  If the number is odd, multiply it by 3 and add 1.  Keep applying these rules until the pattern appears to end.

For example: If you start with 7, the sequence looks like …

7 – 22 – 11 – 34 – 17 – 52 – 26 – 13 – 40 – 20 – 10 – 5 – 16 – 8 – 4 – 2 – 1 – 4 – 2 – 1 …

This is called a “Hailstone Sequence” because hailstones go up and down like this – they start in a cloud as drops of rainwater, then they are pushed higher in the atmosphere by wind where they freeze, sometimes several times, before eventually falling back to Earth.  These number sequences are called hailstone sequences because they go up and down like hailstones.  In 1937 a mathematician proposed his conjecture for these Hailstone Sequences, that for any number you pick, if you follow the procedure enough times you will eventually get to 1. Since then lots of mathematicians have been trying to prove or disprove it. So far every number that has been tried has followed his conjecture, and powerful computers have checked enormous numbers of numbers, but no one knows if there is a big number out there that might break the rule.   So this is classified as an unsolved problem in mathematics.

This, in and of itself, is pretty cool.  Since most problems we give students in math are problems that we (as teachers) already know the answer to, giving them an “unsolved problem” shifts the dynamic away from the cliche “sage on the stage”.  Students were simply asked to pick a starting number and run the sequence.  Then repeat this enough times until you are convinced of something.  I didn’t tell them where to start.  I didn’t tell them where to end.  I simply told them to figure it out.  As expected, some of them were super frustrated (as I would have been).  But they asked questions, they tried different starting points, they collaborated with each other and they all eventually came to the same conclusion as that mathematician did 80+ years ago.  But the coolest part was that after we concluded our time with this pattern I had multiple students ask me, “Ms. Levesque, are there any other unsolved problems in math that we can do?”  

So my question is this: In a world where students can get answers to most of their questions through a quick Google search, how do we teach them to be curious?