Problem Solving, Ingenuity, and a Ten Year Old.

The other night, my ten year old son was proudly displaying the shiny new $10 scientific calculator he had picked up for the upcoming school year. He was asking about some of the functions, so we went through how to use it and what some of them were. He was noticeably impressed that e was on there, being one of his top five favourite numbers and all, right between pi and i (come on… he’s ten… he can do that, lol) and was soon asking about the sine, cosine, and tangent buttons.

So, out came the quick intro to trig and how the functions describe the relations between the angles and the lengths of the various sides of a right triangle. For fun, I suggested that he make a chart of the values from 0 to 360 in increments of 45 (no using the calculator for that – you need to be able to do simple math in your head!) and then calculate the sine of each angle using the calculator. He did, and wouldn’t you know it, the smart little kid seemed to think there was a pattern there :)

So, I figured it was time for the real lesson and issued out the challenge....

“Why don’t you make a graph and see what it looks like?”

He grew quite exited by the prospect (again… he’s ten, lol) until he realised that he didn’t have any graph paper or a ruler. “I can’t do this, I don’t have the stuff I need”, he exclaimed.

I affirmed that he certainly could do this, even without the proper equipment, and that we had a problem to figure out. I told him that it won’t be perfect, but that it’s important to be able to come up with an on-the-fly solution when you're up against a challenge. The fix with duct tape and plywood may not be pretty, but it can still be darn clever and hold you over. He needed a little direction to get going at first, but by asking him few questions he was able to figure it out.

Step 1: Goal

The first step was pretty easy – figure out what your end goal is. In this case we wanted to create a graph of the sinusoidal function. Of course in life and business it can be difficult to figure out what goals you should have, but that was a bit outside of the scope of this.

Step 2: Components

An end goal is nice, but it can be pretty overwhelming to try to tackle it all at once. In this step, you deconstruct the goal from Step 1 into a number of sub-goals. In this case, we need an x-axis, a y-axis, and the points which we already calculated to draw the plot. That’s not looking so tough now… but we need to better define this…

Step 3: Specifications

We have our list of smaller goals which will meet the end goal, but before we advance any further we need to think about what the requirements or specifications are for each of them. What are the defining characteristics of each of those goals? Well, for the axes of an x-y graph we need to have two straight lines that intersect and are perpendicular to each other. We also need to have a consistent scale along them for plotting out our points. And we need to be able to line our points up against the axes.

Step 4: Resources

This one is pretty easy - we look to see what we have available in terms of inputs and resources. It’s basically an inventory taking exercise. In our particular case we had some paper sheets, pens, and a notepad and a few other assorted items. Well… actually we had quite a bit more, being in the living room and all, but listing various dog and children toys is probably is just going to get this conversation off topic. Moving on…

Step 5: Brainstorm

This is by far the toughest stage which requires some analysis and synthesis. We need to figure out how we can use our available resources and inputs to achieve or otherwise affect our goal, its components, and/or their specifications. It sometimes helps to think about what the defining characteristics of our resources are. We have pens and a notepad… pens can be used to write on notepads… there…we got it! We can use the pens to make marks on the notepad so that we have a consistent length for our scale. And the paper happens to be straight so we have some straightedges available. We’re ready to get on with this.

Step 6: Implement

This is where we formulate the plan, implement it, and adjust as necessary. Mark the sides, and top and bottom of the paper at the same distance (which happened marked on the notepad), draw the lines between them using another piece of paper for a straightedge, and voila – our perfectly straight and perpendicular axes have been created. Next up is the scale for those axes. We need 9 points along the x-axis for 0 to 360. The y-axis values are between 1 and -1 and judging by our chart, we can get by reasonably well using increments of 0.5 and a little interpolation. Now, without the standard SI or Imperial tape measure, we of course defaulted to the ten year old pokemon arm width system of measure which admittedly works fairly well (Note, however – measuring heat capacity in terms of pokemon is only going to end in heartbreak). So we got our scale for each axis, can mark down the increments, and we can use two pieces of paper as a sort of t-square to precisely plot our points and connect the dots!

Step 7: Profit!

Well, not necessarily in that sense but it has been an enriching experience. What we really do here is achieve our goal, figure out what lessons we’ve learned, how it could have been done better, document, and move forward.

So there we have it - problem solving so simple a ten year old can do it. He had enough fun to want to draw the mirror of it. Of course, depending on the nature and scope of the problem it may be more involved and we might also do some background research, prototyping and testing, further data analysis and so forth, but the lesson here was how to tackle a problem when not everything is laid out for you to solve it, because let’s face it – nothing in life that’s worth it comes easy.