“You won’t be carrying a calculator with you everywhere you go.” A friend of mine recalled his math teacher telling him that. I’m sure we’ve all heard this or even have said it before ourselves. However, this particular retelling came over twitter, posted from an iPhone, that he keeps with him everywhere he goes.

While it is important to learn basic math skills, it’s also true that our tools are getting more portable as well as powerful. Instead of seeing these as a replacement (“Ha! See you later, multiplication tables!”), I see a great opportunity for deeper math exploration.

Carrying around an encyclopedia in my pocket led to many a question answered. Down highway 101 is a city named Chualar. My wife and I drive past it to visit her grandmother. After years of guessing how it was pronounced, one trip I pulled out my Android phone and went to Wikipedia. For the record is “Choo-a-lar” and the Spanish name of a local plant. For bonus points, go see how Coalinga got its name.

This type of easy access to Wikipedia has been great. After you’ve spent time hopping on IMDB to see just where you’ve seen that actress before, or even doing a quick Google search to check a store’s hours, it’s hard to imagine how we got along before portable computers.

I bet carrying around math tools in our pockets can be just as great. Just imagine what type of questions could be answered by having calculators, Sketchpad, and more all in your pocket.

Scott Steketee recently posted an unassuming sketch titled Measure a Picture to the Sketch Exchange. It includes pictures as well as several number lines and adjustable angles showing their measurement. The sketch, while perfectly usable in desktop Sketchpad, was designed for iPads. You can’t create constructions there, so we’ve created a bunch for you.

While measuring the included house is fun, the sketch really shines when you pick up your iPad and go outside. Take Sketchpad with you, find something cool and snap a picture of it. Import it (or heck, take the picture right from Sketchpad Explorer) and play around.

How tall is that tree? Well let me find out. Why, it’s five times the height of the mailbox next to it. Are the spots on this dog perfectly circular? I wonder what the angles are like on *my house*.

Math is all around us. The tools to understand can be, too. The more we get to play with it, the more we enjoy it. The more we get to answer questions we have, instead of what’s on the test, the more we get to really understand math and why it’s important.

I keep getting the feeling, over and over again, that something about our math curriculum needs to change. That “you will need to know how to do this” excuse seems a bit tired now. Maybe we can construct mathematics curriculum around formulating problems, and understanding their solution?

I couldn’t agree more. I remember hearing that over and over and eventually giving up on ever really understanding the math I was learning.

There’s hope though. That sketch wasn’t created on a whim, but for Helen Crompton, who’s doing a doctoral dissertation looking at using mobile technologies to support the development of 4th grade students’ geometrical thinking.

She wants them to do just what I recommend in the article: Go out, take a picture and measure it. Having some real world use of math as your foundation could be huge for engagement and understanding.

This is what the Common Core State Standards describe by providing students with real-world problems.