I read somewhere that the human mind is no longer remembering as much as it used to because mobile devices are being used as our memories.
Someone pointed out today's devices have internet so we can just look it up if we forget something. We have calendars with reminders that pop up to keep us on task. There are apps that scour the internet for very specific material so we don't have to do that anymore.
So what effect does that have on mathematics and learning? It has some. In many places, students are no longer required to memorize their multiplication or division facts since they can just pop the problem onto a calculator that does the math. In fact, there are quite a few calculators for all sorts of math problems you can use to have them solve it without you ever really knowing the process.
I have the My Script calculator which will solve a variety of problems from simple one step equations to the law of sines and cosines. They just type in the problem and place a set of parenthesis for the variable and it solves it. Most of my students do take time to learn the process but a few rely on the calculator's answer.
Unfortunately, this means they do not develop the number sense needed to know if their answer is even in the ball park. They accept the calculators' answer as the truth. So I'm still working on creating a balance between learning the process and developing number sense with using calculators and asking yourself "Does the answer make sense?"
I've found some great apps which do reinforce skills but my students do not like the ones that provide an explanation of why they missed the problem. They would rather just move on and do the next activity without trying to correct their mistakes. I've thought of providing them with a sheet to write down all work and if the answer is incorrect they have to explain where the mistake was made. The last step would be to write out the correct way of doing the problem.
This might help them slow down and reflect on the type of mistake they are making. I don't think I have students do enough error analysis. At a training I had years ago, they said it was important for students to learn to do the math correctly.
I'd love to hear your thought on these topics. Do you think that deeper understanding is being slowed down by easy access to tools which solve problems for us?