Technology transforms what is possible. I have never learned the algorithm to calculate the square root (I turn 39 this week.) My friends who taught in the math department with me who were older knew how to do it; this was part of the curriculum when they went to school. Calculators made the algorithm of calculating the square root to be dropped from the curriculum.
What shifts in math education does Google allow for?
Using the Chrome browser you can literally ask your computer questions. On your smart phone or tablet, open the Google app and say (you may need to enable)
After saying “Ok Google,” you can ask “What is the square root of 37?”
I am into 3D printing right now (check out the Polar 3D printer). The measurements from Tinkercad are in millimeters. To help me to scale my objects correctly I ask, “Ok Google, how many inches is 5 millimeters?”
My personal favorite is that by asking Google, you can obtain graphs. No graphing calculator necessary.
Ask Google for formulas
Ask Google for how to solve types of math problems.
Instructional Minutes are Valuable
The value in memorizing formulas and cranking out algorithms is significantly less than it was 20 years ago. Yes, students should memorize math facts, but are they crippled in society if they just can not seem to memorize 6 times 7?
It takes time to wait for students to calculate things they can easily ASK Google. This technology is not going to go away and it is only going to get better. Students will, their whole lives, have the ability at almost any moment to ask their technology a question and receive an answer.
Memorizing or following procedural steps does not create critical thinkers or give a deeper understanding of the concepts.
I taught students to graph parabolas. I had them do the proof of the quadratic formula by completing the square. We identified vertices and x-intercepts. We spent a lot of class time doing DOK 1 and DOK 2 level tasks. Follow up with my former algebra students. Ask them to apply a parabola. I would be shocked if hardly any of them could tell me any purpose or value for all that class time we spent. Following steps does not make you a critical thinker and if the goal is not to apply and use the math, there are better ways to create critical thinkers than math formulas. (For example, coding and have kids make things that are useful.)
If we want students to have a better understanding, have them explain and utilize the concepts in a context that matters to them.
If you are spending instructional minutes on things students can ask their phone, you have less time to work with students on developing their critical thinking. You can not talk a kid into being a critical thinker. They need to explain the concepts and have an opportunity for high-quality feedback to help them to dig deeper.
The shift in modern teaching is getting away from telling kids information. Instead, we design the learning environment around asking questions, doing research, analyzing the sources of the information and then doing something with the information.
Instead of students taking notes writing down the quadratic formula, ask something like “How would you use the quadratic formula to determine how high a ball would go up on Venus if you had an initial velocity of m/s at an initial height of 3 meters. Explain your thought process and model this in Google Slides.” Let the students research the quadratic formula, the gravity on Venus and explain how the change in gravity would affect the height of the ball. Spend class time collaborating, researching, applying, explaining, modeling, critically thinking.