Is following along and learning / practicing math directly from a textbook still the most effective way to learn math?
Now that we have devices in our pockets and on our desktops with more and more capabilities that have educational use cases such as interactivity and AR, how would a calculus lesson be made in 2020? Could we just go down the street, aim our devices at cars passing by, or cars speeding up from a stop sign, and see how speed, acceleration, and position relate to each other in real-time? Or aim it at a pool table, bounce a cue ball off another ball and see how vector summation can work in real life? Or input the weight of a cue ball, the type of surface (felt?) and then see how the applied force can be estimated based on how fast the cue ball moves when you hit it? Interactive bits like this as examples and practice mixed in with the text?
I think that's a great way to get an intuitive understanding of the concepts, as an introduction to the subject, but at some point you really do have to sit down with numbers and equations and learn the theory behind it all and apply it to examples that aren't constrained by the reality you can physically experience in a classroom.
You would certainly have to sit down with numbers and equations, but that still doesn’t automatically imply that a textbook is the best way. You can derive numbers and equations via an app for example.
My question is this: if you always had the textbook’s author, who is an expert instructor with decades of teaching experience instantly available, in person, whenever you want a lesson or to be reminded of an equation or want to learn more about a subject, at no harm to him and his well-being: under which situations would you opt for the textbook?
To me it feels like a textbook is one way to store and transfer and spread knowledge, but is it automatically the best way to ever do so? Or is the textbook simply one technology, and we are still searching for the best way to teach as many people as possible with the resources and technologies at our disposal?
Now that we have devices in our pockets and on our desktops with more and more capabilities that have educational use cases such as interactivity and AR, how would a calculus lesson be made in 2020? Could we just go down the street, aim our devices at cars passing by, or cars speeding up from a stop sign, and see how speed, acceleration, and position relate to each other in real-time? Or aim it at a pool table, bounce a cue ball off another ball and see how vector summation can work in real life? Or input the weight of a cue ball, the type of surface (felt?) and then see how the applied force can be estimated based on how fast the cue ball moves when you hit it? Interactive bits like this as examples and practice mixed in with the text?