Evidence: Experience First, Formalize Later
In an effort to reduce direct instruction, I have borrowed the idea of Experience First, Formalize Later in my teaching. This comes from The Stats Medic whom I discovered on Twitter. Their method involves having students experience statistical concepts through self-discovery, generally in groups, then formalizes the experience as a whole class after to make sure everyone's discoveries were along the same lines. I have found this same method extremely useful in teaching all mathematical concepts, many of which require some technological assistance.
One of the latest lessons that I taught in my Math 1 class had to do with finding what creates discontinuities (a.k.a. holes) in rational functions. Have no idea what I am talking about? Play around with the applet below and see if you can create a hole in the function. (I would suggest playing with the sliders for c and d if you need a jumpstart.)
Students were able to create definitions for themselves of what creates a hole in a rational function. They certainly needed more practice after using this, but being able to visualize this relationship without the burden of graphing by hand was beneficial to keeping their attention while maximizing their learning.
Evidence: DeltaMath
DeltaMath is an amazing tool for homework assignments, formative assessments, review because it gives immediate feedback and assistance when students get stuck. A teacher creates an assignment tagged with various standards and students log on with laptops or phones. DeltaMath automatically grades student work and generates unique problems for each student.
Students polled said that they much prefer this method to a typical paper based worksheet, as they get the instantaneous feedback. Additionally, teachers can set the amount of problems that students need to complete correctly before the assignment is finished. Some students who don't need much practice in the subject area may be done after they complete 5 problems, while others who need more practice have to work on 15 in order to achieve 5 correct problems.
This tool is a helpful resource for differentiation with minimal burden on the teacher. Think about creating the same sort of assignment with all of these benefits without technology. It would probably be impossible.