A basic principle of education: always give the concrete before the abstract. In other words, give a new idea to the hand before you give it to the mind.
We are generally awesome at this with little kids. Walk into any kindergarten or first grade classroom in America, and you’ll marvel at the mountains of neatly labeled bins, cubbies, buckets, and boxes that store the resident manipulatives. Early elementary teachers all need a second degree in organization just to keep track of the myriad concrete ways they introduce young children to new ideas.
Then kids reach middle school, and suddenly we expect them to sit quietly, take notes, and understand a whole bunch of much more complicated information.
It’s not a great plan, is it?
No matter the age of your student — preschool, high school, or your grandmother — you have to give the human brain something to hold on to.
One simple application of that in middle school mathematics: have students build three-dimensional shapes to explore the concept of volume. You can use centimeter cubes, interlocking cubes, ice cubes… any cubes, really.
Pro tip: Use a dry erase marker to mark the faces of the cubes and give your student a concrete place to start with surface area.
Â