We don’t do much that looks like “school” in this family, but every once in a while there’s something that comes up that is so quintessentially academic and visual that I just have to take pictures. Hands-On Equations is certainly one of those pursuits. I can’t seem to resist snapping photos of Fiona at work with this program. These are the photos I should put in a Christmas newsletter for skeptical relatives who could never understand unschooling.
Borenson describes Hands-On Equations as “Piagetian learning,” in that children are learning by doing, without direct teaching of principles and theory, but absorbing the concepts all the same. It is pretty neat stuff. Fiona has easily learned the simple basics of what are considered “legal moves” and the whole thing plays out like a game for her.
The program is divided into three levels, with Level 2 introducing negative x and Level 3 introducing negative integers. We’re working through Level 1 fairly systematically to ensure that the rules of play are well understood and are already almost done. We’ve had a couple of short sessions and a couple of longer ones. It is working beautifully for Fiona. She now often “sees” her way to the solution a couple of steps before the end. For instance she’ll see that 2x + 4 = 10 means x=3 just by looking at the initial set-up of the problem with the manipulatives. I’m amazed.
We’re almost ready to start Lesson 6. At this stage the expectation is that students will start working without the manipulatives, instead drawing their symbols pictorially on the page. I’m not sure if we’ll do this step or not. I’m not sure a 5-year-old is as ready for this as a 10-year-old. Plus she loves the game pieces and that’s much of the allure of the program. Although she writes pretty well for a 5-year-old, I also think that sketching out the problem visually would be a lot of pencil-work for her and might detract from the fun of the program. I’m not in a hurry to get her solving algebra on paper, so we might just skip this expectation.