This year I'm taking a class I've already taught for two years and amping it up to an honors level course. It's a ninth grade physics course for students with strong algebra skills, focusing on waves and electricity & magnetism. In previous years the basic lessons were planned at a level where everyone could be successful with some effort, and I tried to provide supplementary enrichment for students who could use a more challenging activity. Now I can build a lot more of the challenge into the lessons themselves. This is the story of an unproductive struggle.
A few days ago I introduced refraction to the students. After going over the outline from the previous night's reading, I gave them beakers of water with pencils as well as whiteboards and markers. We had already done ray diagrams with reflection and mirrors, and I hoped to set up a connection between the demonstration they saw and the behavior of the rays.
Unlike the reflections they identify in mirrors everyday, the students don't see, categorize, and name refraction on a day-to-day basis.
I started by referring to the previous ray diagrams we had drawn, and prompting them to draw a ray diagram for what they see now. I started visiting each table of four students to check on their work. They all started by drawing a exactly what they saw, but not a ray diagram showing the difference between the actual pencil and where the pencil appears.
On my first pass I suggested they change their point of view in the drawing. I suggested they start by showing the beaker from above, and showing an eye to represent the observer. I moved on from each table, but on my second pass to each table I was a little disappointed. I found each table had not added any rays to their diagram, not even an attempt. They had all started talking about other things besides physics, which tells me they found the activity either unclear or too challenging and I need to edit my steps or my instructions. They struggled, and it wasn't productive.
On my third visit to each table I walked them through the steps for the ray diagram. The benefit to this was that each table was able to ask questions at each step and get some individual attention, as opposed to whole class instruction. They did get a chance to struggle with the problem briefly before moving on, and I think that's a good thing. Rather than just applying a set of rules from a textbook without internalizing those rules with their own worldview, they had a chance to wonder how this does fit in with what they know and observe. When students do that and continue on towards an attempted solution, I consider that a productive struggle.
How do you strike the balance between challenge and success that lets a student truly struggle productively without giving up too soon?
Here is a website that helped me explain the broken pencil.