In Honors Advanced Algebra we’ve been simplifying radicals. What’s going well? They get the concept of inverse operations, and that the power and root (they even call it the index) need to be the same. But for many of them, what comes next is just…random. Sometimes they cancel out the power and root, but leave the number under the radical. Sometimes they take it out, but also leave it in (so its there twice). There doesn’t seem to be a lot of rhyme or reason to what’s happening, so its tricky to figure out the misconceptions.
And this might be one of those places where the issue isn’t misconceptions…it’s effort.
I find that confidence issues can be one of my biggest hurdles.
Lack of Confidence: “This looks way too hard. I don’t know what you want me to do. I can’t do this. These are too long/complicated/difficult/etc” Result: Skip it. I don’t know how to do this, so I won’t.
Overconfidence: “Obviously. This is very easy. I will be able to do it, so I don’t need to actually do it right now. I will later. In fact, this will be so easy I do not even need to do my homework on it.” Result: Skip it. I don’t need to do this, so I won’t.
Sometimes, we just need to practice. I suspect most of my students are in Camp 2: Overconfidence here, so if I can make them practice in front of me, they will. But the more I make it interesting and engaging, the less annoyed at me they will be.
Solution: Around the Room. (Some call these “Scavenger Hunts”). Directions below.
Structure: Print out the full document. The first page is for the teacher, mix the others up (alpha order works nicely) and post around the room. Students start at whatever problem they choose (I always tell them no more than 4 students per problem). I have them write the problems in the notebook, with the letter in the margin, but you can also provide a template for the problems*.
Directions: Ignore the top line (we’ll come back to it later). Write the second line (larger font, this is the problem) in your notebook, with the letter in the margin. Solve the problem. Once you have a solution, look around. That will be the top line of one of the other sheets. Go there, and write the letter in the margin, and then the problem. Solve it, then repeat. If you solve everything correctly, you will end up back at the first problem when you are done.
When students are done, just check the letters. If they’ve done it correctly, they will have the sequence you see on the first page. Students find a lot of their own mistakes when they can’t find the next problem, or when they only do four before looping back.
This one was really quick for us, but some take the better part of a period. An obvious caution: Triple check. Resident (student teacher) 2 was not good about this and routinely had multiple mistakes, so students would get stuck because the right answer truly wasn’t out there. Not all of them work well as self-correcting, and it still works fine without it. I just have students come check in with me to check their answers, either in stages or when they’ve finished.
Do you use this structure? What are your favorite ways to get students some practice?
*With most things, once students are familiar with it, they no longer need the template, but the first few times it puts everything in the right place. Muscle memory, I guess?