- One student told me he got his solution in two different ways but didn't get the same result. He asked if I could help him find the mistake, because he had tried and was getting frustrated. I figured it would be better if he compared his results with someone else, so I asked for volunteers to put their results on the board. Not all students have the confidence to put themselves out there on their own initiative, so my role was to be the catalyst. Once one or two graphs were up on the board, the rest followed more easily. Comparisons were made, discussions ensued, mistakes were found. Strength in numbers!
- Whenever I was asked for help, I started by saying "Tell me what you've done so far." First off, this helps them organize their thoughts. Also, while they do this, I have to be constantly asking questions, like, how did you get this result, how did you verify these calculations, what do you know, what are you looking for...and if the answer to any of these is I didn't do that or I don't know, it helps them zoom in on the hole in their work ethic, not their math.
- Even those who are marching along at a good clip can benefit from explaining their work, to me or to a peer, because that can be a practice run at how they will present their solution.
- One student, let's say her name is Claire, listened to one group's explanation of their procedures, then later, while working with a different group, said she hadn't understood the first group's work, and so had figured out her own way. I asked Claire to explain her way to the second group. That group then benefited not only mathematically, but emotionally. She used their own language, AND it was great modelling - here's someone who got stuck, tried out something else, then persisted until she found her own way. I can say "persist!" until the cows come home, but when they see a peer actually doing it, it's got gravitas.
|Nice colour coding by a student!|
- headings for sections
- colour coding
- introduction/conclusion paragraph
- outline procedure first then give details
- validate and show your validation
- do the whole thing paper-free
Offer technical help:
- A student was trying to read points from his graph, which he had created from excel using just a few data points. From his responses to my "find the hole" questions, I guessed that his graph didn't have the accuracy he needed (remember I can't see them, or their work instantly), so I suggested he do it using geogebra, which can produce a graph from a rule. I had already introduced geogebra, and I had told them they could use it for this problem, but I think he was stuck in a rut, always using the same tool, never considering that another might be better for this case.
- Some were working on their final presentation and needed help like how to take a snapshot and paste it into a word doc or ppt, or how to get proper math notation and symbols into the same.
- Of course, it all depends. Pretty much all of the above ideas came to me during and after a class with a highly motivated and active core group of students. They're the spark plugs in the problem-solving engine. But in a class without those spark plugs, where no one ever asks you for help, or no one offers help, none of this would happen without additional prodding from me. Which makes it all feel so old-school to me, so do-this-because-I-told-you-to-not-because-you-want-to. Maybe that's just a question of finding problems that are more engaging for that particular group....
- If you have any other ideas of what kind of help teachers can give students that will truly help them tackle problems, other than explaining the entire solution to them, I'd love to hear them!