Developing Students' Resilience in Secondary Mathematics Classrooms
“I remember the day not long ago when Ruth opened my eyes. We had been doing math, and I was pleased with myself because, instead of telling her answers and showing her how to do problems, I was "making her think" by asking her questions. It was slow work. Question after question met only silence. She said nothing, did nothing, just sat and looked at me through those
glasses, and waited. Each time, I had to think of a question easier and more pointed than the last, until I finally found one so easy that she would feel safe in answering it. So we inched our way along until suddenly, looking at her as I waited for an answer to a question, I saw with a start that she was not at all puzzled by what I had asked her. In fact, she was not even thinking about it. She
was coolly appraising me, weighing my patience, waiting for that next, sure-to-be-easier question. I thought, "I've been had!" The girl had learned how to make me do her work for her, just as she had learned to make all her previous teachers do the same thing. If I wouldn't tell her the answers, very well, she would just let me question her right up to them.”
John Holt in “How Children Fail”
Five suggested ways of scaffolding tasks to bring them within reach of "our" students without doing all the work for them:
Showing a potential map or route through the problem
Latin Numbers
Showing the start of some methods and inviting students to complete them
Odds, Evens and More Evens
A variety of methods (algebraic/geometric) and follow-up questions
Quadratic Patterns
A proof sorting activity
Pythagoras Perimeters
Showing different methods and inviting students to adapt them in order to generalise
Marbles in a Box
We choose to hide the scaffolding under a "Click to reveal..." button, so that students can choose when they want to access it. In the classroom, we imagine teachers might provide the scaffolding in an envelope that students can choose when to open.
Issues / questions to consider:
Where might your students get stuck?
What is the thinking that you think the students must do for themselves?
What's non-negotiable? Where do we draw the line?
Does our scaffolding get the balance right?
Are we offering too much (or too little) assistance?
Does working in this way give students the sense of achievement we want them to feel?
Resourcefulness vs Resilience
Are we addressing the latter, or just equipping students to be more resourceful?
Are students who are offered this type of scaffolding likely to "hang on in there" for longer than they otherwise would?
Is this likely to transfer to problems where students aren't offered such scaffolding?