Speed Is The Enemy!
- Value mistakes
- Talk about brain growth and why mistakes are important
- Give work that encourages mistakes – the key is to offer experiences that are at the edge of students’ understanding
- Don’t share your anxiety about math, your lack of confidence, your bad experiences (that just increases stress/anxiety and keeps the brain from working – or – it makes it OK to avoid math learning altogether)
- Grade differently or not at all
- Dissociate math learning from speed
Do I agree with all of the above – not the exact wording precisely:
“work” – that will be interpreted by most parents and teachers as drill – doing math exercises/problems from a textbook or worksheet; whereas “work” ought to be open-ended exploring which offers unexpected surprises and individual learners make different discoveries which they then share.
“talk about brain growth and why mistakes are important” – “talk” – that’s the problematic word for me – more important is having success at math activities – that success demonstrates to the learner that it’s possible to be successful – talking about why mistakes are necessary for learning doesn’t help a lot; being successful makes a huge difference.
In 1981 Frank Smith published an article in Language Arts, 58 (1): 103-112) (reprinted in Essays Into LIteracy 1983, 95-106). I still think this is an extraordinary piece of writing that sums up the dilemma of teaching.
Smith discusses “the learning brain”:
Learning is not an occasional event, to be stimulated, provoked, or reinforced. Learning is what the brain does naturally, continually. It is only in artificially contrived experimental or instructional situations that the brain usually finds itself not learning – and tolerates not learning. (And even, then, learning is probably taking place, that such experimental or instructional situations are artificial, unproductive, and boring.)
This is the time bomb in the classroom – the fact that children’s brains are learning all the time. They may not learn what we want them to learn. They may not learn what we think we are teaching them. But they learn, if only that what we try to teach them is boring or that they are unlikely to learn what we think we are teaching. Learning is the brain continually updating is understanding of the world; we cannot stop the brain from doing this. The hazard of so much instruction is not that children do not learn, but what they learn.
The important question for researchers is not how we learn, in the sense of the underlying brain processes, but why a brain which normally learns so effortlessly, so continuously, should sometimes be defeated by tasks that are intrinsically not exceptionally difficult.
Smith goes on to discuss three big ideas: Demonstrations, Engagement and Sensitivity.
I have written about this elsewhere.
Demonstrations
[ Journal Entry ]
I’m going to start with “demonstrations”—let me add my 2 cents to Smith’s discussion. What I understand from his argument is that we teachers have no control over the demonstrations we offer. We do what we can to create a learning situation; HOWEVER, what we set up are POTENTIAL demonstrations. What makes something an actual demonstration is a learner’s engagement. In other words, learners are in control of demonstrations—they determine what aspects of a situation they will engage with. What decides whether a learner engages or not is what Smith calls ‘sensitivity’—the learner’s expectation that it’s worth engaging in an experience. And because learners determine what constitutes a demonstration, it means that what I think the situation might be demonstrating may have nothing to do with what catches any learner’s attention; different learners in the same situation are likely engaging in different demonstrations at the same time. Another thing I’ve come to believe is that there is no such thing as NO demonstration—there can be no absence of demonstrations because everything is a potential demonstration–that’s where Smith’s time bomb comes into play—the brain is learning all the time, even if what it’s learning is “not-learning”. (Herbert Kohl writes brilliantly on “not-Learning)
So, supposing that… if we created learning situations so they were like the best kindergarten classroom—helping learners feel confident that nothing, or very little, is beyond their capabilities, to have a reason to shoot at being able to do anything that seems worthwhile, able to explore freely and pursue tenaciously, explore with an open mind, to feel free to take intellectual and social risks—to ask outrageous questions, to make wild and improbable connections, to take on tasks that might require a long time to complete, and even to abandon some tasks unfinished—what might learning be like for learners of any age? Meier’s experience at CPESS showed that enterprises, a collaborative learning community is feasible.
It’s the engaging in tasks that might require a long time to complete—Conroy’s contention that education doesn’t end until life ends, because you never know when you’re going to understand something you didn’t know before—that’s compelling. Another point he makes which I found very powerful is that much of understanding is retrospective—as he puts it
“I remembered what I hadn’t understood…until my life caught up with the information and the lightbulb went on.”
What that means is that learning isn’t uni-directional—learning occurs in hindsight—when something happens that permits a “wonderful idea” and we see a connection that was impossible before. He also makes the point that understanding doesn’t mean resolution—many situations are very complex and although we understand some of the variables at play, we may not be able to resolve what’s problematic in them.
Smith’s article on “demonstrations” is an important one. I keep highlighting several quotes:
Learning is not an occasional event, to be stimulated, provoked, or reinforced. Learning is what the brain does naturally, continually.
This is the time bomb in every classroom—the fact that children’s brains are learning all the time. They may not learn what we want them to learn. They may not learn what we think we are teaching them. But they learn, if only that what we try to teach them is boring or that they are unlikely to learn what we think we are teaching them….
The reason why collaboration is crucial is that we learn by seeing how things are done—demonstrations. That means we need to be in the company of other learners so that we have maximum exposure to the way people go about doing things we might be interested in doing ourselves. It’s that learning brain that’s learning all the time—coming up with those wonderful ideas.
On Learning 