One thing I wanted to point out: I never used the word “measure.” I’m not talking about measurement, I’m not talking about data, and I’m definitely not talking about grades. That’s a whole other pricker patch.

I’m just talking about listening to students’ thinking.

Students’ mathematical thinking is central to all the planning and teaching I do, so I need to create conditions such that I can find out what they’re thinking. That means engineering a reasonable, informative mix of observations, conversations, and carefully chosen products that will give me insights into kids’ thinking and inform my teaching.

The general term for that process is usually formative assessment, but I think Mylène is onto something important when she calls it teacher inquiry. I like that stance. It puts the onus on us in a productive way.

I don’t accept the premise of the quote though. The quality of my tasks are not measured by how much access I get into their learning(i would bold the word I here if I could), but rather how much access my students get into furthering their own modes of understanding and indeed, more importantly, how inspired they are to learn more. When learning becomes fun and they forget they’re learning, I know I’m on the right track, something that is inherently impossible to achieve when they’re busy justifying every line of reasoning or attempt in the process.

I’m reminded of a speech last year’s valedictorian made at commencement this year. He recounted with obvious gusto the FUN in staying for hours after school day after day designing and building a rollercoaster in class… Could I possible have measured all his learning in any format except that of direct experience? No, not if I’m honest with myself and with what HE got out of it. And would it have mattered? Not to him, and if not to him, not to me either.

He’s at the top of his class in Mechatronics at university and doing wonderfully. Can’t measure my pride in his achievements, and I can’t measure how much that roller coaster experience meant to him.

I am not suggesting you look at 120 students’ work for 2 hours each, every day.

I am suggesting that, once in a while, it’s extremely useful to sit with your colleagues and a single piece of work, a few pieces of work, or a full class set of work and analyze it.

If you can’t decipher much about the student(s)’ thought process by looking at the work, you’re left with a couple of related possibilities, neither of them desirable:

1) the assignment was poorly designed for the goal of teacher inquiry into student thinking; or
2) the student didn’t do much thinking to finish the assignment.

This is the kind of reflective work I was thinking about when I read Dan’s summary: “she measures the quality of her tasks and instruction by how how much access they grant into her students’ learning.”

If you accept the premise of the quote, then tasks and instruction that don’t grant access to students’ learning are lower quality than tasks that do reveal students’ learning and thinking.

I am arguing–and I honestly do not think this is controversial–that by that measure, most tasks that most teachers assign are low quality.

Does that help?
Tracy

I feel sorry for your children but aside of that, your comment is a non sequitur to what inquiry learning is all about as it reveals your children’s teachers aren’t doing it. And you seem to get that.

Completely agree with Chester regarding time management and time spent looking at student work. I would never spend 2 hours on any piece of work, never mind discussing it with a colleague.

Less is more. And I think, Tracy, if you go back and re-read what you just said about mountains of useless stuff your children bring home, you just might begin to agree.

Even if you wouldn’t do it–and you make it abundantly clear you wouldn’t–the thought experiment might do you some good.

Actually practice can be the answer most of the time. Why can it not?

Great quarterbacks, who already throw the ball rather well, still practice for hours on end. Practice is, it turns out, immensely important even when you are an expert.

Let’s lose this idea that children have to be learning something new all the time. Learning something old well is often much more useful.

Most of what I see assigned in schools yields no insight into students’ thinking for teachers.

You might be surprised what an expert can do with apparently very little. (It’s pretty much the definition of expert.)

Also, just how much time do you think we have to spend analysing individual student’s work? I have 120 students this year. I have time to do one piece per student every couple of weeks, if I’m going to do it well — actually look for what the student is thinking and providing useful feedback. That’s six hours of out of classroom work. I’m paid for five hours of non-class time a week. So all the lesson preps, curriculum work, pastoral stuff, etc is done in unpaid time.

Imagine you had a single piece of student work and were going to talk about it with colleagues for an hour or two.

Two hours on a single piece of student work. What is it “The Illiad”?

I don’t spend two hours a year thinking about any particular individual student’s work.

I disagree in a big way. My own children come home from school with endless folders of completely useless products. Useless in that they give the teachers no actionable information, no insight into the children’s thinking.

Imagine you had a single piece of student work and were going to talk about it with colleagues for an hour or two. Which pieces of work would lead to rich discussions about students’ thinking and mathematics, and which wouldn’t? If you’d run out of things to talk about in 5 minutes–if the assignment wouldn’t lead to a productive, insightful discussion among teachers–why are we assigning it?

Yeah, practice. Why else? That can’t be the answer for everything.

Most of what I see assigned in schools yields no insight into students’ thinking for teachers.

So I think this is a big, important idea that goes far beyond common sense.

http://edci670.pbworks.com/w/file/fetch/60463828/Hammer_1997.pdf