Can we stop telling them how to solve problems?

Recently observed:

The class was in the middle of a series of lessons centered around developing strategies for multiplying 2-digit numbers by 1-digit numbers. On this particular afternoon, a group of students was working independently on the above worksheet. One student, after reading the first question, wrote 72 + 72 + 72 + 72 in a column in the work space. As he began to add up the numbers, an instructional aide working in the room stopped him and said, "You have to use multiplication to solve this problem. You're learning about multiplication, and it says in the directions to use multiplication."

Obediently, but with an under-his-breath groan, the student erased all his work.

I was not in a position to stop this from happening.

Things like this happen all the time.

If we're going to use worksheets like this, can we at least cut the top off first?

Let the kids work out the problems in ways that make sense to them, not to us. |

Here's what I've wondered when I have read about how insightful math teachers open their students minds to inquiry: what kind of conversations can you have with students to prepare them for the time when they (inevitably?) have a different kind of math teacher? What can tools can a student be empowered with so they don't "Obediently, but with an under-his-breath groan" erase the notice-and-wonder kind of thinking from their minds?

ReplyDeleteThat's a really good question, Paula! I don't think I have a good answer. A child would have to be very confident and secure to be able to at the same time comply (outwardly) but resist (inwardly.) The younger the student the more difficult that would be. But the older the student the more likely that years of mathematical trauma will have just beaten him or her down. But whenever I get discouraged that we're up against institutional forces that far outnumber our own, and that for every one insightful math teacher there are many hundreds more making their students erase 72 + 72 + 72 + 72, I think of the story of the boy throwing starfish back in the ocean. One at a time.

ReplyDeleteI totally agree that if you must give a worksheet, at least don’t tell kids exactly how they have to solve the problems! Using worksheets often in my view is equivalent to a 'starvation diet' for the intellect. Lucy West

ReplyDeleteThanks Lucy. The image of a worksheet as "starvation diet" is a striking one. No real nourishment there. Maybe the fact that they're easy to access, print out, and distribute make them also like fast food. They fill up time but have no lasting health benefits.

ReplyDeleteI agree Joe, I still see this often unfortunately but have seen some bright spots. Its getting better in my schools but still show up in places. This reminds of the need to know your students well and look at what they are doing (see, hear them). If this teacher/EA had been working with Alex Lawson's resource "What to Look For", for instance then they may have known that this student is most likely still in the repeated addition phase of Lawson's continuum and they could have looked at what are some strategies to move this student forward into more efficient working with numbers strategies. So many times I see teachers that do not use this info to inform their teaching. We have had luck this year in one of my primary schools introducing people to Lawson's continuum and resource to help them dig in deep with each student to see where they are on their development to from direct modelling/counting to counting more efficiently/tracking to working with numbers to proficiency. Now these teachers who are digging in, when they see their students working on problems or tasks are able to identify what strategy they are using and how to work with them. Each student could be using a different strategy that makes sense to them but the teacher then undertsands how to help move them. Thanks for sharing again Joe.

ReplyDeleteThanks Mark. You bring up a very important issue, and that's the investment that a district must make in PD for its staff, not just teachers, but support personnel as well. That's time and money. Graham Fletcher often points out that the money a district spends on curriculum might be better spent trying to build the capacity of its staff through introducing people to things like Lawson's continuum, and then helping them understand how to use it. It's heartening to know that your district has made that happen, and that you see tangible results of that effort.

ReplyDeleteJoe, one line in your post made me think about another difficult teaching (and parenting) issue: when do we intervene? You saw an aide do something that felt wrong. Should you say something? If so, at the time, afterward to the aide, afterward to the learner, other? And how should it be phrased?

ReplyDeleteOne reason I find it such a difficult question is that the quality of an activity or interaction depends on the medium term and long term context of that learner and the interaction of that teacher and learner. Without knowing the context, it is almost impossible to say definitively that the activity was bad or the teacher's cues inappropriate.

My best idea is to talk about feedback and intervention in advance, when it doesn't feel emotional or like it is criticizing a mistake. That also clarifies how the person thinks they like to get feedback. However, I always forget to have this conversation until I want to say something!

Thanks for your thoughts, Joshua. You are absolutely correct: I had no idea of the context beyond what I saw happening in the moment. The interaction took place among unfamiliar individuals in an unfamiliar classroom. Mark's comment above about effective PD would (hopefully) be a dose of preventative medicine. In the instance described in the post, I did nothing. I believe that given the opportunity, I would have gone back to the learner.

DeleteI know as parents, my wife and I started out very hesitant to get between our kids and their teachers, and did let quite a bit slide. As they got older, we became a little more vocal, although we would ask them first if they wanted us to get involved. Most of the time, they preferred us not to. But not always, and it was in those times they felt supported by our actions. Not sure if that's helpful. As always, your comments are insightful. Thanks for making me think through this in a deeper way!