Comments on: Eric The Sheep

By: Where do questions come from? | Overthinking my teaching

Where do questions come from? | Overthinking my teaching — Fri, 07 Sep 2012 19:08:10 +0000

[…] So you made me think of your Eric the sheep post. You had a graduate course, or someone who came and spoke in your graduate program who came and had […]

By: Matt Skoss (@matt_skoss)

Matt Skoss (@matt_skoss) — Thu, 13 Oct 2011 11:37:08 +0000

What is also also interesting with this problem from the Maths 300 resource bank (http://maths300.esa.edu.au/) is that the problem subtly changes if:

– Eric sneaks forward x sheep, then the shearer grabs a sheep

versus:

– the shearer grabs a sheep and then Eric sneaks forward x sheep.

Further on Maths 300, I’m interested in seeing how we can use Twitter tags (I use #maths300) to share our pedagogical ‘a-ha’ moments when using lessons from the Maths 300 library.

By: Chera G.

Chera G. — Fri, 23 Sep 2011 02:19:18 +0000

This is an interesting math question. I loved how the students were able to formulate their own questions based on what they thought was going to be asked next. I also loved that they were able to chose the question that best interests them and describe their assumptions. The teachers I know from my own experiences and colleagues do not open up the door for creativity and higher level thinking. Allowing students to chose their own questions and then solve them requires independent thinking and reasoning that fosters growth. I would love to do something similar in my classroom. It’s very interesting that no one chose the same variable.

By: luke hodge

luke hodge — Thu, 22 Sep 2011 00:26:22 +0000

morrowmath: Sure, you could call it part of the reasoning process, grappling, etc. But are you saying that these students were able to generalize the problem in the sense of being able to fairly quickly determine how many sheep are sheared before Eric for large numbers of sheep? I would not have guessed many students could do that without seeing that Eric moves forward three spots each time a sheep is sheared. How did they do it?

By: morrowmath

morrowmath — Wed, 21 Sep 2011 00:11:49 +0000

I don’t think that this is a “difficulty,” but rather part of the reasoning process. One group’s table saw a repeated +2 pattern and represented it this way (the number of sheep jumped by Eric):
2+2+1
2+2+2
2+2+2
2+2+2+1
2+2+2+2
2+2+2+2
The only 3 in this problem is the repeated similar groups of 3 expressions.
This is 6th grade, and they were able to verbally generalize this problem. In discussion, the teacher did ask for conclusions that led to thinking about the changes that happened around a multiple of three, but the students’ reasoning did not lead there. Sometimes you never know where a lesson or mathematical exploration will lead.

By: luke hodge

luke hodge — Tue, 20 Sep 2011 23:33:17 +0000

morrowmath: I think many students would need at least a subtle hint (suggestion to draw or act it out) to “find” the 3 and most would benefit from a very concrete demonstration of why 3 is important. How did the teacher react to the student’s difficulties in the class you observed?

By: morrowmath

morrowmath — Tue, 20 Sep 2011 22:27:14 +0000

I noticed that many of the commentators focused on the number 3, as in “a multiple of 3” and “subtracting by 3 a bunch of times.” I watched a class of sixth graders tackle this problem as part of a lesson study recently. The “3-ness” of the problem was not readily to apparent to any of the groups, although it was to one or two students.
Part of the process of mathematizing a problem or context is recognizing the salient mathematical features. In this case, a change of 3 sheep. Because, as Bowens points out, it’s 3 sheep, but the step nature of the context means that an answer like 16 1/3 can be generated, which makes no sense as an actual answer. What the average student needs, is to recognize a change of 3 first, and why. And we can’t tell them it’s there.
The generalizations to larger numbers of sheep and the divisibility issue are only relevant if the student can see “3”.

By: luke hodge

luke hodge — Tue, 20 Sep 2011 21:34:54 +0000

From one perspective I can see this problem involving an abstraction — introducing variables and/or an equation to solve/model. From another perspective I think this problem is really about removing abstraction. We have abstract procedures for dividing numbers with no context, but here we are presented with a concrete reason and meaning of division — it is quicker than subtracting 3 a bunch of times.

I don’t see the benefit in explicitly using a variable(s) or an equation to solve this problem. Viewing this problem as a division problem seems much more natural. Why introduce all that abstraction if you don’t need it?

Also, judging from the class questions, it appears that there are a few students in the mathematical thinking and problem solving class that are trying desperately to avoid mathematical thinking and problem solving.

By: Allison Krasnow

Allison Krasnow — Tue, 20 Sep 2011 05:17:15 +0000

I remember when Kim used this problem at least 10 summers ago as part of a Bay Area Math Project summer institute. Hearing that she’s still using it, with a new angle, as part of a totally different class, makes me realize that I don’t reuse good problems enough. My teaching could evolve while using the same original problem, but posed in new ways, reflecting how I am growing as an educator. Thanks for posting this…it made for good food for reflective thought for me.

By: Christopher Danielson

Christopher Danielson — Tue, 20 Sep 2011 02:17:52 +0000

Dan writes:

I don't know how she planned to reconcile that difference.

Per our conversation over in my place, I find this to be of particular interest. What was the point of the example lesson? If it was to model learning mathematics through challenging tasks that admit a variety of approaches, then the plans for reconciling the differences among the various problems being worked on would be of primary importance. It's going to be hard to have a group of students learn much from each other's work if they are struggling to wrap their minds around each other's problems. But there may be dozens of different reasons for doing Eric the Sheep with graduate students.