Let me start by saying my students are never the reason for my bad days. Never. Usually my bad days come from the thought that I am not doing enough good for my students in a world that is in short supply of it.

However, instead of discussing the bad in the world, I wanted to share something good from today.

Today my students did their typical good, hard work using math to solve problems they might encounter in their daily lives. But this post is not about them, well, not directly.

It’s about my assistant teacher. She is in her first year at our school and also finishing up her master’s in special education at Hunter College. I really enjoy talking with her about math and teaching. If you are a veteran teacher I highly recommend casually chatting about teaching with a new teacher. It really gets the juices going.

Anyway, so what was good about today you ask?

I’m getting there.

One of my favorite blog posts is from Joe Schwartz, an elementary math coach in New Jersey. Last year he described how to build a better worksheet. The main idea is to eliminate extraneous stuff that exists on curriculum worksheets and doesn’t lead to mathematical thinking. Joe’s post proves to me why he would make a great special education teacher, because it illustrates what most special education teachers do on a daily basis. They have to identify the most mathematically essential pieces of a worksheet or task and eliminate the rest of it that might cause obstacles to their executive functioning. They have to create easy access to hard math. That’s the goal. Joe does an amazing job exemplifying this in his post.

So that leads me to today. As I was reluctantly perusing some EngageNY worksheets for usable content for our measurement unit, my SMARTboard was also on. After several minutes of scrolling my assistant teacher exclaimed, “That would make a good notice and wonder!” She was referring to the following worksheet.

I asked her to tell me more. “Well you just give them that picture and ask what they notice.” I used the I Notice/I Wonder instructional routine with some regularity, so I was pleasantly surprised to hear her use it during our planning time. So we came up with this worksheet work-around.

I think the title may also be unnecessary, but giving the students a hint as to what direction the teacher wants to go in and to frame some of their noticings seems fine to me. Hopefully, after the students are given the opportunity to notice and wonder about this picture, a conversation about how to appropriately measure the paint brush using the cubes will come up organically. And maybe, just maybe, your students will surprise you and wonder something that is just as mathematically interesting as the original direction in which the lesson was meant to go.

Love this! Another great example of how to take a textbook problem and make it something worthwhile. Thanks for sharing.

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Thanks Teresa!

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Thanks for your kind words, Andrew. I love what you and your assistant teacher have done to the worksheet. Now I’m really curious to know what your students will come up with, and how you and your assistant will react if it’s something unexpected. What’s powerful here is that you are letting your students take ownership of the task just as you took ownership of the task’s creation.

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Thanks Joe! I’ll make sure to post about the student responses soon!

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If you really need to cover the points intended by the worksheet, then the heading is probably required. However, I would really be tempted to leave it out. Why:

(1) less guidance frees the students’ thinking. Since you already do lots of notice and wonder, you already see this.

(2) measuring the paintbrush almost certainly misses out on the essential feature of paintbrushness: it can be used to paint things! What could we possibly want to paint? Hmm, there are those innocent white squares just standing there, begging for some color!

Of course, this probably leads one to be more interested in knowing the width of the paintbrush and the paint-carrying capacity, rather than the length.

(3) thinking about it more, a painter might get a some use from knowing how long his paintbrush is. can you think of an application? I have in mind measuring the dimensions of a shape that is to be painted, where the painter puts a little paint on the brush to mark one-brush lengths. This is at least one way to integrate the intended task and the fact that the thing is a paintbrush. Could also open up an interesting conversation about who precise this form of measurement would be and whether the costs/benefits outweigh other choices a painter might make.

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Thank you for your thoughts Joshua. I never thought about the boxes as objects to be painted, but that makes so much sense and makes me think the title is very important to either leave off or keep depending on the goals of the lesson. Our goals are to identify misconceptions regarding measurement, so the title seems necessary now. What do you think?

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Hi Andrew- Thank you for taking the time to post this. I struggle mightily with the EngageNY units because teachers find them so appealing (easy to use?) and I find them so appallingly prescriptive and rote. You’ve deftly opened the door, inviting teachers to see that math teaching and learning can (and should!) be fun, creative, and open-ended, and showing how they can take something which gives a nod to Standards for Mathematical Practice and turn it into something loaded with wide-open SMP possibilities. Lovely.

Thank you, too, Joe, for pushing thinking, always.

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Thank you!

When I send any of my teachers resources from EngageNY, I often have to caveat by saying that they should use some of the tasks and lesson guidance, but to definitely take their students needs and learning preferences in mind during planning. This is a major reason for me to look through the resources critically myself, like we did in this post.

I also wonder what most teachers view as “easy to use.” This is something that I still haven’t figured out, but I am very interested in.

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I really liked your lesson plan. I have seen similar lesson plans before but particularly this one indicates the importance of mathematical thinking-without curriculum worksheets. Can I ask which year group and level your class is?

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Yes, it’s a self-contained high school class of students at around a 2nd grade equivalent level.

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