Monday, November 23, 2015

Should 3 Act Tasks Build Literacy?

I went to the Nashville NCTM Regional session by Graham Fletcher and Mike Wiernicki and they showed this slice of awesome:

You'll notice they covered up the text of a [K-5] word problem only to show the question at the bottom of the chart paper. I thought this was a really slick move to get students talking, thinking, and imagining. If you've been to one of my problem-solving sessions lately, you'll know I'm really encouraging math teachers to push student potential by creating a mystery, layering in the clues, and solving the mystery. Therefore, the slide Mike and Graham displayed really resonated with me. Imagine students taking those stickies off one at a time, creating suspense in the process. More importantly, in my opinion, a teacher can scaffold in the context and literacy demand of the word problem.

Imagine reading one sentence (or one part of a sentence) at a time on that chart paper, as a class or with a classmate, working on understanding the context better and better with each sticky that is removed. However, the resonation of their slide didn't stop there with me. It really got me asking myself, "Can we help students simultaneously build math skills and literacy skills with 3 Act tasks?"

As much as I love how 3 Act tasks make the math accessible to more students because the literacy demand is usually removed, I agree with teachers that voice their concern about this actual feature. Understandably, they're concerned about the literacy demand that many of our state tests demand. (*concern should not be limited to state tests)

Essentially, I'm wondering if there's a natural way to work in the literacy demand during Act 1 and Act 2 of a 3 Act task? For example, let's use my File Cabinet task as an example:

Students watch Act 1:

After we gather student thinking (noticing and wondering a la Math Forum) and have students make a guess, I'm feeling the notion to present students with the textual representation of this task at some point. I'm not sure when that point is, since I badly want to test this out with students. The text might look something like this:
Mr. Stadel is using sticky notes to completely cover a file cabinet in his classroom. How many sticky notes will he need to cover the five visible sides of the file cabinet?
Whether we (the teachers) present the text to students or students help compose the text description above, would this benefit both the math and literacy? Would it detract from the math?

Moving into Act 2:
I think it's still important to have students think of information (identify variables) that is important to know in solving this question. Lately, I've been encouraging teachers to have students formulate a plan without any data, numbers, measurements, or other information. Lately, I've been seeing students just grab the numbers from Act 2 and hastily plow into a wrong plan or formula, getting unreasonable answers. My suggestion: Let's sit tight on revealing the information in Act 2. Get students to formulate a plan or representation first. Maybe make a more precise estimate in the process. After going through that process, maybe we can refine our original text description to something like this that now includes the measurements necessary in solving the task:
Mr. Stadel is using 3" x 3" sticky notes to completely cover a file cabinet in his classroom. The file cabinet is a rectangular prism with a 36-inch width, 72-inch height, and an 18-inch depth. How many sticky notes will he need to cover the five visible sides of the file cabinet?
Now that we know more information in this task, I think the original text should be adjusted (updated) accordingly. To me this feels like we have removed all the stickies from the chart paper Mike and Graham gave us.

Similar to Act 1, I question if this would benefit both the math and literacy?

Since I am putting Act 1 and Act 2 under some scrutiny, it would only be fair to address Act 3 as well. Maybe the literacy in Act 3 seems more intuitive (all relative), but would this be a good time for students to write something that represents their plan from Act 2? For example:
We found the surface area of each side by... We figured that we could divide each side by 9 square inches, the area of one sticky. In doing so we predict Mr. Stadel will need X number of stickies to cover the file cabinet. 
There are two big reasons I was initially drawn to these tasks. 3 Act tasks typically:

  1. eliminate the literacy demand, making the math accessible to more students. 
  2. have Act 3 to validate (or break) the mathematical model we used in Act 2.

I still believe in 3 Act tasks, don't get me wrong. However, I believe we might be able to get even more out of them as teachers. I consider this: at what point do we say to our students,
Look, I first want you to access the mathematics without your english language skills (or lack thereof) getting in the way. We have to keep in mind that our state tests (and other math problems) require strong literacy skills. I think you need to see what this task might look like as just plain text.
Or do we say this at all to students? parents? colleagues? administrators?

Many online colleagues gave input on building literacy into an Act 4. You can read more in the thread here. I support extended opportunities for more literacy like our colleagues suggest (or practice). However, my focus is during Act 1 and Act 2 right now. Help me think this through. Add some thoughts in the comments.


Friday, November 13, 2015

Are You A Mathematician?

I flew out to New York last Sunday. An older gentleman on the airplane sitting next to me saw me working on this idea in Desmos and simply asked, "Are you a mathematician?"

I hesitated. Not sure I know why

I think my hesitation roots from me having this impression that mathematicians exist only at the college level. They do math all the time. On chalkboards. Wear white coats. Have frizzy hair. Stand in front of chalkboards full of symbols and equations. Yes, I know. Very stereotypical.

Why did I hesitate?

Yes, I am a mathematician.
I love thinking critically. 

Yes, I’m a mathematician.
I love building number sense.  

Yes, I’m a mathematician.
I'm scared of math problems in which I lack the skills to solve. 

Yes, I'm a mathematician. 
I love being challenged by a good [math] problem.

Yes, I'm a mathematician.
I love using numbers to make sense of the world around me.

Are you a mathematician?
Yes. Don’t hesitate.