I’ve been thinking about making posters for each of the CCSS Standards for Mathematical Practice and used an image search to see what might already be out there. Since I’m only teaching 6th graders, I tend to find myself in elementary land with all the cute stuff. (Not trying to inflame anyone here…it’s the truth. If you have missed the raging debate on the value of “cute” in elementary education, take a side trip to Matt Gomez’s blog for an update.) Of all that I saw, I think the Grade 6 posters from Jordan School District in Utah are the closest to what I had envisioned. I especially appreciate that they have customized their posters to each grade level, giving content-specific examples on each poster. Here’s a sample of one of the 6th grade posters:
What concerns me are the posters I came across that have tried to simplify the CCSS Standards for Mathematical Practice into single “student-friendly” sentences. Let’s take practice #6, “Attend to precision,” as an example. In the CCSS, “Attend to precision” is explained as such:
“Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.” http://www.corestandards.org/Math/Practice
The statement, “Attend to precision,” is purposefully broad. It was intended to include many different aspects of being precise; precise with language and explanations, precise with computations, precise with symbols and labels. But many of the resources being shared online seem to focus only on one aspect of precision; precision with computation. Some examples:
“Good mathematicians try to be accurate and revise their thinking when they make a mistake.” Math Minds (Teachers Pay Teachers)
“I can work carefully and check my work.” everybodyisageniusblog.blogspot.com
“I can check to see if my strategy and calculations are correct.” Carroll County Public Schools
I’m sure that each and every one of these resources (and many more like them) were created with the intent of making a broad statement easier for young students to understand, but in doing so they have lost much of the meaning of the original statement. In trying to simplify an idea to be “kid-friendly,” the opportunity for students to discuss and explore the meaning of “attend to precision” has been taken away and students are being given just one very limiting definition.
This is a slippery slope that elementary teachers have been on before. Take the standard algorithm for division as an example. A well-meaning 4th grade teacher may tell students, “The big number always goes in the house.” (Translation: The dividend goes under the division bar and the divisor goes on the left. You’re 4th graders and we’re only working with dividends that are greater than their divisors.) But students are left thinking that this arrangement has more to do with the value (or length) of the number, and they have no understanding of the meaning of the procedure they are performing. This serves the purpose of getting 4th and 5th graders to pass a high-stakes test that focuses on procedural fluency, but when 6th graders start working with division of decimals, their misunderstandings are unearthed and they start to fall apart. This is just one example of a “trick” to understanding a procedure gets in the way of true understanding of a concept.
So back to CCSS Standards for Mathematical Practice. Can we afford to allow students (or teachers) to believe that the eight Mathematical Practices can be boiled down to one kid-friendly sentence each? I say no. The Standards for Mathematical Practice are rich and deserve to be left as open statements that can be applied whenever appropriate. I don’t condemn those trying to make it easier for their students, but I do challenge them to take a step back and ask themselves if what they are doing might, in the end, actually make understanding mathematics more difficult and confusing.
Rocking the Boat 