Common Core Math (CCM) Practice Standard 2

Opinion – Embrace CCM

I believe that it is in the best interest of your children to master CCM. Our challenge, yours and mine (as your self-proclaimed guide), is to adopt a growth mindset (we will discuss this in a subsequent post) and to learn, or relearn, the concepts and skills that your children are learning. One reason for parents to learn the standards is that teaching CCM does not come easily or naturally to every teacher – the Internet is awash in complaints about homework assignments and test problems which supposedly reveal the evils of CCM. Perhaps, but they also reflect inconsistent teaching methods, varied student abilities, and inherent challenges of the subject matter.

There is no guarantee that your child’s teacher will excel at teaching math in general or the CC Standard in particular. This should not be a surprise because CCM is still new to many teachers and for those who teach elementary school, not only is it not their only subject – they are certified to teach multiple subjects – they are being challenged at the same time by CC English. This means that betting your children’s math future on the abilities of their teachers is risky. Your children deserve a lifelong coach and I recommend that you be that coach.

Since high-school math teachers are certified to teach math, they are generally ready to teach CCM. Your children will be able to take advantage of such teachers in high school if they arrive knowing that math is a discipline which requires careful analysis and objective thinking. Once you have helped them to get this far, even though you may eventually lose contact with the math they are learning, you will find it normal to continue encouraging them to maintain a growth mindset and to stay the course(s).

CCM Lesson of the day: CCM Practice Standard 2

Reason abstractly and quantitatively.

“Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.”

My Comment

As I understand this step, it refers to moving from the specific (as in, it took me 15 minutes to walk a mile) to the general (as in, r = d / t) and then back again, once I have computed my walking rate. As for reasoning quantitatively, the numbers should make sense; for example, it’s unlikely that I will be able to walk a mile in under 4 minutes.

Process implications:

• estimate

• use abstractions, such as algebraic symbols

Definitions

Decontextualize: move from a specific case to a general principle

r = d / t : this equation tells us that rate = distance divided by time.

Applications and Examples

If I walk a mile in 15 minutes, rate (in miles per minute) = 1 mile / 15 minutes. This will be easier to understand if I notice that 1 mile / 15 minutes is the same as 4 miles / 60 minutes, or 4 miles per hour.