A teacher in a public school in Chicago writes an op-ed on Education Post.org, saying she went from anger to acceptance about the standards in the Common Core.
An alternative strategy for subtraction, typically taught under the Common Core, involves setting intermediate goals of round numbers. It’s like counting back change from the price up to the amount tendered. I’m not so sure, but several teachers say it helps students understand the meaning of the underlying mathematics in subtraction.
“While my own experience with the new standards hasn’t been completely smooth, as I look back on the year, I recognize that a new instructional approach motivated by the Common Core is having a positive impact,” writes Lindsey Siemens, a special education teacher. “I can see my students reaching great heights if I take the time to learn these standards and push student thinking and learning.”
We have been saying exactly the same thing for quite a while. Take the subtraction strategy demonstrated in the picture above. I realize this isn’t how subtraction would be done in the real world, but when it comes to teaching students the mathematical meaning of subtraction, this way sure beats using a calculator.
Besides, subtraction isn’t really what this lesson is about. This lesson is about applying alternative strategies to justify your answer.
Students will have many opportunities to subtract numbers using calculators when they get out in the working world. In second grade, as we showed on these pages last November, kids also learn a subtraction strategy involving a number line. The engineer we quoted in the article thought that was way too much work just to subtract two numbers, but what’s going on here is the teaching that you have several options for approaching the solution to a problem.
That’s true for second graders with subtraction or high school students learning about the use of metaphors in poetry. We quoted Damon Z Ray, an English and history teacher at Hume-Fogg Academic Magnet High School in Tennessee, as saying this:
Under the Common Core, lessons in metaphors take on new life, and English teachers get the space to empower and embolden our students’ ideas. It used to be sufficient to just identify a metaphor in writing, or possibly even one in another artistic medium. Now, we’re given space to create our own metaphors, to actually apply this knowledge to something real that reflects the way a student sees the world.
And the same thing is happening with math: The Common Core is placing an emphasis on students explaining and justifying their arithmetic. Suppose you have to justify that 32–12 = 20. You can’t just say, “I know 32–12 = 20 because it just does.” And you can’t justify your arithmetic by saying, “I punched this and that number into a calculator, and I got 20.”
So, when we teach alternative strategies, we give kids the tools to justify their subtraction. That’s not such a valuable skill, really, when it comes to subtraction per se, but soon it will come to logic, debate, politics, scientific experiments, and the like. Teaching alternative strategies in elementary math, which is what’s important to their lives in elementary school, will only help them strategize when they have to justify more important calculations or positions on issues later in life.