What is Common Core Math? It is math instruction written from a Constructivist Theory.
Every time educators sit down to write a curriculum, they must have a controlling set of ideas, a theory of teaching, that helps them decide what to include or exclude.
For the Common Core Mathematics, that education theory is called Constructivist Math.
Constructivism means that students are expected to work out a problem for themselves, to construct meaning on his/her own.
Mathforum.org says, “Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to ‘transfer’ mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions.”
It’s a theory that is largely supported by mathematicians, but is controversial in its adoption, partly because parents don’t support the changes in instruction.
Traditionally, students were taught toe memorize basic arithmetic facts and times tables. Under constructivism, students are asked to work out the problems for themselves.
This video demonstrates the differences in the approaches; it’s definitely slanted against constructivism, but it still demonstrates much of what needs to be understood.
If you can’t see this video, click here.
Here’s a pro-constructivism comparison, though, of what a lesson plan would look like for a behaviorist math class versus a constructivist math class. It emphasizes the boring nature of rote memory and the imperative for students to understand underlying concepts.
The emphasis on student-discovery, though, means that there is no place in a constructivist math classroom for students to learn basic facts or learn times tables. Parent’s complain that sixth graders can’t make change for a $20 bill. Second grade students are still doing addition and subtraction on their fingers; when they run out of fingers, they are frustrated and don’t know what to do. A sixth grade students knows how to figure out a multiplication problem, she just counts by fours 23 times, a laborious time-consuming process; she gets it right, but at the cost of speed.
In other words, for basic arithmetic, parents and critics say that constructivism math takes the long way round to solve problems that could easily be solved if basic arithmetic facts and times tables were memorized. To put it in mathematic terms, basic algorithms, or ways of approaching a math problem, speeds up the process and increases accuracy; letting kids work out their own algoriths, or using process-oriented math solving does eventually wind up with the right answer, but it’s often slower, more cumbersome and unreliable. The multiple steps involved also mean an extra layer of complexity that may or may not work for an individual student. But in the long-run, process means better understanding of deeper math concepts.
There are fewer criticisms for constructivism math as the math becomes more complex, for example, in algebra and geometry, and most center on the frustrations that students’ experience when forced to “try to figure it out. Some students like the experimentation, but many don’t.
While many math teachers have conservations about the advantages and disadvantages of constructivism math, most are just concerned about teaching the next day’s lesson. As one teacher said, “It doesn’t matter what the theory behind the Common Core is, I still have to teach it, like it or not.”
Likewise, I’m not trying to convince you of the effectiveness of the constructivist approach to math education; I am just pointing out what isn’t necessarily obvious at first glance: Common Core math is based on constructivism theories of math education.