I’ve heard the phrase the “Common Core way” several times this summer, as in “we used to teach math differently, but now we do it the Common Core way”. I want to unpack that idea.
What does the Common Core actually say about teaching and learning? Let’s look at the standards. There are exactly three points the standards make (pg. 3-8) before they dive into the content standards.
Toward Greater Focus and Coherence
To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.”
We can argue about whether the standards actually achieve that goal, though I’m confident they are an improvement over the median state standards that preceded the Common Core.
One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).
We want students to understand, and one tool to probe for that understanding is to ask kids to explain a piece of mathematics. Nothing groundbreaking here.
Standards for Mathematical Practice
The Standards for Mathematical Practice describe the ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years.
The Standards for Mathematical Practice focus on what students should be able to do — to reason abstractly, to construct arguments, to model, to make use of structure. Good to know.
We can also look, separate from the standards themselves, at the key shifts:
- Greater focus on fewer topics
- Coherence: Linking topics and thinking across grades
- Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity
Nothing surprising here. Again, we can argue about whether the Common Core meets these goals, but these are goals worth working toward.
Finally, there are the standards themselves. Does the content of the standards dictate instruction? Let’s look at the progression toward adding and subtracting fractions as an example.
- Develop understanding of fractions as numbers
- Extend understanding of fraction equivalence and ordering
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
- Understand decimal notation for fractions, and compare decimal fractions
- Use equivalent fractions as a strategy to add and subtract fractions
These standards, like many other places in the Common Core, progress across several grades. First students should know what fractions are. The next year they should be able to compare fractions and think about them in multiple ways. Finally, they are ready to perform operations on them.
The standards also give an example of how students can link their previous knowledge to a new topic — using equivalent fractions (also called finding a common denominator) to add and subtract fractions.
This seems only to illuminate the point about coherence — a given grade is not an island, but a piece of a deliberate progression built around our best understandings of how children learn math.
The Common Core Way?
There are definitely differences here from standards that preceded the Common Core. My argument is not that everything is the same. Instead, I’m arguing that many teachers have always had these goals for students, and they represent common sense changes. Focus and coherence? Let’s do it. Standards that link content between grades? Awesome. Students who reason, argue, model? I’m in.
I don’t see any evidence that the Common Core is telling me how to teach. It’s not completely agnostic, but I see no evidence of a “Common Core Way”. The big difference I notice is when, as Dan suggests, I watch the verbs.
The Common Core asks students to understand, to explain, to reason, to argue, to model, to build on their knowledge from year to year, and to make sense of mathematics. It’s not just about what they know, it’s about what students are doing in math class. It’s about the verbs.
Maybe that’s what folks mean by the “Common Core way”. But the standards are still a political lightning rod, and the more they are framed as prescribing a new and different way of teaching math, the more polarizing they will be. Instead, I’d love to focus on the fact that the Common Core names some very reasonable goals for students, that none of these goals are particularly surprising, and that if anything we are raising the bar for what students are able to do in math class. With this focus, I think the Common Core will find more support and less polarization.
There are lots of tools to move students toward these goals. Some of them will continue to frustrate parents, as parents will naturally be frustrated when their children have a tough time with something new. But I think that if we say, “oh, well that’s just the Common Core way,” we’re setting the standards up for failure. Instead, we can frame it as, “I have ambitious goals for your daughter or son — to engage her or him in mathematical thinking, reasoning, and sense-making. It’s going to be hard sometimes. That’s fine — it’s hard because it’s worth doing.” That’s a message that is more likely to resonate with parents, and is faithful to the spirit of the Common Core.
We send a message, which is also my firm belief, that the Common Core is not some directive we received from on high to change everything. Instead, it’s one step forward, and the best tool we’ve got to reach the potential for teaching and learning mathematics for all students.