Common Core is easily one of the most controversial developments in education in the past two decades, polarizing educators, administrators, students, and parents into separate camps.  SWUN Math helps in this area.

But as you can see from our previous posts, Common Core was indeed born of a noble impulse: to make American math education more comprehensive, thorough, and ultimately, more effective. This would have a multitude of positive results, such as building critical talent in the STEM fields and making our population (and in general, our country) that much more competitive on the world stage.

Big picture concerns aside, there are plenty of ways you, as a stressed, overworked teacher, can adjust to Common Core. Read on for three methods to incorporate Common Core into your everyday lessons.


Here, manipulate doesn’t equate to psychological manipulation; instead, this refers to manipulatives, which are physical, tangible objects that can be moved, handled, touched, and grasped (both figuratively and literally) by learners. After all, mathematics, at its core, often deals with abstract principles: only by rendering them into concrete examples (for instance, 2 x 2 can be represented by two groups of two marbles each) can we smooth out the learning process.

At the very least, manipulatives can lead to higher levels of engagement and satisfaction, both from teachers and students. Still, as Jenni Beck points out, one mistake that teachers may make is to use manipulatives not as a central part of their lesson–but rather as a reward for good behavior. In fact, manipulatives are a central part of any successful lesson, allowing students to enjoy and think deeply about otherwise confusing concepts.

Best of all, manipulatives are easy to make can take on a wide range of forms, limited only by your imagination. Make ten frames from egg cartons by cutting off the cover and two egg slots; find the volume of a basketball by measuring the displacement of water when you drop it into a large container; understand fractional equivalents with the help of number lines or graphical representations (like shaded circles and squares).


If there’s one thing we can learn from the education systems of other nations, it’s that at times, teachers should serve as facilitators and enable discussions, rather than lecture.

For instance, Japanese math classrooms are a hotbed of activity; as Elizabeth Green writes in her comprehensive, illuminating article, Japanese schools don’t just use the “I, We, You” (first the teacher does it, then (s)he guides the class, and finally the class works independently) model so common to US schools. Instead, Japanese teachers will use “You, Y’all, We,” starting with a single problem given to the class; first, students try it on their own (You), then in peer groups (Y’all), and finally, in a group with the class (We).

The strength of this model lies in the active process of forming meaning and understanding. Note that students will talk at length, and rather than listening to the teacher lecture, they will question their assumptions and gradually, learn what works (and what doesn’t).

Now that’s not to say that students should be left on their own, without guidance; facilitation, after all, is only possible when used in conjunction with a lecture. Therefore, teachers should incorporate this model as one part of their lesson plans, perhaps replacing the old “I, We, You” structure that they previously used.


By now, it’s clear that memorization is detrimental to learning.

In fact, recent research shows that successful memorizers actually end up being the lowest achievers in math, rather than the highest. For instance, among students who took the PISA tests, a series of skills assessments administered to the member nations of the Organization for Economic Cooperation and Development (OECD), the highest scoring students (usually in East Asian countries) actually reported less memorization than their lower-scoring counterparts in other countries.

Why? Apparently, memorizing facts without understanding them is a short-term solution at best, and doesn’t lay the groundwork for future mastery. As any experienced teacher can tell you, often students will memorize facts before the test, only to forget it after; lost in the process is meaning, understanding–any of the higher-level conceptual thinking that Common Core tries to promote.

Rather than committing facts, algorithms, and formulas to memory through rote repetition, educators may wish to consider cognitive activation. Cognitive activation encompasses a wide range of techniques, with one, key binding thread: these strategies promote deep thinking and learning, rather than simply relying on rote, brute repetition.

Here are some examples of cognitive activation at work:

  • Assigning students problems in slightly different contexts (or with completely different variables), either of which can skew the outcome significantly. For instance, this could be giving your student a fractional equation with different denominators (⅕ +⅑).
  • Ask for alternatives. One example is 5 x 3; this simple equation was the center of a heated controversy over Common Core (essentially, the student wrote that it was three groups of five instead of five groups of three), but teachers could push students to find multiple solutions for one problem.
  • Use interdisciplinary units. Interdisciplinary learning is especially valuable, because it situates math within a real-world context, rather than just forcing students to study equations in isolation. For instance, math teachers could pair up with social studies instructors to create an interdisciplinary unit about taxation in early America: one group of students could be given tax brackets and quotas, whereas another group could be farmers who have to turn over a certain percentage of their crop yields from this year.

However you go about your lessons, these three mindsets and techniques are invaluable to getting the best of Common Core. After all, it’s a truism that Common Core’s rollout has been bumpy, and many educators are still confused about what these new standards mean. Hopefully, with these strategies, you’ll come one step closer to helping your students build a deep, solid math foundation.