In the transition to common core students are being asked to go deeper by building conceptual understanding of the mathematics as well as know how to apply the math to real worlds situations. Students are being asked to do much more than just compute. I would suggest that this is an extremely challenging endeavor for everyone involved and one that is worth taking.

This transition away from memorizing procedures, formulas, and facts is forcing fundamental shifts in the classroom environment. Now outdated, is the teacher standing in front of the class at the whiteboard showing the class to just “invert and multiply” when dividing fractions, followed by students solving 1-47 odd of similar problems. International studies and the United States rankings in mathematics tell us what most of us have already discovered, this pedagogy has major limitations. Solving pages of problems that someone just showed us what to do does not allow for long-term retention beyond the test and is not the math we do in the real world.

Tied to this outdated system is the very simple way to identify and challenge those that were good at math. If a student was good at dividing a three-digit number by a two-digit number I could challenge that student by giving them the next page or by adding more digits to the problems that they solved. For those students that really needed the challenge, we could move them forward an entire chapter or even course. Although this satisfied many people’s need to show that their child is the highest or brightest, I question whether doing a skill earlier, faster, or with more digits is really more challenging.

Looking into our common core math classroom, you may see students working in groups with piles of cubes, building shapes on the latest ipad app, or collectively solving a mental problem at the white board. How can the kids that are good at math be doing the same thing that the rest of the class is doing and still be challenged? The answer is in the opportunities that the work provides and the willingness of the student to be challenged by those opportunities.

Some strategies that I love that promote thinking, conceptual understanding, and problem solving while challenging our top students include number talks, rich tasks or problems, 3-Act lessons, and Claim, Support, Question. Each one of these is worth it’s own attention to truly understand their value but they all share a few key connections. They each present the opportunity to see numbers at their pure form. Numbers can be broken in half, doubled, and reorganized to change the way you solve a problem. These strategies are open-ended and allow for the concept and understanding to go far beyond the mathematics of the grade level. Last, each of these strategies is less about the answer and more about the process and understanding to get the answer. The learning and the challenge happen in the process. The answer is a means to validate the process.

So, is my child being challenged? More than likely they are being challenged if they are being asked to persist, reason, construct, critique, and model. Probably not, if they are still solving pages of similar problems.