6th Grade Common Core Math

Tips and Support for Common Core Math Implementation

The Importance of Conceptual Understanding in Math

on December 19, 2013

Why not just teach the steps?

Students take information from the world using all their senses. Why should learning mathematics be much different? Let’s look at how athletes learn to play sports. Imagine taking a child to watch a professional baseball player for 50 minutes a day and then be expected to win a game. It seems ridiculous because in order to play the sport, the player must feel the bat and gloves in their hands. They must run the bases to determine how long it will take. They need to imagine hitting the ball into the outfield. No matter how much you watch the pros, until you get your whole body involved, there is no way to really excel at the sport. This is not much different than a student watching a teacher for 50 minutes and then be expected to successfully complete their math tasks. Truly understanding mathematics involves more than just memorizing steps or formulas. In order to truly comprehend mathematical concepts, our teaching methods should involve the use of moving and placing manipulatives in order for students to feel and see what is really happening in a problem and therefore be able to predict a reasonable outcome.

What do conceptual learning activities look like? 

Conceptual learning activities often incorporate the mathematical practices.

  • Make sense of problems and persevere in solving them
: When a student asks and demonstrates the reasonableness of the answer, they are using this math practice (and arguably others as well). For example:
    •  “What is 7.245 x 6.18?” A student demonstrates conceptual understanding of mathematics when she or he explains that 850.015 cannot be a reasonable product because by estimating the smallest possible response as 7 X 6, and the largest possible response as 8 X 7; therefore making the product between 42 and 56.

    Image Attribution: by Alana Gilliam

  • Model with mathematics: A student demonstrates conceptual understanding of prime numbers when she or he is asked to prove if a number is a prime or composite number, and she/he creates a model to demonstrate it is prime by building only two arrays to show the different multiplication combinations of the number, while a composite number has more than two.

ResourceWhat is Conceptual Understanding?

Performance Tasks demonstrate Conceptual Understanding

Before beginning a new topic, study the performance based assessment. What are the students truly expected to be able to do conceptually? This should be our “GPS.” We need to have a clear understanding of the concept at hand to effectively facilitate learning.

Do you teach the steps, or do you teach the concepts?

How do you allow students to demonstrate their conceptual understanding daily?

I wanted to give a big thank you to Robyn Gonzales, Common Core Coach and Title I Teacher at SMES, for the ideas, resources, and the wording in the top and bottom portions of this post. 

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