Counting is Fundamental to Mathematical Reasoning

As I write this, The AIMS Center for Math and Science Education is in the final stages of planning and preparing for the kick-off of our pilot program with Kindergarten through Grade 2 teachers. We will start with a week of professional learning this summer. In the midst of synthesizing all that we have been reading and learning, I have been thinking about how to connect what we are doing to the Common Core Mathematics Practice Standards, in particular, Math Practice 2: “Reason abstractly and quantitatively.” Sometimes the eight practices seem a little nebulous because they try to communicate the “habits of mind” we want to instill in our students during mathematics instruction, and the practices encompass Kindergarten through 12th grade. What this practice looks like in kindergarten is very different than what it would look like in 12th grade. I wanted to know more so I decided to look at the California Framework for Mathematics, specifically the separate chapters for TK, Kindergarten, Grade 1 and Grade 2 to see what they say.  When I looked at the first couple of sentences from each grade level description on Math Practice 2: Reason abstractly and quantitatively I noticed something interesting. See below:

Transitional Kindergarten:  Counting things for a reason—or just to get better at it—is important. Young students love to count things and to practice the counting sequence.

Kindergarten: Younger students begin to recognize that a number represents a specific quantity and connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.

Grade 1 and 2: Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.

First of all, creating many meaningful opportunities for young students to count is critical in students’ development of quantitative reasoning (being able to work with and think about numbers). More importantly, it is necessary for students to have a context or reason for counting and be able to communicate that purpose to others so they start to see that math is all around them. For example, students could count to see how many pencils are in a container and connect that amount with a numeral. As students get more sophisticated with their counting they notice that there are 7 blue pencils and 8 red pencils. They might want to be able to communicate what they have counted in a more efficient way “7 blue pencils plus 8 pencils equals 15 pencils all together” or “7 + 8 = 15”.  In other words, students create a symbolic representation of a problem while attending to the meanings of quantities. Believe it or not, that is a lot to hold to in a child’s mind! How can we as teachers support them in their understanding? Stay tuned for my next blog post!

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