Author Archives: Jason Chamberlain

Really? You’re Still Counting? (Part 1)

Counting.  Nothing in mathematics gives us more of a return on our investment.

In my work, I have heard educators unwittingly dismiss the significance of counting with phrases like “they were JUST counting” or “we finished counting as quickly as possible so we could focus on fluency”.  The evidence is noticeable in the classroom as children, at a very young age, try to hide their fingers and count inconspicuously. There is a stigma attached to counting, and particularly to finger use. Many educators and parents feel that children should “know their math facts.” Here at the AIMS Center for Math and Science Education, we say, “Don’t rush it. Let them count…a lot.”

Dr. Les Steffe, early mathematics research guru from the University of Georgia, says, “Kids need to count, count, count.  Count everything.” I’m beginning to see why this is one of his go-to recommendations for teachers. Let’s take a look at the power of counting.

Counting: Number Word Sequence

Proud parents ask their 2-year-old child to show off for visitors.  “Gracie, can you count for us?” Gracie, in a sing-songy voice, recites her number words from one to ten.  Some call this rote counting, which is really just a memorized sound pattern. This type of counting can be done without any conceptual understanding of number.  Kindergarten standards CC.1 and CC.2 can be, and most often are, addressed in this way — without conceptual understanding. Nevertheless, knowing an accurate number word sequence is critical for the counting that will follow.

Counting: Concrete Items

Once children know a number word sequence, they can begin really counting.  Counting is roughly defined as saying one number word that corresponds to each item being counted.  At this point in their counting journey, children must be able to see the items to count them.

Disclaimer: Some educators say that children are already doing ADDITION or even SUBTRACTION (see example pictures below)…but what they are really doing is COUNTING.


Disclaimer: Creating visual models of “addition” or “subtraction” word problems or algorithms has become en vogue as the bridge between counting concrete items and “counting on” (or “counting off”).  Although creating models is slightly more complex than counting the concrete items, the children are really just creating DIFFERENT concrete items to count.  When kindergarten standards OA.2, OA.3, and OA.4 refer to “objects or drawings”, they are still referring to counting concrete items.


Counting lots of different concrete items (including items like objects, patterns, movements, sounds, touches, etc.) provides children with a rich, complex set of experiences that give them the firm foundation they need for the imagined and abstract counting that will follow.  If they have few experiences, they have few resources to draw from.

Next time, we will look at what happens as counters begin to move away from concrete items and begin mentally counting imagined experiences.  Counting in this way is the critical (and most often overlooked) bridge between counting concrete items and counting on (or off).



Sometimes, early mathematics learning is necessary even in college math courses. A week or so ago, a community college math instructor told me, “You all at AIMS should visit my classroom to study a couple of my students.” He knows that we work with children between the ages of 3 and 8, but thinks there… Continue Reading

Not Just a Buzzword

Overloaded with educational buzzwords? Ever hear the newest trendy catchphrase and say, “Oh yeah, that sounds good.” Meanwhile, in the back of your mind, you’re thinking, “What does this even mean?” Here’s one I’ve used: “We need to provide students with rich mathematical experiences.” When we hear this at a conference or in a meeting,… Continue Reading

I Close My Eyes to See

Recently, I had an “Aha!” moment. My colleagues and I were analyzing video from a math interview with a young student, trying to understand what he knows about number. Somewhere in the back of my mind, I vaguely recall my dad gave me an article several months ago that discussed the science behind where great… Continue Reading

The Power of Imagination in Mathematics

I have been reading and thinking a lot about the power of imagination in learning — specifically, learning mathematics. In this and successive blog posts, I will discuss one role imagination plays in helping children form number sense. Merriam-Webster’s definition for imagine: “to form a mental image of (something not present),” is what I mean… Continue Reading

Building the Mathematical Mind

Watching a young child’s mathematical knowledge grow is analogous to watching a house being built. When I was in my teens, my dad, along with my brother and I,  BlogAugPt2 BlogAugPt1built our new home. I remember the exciting days of noticeable growth, such as when we poured the concrete slab, framed the walls, or put… Continue Reading