Number Word Sequence & Counting

Meet the Children Where They Are: Episode 2

Narrator: “Last time on Meet the Children Where They Are: Mr. Unnamed nerdy-looking stereotypical math Research Associate (RA) is down in the mud getting ready to do some math with an unsuspecting 5-year-old child named Bob. Can he find Bob’s ZPC without damaging the child for life? Let’s head back to the construction site where the action is going on.”

(fade out title screen — video of construction site with concrete truck beeping as it backs up)

(fade to videos of various groups of rocks being moved around by hands)

(nerdy-looking stereotypical math researcher narrates)

RA: First, Bob and I made 3 groups of 4 rocks and I asked him how many there were. He pushed 2 sets of 3 together twice to make 6 and 6 and then quickly answered, “12!” I asked him how he knew that and he said he “just knew” that 6 plus 6 is 12. I then thought that he might have been taught some addition facts, but that he didn’t necessarily have efficient strategies for solving additive situations. So I rearranged the rocks to make 4 groups of 3. Interestingly enough, with the added cognitive load of groups, he did not conserve number!

(still screenshot of definition — “Cognitive Load: the total amount of mental effort being used in the WORKING memory; not yet in the long-term or ‘automatic’ memory”)

(fade to video of math researcher kneeling in the mud with a small child — slowly zoom in)

(nerdy-looking stereotypical math researcher continues to narrate)

RA: His strategy for this second activity was to simply count all of them. He came up with 12, so I decided to rearrange them in 6 groups of 2. He decided he would count them all and counted 12 by 1s, but before I could reply he said that he wanted to count by 2s. He counted, “2, 4, 8, 10, 12, 14,” and knew he had done something wrong because he got a different amount than when he counted the first time. Did you notice what he did?

(still shot of Jeopardy logo with Jeopardy music for 7 seconds)

(fade to videos of various groups of rocks being moved around by hands)

(nerdy-looking stereotypical math researcher narrates)

RA: Oops! He forgot to count 6. So he counted again. This time the count was, “2, 4, 8, 10, 11, 13.” He accidentally said the number word sequence by 2s on one of the counts but still touched 2 rocks. Bob looked at me with this very PERTURBED look, maybe even annoyed, and said, “Hmm.”

Narrator: “Will little Bob be able to persevere and solve this problem? What in the world does “perturbed” mean? Find out on the next episode of Meet the Children Where They Are!”

(dramatic orchestra music and fade to credit roll and outtakes)

Mind the Black Box

Here at the AIMS Center, a central focus of our attention is the mathematical thinking of children. It should not be surprising that children do not think like adults. While as adults we agree in theory, our actions consistently seem to contradict this truth. The habitual act of laying our own mathematical thinking onto children… Continue Reading

Playful Learning

The AIMS Center Research Division’s early math team is currently interviewing and videotaping 3 and 4 year olds in order to illustrate the developmental stages in learning to count that researchers have identified. We are specifically interested in collecting video clips that illustrate a child’s path in moving from one stage to the next. We… Continue Reading

The Gift of Mathematics

Earlier this month my colleagues and I had the privilege of attending the National Association for the Education of Young Children Conference in Los Angeles. Professional learning is a wonderful opportunity where one can validate ideas, gain new insights, and network with others in the field. This was my first attendance at a preschool level… Continue Reading

Subitizing, Part 2

In my last blog I mentioned that there are two distinct types of subitizing – perceptual and conceptual. I am fascinated by the subtle differences that students show and what that means about their thinking. Perceptual subitizing is the ability to recognize a number without using other mathematical processes (Clements 1999) and there are four… Continue Reading

Is Early Mathematics Too Academic For Young Children?

Math for young children is much more than saying the number words by rote or memorizing the math facts. I just finished reading an article titled, “Learning Mathematics Through Play” by Anita A. Wager and Amy Noelle Parks. The early learning community has often said that children learn through play and there is research dated… Continue Reading