Number Word Sequence & Counting

Meet the Children Where They Are: Episode 3

Narrator: “Last time on Meet the Children Where They Are: Has Mr. Unnamed nerdy-looking stereotypical math Research Associate (RA) found 5-year-old Bob’s zone of potential construction (ZPC)? Bob has counted 12 rocks and he came up with three different solutions.”

(from title screen — video of construction site with concrete truck backing up) (fade to videos of groups of rocks being arranged by hands) (math researcher narrates)

RA: After waiting for a few seconds to see what he would do, I said, “So, you came up with three different amounts: 12, 14, and 13. Which one is correct?” He said, “I’m not sure.” I said, “Which one do you think is correct?” He said, “I don’t know.” At this point, it looks like we’re stuck. So I made a desperate attempt to prompt him to reflect on his actions. “If you had to GUESS which is correct, which would you guess?” He quickly said, “12,” so I asked why he said that. Bob said, “Because I counted it.”

(still shot of satisfied look on Bob’s face with “Hallelujah Chorus” playing in the background) (camera zooms out as nerdy-looking stereotypical math Research Associate walks toward camera — reminiscent of a political spot)

RA: I thought that I would continue on to the additive situation. I asked him to count out two piles of rocks — one with 5 and one with 4 — and then asked him how many there were all together. He touched each rock in the pile of 4 and said, “6, 7, 8, 9,” with an emphasis on the 9. When I asked him how he knew to start at 6, he said that there were 5 in the first pile. So my next step was to hide one of the piles. Bob counted 7 rocks out into a pile, which I covered with my hand. I then asked him to make another pile with 4 rocks in it. Then I asked, “How many rocks all together?” He counted, “8, 9, 10, 11,” while pointing at each rock in the pile.

Wow! Did Bob just count on? OR, was Bob’s counting of the first collection so recent that he did not need to count it again? What would have happened if Bob had only been told that there were 7 rocks under my hand but had NOT counted them for himself? Would he still have counted on?

Narrator: “Tune back in for the fourth episode will determine where nerdy-looking stereotypical math Research Associate identifies what little Bob’s ZPC is. Don’t miss it!”

(dramatic orchestra music and fade to credit roll and out-takes)

The Forgotten Thirteen

Did you know that the number thirteen is a frequently skipped number in a young child’s early number sequence? According to Karen Fuson’s research in “Children’s Counting and Concepts of Number,” the numbers 13, 14 and 15 are the most consistently omitted numbers. As we work with children at our partner school sites, we are… Continue Reading

Mathematizing: Highlighting the Mathematics in the Young Child’s World

“From the ages of 3 through 6, children need many experiences that call on them to relate their knowledge to the vocabulary and conceptual frameworks of mathematics – in other words, to ‘mathematize’ what they intuitively grasp.” (NCTM/NAEYC 2002, p.16)  So what does it mean to “mathematize”? Mathematize is defined as: To regard or treat… Continue Reading

Shapes Here, Shapes There, Shapes EVERYWHERE!!!

In January, I had the wonderful opportunity to present to a group of 50 dedicated TK/K teachers in Clovis Unified School District. My colleague, Jason Chamberlain, and I provided the research on the importance of children having early math opportunities prior to kindergarten and weaving math opportunities throughout the day. We provided a variety of… Continue Reading

Making the Most of Mathematical Play

If you have been following our early math team’s work with three- and four-year-olds, you’ll know that we’re exploring the ways children develop knowledge and understanding in the context of mathematical play. We’re not interested in “social knowledge”, or the kind of knowledge that requires transmission from one person to another. Rather, we’re engaged in… Continue Reading

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… Continue Reading

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