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 finding that fact to be true.
Ironically, our student who we have identified as Student 13, happens to also fit this stereotype. In preliminary interviews, we quickly noticed this aspect about his number sequence, but what turned out to be challenging was presenting him with tasks that would help him construct a correct sequence. Watch our first try below.
It may be humorous to hear him correct the interviewer at the end, “not thirteen, FOURTEEN.” His sincerity is clear. In his sequence the number 14 follows 12. It is important to mention here that “we can only provide appropriate situations to encourage the child’s experiences. We can never dictate an experience.” (Steffe, Von Glasersfeld, “Helping Children to Conceive of Number, 1985) Especially for very young children, whose attention may be quickly exhausted, it is prudent to realize that the task planned and the task executed may be very different.
Almost two weeks later we conducted another teaching episode. Again we constrained the quantity to 13, but we changed the scenario to help keep the student engaged. Watch our second effort below.
As you watched, perhaps you could feel a little of our excitement. He not only repeated the word “thirteen” but seemed to recognize it as part of his sequence and made the important step of repeating “thirteen” when asked, “How many?”.
In mathematics education there is a lot of talk about perseverance and the need for students to embrace this virtue. The first mathematical practice identified in the Common Core is summarized as, “Make sense of problems and persevere in solving them.” But perhaps we should rewind the math story just a bit more, because what needs to happen before perseverance is perturbation. Perturbation can be defined as “mental uneasiness.” It usually occurs when something or someone disrupts our expected outcome. We have all been there. It does not feel good, but it is vital to the learning process. The desired positive reaction to perturbation is perseverance, and when these two states of mind meet the potential for learning is great.
Our endearing Student 13 is proof that even a four year old can be placed in perturbation and endure. His perseverance and ours paid off. Almost three weeks later we revisit his counting sequence and the change is worth celebrating.
I cannot help but smile every time I watch this small segment and hear him say, “ I like thirteen.” How exciting it is when the theory of the research we study becomes reality in our teaching episodes. I look forward to sharing more of these celebrations with you.