09/11/2026
A six-year-old named Ruth wrote 6 x 6 = 26 on a thank-you card. She got there because she knew 5 x 5 = 25.
Look at what that error actually contains. Ruth believes mathematics has structure. She believes patterns hold. She believes you can figure things out rather than wait to be told. She applied a rule she had noticed, which is exactly what a mathematician does, and the rule happened not to extend.
Correct her fast and you fix one fact. You may also teach her that math is a list of arbitrary answers held by adults, and that noticing patterns is risky.
Goldenberg, Miller, Carter, and Reed argue that teachers have more choices here than they usually take. They sort children's errors into three kinds:
Slips: A momentary lapse of attention. One kindergartner kept writing 34 instead of 30 when adding 6 to 24, even though she counted correctly every time. The starting number was still in her head as her hand moved. Nothing was wrong with her thinking.
Incorrect structures built by correct reasoning: Ruth's card. Sound process, wrong output.
Correct structures applied where they do not fit: A rule that worked before, carried somewhere new.
The teacher move they recommend is not to ignore errors on principle. It is to notice where the child is actually working, and to protect that. For Ruth, that meant handing her dice or counters and letting her build what 5 x 5 means, without touching the 26 at all. The concrete experience does the correcting later, and she keeps her conviction that math makes sense.
Their line worth taping to your planning book: errors can reveal strengths worth preserving, not just weaknesses to fix.
Read the article:
https://www.naeyc.org/resources/pubs/yc/jul2017/mathematical-error-kindergarten
Butte College Child Development and Education:
https://www.butte.edu/academic-programs/coi-sbsc/dept-child-development-and-education/