Categories
Daycare Mathematics Parenting

Two many much

Today was a productive potty day at daycare. The snack bag had more than usual amount. Fleur looked super proud.

They get a piece of candy each time they go. We tried stickers and found it okay but not great. We switched to candy and found it super effective. Daycare went the same route a couple weeks after. The dual environments using the same method has us over a month in without an accident.

Today she showed me the bag. She wasn’t in a rush to eat it like usual.

I asked how many she got. She told me: “Two many much.” I thought she meant too many, but two many makes more sense.

She can count. But, in this moment of triumph, “two many much,” was perfect.

Categories
Mathematics Parenting

Study: Infants recognize counting as numerically relevant

brown numbers cutout decors
Photo by Magda Ehlers on Pexels.com

We play a game: One of us parents will count to five and say that number of fingers are coming after you and tickle Fleur. (My wife does to five and tickles with both hands. I will to five & use one hand or ten &use both.) In true dopamine fashion the smile is largest in the middle (three and eight). It did make me wonder if she recognized the words, but that apparently comes around 3-4 however there is evidence that starting around 14 months they have an approximate numerical system that allows them to recognize it.

Children do not understand the meanings of count words like “two” and “three” until the preschool years. But even before knowing the meanings of these individual words, might they still recognize that counting is “about” the dimension of number? Here in five experiments, we asked whether infants already associate counting with quantities. We measured 14‐ and 18‐month olds’ ability to remember different numbers of hidden objects that either were or were not counted by an experimenter before hiding. As in previous research, we found that infants failed to differentiate four hidden objects from two when the objects were not counted—suggesting an upper limit on the number of individual objects they could represent in working memory. However, infants succeeded when the objects were simply counted aloud before hiding. We found that counting also helped infants differentiate four hidden objects from six (a 2:3 ratio), but not three hidden objects from four (a 3:4 ratio), suggesting that counting helped infants represent the arrays’ approximate cardinalities. Hence counting directs infants’ attention to numerical aspects of the world, showing that they recognize counting as numerically relevant years before acquiring the meanings of number words.

Experiment one: The infants watched a demonstration of putting items in a box some while counted and others using “this” instead of counting. Then the researcher had the child do the task on sometimes two or four objects (two in front and two in back). They measured the search time and found the children searched longer for the two when counted. The supposition here is the counting primed working memory for four items. Or setting a summary representation array using an approximate number system (ANS).

Experiment two: In this one, the researchers teased out the efficacy of the ANS . The two tasks were both counted prior to hiding. This time the search time was measured after the first two were found. In the other, the search time was measure after the third was retrieved. If ANS were used, then they should not distinguish between 3 and 4, which was the result.

Experiment three: The number of objects was increased to 4 and 6 as it should exceed the capability of working memory. It confirmed ANS is likely the component in play.

Experiment four: Same procedures as three but measured like two.

I would love to see this have with more kids and replicated.

Wang, Jinjing & Feigenson, Lisa. (2019). Infants recognize counting as numerically relevant. Developmental Science. 10.1111/desc.12805.