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Experiments by University of Chicago psychologists with deaf people in Nicaragua who learned "homesigns" rather than formal sign language, could not count beyond three. In contrast, people learning sign language learn number words and number concept and understand large numbers. The findings ""suggest that language is an important player in number acquisition." The research is reported in PNAS: http://www.pnas.org/content/early/2011/01/31/1015975108.abstract

"turning molecules into calculators"

This website is K-12 with algebra tiles, fractions and interactive games on the computer. It also has a "grapher" that graphs up to 3 functions. I use it to find x and y-intercepts of lines or parabolas

Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "

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Great directory of tutorial textbook style lessons to point your learners to.

It is great that today children can learn math while playing games.

I was skeptical about playing games, but since I'm a mom of two, I have to choose proper games for my children. I like ABCya https://abcya.pissedconsumer.com/review.html. My kids can learn math and have fun at the same time. What can be better?