Negative numbers are closely related to the idea of symmetry. Students use their perception of visual symmetry to help them understand the abstract symmetry of integers along the number line.
Using symmetry appears to help not just in teaching children negative numbers, but in improving their ability to solve higher-level math problems they haven’t seen before. In studies, participants were likely to incorporate symmetry as an almost automatic part of their thinking. That’s important because many skills – such as decoding words in reading – are more effective when they become instantaneous and reflexive.
The biggest surprise was on what educational researchers call “generativity” – the tendency of kids to apply the ideas of symmetry on their own to problems they haven’t encountered before. They did surprisingly well with word problems using spatial positions, negative fractions, and introductory algebra.
So as it turned out, students who learned to rely on symmetry didn’t simply do better than other students on the material they had just been taught. They also did better on math topics that they hadn’t yet studied.
Research has also shown that the more parents of kindergarteners do math related activities with their children – such as board and card games – the better their math performance in 1st and 2nd grade. The good news is that math skills are learned through practice, and math knowledge is gained through experience. Playing a game makes that process fun and easy. The best way for kids to learn anything is through play.