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Addition and subtraction are inverse operations. So, it is no surprise primary school teachers often explain multiplication via repeated addition and division via repeated subtraction. Yet such approaches become tricky as soon as fractions and negative numbers get introduced. In this presentation, I reveal how long lost ideas of René Descartes and Isaac Newton can be used with children as young as Grade 2. Play a game. Sing a song! The new ideas you will discover explain multiplication and division, from Naturals to Reals, more deeply and simply than ever before, in ways currently missing from western F–8 curriculums.—In 1968 at age 7 in Grade 2, Jonathan Crabtree noticed the definition of multiplication taught for centuries made no sense. Undeterred by failure, he explored hundreds of original source mathematics books and manuscripts spanning 16 languages. Strangely, Euclid’s definition of multiplication, broken upon translation into English in 1570, was never fixed! Thus, the writings of brilliant mathematicians were ignored and the foundations of mathematics education in the West are worse today than in ancient India and China. Having hunted for the lost logic of mathematical minds for decades, Jonathan’s new researchbased ideas make mathematics simpler than ever before.
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