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I can start with how it was/is done in Russia. Logic was taught in Russian gymnasiums as a separate subject in late 19th century. When Bolsheviks came to power they pulled logic out of the curriculum. Logic was reinstated in Soviet schools in late 1940s only to be abolished again by the end of 1950s when Khruschev took over. AFAIK, there is no separate logic ...


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In UK 40 years ago the calculus was really rigorous first studying limits and series, we did virtually proved all results, except perhaps some integrals but we also had to memorize all formulas as we did not have formula sheet in the exams like they have today in UK A level. In Spain it is still like UK traditional syllabus from back then. I was shocked to ...


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Another way to represent addition and subtraction of two fractions is by subdividing rectangles both horizontally and vertically. Say you want to show how to add $\frac{1}{3}$ and $\frac{2}{5}$. Draw three equal sized rectangles. Subdivide the first in threes with horizontal lines. Subdivide the second rectangle in fifths with vertical lines. The students ...


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I have some personal experience. I taught in a school that has Israeli students whose families had moved to the US. These children had Hebrew as their native language. Hebrew is written right to left. I never saw these students struggle with math because they learned to write from right to left. Furthermore all students in my school studied both Hebrew ...


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Here's an interesting attempt in both text and interactive images. Not a hierarchy but rather a "map." The Map of Mathematics. A project by Quanta Magazine. Text by Kevin Hartnett. Design and visualizations by Kim Albrecht and Jonas Parnow. Feb. 2020. Quanta link.                     ...


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Suggestion: Do not bother having students do calculations with two fractions until they can do a comparable operation with a fraction and a whole number. Example: Before teaching, say, $\frac{3}{2}-\frac{4}{3}=\_\_$, ensure they can answer something like $4 - \frac{1}{5}=\_\_$. Make sure all students can draw that on a number line and with area diagrams. ...


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