Category Archives: Algebra on Rational Numbers

People give up trying to understand structure with real numbers

Infinite decimals make people give up thinking.  They don’t believe they can understand an infinite decimal, especially one that does not repeat.  Therefore, K-8 should avoid reals as much as possible. It is natural to think you can understand finite … Continue reading

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School Goals: Naturals Perfect, Rationals Well, Reals wing it

For teaching students from K-?, we should have the following emphasis. Natural Numbers almost perfect.  This includes mathematical induction and proofs. Limitations of natural numbers almost perfect. Rational numbers well.  This includes ordered pairs. Limitations of rational numbers well. Real … Continue reading

Posted in Algebra functions restricted to naturals, Algebra functions restricted to rationals, Functions and ordered pairs, Real numbers, Real numbers difficulties | Leave a comment

Teach Explicitly and Distinctly Algebra on Naturals and Rationals

Algebra is typically taught using a letter x with no distinction as to whether x is natural, rational or real.   Keith Devlin illustrates this thinking by advocating teaching the field axioms instead of the progression from naturals to rationals to … Continue reading

Posted in Algebra functions restricted to naturals, Algebra functions restricted to rationals, Algebra on Natural Numbers., Algebra on Rational Numbers, Algebraic slope and rational numbers, Functions and ordered pairs, Object Oriented Rational Number, Slope concept on rationals, Slope Concepts | Leave a comment