We learn more by looking for the answer to a question and not finding it than we do from learning the answer itself.
Lloyd AlexanderRead
Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.
Interpretation
What this quote means
Mathematics education requires a balance of problem-solving, technical skill, and abstract understanding.
In this quote, Richard Askey emphasizes the importance of a well-rounded mathematics education, comparing it to a stable stool that requires three legs. These components include engaging problems that encourage deeper thinking, the necessary technical skills to tackle complex tasks, and an appreciation of the abstract elements and proofs inherent in mathematics. He stresses that these elements should be developed progressively through a structured program, ensuring that students build a strong foundation in math over time.
Themes
MathematicsEducationProblem-SolvingTechnical SkillsAbstract Thinking
In practice
Example use cases
In a classroom setting to emphasize the need for a comprehensive math curriculum.
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