Textbooks often provide rigorous and formal explanations for complex mathematical concepts. This is unhelpful to the average student.
Textbooks should appeal to the human ability to draw analogies, and build upon simplicity.
Instead of stating concepts, rules, axioms and theorems, they should provide simple intuitive explanations that can help students visualise abstract topics, such as through the lens of geometry.
For instance, calculus seems daunting and abstract, but actually can be explained simply and in an interesting and useful way.
Of course, not every topic can be taught in an intuitive manner.
However, embracing intuition-centric explanations may help lessen the complexity and allow students to appreciate the sublime beauty of the subject.
Conrad Soon Kang Le, 16
Secondary 4 student