Bad math materials correlate to age level?

Suppose that as age level advances students take more sophisticated math courses.

At the same time, let us assume that these more advanced courses have textbooks that leave out more steps and details and explanations.  They have fewer examples and the examples don’t teach the distinctions.

Then the vendors of this, universities, blame it on the students.  They say that students at the age of those taking the courses are challenged by proofs.

We then get a false correlation between age level and doing poorly at proofs.

In effect, the university materials for teaching advanced courses are poor.

Advanced courses stress proofs.

The universities then claim students are bad at proofs at the age levels they take these advanced courses.

So a spurious correlation is created.

The problem is that as courses focus more on proofs, the materials don’t do it well.  The textbooks at college level need to go into more detail. They should also explain why proof steps are needed.  They should teach that.  This is a foreign concept to them.

If the business is to teach why proof steps are needed, then they don’t do it.

 

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About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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