The Conservative Case for Common Core

[tafan]

The first thing we should teach students in math is set theory. Everything else is dependent on that. Plus, set theory is great at teaching logic and reasoning. Furthermore, it sets students up for a rigorous definition of what math is. In K-12, kids are taught how to add and multiply but aren’t taught why they are allowed to do that with real numbers. What is addition? What is multiplication? Furthermore, it bothers me kids are taught subtraction and division when these operations do not really exist and they are not as nice when it comes to laws such as commutativity and the like. Students should not be taught subtraction and division in my opinion.

I have actually had professors who would actually not allow you to use subtraction or division.

They are taught all these laws, such as commutativity, transitivity, etc., but aren’t taught why they apply to the real numbers. Most people don’t have a clue that those laws and operations do not apply to all objects, until they take an upper level math course, such as linear algebra.

You want set theory, then use it your self. Not all mathematics is taught based on the set of natural numbers. Actually, almost no math is taught based on natural numbers.
With the set of integers, or the set of real numbers, subtraction is an operation that most certainly exists and it is just as “nice the laws of communativity and the like”.

Change the domain to real numbers and the same thing applies for division.

Professors not allowing to use subtraction or division? Pray tell: what was the course? A study of Gödel’s incompleteness theorem maybe?

 

[TexCatholic4JMJ]

One very troublesome part of Common Core is the testing. That is where the money is in
this. The teachers then start “teaching to the test”. And, of course, they need to have the
books that teach these methods. By the way, Common Core has its opponents across the
spectrum of ideologues (except maybe communists?!?) not just conservatives.
I have a great deal of respect for Mr. Bennett, but I think he’s wrong on this one.

 

[St_Francis]

One very troublesome part of Common Core is the testing. That is where the money is in
this. The teachers then start “teaching to the test”. And, of course, they need to have the
books that teach these methods. By the way, Common Core has its opponents across the
spectrum of ideologues (except maybe communists?!?) not just conservatives.
I have a great deal of respect for Mr. Bennett, but I think he’s wrong on this one.

This is a very good point, because as I understand it, the SATs are going to be aligned with the CC curricula. This will necessarily lead to private and parochial schools’ changing tgeir curricula to match, because part of the big draw is that the students will get good grades on the SATs and into academically acclaimed colleges, etc.

 

[freeRadical]

You want set theory, then use it your self.

What is your problem?

Not all mathematics is taught based on the set of natural numbers. Actually, almost no math is taught based on natural numbers.

Set theory is the foundation of mathematics. What are the real numbers? They are a set. What are addition and multiplication? They are operations defined on sets. They are both meaningless without the rigorous concepts of sets. Furthermore, set theory is more than just the natural numbers, I don’t know why you brought that up.

A lot of math is taught on the natural numbers. Ever heard of sequences, series, real analysis, etc.?

With the set of integers, or the set of real numbers, subtraction is an operation that most certainly exists and it is just as “nice the laws of communativity and the like”.

No. Only addition and multiplication exist. There is no such thing as subtraction and division. Anyone who works with ordered fields, of which the real numbers are, knows that only addition and multiplication exist.

Change the domain to real numbers and the same thing applies for division.

The real numbers are an ordered field and, as such, the only two operations defined on them are addition and multiplication. So, there is no such thing as division even when you include the real numbers.

Professors not allowing to use subtraction or division? Pray tell: what was the course? A study of Gödel’s incompleteness theorem maybe?

My linear algebra professor didn’t allow it and my real analysis teacher definitely didn’t allow it. They both hated subtraction and division and thought that they shouldn’t be taught.

 

[freeRadical]

You want more proofs: grade 8 requires that all kids be able to prove the Pythagorean Theorem and its converse. This is a step up, not a step down in basic math taught to eight graders. I do not remember any of my eigth grade kids having to prove the Pythagorean Theorem.

The Pythagorean Theorem is a cakewalk to prove.

It is my gut feeling, after having read the math standards is that the common core is an attempt to do what you say is needed. Read the standards and tell me that I am wrong.

You’re wrong.

I have had 2 kids who had completed the first two semesters of Calculus before their first semester of engineering school. Is there calculus in in the high school standards? no. But that does not mean that high schools cannot teach calc I and calc ii.

At a minimum, calculus of a single variable should be required of all students in high school. That, and a class on logic.