What are your views on whether mathematics should be revised and why?
Mathematics is built into the universe--it doesn't change. The way we teach it, however, is subject to all sorts of silly fads. I like the Japanese approach of letting students struggle with problems for a while before helping them evaluate solutions. American teachers tend to give formulae so students can pass end-of-grade tests, but don't mak students do the hard work of thinking through problems--or, in other districts, students are given exercises in "thinking skills" even when they haven't been made to memorize math facts that would give them something to think about.
We need to study the best math teachers in the world, then encourage all math teachers to teach that way.
I don't really know what you could possibly mean by this. Mathematics is not the type of thing that people get to just come up with, you know. So, it can't be "revised" in the way that laws or books can be revised. The question to me seems similar to asking if you think gravity should be revised, or perhaps purple.
Maybe more clarity in how your question is put would help people to answer it better.
I think that revision of mathematics should be avoided but my be occosionally necessary.
An example of what should be avoided is the intuitionism of the early twentieth century. Basically, intuitionists argued that the law of the excluded middle (LEM) should be denied. LEM says that either P or ~P is true for any proposition. Obviously the denial of this principle would mean massive revisionism in logic and mathematics.
On the other hand, in August I went to a lecture given by a well-known (in set-theory circles) professor of mathematics at CUNY and NYU, who argued that Cantor's continuum hypothesis (CH), and its generalization, the aptly named generalized continuum hypothesis (GCH) would never be proved true or false because there has been too much research into extensions of set-theory (ZFC) in which GCH holds and others in which it doesn't. (CH and GCH are independent of the axioms of ZFC)
I would hold that there is the possibility of a new axiom, probably an large cardinal axiom or stronger axiom of infinity, being added to the the traditional axioms and be accepted as true, that decided GCH one way or the other.
This is I suppose, because I am a truth value realist, which is to say that I believe that all coherent mathematical statements have an objective truth value, independent of the extent of the current research.
My belief is that mathematics does not necessarily need revising; however, what does need revising is who is teaching it and how it is being taught. It was my experience while in the school system, that there are many teachers in the math classrooms who are clueless about math, clueless how to teach it, and clueless as to how to get their students to understand mathematics.
I would love to see mathematics specialized or departmentalized at every grade level to include Kindergarten. We set teachers and students up for failure when we place teachers in classrooms to teach subjects that they frankly don't understand themselves. Teachers should not be teaching subjects that they do not know or understand. It's not fair to them or their students.
I was very blessed upon transitioning from middle school to elementary school. My first year of being in elementary school was quite frankly overwhelming. It was mind boggling to me how teachers were expected to teach the same students all subjects all day five days a week. I introduced the middle school concept of specialized instruction to my other 2 team members who eagerly embraced it and so did my principal.
What made it work so beautifully for our team was that one teacher was specialized in Reading/Language Arts, the other was specialized in Science and Social Studies, and I was specialized in Mathematics. It worked like a well-oiled machine!
The bottom line is teachers struggle with teaching subjects for which they are not passionate or knowledgeable. I know some of you are reading this thinking how can a teacher not know all subjects well. The fact of the matter is, when teachers are enrolled in college to earn their teaching certifications, they are not taught content. They are taught how to teach content and given strategies, pedagogies, theories, philosophies, etc of teaching.
So my vote is, instead of revising mathematics; let's specialize the instruction and put passionate, talented, knowledgeable math teachers in classrooms from Kindergarten - 12th grades.
Haunty asked a very pertinent and relevant question considering students performances collectively in the mathematics classrooms and on standardized tests across the country today. It is my desire to see mathematics specialized or departmentalized at every grade level including Kindergarten. read more
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