Is there a way to classify a math program as classical?

[gandpsmommy]

I'm just curious. I have been thinking a lot about curriculum and about prioritizing subjects, etc. Is there anything that makes a math program more suited to classical education? I know that Miquon math, for instance, uses a rather Montessori approach.

[angela in ohio]

A math program that focuses on the "grammar" of math first (learning facts, basic skills,) I would think.

[dragons in the flower bed]

Is there anything that makes a math program more suited to classical education?

 

Yes, there are two defining criteria (or just one and the other's wrong, but let's not go there, please) --

 

1) Neoclassical and/or WTM hs'ers would say that if a math program focuses on the facts (grammar) in the early years, the relationships (logic) in the middle years, and communicating with or application of math (rhetoric) in the later years, then it's a classical program. I think Logos School publishes a grammar of math program.

 

2)Traditional classical hs'ers would say that if a math program is grounded upon, if not strictly limited to, the wisdom and learning of the ancient Greeks and Romans and their languages. A year spent with Euclid or Pythagoras would be a classical math program. Wildridge publishes two middle school software programs which teach math via music theory and astronomy, just like the ancients did.

[Myrtle]

Yes, there are two defining criteria (or just one and the other's wrong, but let's not go there, please) --

 

1) Neoclassical and/or WTM hs'ers would say that if a math program focuses on the facts (grammar) in the early years, the relationships (logic) in the middle years, and communicating with or application of math (rhetoric) in the later years, then it's a classical program. I think Logos School publishes a grammar of math program.

 

2)Traditional classical hs'ers would say that if a math program is grounded upon, if not strictly limited to, the wisdom and learning of the ancient Greeks and Romans and their languages. A year spent with Euclid or Pythagoras would be a classical math program. Wildridge publishes two middle school software programs which teach math via music theory and astronomy, just like the ancients did.

 

Let me throw this idea out there as another possible interpretation. :) Perhaps the trivium was not about math and historically the mathematical sciences were part of the quadrivium, not the trivium. Although if you want to apply the trivium as "stages" rather than as content areas then it might go something like this:

 

Grammar stage - Basic mastery of the algorithms of arithmetic.

 

Logic stage- Learning why those algorithms work and learning mathematical justification. For example, rather than only applying "invert and multiply" to solve a problem about pies or plumbing, the student in the logic stage studies why this algorithm works the way that it does and can derive it from first principles.

 

Rhetoric stage would build on the student's knowledge of first principles and the student would make original mathematical arguments in support of the truth of a propositions about mathematical objects.

 

The culmination of this in a classical education was in fact synthetic geometry and not anything like Calculus. At the time when classical education and Latin grammar schools were popular the foundations of algebra and calculus had not been discovered (they still relied on Euclidean axioms of equality for justification) and entire fields of math, such as topology, didn't even exist.

 

When mathematicians say that students learn math "heuristically" they mean that the student is not learning the proper mathematical justification for what they are doing. When they use the word "rigor" or "rigorous" to describe a math book they mean that the student is learning the proper mathematical justification that motivates an algorithm. When the rest of us use the word "rigorous" we mean that the program has lots of hard problems.