Within the context of the core curriculum, "basic literacy" tops off at about "algebra 1/2" ... functional intelligence about simple formulas and their equatings. When that much is fully common-sensible too students, they are well prepared to survive the rest of the (K-calculus) core curriculum ... even if the rest makes little mathematical sense to them.
But from HS algebra through calculus, the rate of dropout from curricular mathematics is staggering. The primary cause is that the curricular presentations largely fail to make the content mathematically sensible to the students, themselves ... which is enough to cause hoards of strongly mathematical minds to shy away from math-dependent studies.
Bob's query has two answers, depending on how his question is interpreted. For one, make the entire curriculum fully common sensible to all normal students. It cannot be done by traditional modes of "curriculum reforms" ... which have been quite disastrous. It is imperative to get serious about clinical research in how humans most naturally learn mathematics as common sense. Unfortunately, that "solution" presently seems to be decades away.
Meanwhile, it is possible for individual teachers, parents, and students to progressively learn the art of discerning and invoking the common-sensibility of the same mathematical topics that are attended in the core curriculum. It is an art that a very meager minority of students and teachers seem to learn, on their own. The rest must be given some steerageway and guidance. That is one function of clinical mathematics instruction that is not shared by instruction of "classes" of students or by traditional tutoring.
The first such step (for the student or the teacher) is to acquire a better-than-scholastic perspective about the very nature of mathematical knowledge and of personal mathematical growth. The best way to achieve that is to try to guide someone else to learn some new mathematical topic ... without actually telling that mathematics. You might not like "discovery" as a way of teaching ... but it surely is the best way to find out about when mathematics is common-sensible and when it is not.
I wish I knew of a knowledgeable monograph on "How You Can Grasp the Common Sense That Underlies the Mathematics Curriculum."
From: Robert Hansen Sent: Thursday, August 30, 2012 7:54 AM To: Clyde Greeno @ MALEI Cc: email@example.com ; Richard Hake Subject: Re: Martin Bickman On The Needless War Between Traditionalists And Progressives
And for the unfortunate human beings that go much further than basic literacy, what do you suggest?
On Aug 30, 2012, at 3:11 AM, "Clyde Greeno @ MALEI" <firstname.lastname@example.org> wrote:
They compel us to re-define "the basics" so as to focus on making "basic-literacy mathematics" fully common-sensible to all normal human beings.