Most of the discussion on Chapter 4 seemed to center around the goals for elementary and secondary school mathematics. So, here is the view expressed in Everybody Counts. See how it compares with your own:
Elementary School: "ELEMENTARY SCHOOL IS WHERE MOST CHILDREN LEARN THE MATHEMATICAL SKILLS NEEDED FOR DAILY LIFE. Formerly, shopkeeper arithmetic was an adequate objective since, for most people, mathematics in daily life required little more than arithmetic. This is no longer true. Calculators now do most of the arithmetic needed for daily life, while a technologically dominated society requires that everyone have a good grasp of chance, of reasoning, of form, and of pattern. WHILE THE GOAL OF ELEMENTARY EDUCATION HAS NOT CHANGED, THE MATHEMATICAL OBJECTIVES APPROPRIATE TO THIS GOAL ARE VERY DIFFERENT NOW FROM WHAT THEY WERE HALF A CENTURY AGO. THE MAJOR OBJECTIVE OF ELEMENTARY SCHOOL MATHEMATICS SHOULD BE TO DEVELOP NUMBER SENSE." [Caps are mine. The reader might be interested to go on and see the author's explication of this objective]
Secondary School: "Secondary education is where students begin to learn the mathematics they will need for careers as well as the mathematics required for effective citizenship. Whereas, traditionally, secondary school has been characterized by the introduction of algebra as an extension of arithmetic, contemporary society requires much greater breadth from secondary school mathematics. THE FOCUS OF THE SECONDARY SCHOOL CURRICULUM REMAINS--AS IT SHOULD--ON THE TRANSITION FROM CONCRETE TO CONCEPTUAL MATHEMATICS. As students' understanding moves from numbers to variables, from description to proof, from special cases to general equations, they learn the power of mathematical symbols. In a very real sense, THE MAJOR OBJECTIVE OF SECONDARY SCHOOL MATHEMATICS IS TO DEVELOP SYMBOL SENSE." [Again, caps are mine]
Finally, although I did not ask a similar question about college mathematics, there is a fairly lengthy section on that topic. Among other things the author concludes: "IF IT DOES NOTHING ELSE, UNDERGRADUATE MATHEMATICS SHOULD HELP STUDENTS DEVELOP FUNCTION SENSE--A FAMILIARITY WITH EXPRESSING RELATIONS AMONG VARIABLES."
Thus, what we have are: 1. Number sense, 2. Symbol sense, and 3. Function sense
I will post Chapter Five questions on Monday.
Rob Ward/Western Washington U/Bellingham, WA 98225 firstname.lastname@example.org