services on the market would be at a premium, with prices high
enough to exclude at least the lowest-income strata of society;
if the less affluent could afford some market-based education,
it would be of a substantially inferior quality to that received
by wealthier consumers of educational services; and
lack of a universal curriculum and standardized criteria of
achievement would render the market incapable of providing the
equality of opportunity that public education, however unsatisfactorily,
at least aims in principle to ensure.
Argument 1: Affordability
§111.35. Precalculus (One-Half to One Credit).
- Knowledge and skills.
- The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions. The student is expected to:
- describe parent functions symbolically and graphically, including f(x) = xn, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = ex, f(x) = |x|, f(x) = ax, f(x) = sin x, f(x) = arcsin x, etc.;
- determine the domain and range of functions using graphs, tables, and symbols;
- describe symmetry of graphs of even and odd functions;
- recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and
- investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.
Argument 2: Quality
Argument 3: Opportunity
along the same antiquated lines of a mere transmission of knowledge, there is little to be hoped from it in the bettering of man's future. For what is the use of transmitting knowledge if the individual's total development lags behind?
One is mentally an individual only as he has his own purpose and problem, and does his own thinking. The phrase "think for oneself" is a pleonasm. Unless one does it for oneself, it isn't thinking. Only by a pupil's own observations, reflections, framing and testing of suggestions can what he already knows be amplified and rectified. Thinking is as much an individual matter as is the digestion of food. [Moreover], there are variations of point of view, of appeal of objects, and of mode of attack, from person to person. When these variations are suppressed in the alleged interests of uniformity, and an attempt is made to have a single mold of method of study and recitation, mental confusion and artificiality inevitably result. Originality is gradually destroyed, confidence in one's own quality of mental operation is undermined, and a docile subjection to the opinion of others is inculcated, or else ideas run wild. (p. 311–12)