On Mon, Oct 8, 2012 at 1:23 AM, Robert Hansen <firstname.lastname@example.org> wrote: > > On Oct 7, 2012, at 5:16 PM, Paul Tanner <email@example.com> wrote: > > If "the standards" means the minimum requirements for passing on to > the next grade and then graduating from high school, then the claim > that "they lowered the standards and negated the strides of the > previous generations" is a baldfaced falsity. > > There used to be no exit exam for any grade, period. Now there are for > many grades, and for high school graduation they get harder as time > goes on in that each incarnation covers more material or the > combination of end-of-course exams covers more material. (The first > high school exit exam in FL in the 1980s was just arithmetic, no > algebra at all. Now there are exit exams on every math course that > they have to have to take to graduate, including algebra and > geometry.) > > > This is a ridiculous statement. ... > Just having students take algebra and an exit exam means NOTHING if the > standards are crap.
Utter, utter, insanity.
Because you are tacitly claiming the utter insanity that those who never took Algebra I or Geometry 40 years ago would have been able to pass the Algebra I and Geometry exit exams today without ever having studied these subjects - you are tacitly claiming the insanity that people who never study a subject would be able to pass comprehensive tests on that subject without ever studying it.
Those that never took algebra would be like my brother and a whole bunch more people I know who never took algebra back then - they would not have been able to answer even a single algebra question.
Utter, utter, insanity.
> There wasn't exit exams before because there was no need > for them. >
The first exit exams in FL were in the early 1980s. The first exit exams had NO algebra on them. It was like that for many years before they started putting algebra on them and only after they required everyone to take and pass Algebra I to graduate. Now it's Geometry and now soon even Algebra II.
And what about those who never took algebra, they would be able to pass today's comprehensive algebra tests without ever studying algebra? I repeat: They that never took algebra would be like my brother and a whole bunch more people I know who never took algebra back then - they would not have been able to answer even a single algebra question. You tacitly put forth this utter insanity that they would have been able to pass today's comprehensive algebra tests without ever having studying algebra.
> > And this: The math classes in the middle school levels and the algebra > classes up through Algebra II are much harder than they used to be in > that they cover more advanced material. I already proved in past posts > this fact by comparing the content of Algebra I and Algebra II texts > from today to 40 years ago. >> > > Which texts?
Compare the older texts to today's texts. It's pure fact.
You really need to go to the library or even just ask people who have been teaching high school all through the last part of the 20th century into the first part of the 21st.
Consider the Harcourt Brace Jovanovich Algebra 1 and Algebra II textbooks published back in the 1980s. These textbooks were exactly as I remember the textbooks used by my high school years in the 1970s. The rate of algebraic material coverage of the Algebra I and Algebra II sequence was so slow, the quadratic formula was introduced only towards the end of Algebra II. There was no mention at all in the Algebra II textbook of these things at the precalculus level needed as prerequisites for calculus, which would include advanced treatments of polynomial functions (and including such topics as the binomial theorem) and would include the transcendental functions (exponential functions, logarithmic functions, trigonometric functions). Back then in the 1970s, the community college for our whole county required a precalculus class at the community college as a prerequisite for calculus because of the fact that Algebra II as taught in the high schools throughout the county did not contain this precalculus level material that was needed for calculus and because most who went into the college did not take a precalculus-level math course in high school since it was not offered most of the time in most of the high schools back then in that county.
Again: There is absolutely no comparison between the topics covered in that Algebra 2 textbook in early 1970s in my old high school and that Harcourt Brace Jovanovich 1980s Algebra 2 textbook and the topics covered in, say, "Algebra 2: Applications, Equations, Graphs"; Larson, Boswell, Kanold, Stiff; McDougal Littell:
Real Numbers and Number Operations Algebraic Expressions and Models Solving Linear Equations Rewriting Equations and Formulas Problem Solving Using Algebraic Models Solving Linear Inequalities Solving Absolute Value Equations and Inequalities Functions and Their Graphs Slope and Rate of Change Quick Graphs of Linear Equations Writing Equations of Lines Correlation and Best-Fitting Lines Linear Inequalities in Two Variables Piecewise and Absolute Value Function Solving Linear Systems by Graphing or Algebraically Graphing and Solving Systems of Linear Inequalities Linear Programming Graphing Linear Equations in Three Variables Solving Systems of Linear Equations in Three Variables Matrix Operations and Multiplying Matrices Determinants and Cramer's Rule Identity and Inverse Matrices Solving Systems of Equations Using Inverse Matricespe Graphing Quadratic Functions Solving Quadratic Equations by Factoring and by Finding Square Roots Complex Numbers Completing the Square The Quadratic Formula and the Discriminant Graphing and Solving Quadratic Inequalities Modeling with Quadratic Functions Using Properties of Exponents Evaluating and Graphing Polynomial Functions Adding, Subtracting and Multiplying Polynomials Factoring and Solving Polynomial Equations The Remainder and Factor Theorems Finding Rational Zeros Using the Fundamental Theorem of Algebra Analyzing Graphs of Polynomial Functions Modeling with Polynomial Functions nth Roots and Rational Exponents Properties of Rational Exponents Power Functions and Function Operations Inverse Functions Graphing Square Root and Cube Root Functions Solving Radical Equations Statistics and Statistical Graphs Exponential Growth and Decay The Number e Logarithmic Functions Properties of Logarithms Solving Exponential and Logarithmic Equations Modeling with Exponential and Power Functions Logistic Growth Functions Inverse and Joint Variation Graphing Simple and General Rational Functions Multiplying and Dividing Rational Expressions Addition, Subtraction, and Complex Fractions Solving Rational Equations The Distance and Midpoint Formulas Parabolas, Circles, Ellipses and Hyperbolas Graphing and Classifying Conics Solving Quadratic Systems Introduction to Sequences and Series Arithmetic and Geometric Sequences and Series Infinite Geometric Series Recursive Rules for Sequences The Fundamental Counting Principle and Permutations Combinations and the Binomial Theorem Introduction to Probability and Probability of Compound Events Probability of Independent and Dependent Events Binomial and Normal Distributions Right Triangle Trigonometry General Angles and Radian Measure Trigonometric Functions of Any Angle Inverse Trigonometric Functions The Law of Sines The Law of Cosines Parametric Equations and Projectile Motion Graphing Sine, Cosine, and Tangent Functions Translations and Reflections of Trigonometric Graphs Verifying Trigonometric Identities Solving Trigonometric Equations Modeling with Trigonometric Functions Using Sum and Difference Formulas Using Double-Angle and Half-Angle Formulas
The comparison is so overwhelming between now and 3 or 4 decades ago in so many schools districts, Algebra I and Algebra II now covers so vastly more material than 3 and 4 decades ago in so many school districts, it is pure fraud to claim that minimum standards are no higher today than they were 3 or 4 decades ago in terms of what these courses cover in so many school districts - just as it is pure fraud to claim that the minimum standards required for high school graduation today are no higher than what they were 3 or 4 decades ago in so many school districts.
And not only that:
The percentage of the population taking advanced math has exploded compared to 40 years ago. We've been through this before, you claiming that more people took calculus back then when I proved from even your citations that the total taking calculus now is three times greater than it was.
Example: Many high schools all over the country back then were like my high school then - and mine was a relatively large one, not far from a thousand for just the three grades starting at 10th: No calculus courses, some years not even enough students to even have just pre-calculus after that low level Algebra II I spoke of. In my senior year, there would have been only about a half dozen students that were planning to take that precalculus class, and since that was not enough students, it was not offered.
>> And also this: The minimum college math requirements to get certified > to teach math at either the middle school or high school levels are >> vastly higher than they used to be 40 years ago. > > > Again, this means nothing. You are telling us the POLITICAL requirements. I > am talking about the actual requirements. The requirements that a parent > like me looks for. >
You simply do not know what you are talking about. I guess you would rather go back to the "good old days" 40 years ago when in FL the highest level course required to get certified to teach high school was just Calc II - when now the minimum is that we have to take not just Calc III but several courses post-Calc III.
What you say is so insanely dumb, such an incredible complete denial of fact after fact after fact - everything in my prior post http://mathforum.org/kb/message.jspa?messageID=7902143 is just plain fact - as to the large increase in the MINIMUM standards imposed on the whole population of students and teachers, one really wonders.