Not much to cheer about, it seems. Math coaches, technology, interdisciplinary studies.... and Project Lead the Way:
Another crowd pleasing testimony came from Dr. Wanda Talley Staggers, Dean of Manufacturing and Engineering, Anderson School District Five, Anderson, South Carolina. She is involved in a program called "Project Lead the Way™". Pardon my cynicism but it's hard for me to not notice the trademark symbol after the title. This program provides pre-engineering type classes in middle and high school that can only be taught by teachers who have been certified by this trademarked program trains such teachers, and testified that "After six years of training high school teachers during the Project Lead The Way™ Summer Training Institutes across the nation, I have heard overwhelmingly from teachers that they come away from the experience with a rejuvenated interest in teaching."
Maybe so, but the key is whether the students in Project-Lead-the Way™ courses will learn any math or simply be entertained.The program is based on the premise that students don't take a lot of math because it's too removed from the real world.The solution? Hands-on project-based courses that involve the students.In order to take such classes, however, they must be enrolled in regular math classes—thus a carrot and stick approach. The program has not been field-tested or validated, and is too young to have data showing whether this strategy is likely to work.Plus problem-based learning, tends to be rather discovery-heavy despite teachers' best and stated intentions that they use a "balanced" approach—the type of balance where someone's finger is on the scale.
Chairman Miller (D-CA) saw the value of this type of program and made a leap from math connecting to applications of math, to math connecting with everything.He rhapsodized about a school he saw in Oregon that became a math academy through an interdisciplinary approach.All courses were interrelated—students had to understand the mathematics of history: distances between cities, depth of the oceans.
I ran that one by Ed, a person who is, by profession, an actual historian as opposed to a Congressman. Paraphrasing: Ed says that measuring the distance between cities in a history course defeats the purpose of history because throughout most of history distance is relative to technology. For example, the distance from Marseilles to Alexandria is 1500 miles; the distance between Marseilles and Paris is 400 miles. But in the ancient world in the Middle Ages, Marseilles was for all intents and purposes much closer to Alexandria because of the ease of shipping in the Mediterranean and also because, culturally, until fairly recently the Mediterranean ports had more in common with each other than Marseilles did with Paris. Marseilles wasn't integrated into the French kingdom until the late Middle Ages. There were no decent roads from the Mediterranean parts of France to Paris. It was an incredibly arduous trip. But it was relatively easy to get from Marseilles to Egypt. The Mediterranean Sea was protected from storms and bad weather, and it was fairly rare for a ship to be lost at sea in the Mediterranean.
Or take the words, "Dr. Livingstone, I presume."
It took 6 months for these words to travel from the center of Africa to the nearest telegraph station. From there, it was only a matter of hours until these words had traveled to all parts of the world linked by telegraph.
To have students in a history course "calculate" the physical distance between cities is to willfully have students overlook the cultural and technological factors that make distance meaningful. It's not just a waste of time, it undermines and subverts historical thinking; It is the opposite of historical thinking. It is harmful.
Does anyone else notice a lack of focus on CONTENT here?
ReplyDeleteJust to reiterate:
Source: National Mathematics Advisory Panel, 2008.
Recommendation: The Panel recommends that school algebra be consistently understood in terms of the Major Topics of School Algebra given in Table 1.
Recommendation: The Major Topics of School Algebra, accompanied by a thorough elucidation of the mathematical connections among these topics, should be the focus of Algebra I and Algebra II standards in state curriculum frameworks, in Algebra I and Algebra II courses, in textbooks for these two levels of Algebra whether for integrated curricula or otherwise, and in end-of-course assessments of these two levels of Algebra.
The Panel also recommends use of the Major Topics of School Algebra in revisions of mathematics standards at the high school level in state curriculum frameworks, in high school textbooks organized by an integrated approach, and in grade-level state assessments using an integrated approach at the high school, by Grade 11 at the latest.
Table 1: The Major Topics of School Algebra
Symbols and Expressions
Polynomial expressions
Rational expressions
Arithmetic and finite geometric series
Linear Equations
Real numbers as points on the number line
Linear equations and their graphs
Solving problems with linear equations
Linear inequalities and their graphs
Graphing and solving systems of simultaneous linear equations
Quadratic Equations
Factors and factoring of quadratic polynomials with integer coefficients
Completing the square in quadratic expressions
Quadratic formula and factoring of general quadratic polynomials
Using the quadratic formula to solve equations
Functions
Linear functions
Quadratic functions—word problems involving quadratic functions
Graphs of quadratic functions and completing the square
Polynomial functions (including graphs of basic functions)
Simple nonlinear functions (e.g., square and cube root functions; absolute value; rational functions; step functions)
Rational exponents, radical expressions, and exponential functions
Logarithmic functions
Trigonometric functions
Fitting simple mathematical models to data
Algebra of Polynomials
Roots and factorization of polynomials
Complex numbers and operations
Fundamental theorem of algebra
Binomial coefficients (and Pascal’s Triangle)
Mathematical induction and the binomial theorem
Combinatorics and Finite Probability
Combinations and permutations, as applications of the binomial theorem and Pascal’s Triangle
PLEASE NOTE: When the word "connections" is used, the report explicitly states "connections among these topics"
The focus is on CONTENT!
To have students in a history course "calculate" the physical distance between cities is to willfully have students overlook the cultural and technological factors that make distance meaningful.
ReplyDeleteI think it depends on exactly how calculating the physical distance between cities is done. For example, if they included the calculations of time to get between cities, then that's the basis for Ed's discussion of the time it takes or took to get between cities.
And I find that famous graph of Napolean's invasion of and retreat from Russia fascinating, even though that uses distances.
"PLTW approach adds rigor to traditional technical programs and relevance to traditional academics."
ReplyDeleteWhat they are saying is that more is better. Why not just extend the school day?
FAQ question and answer:
"Why does PLTW have a math requirement for students enrolled in its program?"
"By taking the highest level of college preparatory mathematics they are capable of successfully handling in all four years of high school, students will develop a solid background in math skills and concepts, will be prepared to take each level of the PLTW program, be prepared to succeed in the entry level mathematics course in college, avoid regression between high school and college by taking math each year of high school, and will have a solid background for engineering/technology."
OK, so PLTW is really "more" on top of college prep math, which they define as the calculus track.
"...will be prepared to take each level of the PLTW program,..."
Traditional calculus track math courses PREPARE kids to take each level of PLTW.
They just now have to get the kids on that track in the first place. The rich get richer, the poor get poorer. It makes me wonder whether many really understand how PLTW works.
I can imagine students who are excited about their PLTW classes, but can't understand why they need to put the work into their regular math classes. Ergo, the FAQ question above. They miss the fact that hands-on PLTW-type projects are about "technology", not engineering. Many apparently don't know how much math (above calculus) is required for engineering schools. Engineering schools are not glorified vocational schools. Engineers don't just test structures (popsicle stick or otherwise) with guess and check. They apply theory and calculus to determine moments of inertia, shear forces, and bending moments.
In any case, I prefer this separate approach to real-world applications, especially if the PLTW-type add-on is optional. If this is part of the regular classwork, then content and skills get watered down. Neither can be done well. That doesn't mean that I think tht PLTW is a good program. It just means that the student can quit at any time without any issues.
Thanks for posting this. FYI, the article can be found here.
ReplyDeleteIt has always baffled me that people feel the need to 'connect' math to some arbitrary context when the history of mathematics is its own context. Every single discovery in mathematics was born of some real world stress from our past.
ReplyDeleteMathematics is arguably human kind's greatest achievement. It is wrapped into our language, our history, our culture, and virtually every other discovery we have ever made. Yet instead of teaching these stories as part of this tapestry we teach it like it was dropped on us by space aliens.
I sat through a discussion once where a consultant was berating us for not using the pictures in the math book to advantage. Yikes!
Those pictures aren't the context that would make the lesson come alive. But a story about the first caveman struggling with how to divide up his catch into parts less than a whole, now that might make a compelling context.