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Algebra As A Gateway Subject
Spock the Baptist writes: "The Washington Post started a two article series Sunday, and Monday August 18 and 19 2002. The articles deal with something that the math, engineering, and physics faculties at colleges, and universities have long known. Algebra is a 'gateway subject' for math, science, and technology, and secondary schools in general are not doing a good job teaching algebra."
The way the indignant parents act about this is the worst of all. If it were up to me, a probability and statistics course on top of trig (including spherical trig) and a C programming course (but not calculus) would be mandatory to graduate high school. The way parents get all huffy about their kids homework, taking their own ignorance personally I suspect, it is unlikely to come to pass.
Are there any other states where it is possible to graduate high school without algebra?
Apparently English is taught *incorrectly* as well.
Taught wrong. Jesus.
yes, and al'Khwarizmi is the origin of our word 'algorithm' via french algorisme
In an effort to overcome our country's mathematics woes, the National Council of Teachers of Mathematics (NCTM) put together a monumental group of standards and principles revolutionizing the way that Mathematics is taught at the High School level.
The NCTM-based curriculum is different. Some teachers and college professors believe it to be weak on mathematics because it doesn't look like the curriculum they grew up with. Traditional curriculum (teacher does a couple examples, students practice solving 30+ problems similar) has not been good enough though.
The new curriculum, based on psychology and education research from the latter half of this century, focuses on understanding in addition to the traditional acquisition of skills. It is mathematics rich with connections to other areas, and deep in content. Students start in 6th grade learning basic algebraic concepts, number theory, geometry, probability, etc. Obviously mastery of all these concepts does not happen in a single year. In fact, the curriculum spirals around the same concepts, building new understanding and making new connections with each pass so that, ideally, when students graduate their skills AND understanding will be better than that of previous generations.
Sometimes this math is called "Fuzzy Math" or the "New 'New Math'". Some educators, professionals, parents, and children feel the curriculum is weak on "real math." My concerns were similar before I started teaching the Interactive Mathematics Program (IMP).
Between 9th and 10th grade, students master basic algebra, learn the basics of the trig functions, work with standard deviation and the chi-squared measure, build and solve and maximum profit linear programming (something most math majors don't do until grad school), derive and prove the pythagorean theorem, work with exponential and logarithmic functions, do all sorts of number-theory related problems, and so much more. Still IMP and other standards-based curricula have their problems. In my opinion, although there's plenty of problem-solving and understanding-based activities, there needs to be more traditional skill work. I supplement my lessons with such work where appropriate. Any teacher worth their stuff would do the same. Additionally, the curricula is very wordy, which is fine for middle-class suburbanites, but when you're teaching in a city where 25% of the students don't speak english as their first language, and 75% are in poverty (typically correlated with smaller vocab and weaker reading/writing skills), a wordy curriculum is just one more thing making it tough to teach/learn math. In sum, there's a lot of hostility from the non-math-teacher world toward this new curriculum because it's so different. But, with the abismal performance of American mathematics when compared internationally, it can't be business as usual. The curriculum is already working well in the classes I've seen. And the research points to positive improvements after curriculum implementation (no large study has been completed as far as I'm aware). NCTM-based curricula is no panacea, but it's a definite improvement over the more archaic traditional curricula.
"Blame it on the other guy" sounds snappy and dismissive, but actually it misrepresents the situation.
I am resposible, at the beginning of the year, for assessing student proficiency and providing remedies for those students who seem to struggle with basics. Coming new into a distict, however, makes that assessment more difficult, because I don't even know where to begin looking for student proficiency with past material. I continue to be responsible, through the year, for doing whatever somersaults I need to do to make sure that all of my students are acheiving.
So there is certainly no buck passing here...
That said, three practical facts apply which impact what I am able to do in the year:
1. I am a finite man with a finite amount of time.
2. My average Algebra I class size is 30, and I have 45 minute periods.
3. I inherent the best and the worst teachings that my students had before me.
Thus, it is not "passing the buck" to prescribe curriculum changes in the grades after mine. The proficiency that my students have 1st day of school will impact the whole year.
One of the things that seriously separates humans from other animals is our ability to think, and to think abstractly. Too often the comments are made about algebra- "I'll never use this..." "What is this good for?"
Even if algebra problems per se never occur in whatever "real life" people end up having, the ability to think quantitatively is essential for an reasonable person. Thinking more abstractly about problems of many kinds is essential- for developing efficient code, for having a reasonable business plan, for managing one's person finances, for voting in a responsible way, and basically for being a productive member of society. The evidence for poor critical/mathematical thinking is everywhere- people falling for Ponzi schemes, short-sided economic policy, unwise credit-card debt, bad laws, ridiculous jury decisions, and the list goes on. The proper perspective about mathematical reasoning is that it is fundamental for most productive people, and essential for all citizens.
Unfortunately, this perspective is usually not instilled by our current generation of underpaid, frequently under-qualified (more than half of the math and science teachers in CA have "emergency certification", which can be extended indefinitely since there is no adequate supply of properly trained and willing math and science teachers.) Instead, students are often exposed to math teachers, who, to be honest, don't actually like math or understand its central role as a foundation for science and modern reasoning. Kids are smart- if a teacher doesn't like math and is just going through the motions, they pick up on that. And given the sympathy that students get from parents, teachers, etc for the horror of "word problems" it isn't a surprise that mathematical reasoning skills are a consistent weak point of students at all levels in the US.
Everyone agrees that more resources should be directed at education, but people have been agreeing on that for at least 30 years with much of the same problems enduring. Good education is more expensive an investment than many decision-making bodies are willing to undertake, and that shows in the wide disparity in education between the "haves" and the "have nots". Until there is a significant change in how much energy and money people are willing to invest in education, it seems that these phenomena will continue.
It's psychosomatic. You need a lobotomy. I'll get a saw.
You have never read Dewey.
Dewey's first insight was to argue that learning by rote was a bad -- poor -- inadequate -- way to learn.
Your description of Dewey's thinking is exactly the opposite of what he said and wrote.
Interestingly enough, our word Algebra comes from the book Hisab al-jabr w'al-muqabala written by a Middle-Eastern man named Abu Abd-Allah ibn Musa al'Khwarizmi around 830.
And "Algorithm" came from his name "al-khwarizmi"
alkwarizmi -> algorism -> algoritm
another onteresting fact is, he live in iraq, where encryption algorithm are forbidden to enter their country...
(US export law)
-- Hasbullah bin Pit (sebol)
Let me quote from this page
You can find Dewey's book Democracy and Education at this page.
The problem in our system is not that Dewey's arguments prevailed, it's that they did not.
Hopelessly pedantic since 1963.
"It's like asking why Beethoven's Ninth Symphony is beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."
Paul Erdos, Hungarian mathematician