To be honest, this introduction, rather than inspiring me to want to read the rest of the document, makes me skeptical of the whole documents value. This is because it opens with a plethora of unsupported assertions. For instance:
To compete successfully in the worldwide economy, today’s students must have a high degree of comprehension in mathematics.
Who really believes that this is true? I would agree that being good at math is pretty helpful to being successful - especially in certain fields. Still, we all know that lots of people are successful without having any skill in math at all. So after reading just a paragraph or two, my nonsense filters are already up at full strength.
Here's another assertion that puts me off:
Proficiency in most of mathematics is not an innate characteristic; it is achieved through persistence, effort, and practice on the part of students and rigorous and effective instruction on the part of teachers.
Anyone who has taught math for more than a week knows that some students find this stuff easy, and some find it almost impossible. Maybe the students who have a really hard time have had bad instructors in the past or haven't tried hard, but I doubt this is always the case. To dismiss out of hand the role of innate ability seems disingenuous.
Later in the introduction they talk about the skills required to do mathematics beyond learning the content of the standard itself:
Problem solving is not separate from content. Rather, students learn concepts and skills in order to apply them to solve problems in and outside school. Because problem solving is distinct from a content domain, its elements are consistent across grade levels.
Now here we get to the heart of the weaknesses inherent in these standards. The standards explicitly leave out any direction about how math is to be taught. So, most teachers treat the standards as a "laundry list" of different kinds of problems the students must perform before passing a subject. Therefore, whatever teaching approach gets the students through the list fastest is best. Unfortunately, I fear this motivates teaching each item on the list as a procedure to be performed by rote with little understanding of the underlying reasoning or methods of thinking because this gets students through the content quickly.
This is not to say that standards are useless or harmful. But they are certainly not a panacea to providing high quality teaching.
By the way, the elementary school standards do make an effort to address mathematical reasoning through different "strands" of math standards at each level. Whether the application of reasoning can be measured (and measurement is key to gaging success in implementing a standard) I do not know. This practice pretty much ends at grade eight. So, I wonder if the traditional secondary school curriculum of "Algebra I, Geometry, etc..." really serves the students that well.
At the end, the introduction talks about the positive role technology can play to assist learning in the math classroom (through visual tools, graphing calculators, etc.). It is a shame that schools have not taken this possibility more to heart.
It is interesting to note the difference in the standard as it transitions from K-7 to 8 and above. I'm not sure the difference is positive since the earlier emphasis on specific mathematical reasoning techniques is dropped. The argument for this is stated at the grade eight introduction:
Mathematical reasoning and conceptual understanding are not separate from content; they are intrinsic to the mathematical discipline students master at more advanced levels.
My answer to this is "maybe, maybe not." Students can learn an amazing amount of stuff by rote, and they are often taught things that way.
Some elements of the standard are redundant across topics. For instance, rational expressions are taught in algebra I and algebra II. I don't think this is a bad thing and fits the model of "spiral learning", but I think the standard could be a lot more specific on how each topic is built upon at each level.
In fact, the standard is all written at such a high level that its usefulness is hampered. What this standard needs is a comprehensive set of example problems that students should be expected to solve at each level. Really, what I would like to see is a standard textbook developed by the state and made freely available to all on the web - but that is a topic for another day.
I found NCTM overview to be much more helpful than the cliche ridden state standards introduction. For one thing, the overview has a more realistic and inspirational argument for teaching math:
...those who understand and can do mathematics will have opportunities that others do not. Mathematical competence opens doors to productive futures. A lack of mathematical competence closes those doors.
This is true I think. Having math skills opens doors. Not every door requires this skill, but those who do not have it will have these particular doors closed to them forever.
I like the fact that the NCTM emphasizes mathematical principals as well as a set of standards. I also like the fact that they have a set of "process standards" to go with the content standards.
Of course, I can't actually evaluate any of their core material because I would have to buy it first. This to me is beyond frustrating. The NCTM claims to represent 100,000 math teachers. Wouldn't those math teachers like to have material that is free and readily available on the web to anyone who wants to use it? I think this is where education ultimately needs to go. This idea of buying over and over again the information we need to do our jobs is preposterous when information should be free.
When I get the time, I need to go to the library and check out this material to evaluate it more fully.