tag:blogger.com,1999:blog-30226356.post115169381791018628..comments2024-02-16T23:32:12.073-08:00Comments on The Exponential Curve: NCTM standards vs. California Algebra standards?Dan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-30226356.post-1151798806109962612006-07-01T17:06:00.000-07:002006-07-01T17:06:00.000-07:00I agree that the CA standards are rigorous. I als...I agree that the CA standards are rigorous. I also think that the skills outlined in the standards are critical to being able to solve more complex problems in each subject area. I've read through a lot of the framework, and I think it is well written and quite reasonable. I haven't found anything in the framework that I object to.<BR/><BR/>However, if something that is not tested is not taught, I don't think it is correct to necessarily blame the teacher. The standards for each grade level are written with the assumption that the standards from the previous grade levels have been adequately mastered. This is clearly not the case for the majority of students (otherwise, there would not be such high levels of failure on the CA exit exam, which barely even touches high school level math).<BR/><BR/>Therefore, as a 9th grade Algebra 1 teacher, I am faced with a daunting list of standards, which I would love for my students to learn - and they, I, and my school will be judged based on how well they learn them. I have the problem, though, that I must spend a huge amount of time teaching standards from lower grades that students have never learned. This eats away from the time needed to teach the current standards at just a procedural level, let alone a conceptual level. <BR/><BR/>The framework emphasizes that three components of math education are critically integrated: procedural knowledge, conceptual understanding, and problem solving skills. However, the standardized assessment that students take is almost entirely composed of procedural level questions.<BR/><BR/>In our algebra 1 classes, we used to do a Problem of the Week assignment to really develop students' thinking and problem solving skills, but we had to drop this. They were so weak in their problem solving abilities, that the amount of time going into developing them (though I think this was time very well spent) was making it impossible to make any headway into the list of content standards. We still work on traditional word problems, but these are pretty formulaic and don't really push the boundaries of critical thought. We also have to spend a lot of time developing pre-algebra concepts (this is in addition to the separate numeracy class that students concurrently take to develop their basic arithmetic skills). Add to that the fact that the STAR tests occur when there is still over a month of class left, and yet they test the entire year's worth of standards.<BR/><BR/>Given all of these constraints, we've had to strand out the concepts vertically among classes. Some things we have just accepted we will not teach in Algebra 1 (i.e. rational expressions, absolute value equations, fractional exponents), and will instead push to Algebra 2.<BR/><BR/>And, in the high stakes testing climate that we now have, we do look at the blueprint (the document that shows how many questions relating to each standard that will be on the test) to make decisions. For example, here is standard 21 from algebra 2:<BR/><BR/><B>Students apply the method of mathematical induction to prove general statements about the positive integers.</B><BR/><BR/>According to the blueprint, there is one question every three years on the STAR test relating to this standard. I think mathematical induction is fascinating and really develops critical thinking. But to really teach students mathematical induction takes a lot of time. How can I justify spending that time, when so many other standards are tested much more heavily?<BR/><BR/>In summary, I don't think there is a problem with the skills that are listed in the standards. I think there is a larger systematic problem that the standards are a part of.Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-1151709796790644122006-06-30T16:23:00.000-07:002006-06-30T16:23:00.000-07:00California's standards are pretty darned rigorous....California's standards are pretty darned rigorous. <BR/><BR/>As for your statement that "if it isn't tested, it doesn't get done", that's a reflection more of poor teaching than on the standards themselves. <BR/><BR/>If you read the CA Framework in addition to the standards (the standards come in a stand-alone book or as Chapter 2, I think, in the Framework) your concerns about application and higher order skills will be assuaged.Darrenhttps://www.blogger.com/profile/15730642770935985796noreply@blogger.com