Educational standards are individual to the States and are adopted by each State legislature. If, someday, there are national education standards, it will probably require an Act of Congress that both adopts those standards and denies the States the right to modify them.
Teachers do not decide what is taught in the classroom. Teachers can decide on the timing of lessons, their flow from one to another and the actions necessary to translate teaching into learning, but the substance of a year's worth of learning is provided by the State.
Because the States adopt education standards, a political act, these standards have the implicit approval of the voters of each of the States. The voting-age population has decided, through its representatives, the timing, the scale and the specifics of what adults expect schools to do with school-age children.
The Tutoring Room, at least for a while, is going to consider what an eighth-grader is supposed to know while registering for high school.
The diary continues in a moment.
The Tutoring Room is a service diary for all kossacks who are engaged in education as a student, a teacher or someone important in a student's or teacher's life. Ask a question; it doesn't have to be about math. Answer a question; maybe you can rephrase a question so that everyone can consider it in a different way.
This diary series is allied with plf515's Daily Kos University series and cfk's Bookflurries:Bookchat series. They have agreed to offer tutoring services as well. If you have a diary series and would like to be allied in this education service, please let me know. I strongly recommend that all readers should visit The Teachers' Lounge on Saturday mornings.
While the States of Illinois and California have given me teaching certificates and the No Child Left Behind Act has labeled me as a "Highly Qualified Teacher," I am not a university-trained expert on curriculum, educational psychology or educational process. I'm a teacher who has spent years using and considering the standards for my subject. Because I am an intellectually curious adult, I have compared the standards for my subject with the standards of the other subjects taught to the same students. In essence, I want to know what the legislature had in mind when the standards were adopted.
My subject is Math and I teach both Algebra and the transition from arithmetic to Algebra. Completion of first-year Algebra is, by law, what is considered normal for an eighth-grader moving on to high school.
What is an eighth-grader supposed to know?
Equivalence
There is a difference, subtle perhaps, between being equal and being equivalent. Equal implies two things are the same; equivalent implies two things may look different but they have the same value.
For most if not all educated people, equivalence is seen most in the fractions, decimals and percents triangle. Fractions can be converted into decimals, decimals can be converted into percents and so on. A particular number can be shown in each of these three ways; it is the same number but its meaning and usage changes. A tax of 5% (five percent) is the same thing as .05 (point zero-five in common usage, or more accurately five-one hundredths) which is the same thing as 5/100, which in turn can be "reduced" (a word often misunderstood by young people; the fraction does not become smaller; common "factors" have been removed) to 1/20 (one-twentieth).
Before an eighth-grader can be trained in Algebra, he or she is expected to have a strong grasp of equivalence. This can be shown in data analysis (mean, median and mode all show forms of the concept of "average"). Exponents, the "powers" of numbers can indicate a rapidly growing value or one that is diminishing, are used in scientific notation to show both very large and very small numbers as well as growth and decay problems. Simple equations are used to show that one-side equals the other-side and is therefore true if a particular number is identified, while all other numbers would make the equation false.
Consider, for a moment, that a typical twelve-year-old is expected to grasp and use the idea that something can be true in many ways and can be shown to be true in many ways. As a parent, I can laugh about how my daughters (ah, me too) became practiced liars somewhere before becoming teenagers. They weren't liars, of course; they were practiced at presenting versions of the truth. Math class reinforces this.
Pre-Algebra
In future diaries, I'm going to expand on equivalence. I will give examples of how a pre-Algebra student is trained in equivalence. This will lead to Algebra itself.
As a preview, let me say that first-year Algebra can be grouped into a triangle of equations/inequalities, solutions and graphic representations. Understanding equivalence is required for a student to see that an equation can tell what a graph will look like and a graph shows the solutions that make an equation true; these solutions establish a pattern that can be shown in an equation. Language, facts and patterns create the Algebra I teach.
An educated eighth-grader is supposed to know how to solve linear equations and inequalities, absolute value equations and inequalities, quadratic equations and inequalities and so on; they are supposed to understand the subtle difference between solution and answer and they are supposed to be able to graph the whole thing.
Ahem. Consider that when you look at the junior high school students hanging out at the local mall.
More to come. Any questions?