Once again, as much as I want to, I can't escape discussing politics, as even the name of this blog is political: "Right on the Left Coast: Views From a Conservative Teacher." But that's the problem -- the debate about Common Core is inherently political, and since the more liberal of the two major parties first proposed Common Core, naturally its opponents are more likely to be conservative.
The author is Darren Miller, and as the title of his blog implies, Miller is a West Coast teacher -- indeed, he is, like me, a high school math teacher from California. Here is the link to his blog entry from last week:
So Miller's district is, like many others in California, considering teaching Integrated Math. The district will try Integrated out this semester, and then make the final decision for this fall. Miller is clearly concerned about the transition to Integrated Math.
Let me remind you that Integrated Math is not a prerequisite of Common Core -- at least, it isn't here in California. Nonetheless, many California disticts are using Common Core as a reason to switch to Integrated Math. Therefore, my own opinions of Common Core and Integrated Math are separate -- I'm mixed on Common Core, but have nothing against Integrated Math.
Naturally, Miller is concerned that Integrated Math reflects a lowering of standards. Indeed, one of the commenters -- of course, that commenter is "Anonymous" -- writes that colleges won't want to accept students who took Integrated Math:
i feel bad for everyone who tries to apply to out-of-state schools that look for two clear algebra requirements and a clear geometry, with pre-cal, cal being an added bonus. how hard will it be to explain, "well, my classes were a mix"....
that might interrupt some students college dreams. not all states' colleges are friendly to california's changes.
Now here's the problem that I have with this commenter -- the United States is an outlier when it comes to traditionalist classes such as Algebra I, Geometry, and Algebra II. Most countries, including those considered to have superior math programs such as East Asia and Singapore, actually have Integrated Math programs. So introducing Integrated Math make us more like the nations that we want to emulate, not less!
Suppose an international student from East Asia or Singapore applies to a math program at an American college. Since secondary math is superior in those nations, one would think that an American college would leap out of its skin to admit the student. But based on what our anonymous commenter wrote, many colleges wouldn't admit the East Asian student, because the student's transcript doesn't contain "two clear algebra requirements and a clear geometry," classes that aren't taught in the student's homeland.
Once again, let me post the link to the Singapore secondary math standards, and I dare you to find the two clear algebra requirements and a clear geometry in the standards:
Now let's return to Miller's original post. We see that part of the reason for considering Integrated Math to be inferior is the ability of the students to reach AP Calculus:
Then we talked about all the courses we'll need to offer. It's more than Integrated 1, Integrated 2, Integrated 3, Pre-calculus, Stats, and Calculus. See, according to the Common Core standards and guidelines, students are not supposed to be accelerated in middle school. Get that? The smart kids will be kept back with everyone else, because, fairness! Our illustrious district will allow middle school students to accelerate one grade in middle school, meaning 8th graders will be allowed to take Integrated 1. (Those would be the smart kids; under California's old standards, those would be the on-track kids.) So if we want kids to be able to take AP Calculus AB and/or BC in high school, we need to accelerate them in high school.
And so we see the problem -- just as Common Core has become intertwined with Integrated Math, the latter is intertwined with the inability to reach AP Calculus. If Miller could see how other districts have already implemented Integrated Math -- such as my own district -- he would notice how freshmen in ninth grade are working out of eighth grade packets. He would be rightly concerned that these students have little shot at reaching calculus.
I don't necessarily agree with Miller's use of the word "on-track" to refer to California's old standards, in which the 8th grade standard was Algebra I. I don't like the idea that a student has to master the quadratic formula, which very few adults have mastered and only workers in STEM subjects actually need to know it to make a living, just to be considered "on-track" in eighth grade.
But I've already posted my Singapore compromise, in which the Singapore standards are given as a good replacement for Common Core. My plan gets students to calculus in senior year via an integrated pathway, but the 8th grade course does contain a lot of Algebra I.
Recall that we are devoting only two weeks to each chapter during the second semester. So it's already time to start reviewing for the Chapter 12 Test.
As usual, most of these problems will be from the "Chapter Review: Question on SPUR Objectives" section of the U of Chicago text. I had to skip around in order to avoid the problems that relate to area or volume, since these involved the skipped Chapters 8-10. In particular, I included ten straight problems from the text, all in the thirties, since this stretch of questions avoids area and volume. I also decided to modify one based on Question 13 from Section 12-6, even though it's originally a question about area and volume. This is only because the question is about a statue of Martin Luther King, Jr. -- today is the civil rights leader's birthday and the reason that there is no school Monday. I decided to change the question to describe the MLK Memorial in Washington DC -- a statue that didn't exist at the time the U of Chicago text was printed.