Gifted Issues Discussion homepage Forums General Discussion Common Core

Yes to everything you wrote.

The better mathematics textbooks in the US have proofs outside of geometry as well. Unfortunately, the mainstream textbooks in this category tend to be older. For example, the high school math textbooks by Richard Brown include proofs outside of geometry (see Algebra 2 here) . Newer programs like AoPS are outstanding math courses and textbooks.

College placement tests for math (and English) are *all* multiple choice questions.

I have been taking classes here and there at the local community college. I passed the English placement test with flying colors (qualified for the honors program, although after hearing me ask for information the exam proctor tried to redirect me to the ELL placement test, ah!). To validate an associate degree I would need to either test out of math or take the one math class I never took in my previous educational career (statistics). That multiple choice test scares me. I am rusty, forgot a lot of theorems, and am used to working on long proofs for everything (slow!)... but landing into remedial math would be a huge blow to my pride .

But you are presumably way more than 10 weeks out of secondary school, unlike most people who take that test. Obviously, someone who's been out of school for a while should have to study, but IMO, someone who just finished four years of math several weeks ago shouldn't have to study to pass (not get an A on) the placement test.

Yes-- it's just that in the US, high school geometry was a sort of last bastion of the form (constructing proofs, I mean).

Seeing it pass from core instructional practice even there is beyond the pale for me personally.

I do not find mathematics "easy" by any means, either.

What is the name of the math placement test? Two commonly-used tests are the Accuplacer and Compass. There are resources to prepare for these tests. Can you test out with a high-enough score on the SAT or ACT or SAT Math subject test (level 1 or 2)? There are tons of study materials for these tests.

I'm going to attempt to tread lightly here and suggest, with all due respect, that learning to construct mathematical proofs (and I mean authentically learning it, not filling in blanks with the right theorem/postulate, but actually constructing the logical progression one's self); results in a kind of global learning of a different way of thinking or approaching material.

It's that mindset which is most directly utilized in every physical science. Less so, certainly, in engineering disciplines than in their companion sciences, because of the difference between engineering and science. Still, it's that gestalt that is what students should be getting out of math instruction. It's a metaphorical toolbox to keep things in. While it may not seem as though one uses the tools labeled "geometry" one may well use other tools in that box-- as you note, trigonometry, for example. All of that belongs in that toolbox; what students gain from working proofs isn't a single, simple skill such as "the ability to use algebraic concepts to compute vector quantities with precision." It's more about the toolbox.

In short, I believe you when you say you haven't used any THING that you learned in geometry. But I'm also a bit skeptical that nothing you got out of geometry was even indirectly useful in support of other study.

It's rather like learning literacy. "Reading" is such a roomy toolbox that at some point it ceases to be a thing of its own, and becomes a box to hold all kinds of other specific tools.

I can't remember what geometry was about.

I just know that I had to take it to take the upper level algebras.

Whatever I do, I generally do automatically. I normally can't show my work because I can't tell you what I did. I just know that the answer is accurate because it feels accurate.

This is why I *loved* math multiple choice tests. All I needed to do was pick the right answer, and it was generally obvious.

So, teaching is not an ideal profession for me.

Yes, I perhaps should have clarified that the emphasis is less overt in the one than in the other. The focus in the science disciplines is on the process itself (with considerable reflection/feedback related to that process), whereas in engineering it is on the solution to _____ problem, and the feedback tends to be more binary. If that makes sense, and notwithstanding the cliches regarding engineers who can't see the forest for the stand of trees they happen to be navigating... which mostly seems to be exemplary of BAD engineers, from what I can tell. Just as kcab notes, good engineering requires a big picture (forest) too.

I think that is why engineers can lose sight of the fact that the same logical framwork scaffolds both things, though. Focus on outcomes rather than process allows the process to disappear.

Of course, I didn't see any actual STAR test questions. I have downloaded before old actual STAR test questions, which the state of California releases. They really do ask about telling time on the second grade (end of the year) test!
I'm not surprised if they are dumbing down even more math requirements for California. So many kids can't do basic math. I guess the solution is to make the standards lower so everyone will pass!
My kids will likely take two years of AP Calculus in our California public high school, when they get there. So I'm not going to worry if the other kids can't even pass Algebra!

Here they say they have shifted things around a lot, so that the content of the courses is no longer what you would expect from the names. That said, I will be watching closely to make sure that "common core 8" really does look like "algebra 1" to me, as promised.

And yes, based on reading the above, going to be watching geometry extra closely too. I value the logic teaching that is supposed to come with math. Sigh.

MON, here, the shift was moving material earlier in the curriculum, not later. The shift you describe sounds like the opposite of what our district claims to be doing. To meet the same standards. Curiouser and curiouser.

DeeDee