I applaud Dan of The Exponential Curve for being honest in answering a question I asked of him. But I encourage you to read his post and see if you share my concern that he's participating in "course title inflation".
I know that this is a touchy subject, and I don't create this post to pick a fight, point fingers, or criticize. My concern is genuine, and I would like other input on the topic. While I won't speak for Dan, I'm sure he would welcome such input as well.
Because DCP was designed as a college prep school for students who were doing poorly in middle school, the students we get all have significant deficits in their math and reading skills (the average is about 5th grade level). This means that we have to start students out with a lot of remediation and support, and then quickly ramp them up so they are caught up by the time they graduate (thus the name of my blog).
We teach Algebra 2 in 10th grade, and students still need a lot of scaffolding. Our Algebra 2 classes - both regular and honors - are real Algebra 2 classes, and the curriculum is driven by the state standards. However, our students at this level, despite their hard work, can't compete with same-aged students who had a good elementary and middle school education. The honors class I teach can't look exactly like the honors class I took when I was in high school - although I'm doing my best to push it in that direction.
Algebra 2 - even if UC/CSU approved as an honors course - does not earn students an extra point on the matrix, so it doesn't contribute to the grade inflation problem. Our students who take the honors class will actually get a lower grade than they would have gotten in the regular algebra 2 class, and their extra effort will not be rewarded on the matrix.
I think the honors designation has to be there, because the students who choose to take the class are working much harder than the rest. They are taking the most challenging class that they have access to, with no reward except for the knowledge that they will be better prepared for higher level math. Colleges need to know that when looking at their transcripts, so I think it is appropriate to call the class honors.
The real question, I guess, is whether "honors" can or should be defined universally in this case. Clearly, I don't think so, since students don't get a boost in their GPA. All schools are different, and I think they should be free to set an "honors" bar appropriate to where their students are.
I see AP classes differently. Students earn an extra point in their GPA, and there is a clear and understood universal standard to which students must be held. For this reason, my school is debating whether or not the calculus class we offer next year should be AP or not. If we find that our students are not able to do full AP level work, then we won't call it AP.
Standards are well and good, but often meaningless in the bigger picture. If the guy who blogs at Exponential Curve really wants to see how he's doing with respect to preparing his students for what's next, he ought to let them get a workout on the appropriate math placement test from a local community college or on a sample ELM exam from the CSU.
For all I know, he could be the next Jaime Escalante, but I'd be willing to wager that his students scores on such instruments would be lower than he might expect. This, in spite of the fact that the ELM, for example, only tests through algebra 1 and geometry. See, for example:
When I taught high school I used to occasionally give such assessments to my students. The last year that I taught I had a bunch of senior would-be calculus students sit for the MDTP calculus readiness test. Out of the 20 or so who sat for the exam, maybe 6 passed.
At the community college, we hear stuff like "But I had AP calculus in high school," or whatever, all the time. Typically the students are telling us this when they come in to complain about why the're being placed in beginning or intermediate algebra on account of their placement test score.
I understand that you don't have a lot of wiggle room when it comes to how you address the state standards. But you should know that it is not at all uncommon for some kid, fresh out of high school precalculus or algebra 2, to show up at their local CSU or community college and score low enough on whatever placement test is being used to put them right back in beginning or intermediate algebra.
I'm just sayin'...
Anonymous, thank you for your comment. It's nice to have a "higher ed" perspective.
I, too, give the MDTP tests to my students. Extremely valuable feedback. You might be surprised to learn that when I asked last year, the folks at UC Davis told me that the MDTPs were now aligned to California's K-12 math standards. That certainly doesn't make them any easier!
The standards are only valuable if they're taught. In other words, you can call Algebra 1 a "pre-calculus" course if you want, but the students are still only learning Algebra 1 material. If you keep away from grade inflation (always tempting, and always a threat) and course title inflation, I think things will be fine. Give in to either of those, however, and the ELM is going to boot your students back into remedial math.
On a related note...
We teach Algebra 2 in 10th grade, and students still need a lot of scaffolding.
Is scaffolding the same as teaching? Or are there sheets of plywood and lengths of steel tubing in the classroom? Is a classroom a classroom or is it a learning environment? Is a student a peer or a learner? Do learners learn or do they construct knowledge? And do they need sheets of plywood and lengths of steel tubing to do it?
"Give in to either of those, however, and the ELM is going to boot your students back into remedial math."
Judging by the number of students who enroll in these remedial courses every year-- just at the California community colleges alone, about 130,000 students take beginning and intermediate algebra each year*-- there are a lot of people giving in to these temptations.
I'm sure there is some double- and triple-counting going on behind the statistic, as the average success rate in those classes is around 50%, but even so, it is pretty clear that there is a difference between what is said and what is done in edu-circles, K-12 and higher ed alike.
Anonymous, I agree that grade and course title inflation are definite problems in K-12 education--which is why I addressed the problem in this post.
I can't tell if you are just making a joke, or if you are seriously implying that "scaffolding" is meaningless edubabble.
If it's the second, it's important to understand that "teaching" doesn't actually mean anything specific, because it takes on so many different forms and it has so many components. Scaffolding refers specifically to analyzing a concept, breaking it into a sequence of smaller objectives, and then creating classroom activities (lecture, pair work, discovery, etc.) that will help your specific students reach those objectives. I have seen (and given) plenty of lessons where there is "teaching", but a lack of appropriate scaffolding.
As a concrete example, the first time I taught piecewise functions, I thought the students would be able to understand it easily, since they could graph well. The lesson I planned went horribly, and few students learned how to graph a piecewise function. I looked at the work they were producing, and I realized that their concept of domain was not well established, and that was the root cause of their errors. So this year, I am providing increased scaffolding: we will spend a lesson working on domain and range, where students also graph single functions over a restricted domain. Then, when it is time to learn piecewise functions, they will have the proper scaffolding in place, and the objective will be more easily met.
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