Are there any examples of what a person who couldn’t pass Algebra II is capable of doing in the new paradigm? We’ve already seen tests dumbed down, but statistics is no joke either. I have seen people with advanced degrees make unfounded claims because they didn’t realize one can’t always fit a straight line to a set of points. Just handing someone a graphing and statistics package doesn’t make them a qualified analyst.

I love the part about Legislators not being able to require a test that they can’t take and pass. Is that a good metric for testing in general? Should we be able to validate our testing by giving it to “professionals” and seeing how they score? For example, giving an algebra II final exam to mathematician, physicist, chemist, biologist, psychologist, and sociologist (drawn from the strip at xkcd.com/435 ). Each of those fields uses different types of math more frequently than others. If the professional sociologist or psychologist can’t pass an algebra II exam, is that a suitable requirement for their field? (No offense intended to those professions, it’s just my understanding that they use statistics much more frequently than polynomial long division).

That would be a good experiment. Of course the professionals might not want to take the test and be embarrassed by a low score, but it could perhaps be anonymized. What do you think?

I agree! Consider me convinced. Thanks for disseminating his very sensible plan to a wide audience. Algebra 1 and 2 have been in sore need of a sanity check, and better alignment, less overlap for – I don’t even know. Decades, I would bet.

I just don’t know who actually needs to be convinced in order to make it happen! In NY in 2005, it was supposedly these people. But from what I hear, the input of the classroom teachers involved was more or less ignored. In NY we can’t just design and teach whatever courses we want, because in Alg 1, Alg2, and Geometry there are statewide final assessments, and a kid’s score determines the fanciness of the diploma she is awarded. I don’t have a list or anything, but I imagine many other states have moved to such a model since NCLB.

So who really makes those decisions? Does anyone know? I would like to know. I imagine a shadowy network of bureaucrats and test publishing executives.

Leinwand asked, why are most Algebra II final exams balanced towards the verbs:

* Simplify,
* Solve,
* Factor,
* Graph.

… when math is ever so much more about being able to:

* Find,
* Display,
* Represent,
* Predict,
* Express,
* Model,
* Solve,
* Demonstrate.

Is solve supposed to be on both lists?

My guess is there’s a verb-focus on finals because it’s easier to grade the first 4. Even if you don’t go for multiple choice, it’s still easy to give partial credit for work shown. The 2 lists above is more about convergent and divergent thinking/production. Students should be developing both types of skills in the classroom. Convergent production limits the outputs (easy to grade). Divergent production can produce many outputs (in too many formats to easily grade reliably).

If the question is why algebra 2 classes have a verb focus. My guess would be that algebra are the foundational skills for the more interesting application questions in calculus.

I think your example gives a good reason for why algebra 2 shouldn’t be a requirement for attending a state college (for some majors). The solution is to change the admission requirements not dropping long division from algebra 2.

I do agree with finding alternative rigorous mathematics pathways to college.

New rule: “Legislators can’t require a test that they themselves don’t take and publish the results of on their websites.”

It’s easy to beat up the legislators, but that is not a good policy. I did smile when I first read it.

If you’re looking for an example from Leinwand of the “old dialect,” here’s one: rationalizing roots in the denominator of fractions. Here’s another: the conjugate in the same context. Can anyone make a case for that?

Easy for the teacher to grade :D

Gotta run to work. Might have a post down the line.

Great Post! I couldn’t go to Asilomar this year, but you really brought it home to me. I particularly liked the Algebra 1 and II syllabi as they reflect a lot of what I have been thinking about for these past years as a teacher of 8th grade algebra.

I hate teaching rational expressions, and yet, if I don’t, my students aren’t placed in the next class after Algebra (Geometry or Math 2) in their freshman year. They then feel like they weren’t taught correctly.

The vicious circle of demanding more and more out of developmentally in sync kids needs to be challenged.

Thanks

If the question is why algebra 2 classes have a verb focus. My guess would be that algebra are the foundational skills for the more interesting application questions in calculus.

For a large number of students, Algebra 2 is the end of their mathematical careers. Shouldn’t it be looked at as more than just foundational? And can’t the course be interesting enough on its own, rather than just be a prerequisite for calculus?

@Riggins Have you seen Arthur Benjamin’s recent TED talk about changing math education?

I’m with Mr. H:
I think your example gives a good reason for why algebra 2 shouldn’t be a requirement for attending a state college (for some majors). The solution is to change the admission requirements not dropping long division from algebra 2.

We’re still trying to make everybody good at everything. That wasn’t the model for most of history. We accepted that some people like and do better at some things than others. We encouraged some sort of foundational skills in all areas and then…let them advance and excel further in the things that interested them, whether it was math or science (providing the motivation for math too) or literature or basket-weaving or inventing or…

Then again, perhaps this is 3.5 months of middle school math in a high poverty, inner city school speaking. Right now, I’m most interested in developing *thinking* skills. And by that, I’m talking about basics of thinking: taking a minute to picture the problem, or really understand what the question is asking, etc. Harder, of course, when many kids are reading below grade level by several grades and their ability to read aloud is not an indication of their comprehension, which is usually lower. Of course, I’m just as concerned with their scores on the state test, by which we’ll all be judged. The thinking skills certainly can’t hurt them on that, but there are those who would prefer not muddying the water with too much thought.

Sigh.

Math tests for legislators is so funny! I would be surprised if 25% could pass the state Algebra I exam, let alone II.

My husband went to Boalt Hall. Law school is the top pick for those on the policy and politics track, which was why he went there. He’s also a math-phobe claiming an inability to do math once he got to fractions. The only math required for law school admissions at that time (LSAT) was a section of logic problems similar to those you find in Dell Puzzle magazines. It was all logic, no numbers or symbols.

One lovely spring day in Berkeley the students were “off-task” in some truly boring first year class (Civil Procedure, Tax Law, or Contracts). The teacher asked what they were all doing there at one of the top ranked law schools in the country if they weren’t interested in law? One student raised his hand to share this nugget, ‘I didn’t have to do math.”

That will be a super majority of elected officials. If they went to school beyond their Bachelors (likely in PoliSci, with just a glossing of statistics), they went to law school, and they went there to become a politician, and because they didn’t have to do math.

Leinwand’s slides talk about the Common Core State Standards Initiative.

Dan, was your impression that he liked those or was he using them as an example of the old school.

Was there a set of standards he suggested using as a model?

Bad Algebra curriculum and bad college requirements are on one end of the issue. There is another pole. I am reading an amazing book,Mindsets by Carol Dweck. She quotes Benjamin Bloom, “After forty years of intensive research on school learning in the United States as well as abroad, my major conclusion is: What any person in the world can learn, almost all persons can learn, if provided with the appropriate prior and current conditions of learning.”

I did volunteer tutoring at a community college a few years ago–non-credit math classes for those who didn’t pass the placement exam for Math 100. It sure seemed like a waste of time for those students to have to take the Algebra classes “learning” things that they won’t ever think about again. I decided I would have a greater impact tutoring elementary school students instead. This is the other pole.

I don’t think we are addressing the real cause of why so many students are failing math placement exams at the college level; in my state it was 84% in 2007! If we had math entrance exams for middle school (not something I am endorsing), we would see the same problem; in my state, 63% of fourth graders and 75% of eighth graders were below grade level on the NAEP Math test. The majority of elementary school teachers are poor at math. We need to push for math specialists in elementary schools and open up math to a far more students.