Yes, I’m cynical.  But am I cynical enough?

I’m sure I’d be in the minority on this… but for the same reason, I’d also require at least a semester of Geometry (with proofs, not the watered-down “integrated” geometry at our local high school) for every student, not just the college-bound.

Mark Roulo, I think that algebra should be required because there’s always the chance that a kid will change their mind later on and want to do something that requires the maths background.

Okay … but required in 8th grade??

[Yes, I realize that 8th grade algebra appears to be what the rest of the world would consider to be a remedial track, but the US has typically had algebra in 9th grade for a long time ... do we think that moving it up a year will create *more* success for kids doing math? (Actually, it might if the main problem was that the kids were bored ... I don't think this is the primary problem).]

I’d be very happy to see 9th graders consistently learning algebra well.

-Mark Roulo

Mark Roulo, I think that algebra should be required because there’s always the chance that a kid will change their mind later on and want to do something that requires the maths background. Also, doing algebra means repeating the more basic maths skills, which looks to be valuable for long-term retention of those skills.

So you think that kids should be knocked out of the option of going to college by 8th grade?

Dennis hasn’t said that it should not be offered. He’s pointing out (I think) that *requiring* it is a ‘whole nuther kettle of fish.’

-Mark Roulo

Taking Algebra in 9th grade does not eliminate the college option. I took it in 9th grade and did well in it, eventually “acing” calculus in college, and ended up getting my BS in Finance and Economics.

So you think that kids should be knocked out of the option of going to college by 8th grade?

I am in favour of vocational training. But people change their mind all the time about what they want to do in their lives – and the one thing I know that prevents the most people from doing what they want to do is a lack of sufficient maths preparation. One of my parents’ friends left high school at age 15, got a job at the post office, one year later chucked it in, over his father’s objections, and went back to high school (had to sell his motorbike to do so as his father refused to fund any more education), now is a scientist. A friend of mine did his technician engineering qualification (non-uni) and now wants to do his bachelor of engineering, and is having to go back to high school for some more mathematics. My mother burned out of maths at age 15, and avoided it right through uni, until she needed some help with her honours year thesis, and met Dad, but she found herself needing more maths when she started a business with a friend even more maths-phobic than her.

Plus the advantage of taking algebra is that practising algebra helps engrave arithemetic more and more deeply into your brain, without the dullness that sheer drill entails. In Dan Willingham’s book “Why students don’t like school” he presents evidence that what matters for long-term retention is practising something beyond the point of knowing it. On page 89 of the book he shows a graph of how much people remembered of algebra, given the number of intervening years since they’d studied it, the lines in the graphs are broken down by how many maths courses the people had taken. The people who had taken maths courses beyond calculus didn’t forget their algebra. Even 55 years after their last maths course, they still remembered as much algebra as people who had taken their last maths course 5 years ago.
Meanwhile students who had gotten an A in algebra and then never taken another algebra course again forget algebra as quickly as students who took a C and never took it again. They remember more at any given year, because they knew more to start with, but the forgetting curve is there.
This indicates that if you want students to be able to do arithmetic like percentages, fractions, etc, 10 years after leaving school they need to keep practising it. And what’s wrong with teaching them algebra as a way of maintaining attention while getting the practice in?

But even when I attended school with one diploma, there were signals available to separate those who took challenging classes from those who attended. Being an “honors” graduate was the clearest signal; in those days before AP classes were offered at the school, certain classes were designated “Honors Classes” and the GPA number for that class was increased by one (i.e., an A in an honor class was worth 5 points, a B worth 4, etc.). The main purpose of this scheme was to deter people interested in college from getting a “perfect” 4.0 by taking home ec and consumer math instead of trig, physics, etc. Consequently none of the honor graduates (top 10%) had a GPA below 4.0.

Do we really want to set up a system where those kids can’t graduate from high school even if they’re making a reasonable effort?

Maybe that’s the wrong question.  Maybe there should be different grades of diplomas with levels of achievement listed, and those students’ achievement in math should be given as “below basic”.  Different regular and honors diplomas would be good too.

College is an extremely expensive and often wasteful way of getting a meaningful credential, and the more we can eliminate the need for it by going back to what a diploma used to mean, the better off we’ll be.