Only one more week before the kids come in. Four classes of Algebra II (three of them are for freshmen who passed Algebra I in middle school) and one class of AP Stats. So far the rosters are manageable, between 25 and 30 kids per class. What do I want to do with them? What do I want them to get out of their respective courses by June?

I want them to delight in thinking. I want them to delight in thinking mathematically. I want them to stretch their brains. I want them to grow mathematically. With all due respect to all the great middle school math teachers out there, I think that to some degree we infantilize these kids. A poster with glitter, with an illustration of the Pythagorean Theorem and the formula next to it is NOT the same as understanding how to apply the Pythagorean Theorem.

Math is about solving problems – that is all. Too often what we do in math is boring and repetitious. The textbooks rarely have challenging problems. We are giving the kids recipes, but we are not teaching them to cook. We are teaching the kids to make a French onion soup, we have them do it 30 times until they get bored with it, but we never ask them “What do you do if you run out of onions?”

The situation is less dire in AP Stats – I continue to have a tremendous respect for those who put the course together, who wrote the main textbooks and who are coordinating and grading the AP Stats exam. But in Algebra, arguably the foundation stone of mathematics, we (as a country) are falling behind.

Take a look at some of the textbooks American schools used in the 60s. Take a look at Smith and Fagan’s “Mathematics Review Exercises”, at Weeks and Adkins’ “A Course in Geometry”. Those had truly challenging problems. What happened? Have we become dumber? Take a look at Singapore’s “New Syllabus Mathematics.” Those are good problems! Take a look at today’s Exeter problems. How come we don’t have more teachers using them?

Of course there are explanations. As a nation, our classes are more heterogeneous, and in general we expect everybody to graduate from high school with Algebra II and Geometry level mathematics (at least), whereas 40 years ago we did not expect everybody to do so. We have provided opportunity for more, but we have at the same time lowered the quality and rigor of our courses. And of course there are the standards – and we are evaluated on how our kids perform on those standards. We are truly in Lake Woebegone – where “all children are above average.”

Indeed there are many causes that one can list to explain the decline in math education – from parents, to administrators, to politicians, to video games and so on. But I think we – the teachers – bear a heavy burden also.

We have failed to hold the line.

We are coddling the kids, we try to make it interesting, painless,visual, relevant and in the process we have sacrificed rigor. We need to ask more of them…and more of us.

Wow! First of all, I think this is the first time I have read someone else’s blog where their school also does Alg1 – Alg2 – Geom. This is our 3rd year since we switched to that sequence. I found that as I read your comments about what you want your Algebra 2 students to do that those are things I want also. I guess I never really verbalized it before, but as I read the second paragraph, I thought to myself “Yes! Yes! Yes! 100% YES!” Your statement “Math is about solving problems – that is all:” really hits the nail on the head. I think the sooner that more people come to that realization and allow us to treat mathematics that way (and get away from the whole testing crap), the better off our students will be. I know as I have talked to business people and heard business people speak about education, almost every single one of them has emphasized that we need good problem solvers. Unfortunately, it seems that the emphasis right now is in having students complete through a certain course (in Ohio, it’s Algebra 2 – all students beginning with the class of 2014 must have 4 credits of mathematics, including Algebra 2 or it’s equivalent).

So how do we get students and the focus of Algebra 2 back on solving problems? How do we structure the course to accomplish this? As a 19-year veteran teacher, I wasn’t taught how to teach this way in Teacher Ed School. I’ll be curious to read more of how you accomplish this in your classroom. I’m working on it as well (and blogging about it). Thanks for sharing!

–Lisa

An Old Math Dog Learning New Tricks

(oldmathdognewtricks.blogspot.com)

I disagree, although I can certainly be convinced otherwise, that sacrificing rigor is what’s gotten us here. The greater enemy is “coverage.” I actually look at an Alg textbook now and they’re asked to learn far, far more stuff than I ever did in my Alg class (which incidentally, was in 8th grade, the advanced class then, now it’s the standard class for California 8th graders and Geo or even Alg 2 is considered advanced. The pushing down of what’s considered “grade level” is another enemy). Far worse is the cramming of junk into what’s considered Algebra.We’ve got these 300+ page textbooks that contains hundred of different California standards and they only graze the surface of each. Other countries address fewer topics but teach them at a far deeper level.

Lisa,

Thank you – I follow your blog and I learn a lot from it. As to the “how”, here is what I am trying: sending my exams/quizzes to the main middle school teachers in the district (those teaching Algebra I to 8th graders); sending my exams/quizzes to my fellow Algebra II teachers at the HS, giving the kids a basic skills math test on the second day of school and communicating the score distributions to all of the above. Does it work? Hopefully… in the long run…perhaps. I am interested to see if the Common Core Standards will help.

Jason,

YES – for sure, the “mile wide and an inch deep” problem is also fundamental. But where were we (the teachers) when these standards were adopted. Could we not see that we would lose rigor by trying to cover too much? As far as I am concerned – since I come from engineering – I know what is needed and I try to do my own stuff; I emphasize what I consider important and let the chips fall where they may for the other topics. Thank you for your thoughtful comments.