# Algebra – do we start too easy?

I am teaching algebra again next year. Not that I mind algebra. Quite the contrary. I think it is vitally important that freshmen receive a strong foundation in algebra, and in many ways this is more of a challenge than teaching, for example, precalc. Further, I don’t mind teaching freshmen. (Although once I did, but that’s another story)

So here’s the question: The beginning of my course covers ground that most, but not all, have already seen, though not at the depth I will be covering the stuff. And this is transition to high school time. I go a bit slow, and concentrate on good behavior, work habits, organizational skills, etc. But that means that it is relatively easy to earn very high grades for the first and even second marking periods (we have 3/term, 6/year), and build up a false sense of confidence. When we hit factoring, every year, one or two or even three kids in each class will get caught ‘napping,’ iow, will not pay attention because everything up to this point has been easy, and become lost. It happens so fast that some of these kids never get back on track. (Btw, this is very much a boy thing).

So what to do about it? I already warn them in advance. Plus these are 9th graders, 13 year-olds. They are not much advanced past the stage where they hear: “Don’t touch that, it’s hot” and proceed to immediately touch. I don’t want to make the beginning much tougher. What I do now works well with most kids. Those 4 – 8 weeks at the beginning are really a nice time to lay down good foundation, clean up work and make it more uniform (eg, transposition instead of pendant addition).

Have you experienced this? What do you do about it? Or even if you haven’t, do you have ideas/suggestions?

This is interesting. I found the classes I took at university were also structured in this manner.

First few weeks are really straightforward, almost laughable. You’re lulled to sleep. Then, suddenly, things go haywire. I don’t think the university cares all that much. 9th grade, however, there’s a perception of teacher as “nurturer”.

Is it still the “No Child Left Behind” philosophy in the States?

I have taught ninth graders for years. They all come in thiking either they know it all or that it is too hard and they will never pass. To gain their interest, i sometimes use the text that I use in my college algebra class. Of course I pick the problems that are on their level. This book seems to gain their respect and hold their interest. I also throw in lots of word problems and applications that take the basic stuff to more interesting levels. The hard part is not losing the weaker kids along the way.

For those for whom it is “too easy” at the beginning, you could try pairing them up with students’ needing some remediation. Acting as a peer tutor may deepen their skills and the others may get up to speed more quickly.

Involve your students in the discussion the very first week of school. Talk with them about your perceptions. See what solutions they come up with. You may be surprised with what they suggest.

My experience is that students really want to be part of the process especially if they see results from their efforts

P’ed OT, yeah, maybe a little more emphasis on the stranger looking stuff might help. But essentially, I test easy at the beginning, to help build confidence in themselves and trust in me. They do what I say, and do well. If I made the work significantly harder, I might break that, and that is something I’d rather not do. So while I try what you suggest, I need to tread carefully.

Jackie, these are generally weaker boys in the class, who usually are coming from middle schools where they were the best. They are not likely good enough to tutor anyone else. The problem is sort of that the class is easy for everyone, but the strong kids respect the foundation that is being set (same problem as last year, but no numbers, only variables; or same problem as last year, but embedded in another problem situation) but for the weaker kids, they only recognize that they have the right answer. It’s the weak kids who get cocky.

Karen, I just saw what you wrote. I think I need to do that, and more explicitly than in the past. Thank you (and to everyone else who commented)

How about one hard problem on every test, so a B (or even and A-) comes fairly easily, but an A doesn’t?

Or a way of canceling out one or two bad grades by the end of the semester — perhaps a cumulative test which can supercede the tests that went before it?

— Rachel

Don’t get me wrong–I test easy. I just teach hard to keep them interested. Besides, lots of the college stuff is even easier than the hs stuff.

Have a great vacati.on

My thought would be to keep testing easy, but make a little of the homework hard. One or two really challenging problems each time to keep them from getting cocky, and of course to help them develop better problem-solving skills within the easy topics.

Can you take the time to examine some of the history of the concepts of algebra at the beginning of class? I taught a “History of Mathematics” class at my University this past Spring, and several students were completely astounded at the way problems were phrased before algebraic notation became common. The old mathematics texts (before 1500 or so) and the Renaissance mathematics texts are illuminating to my algebra classes because of the convoluted language. Then we rewrite the problems in modern notations and everything seems so much easier…

Jackie wrote “For those for whom it is “too easy” at the beginning, you could try pairing them up with students’ needing some remediation. Acting as a peer tutor may deepen their skills and the others may get up to speed more quickly.”

Please, don’t do this, especially at the start of the year. This only sends advanced students the message that you don’t intend to teach them at their level, and invites them to check out entirely. Advanced students deserve to be taught and challenged every bit as much as other students, and should not be asked to act as unpaid teaching assistants.

My first thought was: if someone is finding algebra easy, that’s a good thing. If they indeed are quick to grasp the subject, what suddenly happens that catches them napping.

Without sounding simplistic, I’d like to caricature 2 types of kids:

a) Kids who are quick on the uptake, but don’t think deeply enough about issues: You know the type, I was one of them! These kids need to be shown different ways of manipulating the content, that usually builds depth. otherwise they become what I call expert test-takers, maxing the lower 3 levels of Bloom’s taxonomy, but failing the upper 3.

b) Kids who aren’t highly strong in the logical-mathematical area, but have found the early portion of algebra to their taste: These kids are the one’s who need more attention and advice. They need to be told that gears will change quickly and they need to cope. I would recommend individualised help and possibly scaffolding through take-home work.

Warm regards,

Vivek

Well since ability grouping is practically a felony these days…

Seriously, no matter what you do or where you start in your class, the same kids will probably still struggle with math. (btw… is it caused by lack of automatic recall of math facts?) If you could narrow down the exact cause of the problem, then you could intertwine the needed foundation skills in with the regular curriculum.

The lack of fact recall is not an issue here. My gut says it has something to do with prior training being procedure-based rather than meaning-based (really, it’s just a matter of degree). And a big part of what I am doing is raising the level of abstraction. Kids who are focused on “the answer” miss that something more important is going on.

You know, some of these kids come to me and solve 7x – 23 = 138 with some arithmetic scribbled off to the side.

Thanks for all the advice. Certainly I will continue to think it over. The “one hard” test question is interesting. And I will definitely have an explicit conversation about this at the beginning of the year, with the entire classes.

I just found your blog and am trying to understand what’s going on in high school math these days (I homeschool a 3rd and 4th grader), and I am in particular wonder what you mean when you say kids come to you and “solve 7x – 23 = 138 with some arithmetic scribbled off to the side.” As opposed to what, doing it in there heads? Using a calculator? What does this have to do with the previous paragraph about “procedure-based” vs “meaning-based”?

— just curious

As opposed to something like this

7x – 23 = 138

7x = 138 + 23

They do arithmetic, and never gain control of variables. They are able to get good answers, as long as the symbolism does not become complicated. And generally they are caught completely off-guard by quadratics, which don’t yield to mental arithmetic.

Whoa! I know this is an old post but, that last example really hit home for me. That post is about me. That is how I do math. I was able to get good answers, as long as the symbolism didn’t become complicated; something it did during Pre-Calc2 (which I failed)! What must I do to relearn so that I can break this barrier and move on into Calculus and beyond?!

Again, this reply is also old, but to Jim,

Start over at either Pre-Algebra or, preferably at Elementary Algebra. If you know basic Arithmetic, then Elementary Algebra teaches you to generalize using variables instead of exact, known numbers. As you study and learn the properties of numbers, you will know how to unscramble almost any equation or inequality given to you.

I’m a student @ Burton Middle and we are starting Algebra in 8th grade, but my math teacher is starting us off early. It sucks! We first did the lesson on Foil and then he gave us 30 problems to do overnight. I don’t want to sound as if I’m complaning but most of us thought oh its just regular math if watch one problem I’ll be fine. Not going to happen. Tell your students that its is harder and don’t give them homework to do that night. Reteach the lesson brefly the next day, then give the classwork and homework.