I had a whole other post planned for today, but it got bumped because yesterday I, like many of you, read the strangest op/ed piece that I think I’ve ever read in the NY Times. And that’s saying something. In the piece, *Is Algebra Necessary?*, author Andrew Hacker suggests, in a nutshell, that algebra is too *hard* to require it of students as widely as we currently do. Dr. Hacker states that as many as six million high school students and two million college students daily struggle with algebra and asks, “Why do we subject American students to this ordeal?”

Apparently many took issue with Dr. Hacker’s questioning of the relative importance of algebra, because, with 475 comments posted to the online version, comments there are already closed. And are there ever some scathing comments there questioning, not only Dr. Hacker’s premise, but also his sanity. I’ll let you read those protests for yourself.

The thing that was so shocking to me was that *nowhere* in the article was the question of how we *teach* algebra called into question. If we really do have eight million learners struggling with algebra on a *daily* basis, maybe we need to fundamentally shift how we’re approaching the algebra curriculum.

I’m not a math expert. I did well in algebra I and II and in trigonometry. I did terribly in geometry. I had to take three quarters of calculus for my undergraduate degree in psychology and I failed the second quarter, thus taking FOUR quarters of calculus in total. Generally, I’m a pretty competent learner. But I can tell you that a big part of my failing that second quarter was the fact that it was taught in a lecture hall of 350 students by a professor who faced the board during the entire class, scribbled notes on it and mumbled his way through the “explanations.” Those were the days before online or distance programs were available. Heck, I didn’t even own a computer….I had one of those old Brother word processor devices that was one step up from an electric typewriter!

And maybe it’s my hubris, but I still don’t believe that calculus is just too difficult for me to understand. Nor do I believe that algebra is just too difficult for those eight million learners Dr. Hacker refers to. I’ll leave it to others to debate whether or not algebra skills are truly useful or applicable in the so-called “real world.” (Though I can honestly say that I still use algebra to figure stuff out on a regular basis.)

Sure, there are some learners who are, due to organic issues, simply unable to learn complex concepts. But I truly believe that we can design an instructional program that will work for the bulk of those eight million. What if we designed an online program that was self-paced, adjusted to the performance of the learner, providing ongoing performance tracking and reporting, gave learners immediate and meaningful feedback? What if we had….dare I say it…*Programmed Instruction* for algebra?

It’s one thing if we, as a society, decide that a subject isn’t “core” enough to teach in schools. You won’t hear me advocating for the teaching of function theory or partial differential equations (yes, I had to look those up) in high school. But by the same token, students not doing well in a subject is hardly reason to drop it from the curriculum. Then we are on a slippery slope, aren’t we?

Let’s move on from blaming the student and…here…blaming the subject itself…and move on to the real question: What is the best instructional method for teaching complex concepts and learner repertoires?

Thoughts?

*The image included here appeared with the original article, “Is Algebra Necessary?” and credit is due to Adam Hayes.*

**Update 7/31: ****After quite a few “offline” conversations on twitter and facebook, I wanted to offer the following youtube resource to math teachers. You can follow Dan on twitter (as I do) @ED_re4mr and feel free to contact him to find out more about learning to implement his methods! **http://www.youtube.com/watch?v=YZKHBZXgPQU

I agree with you whole-heartedly, Karen. It is not the subject that is the problem but the way it is taught. I tutored math for 4 years at a 2-year college here in Indy and I was floored by the number of students that were not able to do basic math computation let alone any kind of algebra. That said, with persistence, the right attitude and instruction, I saw many students who thought they’d never pass their math classes not only pass but get A’s & B’s because someone finally explained it in a way they understood.

One of the things I enjoyed the most from my time in the tutoring lab was seeing how differently people’s brains worked. And when it finally clicked, you could see it.

But back to instruction, when you get into college, most math courses are taught my mathematicians. Just because you can do something does NOT mean you can teach it. There needs to be more rigorous teaching standards. I also often thought there should be Algebra courses for majors and non-majors.

Not to mention that a lot of elementary school teachers were bad math students and don’t like math. That’s the first introduction that children get to learning math. I’m a HUGE proponent of having a dedicated math teacher at every elementary school. It should be the one subject that should be taught by a specialist.

Most of the students I saw fail while I was tutoring was because of their attitude. They spent so much time saying they were bad at math or hating math that they had no capacity left to actually learn it. Those attitudes are instilled early. Get to them while they are young and you could change the whole course of their learning.

Can you tell I’m passionate about this subject? GO MATH!!!!!

Christy, these are great thoughts and I appreciate your contributing. One piece that I want to pick up from you, in particular, is the impact of early failures on later success. We see soooo many kids who reach middle school unable to read or do basic math. And, to your point, they’re done trying. They’ve never been successful academically, so why bother? But when we are able to give these kids effective instruction it is amazing how we’re able to turn them around! Being successful is hugely reinforcing for them!

I often hear folks talking about the “benefit” of making errors in learning. But we don’t often talk about the damage a prolonged error history can do. It doesn’t take a long before kids believe “i’m not good at math” or “i’m not good at reading.” We do kids a huge disservice allowing that to happen. But as long as we continue to take the position implied by Hacker’s article, “Oh, this is just too hard for most kids,” we will continue to produce kids who lack confidence and competence.

I completely agree. I saw that time and again with the adult learner’s I worked with. So many wanted to get a degree but quit because of math but I say it was because of their attitude towards math rather than math being to hard to learn or them truly being unable to learn it.

This really is an ongoing issue…

Several years ago now (I’ll estimate by saying 10years), my sister asked if I would speak to some of the girls in her Girl Scout Troop who found Math too hard and they were having their parents petition them out of their math classes (all types of math fyi). I was asked if I would speak to the young ladies to explain that it could be the way in which they are learning the material rather than material itself… I started with the teachers first, who explained how boring math is and how difficult it was to teach… My advice to them? “Math IS hard, just like every other lesson we NEED to know in this world — it you find a subject boring and too difficult, then please excuse yourself from teaching the it and let someone who is excited by the topic in to teach students.” Then I gave the young ladies my contact information and offered 1:1 discussions if needed. Following that up with a trip to the school board… sadly, that is about where it ended.

The young ladies did reach out and we turned some of our 1:1s into group discussions. They took it upon themselves to meet up after their weekly Troop meeting to review any trending “issues” I saw them having. They kept a file of their notes and left it with my sister, so future girls can learn from their lessons.

WOW. Kathie, this is more disturbing to me than the original article I cited! If the

think that math is boring and difficult to teach, what chance do their students have?!? Those girls were so lucky to have you as a resource….I wonder if any of them will have careers in STEM!teachersI was really fortunate, in retrospect, to have a VERY strict algebra I teacher, who loved math, in 8th grade. At the time we all hated her class because she didn’t take ANY nonsense and we worked our tails off. Getting an A in her class really meant something. And if students struggled, she kept them after school and worked with them one-on-one. The upshot for me was that I was in great shape for algebra II when I got to high school the next year. And she is one of the few teachers who I remember. Thank you, Ms. Gladys Turner, wherever you are!

While Kathie’s interaction with the teachers is disturbing, I would argue that it is more common than most people would imagine, which is precisely why I advocate for dedicated math teachers for elementary schools. I too owe a huge thank you to Ms. Turner. She was a truly great teacher!!!

I have so many teachers that deserve a big thanks and a “take a look at what you helped me become” — but I’m going to point to Mr. Horzelski (4th grade). Back in the dark ages, when I was in elementary school, I think he would have made Christy proud. Although it was just a singular class to teach all topics, he would take each topic, break us into groups depending on where we were with regard to each subject’s lesson book.

When the highest tiered group finished their coursework, they would work with the next tier down to help understand that coursework, etc. The bonus for the class was if all groups finished their coursework prior to the scheduled time, then the entire class could have bonus indoor recess (chatting together, dancing, whatever as long as the class as a whole behaved). Each of learned lessons in teamwork, as well that we are all really good at something.

When he could get parents, relatives, or his own industry friends to visit, he would invite them in and have them walk through a subject which they felt best supported their current job. It was a great way to work within the system he had to work with and gave us kids some insight to careers. 🙂

Nice!

Wow! That’s really cool!!

Bravo, bravo!!! How often during my 38 years in education did I see all of the above. I once told an administrator that learning (and test scores) would not improve until he hired good teachers. Needless to say, that was not a popular concept in an inner city school – but I knew there was nothing in the water that was preventing those kids from achieving.

Fran, I think that comment would probably be just as unpopular today! (I’m so glad that you, as a former teacher, said it, and not me!)

I know that many, many teachers out there are great! But when we come across teachers like the ones that Kathie described, what can we do to get them excited and passionate about teaching math (just as an example)? Is it too late for them? Should we examine Christy’s point that not all elementary school teachers should be teaching all subjects due to varying levels of expertise and affinity?

Just like kids are products of their environments, so are teachers. Are we doing teachers a disservice in their current teacher training programs? I know of many teacher training programs that spend numerous courses covering pedagogy and history of teaching. Is this time well spent? Should we spend more time on advanced subject knowledge and courses that focus more on execution of instruction? Just like kids, teachers don’t just show up hating or not understanding a subject. There’s a whole history there. And for teachers like the ones we’ve mentioned here, what were the contributing factors that made THEM so awesome? It seems that somehow between our teacher training and our selection criteria we must be able to create a better environment for both the teachers and the students, doesn’t it?

Bizarre is not just a word. We are talking about a basic building block for math. Of course not everyone will be a mathematician, but not everyone will be literary major either. I have an idea, lets not expose any student to Shakespeare, why in todays world do we need to know about him? Understanding what he meant by translating from “old” English to modern is an exercise that can be daunting by your average 9th grader. But, with the right attitude and teacher it helps us understand that even then people had the same fears, hopes and dreams. Algebra is a language that explains the world. It helps us think abstractly, why????? Because, it probably was the first subject that made us think in a way that wasn’t comfortable. We are talking about a 9th grade subject like it was differential equations a college course that is needed by select few.

Thanks for those thoughts, Steve. In truth, I’m starting to wonder if Hacker’s article might have been entirely rhetorical? Dare I hope?

Funny you should bring up Shakespeare. Requiring Shakespeare was a matter of some debate on another of my posts, https://karenmahon.com/2012/07/10/three-revised-things-to-unlearn-about-learning/, where two teachers were debating the merits of context for application of skills.

I admit, I’m baffled.

Karen,

Seems we all had the same thoughts around the same time.

Your post, and the insightful comments, all resonate. Especially the comment about teachers who find the subject uninteresting, and decide this is what they will share with their students.

I would not want to over-generalize from one incident, but as we all seem to agree, if the kids are not learning, then we need to examine the material we deliver and how we deliver it. Otherwise we’re no better than Aesop’s fox, denouncing as too sour the grapes we just could not reach.

But then we probably don’t need to teach Aesop either. He’s Greek and dead, so he doesn;t matter, right?

Thanks, Matthew, for checking out my post and for commenting. I really like the Aesop’s fox analogy….can I use that? 🙂

Hi Karen,

I read Dr. Hacker’s Op-Ed piece too, with much dismay. I’ve also read many of the blogs that took issue with his piece. While I agree mostly with the points made by those blogs, there are others points not mentioned, which to me underlie the failings of the teaching of school mathematics.

Firstly, it seems to me that there’s a misguided emphasis on practical “real world” problems. Children have the capacity for play, and it’s with this play that children learn the valuable skills needed in later life. Math in school should not be about solving “real world” problems, but rather doing actual mathematics (arithmetic in grade school and algebra, geometry, and trigonometry in high school) and–what’s most important–becoming comfortable working with (read: playing with) abstractions. But in order to get comfortable with abstractions, the kids have to practice. This brings me to my second point.

There seems also to be a trend these days to want to provide kids with “number sense” by either coming up with new ways of explaining things, or worse, by pretending that solving “real world” problems is giving them quantitative skills. This to me is a big mistake. There’s a somewhat famous anecdote where John von Neumann–a very famous mathematician–said this to someone who complained about not understanding a certain piece of mathematics: “Young man, in mathematics you don’t understand things. You just get used to them.” The best way for kids to get “number sense” is by allowing them to get used to working with numbers. This means, for grade school kids, doing addition, subtraction, multiplication, and division, and not just with integers, but with fractions too. (Proficiency working with fractions is much more important then decimals when transitioning to algebra.) By handing kids calculators arguing that the “real world problems are what’s really important” is denying these kids the opportunity to genuinely develop “number sense” if that expression is to have any meaning at all. In fact it’s criminal!

If kids don’t know their multiplication table by heart and are not comfortable working with fractions, how can we expect them to learn algebra, which is the next level of abstraction? It’s like expecting a kid to play good ice hockey when they can barely skate. How can one be able to figure out when to pass and when to shoot if the front of their minds is consumed with not falling. High school algebra is no different.

I could go much further, but this comment is already far too long.

William

Thanks for those thoughts, William. I can’t disagree with you. Certainly it isn’t possible to teach the application of skills (i.e., solving “real-world” problems) without teaching the basic component skills that are required for application to be possible. And I agree that there seem to be many education professionals today who want to skip that “boring” stuff at the beginning.

I am not a math subject matter expert and I haven’t read the math education research extensively, but I CAN share this anecdote that I think you’ll appreciate: A friend was working with a special education student and his family, consulting on goals for he Individualized Education Program. The parents wanted the student to learn about money: how to identify money, count money, give the appropriate change to a cashier, etc. The school staff in the meeting said, “Why does he need to learn about money? Just give him an ATM card.” Crazy.

Bravo! Bravo! Any successful elementary teacher knows how important this is and they also know that presenting any math concept initially by using concrete objects is an important step that should precede the memorization of math facts.

I completely agree, William. I recently started tutoring elementary school children and was appalled by how mathematics is taught to them these days. What happened to rote learning? While it may not have been appropriate for all subjects, it most certainly is for math. In order to succeed beyond the basics in math, you have got to be able to add, subtract, multiply and divide quickly. Great hockey analogy, too!!!

Karen, that ATM comment is the height of absurdity, which is probably why it is so true of so many in society today.