Why are we still teaching algebra?

[Dan Friedrichs]

The aversion to "common core"-type instruction confuses me. Do people think this was pulled out of thin air? Of course not. Experts in pedagogy developed these approaches, tested them in real students, assessed what worked best, and it was adopted by those who saw the value of the results. It's not some bureaucrats making things hard for fun - these techniques come from experts in teaching and learning who have evidence to show this works. If it didn't work, why would it have gotten so much traction?

Aside from that, in a highly-innumerate country (like the US), it's difficult to understand the logic of staying with the status quo...

[Prashun Patel]

I just don't believe that the ability to explain logic is not for everyone a prerequisite for understanding, using, and extrapolating logic. In theory a good teacher guides, but in practicality, good teachers are not always present. Even in my relatively well-heeled district, the good teachers are hit and miss.

I'm not demeaning the centuries of development that got us to this kind of education. I am saying it's time for it to evolve. I'm not an education scientist, but I do have 2 bright kids that have bumped into obstacles with common core in the past 3 years. So, believe what you want, I think some flexibility and evolution is due.

[William Adams]

The problem is, education bumps into legal problems in terms of access and so forth --- what else can one make of the school system which I attended for 3rd and 4th grade (which allowed me to take 8th grade English, math, and science classes, and would have released the 4 year cap if I'd stayed there until 8th grade so that I could've started on college classes --- all the teachers in the High School were dual-accredited w/ a local college) because it provided unfair advantages to the disciplined and gifted students, while unfairly singling out the lazy and average to seemingly be held behind, or at least that was my interpretation of the Mississippi State Supreme Court case which ruled the system illegal.

Still waiting for someone to work out what the best public domain textbooks were, put them up somewhere that everyone can have access to them, and just be done with it.

[Edwin Santos]

That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind. The fact that this is labeled as an algebra problem and the initial equation looks like one masks the reality that this "problem" is part of the "new-new-new math" methodology being taught in elementary schools in recent times.

Jim,
Would it help to think about Math in the same terms as thinking about teaching English? Math is a language of expression and to call the steps illustrated useless operations and strange thought processes would be like turning to English and objecting to synonyms and metaphors on the basis that we don't need multiple ways to say the same thing (some of which might be unfamiliar and hence strange).

I can completely see where these steps come across as questionable in a simple equation example, but like others have pointed out, the idea is for the student to understand the building blocks of the language so that when the equation becomes more complicated (and it quickly will), these rules and steps will guide the way when things aren't simply intuitive.

Can you imagine someone suggesting doing away with teaching students about verbs, nouns, modifiers and the other technical building blocks of language because we don't really think about them in daily practice, we just intuitively talk? Understanding these technical building blocks allows the educated student to express themselves in different and subtle ways that makes greater use of the breadth of language, and will open doors for them throughout life. The more complex life becomes, the more valuable this ability will be. Math fluency works in much the same way with regard to problem solving.

Not trying to change your mind or say you're wrong, just offering a alternate point of view of why there might be method to what you're perceiving as madness.
Edwin



EDIT - Education is subjective and ultimately I think it's a parent's right to form their own opinions. A parent can delegate to the local school district, or if they are motivated enough, pursue other options like home schooling, charter schools, private schools, online supplementation other hybrid approaches. There are certainly many more options available than there were in the past.

[Jim Becker]

Edwin, the example in this thread is really, really mild compared to a lot of the "stuff" that's being taught in the common core type curriculums. (there are multiple versions...my local district used/uses "Everyday Math" developed, I believe, out of the University of Chicago which happens to be Professor Dr. SWMBO's undergraduate alma mater) My experience with my kids echos Prashun's experience with his kids. My younger is a math wiz (like able to do mental math at an almost savant level sometimes) and still struggled with the very obtuse and multiple methodologies she was subjected to for developing solutions to math problems in elementary school. And as I mentioned, neither I nor my spouse could be of much help...and The Professor does calculus and heavy statistics nearly daily. So many other parents expressed the same concerns. The district has backed down a little and started also teaching the more traditional ways, which the teachers also appreciate. They get frustrated when the kids can't do their homework even with whatever help parents can lend!

[Lee DeRaud]

Asking 5th graders if they anticipate needing to know algebra for their future career plans seems foolish.

The very concept of "the future career plans of 5th graders" seems foolish.

[Lee DeRaud]

I can't imagine stopping Math education pre-algebra.

Yup. That would just be arithmetic, at which point you might as well just have a class titled "How to install a calculator app on your phone".

[Mike Kreinhop]

The very concept of "the future career plans of 5th graders" seems foolish.

The German school system does exactly that. All children attend Grundschule through the fourth grade. At the fifth grade, the school system branches out to Hauptschule (grades 5-9), Realschule (grades 5-10), and Gymnasium (grades 5-12). Hauptschule and Realschule are a mix of classroom and vocational training that lead to apprenticeship and employment in the career path chosen at the start. Gymnasium (pronounced gim-na'-zee-um) is the academic path for university.

I certainly didn't know what I wanted to do with my life at the start of the fifth grade, but this decision is routinely made here. Once a career path or trade skill is chosen for the child, it seldom changes. However, high performers in Realshule sometimes have the opportunity to change to Gymnasium and go on to college.

[Tom Bender]

So in engineering school We solved engineering problems using calculus. That absorbed HALF my energy. Then I worked in engineering for 40 years. Never met an engineer who used calculus for anything. Yes there are a few I did not meet who do but to force every engineer to burn so much energy on something almost arcane is inappropriate. What would have helped more would have been courses in;

Accounting

Languages

Politics

Planning

Law

Patents

Ethics

etc.

Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.

[John K Jordan]

...That time in my case would have been much more profitably spent studying statistics, which I do use all the time. Living in a country where "all the children are above average" it seems that the concepts are widely missing.

That's probably true! As are our national delusions.

Another valuable math skill, depending on your interests, is linear algebra. Learning matrix math was key in developing software to process and then display vector graphics on bitmap screens and other output devices (e.g., a good exercise is write your own flight simulator software). My second bitmap display hardware (in the '70s) was capable of 512x512 b/w or a 256 pixel square in several shades of grey - geek nirvana! Color then: a dream.

[John K Jordan]

The German school system does exactly that. All children attend Grundschule through the fourth grade. At the fifth grade, the school system branches out to Hauptschule (grades 5-9), Realschule (grades 5-10), and Gymnasium (grades 5-12). Hauptschule and Realschule are a mix of classroom and vocational training that lead to apprenticeship and employment in the career path chosen at the start. Gymnasium (pronounced gim-na'-zee-um) is the academic path for university.

I certainly didn't know what I wanted to do with my life at the start of the fifth grade, but this decision is routinely made here. Once a career path or trade skill is chosen for the child, it seldom changes. However, high performers in Realshule sometimes have the opportunity to change to Gymnasium and go on to college.

Our friends in Italy tell me their educational system is similar. In what I think we would call "junior high" they have to decide on which "high school" they want to attend, each with the same core education but with a different focus. Two of our young friends chose art school; one chose language school. (There are others.) The girl who chose language school now speaks seven languages and spent the summer in France and Russia honing her skills. Our art-student Italian house guest came this summer to work on her English and visit art museums. From what she told us the course of study seems far more extensive than what we have in the US. She said in graduating from any of the schools the student has enough of the basic education to go into law school, medicine, anything. It sounded to me that by they time went to university they might already had the equivalent of an undergraduate degree here. I'd like to learn more about the educational systems in other European countries.

JKJ

[Dan Friedrichs]

So in engineering school We solved engineering problems using calculus. That absorbed HALF my energy. Then I worked in engineering for 40 years. Never met an engineer who used calculus for anything. Yes there are a few I did not meet who do but to force every engineer to burn so much energy on something almost arcane is inappropriate. What would have helped more would have been courses in;

Accounting

Languages

Politics

Planning

Law

Patents

Ethics

etc.

Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.

As an engineer, I am horrified at this statement...

To me, your list of topics is heavily weighted towards practical skills. A university education is training to teach yourself those practical skills.

I had often wanted for more practical statistics education, as while I took calculus-based statistics in engineering school, I didn't immediately understand how to apply it in practical situations. I later realized that I had the tools at my disposal to teach myself how to apply it, and more importantly, understand it. Had I taken an introductory statistics course, I might have been able to practically apply it, but I would have just been "turning the crank" on a machine that someone else built for me, rather than understanding it.

[Lee DeRaud]

Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.

On a personal level, I am truly glad some people think that way. I started with an MS in math, and spent a 30+ year career in aerospace coming up with out-of-the-box solutions to the problems that arose when those "narrowly-focused experts" dug deep holes and lacked the imagination to get out.

[Rod Sheridan]

When I was in high school in the seventies, we had a 3 stream system that took you to University, college or trades and I'm not sure what the lower stream was meant for....Rod.

[Andrew Pitonyak]

use it all the time.... For example, which box of cereal gives me the most for my money with this coupon? Pretty easy to do...

I wanted the Internal Rate of Return for my investments based on irregular intervals, deposits and withdrawals.... My spreadsheet did not have a built-in function to do it, so, I derived it then implemented it using a macro. OK, that was more than simple algebra because there was not a closed form solution easily available.

I showed a girl how to calculate simple interest rates and she figured out that when she borrowed money from a friend that her friend had charged her 100% interest on a three month loan. She had no idea how much her friend had charged her. Then again, her friend may not have had a clue either.

Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.