# Why Is Algebra Necessary?

If it even is necessary, how can we teach it better?

“Is algebra necessary?” It’s a question that crosses the minds of many students struggling in high school and college math classes.

Professor Andrew Hacker wonders the same thing. His opinion piece about the math we teach to students has started a big conversation about how schools prepare people for the real world.

He wonders whether this stumbling block forces kids out of school early...whether it really helps with the 21st century tools we need.

His critics - and there have been several popping up in the last week - challenge many parts of his argument. And one of the more compelling questions being asked is "Why is any course necessary?"

Why do we need to read Hamlet, or learn about ancient European history?

What could - or should - change about the way we teach math? Only hours after the curiosity rover lands safely on Mars - is now the right time to be talking about backing off our math requirements? Can we cure our nation’s “math anxiety?”

Today, we talk about the role of not just algebra, but calculus and geometry as well. We look at what can be learned about the education system as a whole.

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This episode originally aired on August 6, 2012.

## Comments

## Is Algebra Necessary -- Is Hacker Joking?

Algebra, and mathematics in general, is as much a part of the shared cultural heritage as is poetry, yet no one is asking the same question about poetry: should we teach poetry in schools?

My answer to that question is yes, despite the fact that I despise poetry, and consider the time spent on poetry in junior high school and high school to be totally wasted.

## Email from Marilyn

I went 12 years to grammar school and high school taught by Nuns. There weren't many choices.

We approached Pre-algebra and then Algebra as a process to solve problems. Thru the years I

counselled my children, and now my grandchildren that algebra teaches you to think logically...

similar to learning to think using the Scientific Method: Step by Step!

## Email from Brett

One example...

Where would you like to travel in the USA?

How many miles away is (Yosemite, Grand Canyon, whatever)?

How many MPG does your vehicle get?

How long will it take to get there?

How much money for Gas will you need?

Food? Shelter? Maintenance?

John wants to go there, as well, what savings with carpooling?

Cost of convenience?

Sharing experiences with others?

Define VALUE ...

SO Much More...

## Email from Rob

I went to college late in life and graduated with an accounting degree when I was 37. I was astounded and appalled while taking college level math classes that the 19 and 20 year old students could not do BASIC math without the use of a calculator. During classes we would be doing problems on the board and get to a basic multiplication problem and there would be nothing but calculators clicking when the instructor asked the class to multiply by TEN !! Is algebra useful in every job probably not, but it is undoubtedly useful and necessary to promote the use of our brains.

## Email from Barry

I find when I am helping grade-schoolers with their math that they seem to memorize symbol manipulation rather than understanding the concepts that allow these symbol manipulations to work. A more conceptual approach would be more successful. If you study to remember, you will forget, but if you study to understand, you will remember.

## Email from David

A couple of main thoughts.

1) Algebra teaches abstraction. The concept that X equals something unknown or anything. There is nothing else that I can think of that teaches abstraction in High school. I think that society are currently having a problem in understanding abstraction in general, leading to some of the break downs right now for instance in bi-partisan.

2) A comment about why literature was thrown out earlier. Personally I hated lit because I always interpreted the stories/poems/etc different than the teacher. But it was a sold class b/c it expanded my empathy and understanding of "the Other".

I'm a big believer of the Renaissance Man concept, if not to an expert level. Beginning biology can help w/ understanding medicine, evolution, etc. Math can provide a huge base for other things. Lit for new life experiences and History for _why_ people did what they did. Physics for reality.. The quote I love is:

"The single most important element in the maintenance of a democratic system"... "The better the citizenry as a whole are educated, the wider and more sensible public participation, debate and social mobility will be. Any serious rivalry from private education systems will siphon off Élites and thus fatally weaken both the drive and the financing of the state system. That a private system may be able to offer to a limited number of students the finest education in the world is irrelevant. Highly sophisticated Élites are the easiest and least original thing a society can produce. The most difficult and the most valuable is a well-educated populace."

John Ralston Saul, Doubter's Companion: A Dictionary of Aggressive Common Sense, Penguin, 1995.

Anyways... Love the show. Wish I could have gotten on the phone.

## Facebook comment from Chris

I'm sorry to say it, but Prof. Hacker is well-named. He preaches ignorance and know-nothingism and does so ignorantly. This show, repeated today, in my opinion, is as marginal as you have ever aired. As with Colin's 9/11 deniers show, if done at all, it should have been with capable exponents of views opposing the proponent of the contrarian view able, in real time, to debate and to confront him. His flimsy case, in my view, would melt under the pressure of cogent, factually-based, coherent argument, argument informed and structured, by the way, via good mathematics education for these opponents.

PS: Advanced Placement classes are NOT keyed solely to multiple choice portions of the exams for their subjects, since students wouldn't do very well on the large essay and short-written-answer parts of those exams. And, finally, his claim that math professors creating derivatives, credit-default swaps and similar instruments is an indictment of math education is so laughable as to dismiss him from serious consideration if ever he merited it.

We need many, many more STEM-capable students and workers, not fewer. Argh. Fie on this man. And more to the point, please have controversial guests with new and contrary views and ideas. But if they are preaching views which goes so pronouncedly against responsible consensus, views which likely would encourage destructive mindsets and conditions (such as countenancing math illiteracy) at least have them confronted with capable opponents.

## Email from Marina

Of course algebra is necessary! I’m a housewife, and recently had to use it to figure out how to make sure my flower garden was a rectangle with nice square 90 degree angled sides – try figuring that out without knowing: a2+b2=c2!

Everyday uses abound.

## Email from Phyllis

OF COURSE WE NEED ALGEBRA! THE PROFESSOR'S PROTESTATIONS ARE MERELY A COVER UP FOR FAILED TEACHING.

## Email from Rebecca

I'm really, really concerned that — at a time when the general level of understanding of math and science is SO challenged in the American public, your guest is arguing for reducing the level and quality of what is taught in classrooms. His argument is really dangerous for the future or our democracy, as it continues us down the slope of "dumbing down" that we're already following, to our peril. We have a significant portion of the public now questioning the credibility of science, which has math at its core, and that skepticism is arguably endangering our future. We may well be able to teach math better, but to argue to cut it out is very short-sighted!

## Email from Abby

I went to public school in Guilford, CT and was required to take algebra 1, geometry, then expected to take algebra 2 and calculus. I had great teachers and even a private tutor but could not pass algebra 2. It made me believe that I was "not good at math", until I discovered I was excellent at statistics. From my statistics course my SAT math score improved 100 points. I went to Skidmore for psychology and was successful in graduate level statistics. I am now a online marketing analyst. I should not have been felt forced to master algebra 2 in high school. It was more detrimental to my success that I thought I was "bad at math" than it was that I didn't take algebra 2.

## Email from Fran

As a recently retired high school math teacher, I was furious about the article written by Andrew Hacker. I was disappointed in the discussion that followed on your program. I won't go point by point because it would take too long.

However, I cannot believe that not one person mentioned that being challenged and learning how to deal with difficulties and disappointment is an important life lesson. Not everything is easy or fun. Not everything we learn has to be applicable to our current experiences. There are many subjects that I have taken (and struggled with) that I will never use and seemed pointless to learn. What my educational experiences taught me, and what I DO use daily, is the idea that expanding my mind is important and that I must do my best to learn things I do not know or readily understand.

I'll end with a quote from Philip Roth's The Human Stain p.330

Reading the classics is too difficult, therefore it’s the classics that are to blame. Today the student asserts his incapacity as a privilege. I can’t learn it, so there is something wrong with it. And there is something especially wrong with the bad teacher who wants to teach it.

Substitute "Algebra" for "classics."

## Email from Robert

Algebra is, of course, is necessary - but not for everyone. Teaching algebra and other forms of math application should be done in context. If a student elects science or statistical based courses, the math application should be taught from within the context of its actual application.

In high school, in the same week, I took a math exam based on 100% logarithms and a chemistry exam based 100% on logarithms and got a D in the math exam and a B+ on the chemistry exam. In the chemistry exam, I was looking for "real" answers to actual, proposed problems.

## Email from Allyson

Perhaps this viewpoint of your first guest would apply to more advanced math; however, I cannot imagine every student not taking some basic form of algebra or geometry.

I was a double major in biology and psychology and have a masters in epidemiology… so I of course did not have one semester where I did not use algebra. However, many of my classmates, even if they were literature, art history, etc. majors, they had to take basic science and social science classes as part of the liberal arts curriculum. Sociology, economics, basic bio or chem all require basic algebra.

Even if you don’t spend one more day in school past high school… if you want to build a fence, or a bench or planter for your deck… or if you want to figure out which debt to pay off first if they have a different interest rates and different fees… basic geometry and algebra can help in many ways in day to day life.

I think the problem is that math classes are not taught in an engaging manner for those students who don’t “naturally” love mathematics. But to “give up” on teaching mathematics in high school is concerning to me.

## Email from Mike

Of course we should stop making Algebra mandatory. But why stop there? Most people won't use science, or history, or civics/government or need to read anything more complex than USA Today.

So lets keep kids in school by not teaching them anything at all.

The real reason no one uses Algebra in America is that we are so bad with math already that all the jobs that require hire level math are shipped overseas. So let's aggravate that situation! I'm sure the South Korea, China, India, Singapore and Russia would love all the new business.

## Email from Mary

Our high school curriculum states that the goal for most math classes is to teach logical thinking. My daughter just spent an entire year in Geometry doing proofs. After you've shown that you can do 10 proofs, what's the point in doing 50 more?

Yet the school does not offer a course in classical logic... (for example, the relationship between case and effect versus coincidence.) There is also very little on statistics. A 21st century citizen who cannot pull apart the illogical statements in our public discourse or in the many "scientific studies" published in the mainstream press cannot effectively participate in our democracy.

Logical thinking and numeracy skills are certainly important, but there are many ways to get to that goal. I think our high schools need to stand back an re-evaluate their curricula for the 21st century, and not fall back on the way they've done it for the last 50 years.

## Email from Rob

I once read that the first three years of high school math education could be replaced by giving every student a $3 calculator and teaching them how to use it.

## Email from Greta

Your guest today shames the good Hacker name. He cannot even pronounce Toyota. He is arguing that only 5% of jobs require STEM skills --um, the GOOD jobs that we cannot fill in the United States without importing labor. Goodness, algebra lets you figure out equivalent ratios --e.g. if I need a cup of flour per egg, how many cups of flour per three eggs --this is not rocket science that normal people cannot use. Ug. I've never felt disgusted with Where We Live, I am a huge fan, but if someone writes an article for the NYTimes (which I respect), this is proof that they don't necessarily deserve to be a guest on your show.