Eighth-grade algebra debate continues online

The Times on Monday revisited the debate over the state's new eighth-grade algebra mandate. The piece recounts how Tom Loveless, a senior fellow at the Brookings Institution, has concluded that such mandates do more harm than good by forcing difficult math on the unprepared, while slowing down the progress of more advanced students. His findings have generated many responses. Read on for a sampling.

-- Howard Blume

Lance seems to side with researcher Tom Loveless:

Take a look at the state scores and you will see that it is even a stretch to argue that our gifted students will be successful with this rule. Right now, their percentages on algebra are not that great.

It is the job of a factory to produce identical product, and the job of a school to help students with their individual needs. All this algebra mandate will do is drive more people out of the system.

Arnie, from Reedley, Calif., wanted to comment on this line from the article:

"Students who take algebra early have a leg up on college and career."

Well, yes. That is true. But this is not a causative relationship. Of course, smarter students are prepared earlier for more rigorous math and smarter people do well in the modern world when they leave school. But that doesn't imply that algebra is the solution. Algebra is a thermometer, not the fire itself.

Another reader, Deborah, also spun off on that sentence.

Correlation is being confused with causation here.  These students take algebra "early" because they are good at math.  Taking algebra in eighth grade does not cause a student's mathematical aptitude to increase. 

I didn't take algebra in eighth grade because I wasn't ready for it.  I had neither the interest nor the ability to be successful in algebra at that age.  Yet I have college degrees in physics and computer science. 

Shelley see harm in pushing students, including her daughter, too quickly.

Why are we doing this to our kids?  I have a daughter who is a senior in high school this year.  She was pushed ahead into algebra in eighth grade through an honors program.  It was her first C in her life and set her up for math mediocrity for the rest of her math classes in high school.  Now she’s struggling with the math portion of the SATs because she took algebra and geometry so long ago and didn’t fully understand it, because she was placed in an accelerated class with the math geniuses.  I would fight this program as I don’t think that it benefits anyone.  If kids take algebra in eighth grade they are [having] to take trigonometry in 12th.  Very few will make it that far.

William has an issue with modern teaching methods:

Part of the algebra problem might be the "new math" approach gradually adopted in the U.S. after Sputnik.  A close friend of mine could not learn algebra the new math way.  So, he got himself a 1950s math book, taught himself algebra, and is now a brain surgeon!

Often, theory is a straitjacket to educators, rather than a signpost.  They assume that new is always better, and so throw away the baby with the bath water. I have been a teacher for 16  years and have seen this folly time and again.  After broken homes, bad pedagogy is the next major reason for the failure of our schools. 

You can be sure that the third-world students putting us to shame in algebra, did not learn it via the new math, but in the traditional, tried-and-true way.  I am all for improvement, but to change and to improve are different.  Alas, textbook sales drive education more than sound pedagogy.  

(Note: Loveless, the researcher, specifically takes issue with California's math curriculum of the recent past. But he also sees much improvement in the last decade.)

Reader Norman also thinks math instruction has gotten worse and that taxpayers get a raw deal.

When I went to school in the '50s junior high was seventh and eighth grades and we had algebra in 8th, also general science. What has happened to our schools and the students? They [school administrators] keep asking for more money yet educate less for all they get. It is time to shut off the money spigot and demand results before they can get more. What we need is more and better qualified teachers with less administration, which is where all of this money is being spent. We don't need high-paid talent in offices, we need them in the classroom where things can actually be fixed. My school administration was the principal of each school (who also taught some classes as well), a superintendent and his secretary, who also ran the high school office. That did just fine and we all qualified for college, those who wanted to go.

This reader, who asked not to be identified, sees teacher qualifications as a central problem:

Algebra misconceptions: that it's mysterious, that it's tough, and that it's "real" math.

I've informally taught first lessons in algebra to 7-year-olds, and they've had no problem. (I'm in my 60s, with a BA in math from long ago but working in an unrelated field.)

My guess is that teachers learned to regard algebra as scary, and in turn they pass their own math anxiety to their students. Make no mistake, that anxiety is far more damaging than ignorance.

Of the subjects historically taught in our schools, the classic example of real math is not algebra but geometry; however, this is now taught in such weakened form that I don't know if students benefit from it. High-school algebra is just manipulations. It's valuable! Fascinating things can be done with it (and with arithmetic)! But such things are generally not done, partly because many teachers do not understand enough math themselves. (A long-time LAUSD math teacher with a Ph.D. in math used to say that no other teachers in the district knew math. No doubt this was an exaggeration.)

I volunteer-taught math one hour/week in a public elementary school, in a variety of classes from 3rd grade on up, and I never found a student who couldn't do everything we talked about. One student would understand an idea before it was half out of my mouth, while another required three repetitions and personal attention in doing the exercise. But every single student could do everything. This is not because I'm a great mathematician or teacher; but I do like the subject, and I did know enough about it to prepare reasonably good lessons each time. Of course I had the luxury of time that real
teachers do not have. (Most teachers I've seen are angels of patience and work endlessly, not to mention paying for necessary school materials out of their own pockets.)

I know a young man who attended an LAUSD magnet school, and in his 8th grade honors geometry course was taught something that was not only false, but famously false (trisecting an angle with compasses and straightedge). He retailed it to me, and I took the teacher up on it;   and the teacher realized that he had been in error. Two months later I learned that He Never Told The Class. There's no room in education for intellectual dishonesty!

Conclusion: We should consider whether our top priority should be educating the teachers, helping them to acquire mastery and thus reduce their math anxiety.

A college math professor in North Carolina finds that even his calculus students are deficient in algebra. 

As a professor of mathematics in an excellent liberal arts university who graduated from high school in the Southland, I would like to add a somewhat different perspective.  I took algebra I in the ninth grade.  The algebra courses that I took in preparation for my college calculus courses were excellent and I ended up getting a Ph.D. in the mathematics.

The number of students that I teach who have taken calculus in high school has increased but the corresponding skills in algebra has decreased. Time is a zero-sum game; time spent doing one thing is time not spent doing something else.   I have students who have taken the AP courses in calculus in high school but are completely unprepared for calculus in college because their skills in algebra are abysmal.  These students cannot do college calculus because they cannot do high school algebra.  They cannot do high school algebra because they were pushed through the subject when they were academically ill-prepared to to so.  Many of these very good students come to college and enroll in a one-semester course of calculus.  Enrolling in additional mathematics courses is out of the question because they just cannot do the work.  What is the point of pushing these students through all of these upper-level math courses in high school if they are unprepared to continue their studies in college?  Most of my students would have been better prepared to study mathematics in college if they had spent their high school years practicing their algebra skills and enrolled in their first calculus course in college.

While I am sure that Gov. Schwarzenegger is well-intentioned with respect to increasing skills in mathematics, what we do we should do well.  Making all students learn algebra in the eighth grade is, in my opinion, a recipe for disaster for mathematics at the college level.

Donald had a question and a point to make:

As a former Californian and a working scientist using algebra daily, I have questions about this policy. When you say mandatory eighth-grade algebra, does that mean students can’t start algebra earlier? I started algebra in seventh grade and finished all math courses available in my high school in 11th.  I was often bored in math class due to the sloooow pace (this was in the advanced track).  No way should any students who don’t have arithmetic mastered be put into algebra classes along with students who are really ready to move forward. Their presence will be actively harmful to the other students.

It is a fact that people have different levels of math ability and one-size-fits-all will have a very harmful effect on the top students who are able to and need to move faster and who will be the future scientists and engineers.   

To answer the question: Students can still take algebra in seventh grade, but the eighth grade state math test will be algebra for all students starting in the 2011-2012 school year. The expectation is that school districts will be forced by this policy to make sure students have taken algebra in the eighth grade, if not sooner. For some time, the official eighth-grade state math curriculum has been algebra, but eighth-graders were not required to take the course. And they also weren't required to take the algebra test.

Don thinks third grade would work just fine for algebra, if it were well taught.

I'm 67 years old and took eighth-grade algebra.  My two children learned algebra in the third grade.  My daughter ended up taking advanced calculus at the age of 16 at UC Berkeley, and is now a veterinarian.  My son skipped two years of grade school and was admitted to UCLA as a physics major with a minor in pre-med two years early.  He graduated with honors in record time.

In 1967 I took a nine-month postgraduate class in physics from Richard Feynman.  At the break Feynman and I both headed for the coffee machine.  He told me about how his child's school district asked him to examine the eighth-grade math-science curriculum.   Feynman told me that the key to getting kids to understand math is to realize that math is a subject where learning one step requires understanding the previous step.   Maybe the student was not paying attention when the crucial concept was explained.  He said that all that was needed to help a math student is to talk to them to find the step they missed, and explain that step to them.  Then they'll understand.

When my oldest child was born, I was an artificial intelligence researcher.  My theory then and now is that younger children are better able to understand advanced math concepts.  Arithmetic is boring for someone who has advanced math understanding.  I encouraged both of my children to cheat and use a calculator for their homework when possible.  Boring them with arithmetic drills will turn them off.

Algebra should be taught in the third grade.

Comments

[Klint]

I agree with Don, partially, on students needing to learn and understand mathematics, step by step. However, I disagree with the fact that the algebra should be taught at 3rd grade.

I was born and raised in South Korea where the country ranks consistently at top 3 in Trends in International Mathematics and Science Study(TIMSS) math tests. I graduated from middle school in 1987 and admitted to one of the best high schools in the nation. Back then, S. Korean middle school students were required to take entrance exam to advance to high schools.

Korean education system back then was very different from the way the school system works here. There was no such thing as not-passing-the-grade concept in Korea. If you were going to school and was physically there for a whole school year, you were guaranteed to proceed to the next grade no matter what your grades were.

Now you may argue that this may seem illogical but I am the perfect proof of this system working at its finest. For example, it would have taken me forever to graduate elementary school if there was such thing as a failing-a-grade system as I was not a very good, academically, student until the 9th grade. I never did my homework for the first 6 years of my school year and was always the last or second to the last in the class in grades. At 7th grade I was in top 50th percentile in grades.(in Korea, the shool posts top 100 students on the board - I never made this board until the 9th grade. Also they tell you exactly where you rank at in school that has approximately 650 students per grade and about 55 - 60 students per class) At 8th grade i was in top 30th percentile and top 10% consistently in 9th grade and took the entrance exam to one of the best high schools in the nation and was admitted.

I think it's illogical for Don to presume that algebra should be taught in 3rd grade. The comment he made - "My theory then and now is that younger children are better able to understand advanced math concepts." is further from the truth in my logical view for the most kids. Each student excels at different subjects at a different time in his/her life. And I do not believe that this 'time' is in elementary school. Elementray school should be just exactly that.. elementary not advanced. Let the kids play and have fun in their elementary school and teach them basics so they could learn advanced stuff in middle and high school and further their education in University. As far as I could remember, the only few things I learned in elementary school is to learn to read, write, add, subtract, multiply and divide. So I comment - My theory then and now is that younger children are better able to understand having fun than advanced math concepts.

[Herb]

I can add that more algebra is being taught and less learned than ever (I teach algebra one to ninth graders). Each class has more than half of the students who don't know basic arithmetic. Most of my energy is spent on management. The district (LA) does not help by insisting on fuzzy, group-based, project-based methods rather than practice to the point of automaticity. Mandatory universal algebra is a beutiful idea. So was communism.

[Alvin]

Here are my suggestions after reading above comments..
1) Prepare teacher better to teach Pre-Algebra. Make the topic interesting, use real life example and help students erase the notion that Algebra is difficult.
2) Prepare students for 7th grade with Pre-Algebra.
3) Get parent involved
4) Teach Algebra at 8th Grade.

The world is not going to stand still while we debate over Algebra. Many countries are teaching Algebra at a younger age. If we are to compete globally and be the leader we should do it quick. Algebra is the very foundation for higher Math like Calculus. If they cannot do Algebra, they will not do well in Calculus.