Problems with Middle School Math

I guess this explains why the intro physics students I see are so bad at algebra...

I think it's more than that. Yes, teachers who don't understand algebra certainly aren't going to help, but I think that teachers who do understand algebra frequently don't do a good job of imparting that understanding to students, just as Eric Mazur and others have observed that even though they understand physics, students who get good grades in their classes may not have really understood what they learned.

Too much of teaching in science and math centers around the learning and memorization of rote facts and procedures rather than actual understanding. And, yes, it's much harder to figure out how to teach actual understanding, and much harder to figure out how to test for it....

I'll worry about this Terrifying Report after we get parents to actually send their kids to school every day, come to parent-teacher meetings, make their kids do their assignments, et cetera.

There are a number of teachers-- I know this from personal, if anecdotal, experience-- who are actually terrified of mathematics. I learned math despite having been taught by these people.

(More specifically, I learned almost nothing about math in grade school, because the teachers there were by and large even afraid of arithmetic. I learned math in high school, because the math teachers there, at least, were not only not afraid of it, but actually liked it.)

I left college and university teaching (Math, Astronomy) in part because so many of the students seemed under-prepared in arithmetic and algebra. I taught summer school High School algebra to students who would be unable to graduate until they learned this subject.

Whenever I discuss this with other teachers, they ask: "what makes you think that the problem starts in High School?" The report shows that, indeed, middle school may be a more severe problem.

I am about to begin my second quarter in a College of Education, towards full California credentials to teach High School Math and Science. The first quarter included my observing 45 hours of high school instruction, different high schools, different teachers.

Some teachers knew the material better than other; some knew techniques of classroom management better than others.

There is still a question, in my mind now, that "people with a math degree but no 'background in pedagogy'" can or can't teach middle school or high school. The California credentialing system used to (according to a Jerry Brown state school board appointee with whom I conversed) have a loophole for "verifiable eminence" whereby provable experts in various fields could have credentialing waived, and be allowed immediately into the classroom. This is no longer possible in California.

I have taught over 2,000 students in various subjects since 1973. I have a Math degree (among others) and know the subject better than any of these teachers that I oberved (including department chairmen). But some of these teachers were better trained than I in pedagogy.

A common sense position for improving Math education in the USA is: (1) do better at teaching Math to teachers; (2) do better at teaching pedagogy to teachers; (3) do better at involving parents and the community. As to how one does this, experts differ.

The report shows different goals, styles, and statistical distributions in different countries. There are also changes over time in each country.

I will not take the time here to rail against the "No Child Left Behind" policy of the Bush White House, as I have yet to find a single teacher who believes in its efficacy.

I close with a quotation, associated with a promising methodology, with which I strongly agree.

"Imagine the following situation. For twelve years you are forced to acquire skills in using some tools that become more and more intricate, complicated and finally utterly unwieldy -- like some gardening tools -- trowels, shovels, rakes, hoes, all the way to combines. You practice using them in a gym, with a patch of soil about 1 foot by 1 foot in size and about 1 inch deep, and you are NEVER EVER allowed to get to a real garden and use your tools and skills there. Would you love and cherish your tools? Would you strive to learn and perfect your skills? Preposterous as it sounds, this is exactly what our K-12 math education currently is. Kids are forced to learn algorithms and techniques without ever being allowed to apply them to a situation for which these algorithms and techniques were invented.
We believe that this is a main cause of the present crisis in math education, and the only way out of it is by opening the doors of a real and beautiful garden and letting our students do their best in cultivating it. This is what problem solving is about..."

Tatiana Shubin, "The Teacher's Circle: an AIM initiative", AIMath. The Newsletter of the American Institute of Mathematics, Autumn 2007, p.8.
Avaiable as PDF online.

I had 9th grade algebra in 1962-1963, and it was all rote learning.

In 1966-1967 I had two quarters of college calculus, getting a C and a D. That ended pre-med for me. I had been trying to learn everything by rote.

It wasn't until after my formal education ended that I discovered algebra had practical uses. I later went on to teach myself calculus, not out of curiosity, but to solve real problems.

At this late date, I am still sore about my crummy education. I was cheated.

I suspect that, like any subject, math is best taught by a teacher with a solid understanding of the topic, who can engage with the students. Right? First you have to get them to listen, then you need to be able to tell them something. But it seems to me that the understanding part has to come first. I've had plenty of classes with teachers that couldn't connect, but if they know what they're talking about at least you might learn something.

I'm a bit confused by one point in this report. Are middle school math teachers required to have a math degree or not? Because I can't imagine how someone would pass advanced calculus, differential equations, etc., and not grasp basic algebra.

I'm a Canadian high school physics and math teacher. In order to be a teachable subject, one has to have at least a minor in mathematics. That means a couple of years of calculus. I've never come across a math teacher who didn't understand algebra. On the other hand, there is a belief within schools that some people have, that anybody can teach math, whether they have a background in it or not.

There are always good math teachers to take on pre-calc, but sometimes the least mathematically-sophisticated streams are covered by someone with no particular background in math or science, just as occasionally, gr. 10 general science will be covered by someone without a science background (but not usually, thankfully). In middle school they seem to relax the standards (more). Ideally, one should have a math background, but sometimes they say, it's only algebra, so they'll give the job to whoever. There are no streams in middle school here, so this affects everyone.

To do a good job teaching any subject at all, you have to have a much deeper understanding than your students, so that you can approach the subject from different ways and help them achieve conceptual understanding. Math is more than just algorithms. If this realization isn't made in the course of a math degree, it should be made in teacher training courses. I was fortunate enough to supplement my math education with some really great math, physics, and science education courses, all taught by the same professor who I came to greatly respect.

Rob, if you think rote learning is bad, just wait until the kids show up who never even got that! "Look Say" reading meets math ed, where guessing replaces logic.

Waterdog, you don't really want to know. Specific requirements vary from state to state, and everyone reading this who has any interest in the future of the US should find out what they are in your state. In mine, the requirements for SECONDARY math ed look a lot like a watered-down math major with most upper-division classes replaced with pedagogy in the college of Ed. The requirements for K-6 are a joke. I put it roughly at the level of rote learning of 9th grade algebra I (defined by what was in that subject when I was in school), and then only while they are actually in that math class. After that it is all about pedagogy.

Jonathan, I have little doubt it starts in middle school. I've picked up a few sections here and there of a "college" (scare quotes fully justified) math class that is roughly at the 9th grade level. (Linear inequalities, point-slope formula, that sort of thing.) It was inevitable that you would get a student dealing with a horrid case of math anxiety. Applying a technique picked up from a colleague would just as inevitably turn up the fact that the student did fine in math, even liking it, until middle school. What teachers did to inflict that anxiety was horrifying. (Think about how bad you would have to be for a public school system to fire you within the first week of the semester.)

The problem begins in K-12, which is where the future teachers learned to hate math. Data I saw at the Uni that published this article showed that future teachers were being drawn from the bottom 10% of the university population, something that has probably not changed. A few years ago Profgrrrrl told a story about overhearing students at another Uni talking about math ed final exam: It wasn't too bad except for the parts that involved math said the future el ed teachers, and they were really happy they would not have to do any math ever again.

Re: #8, CCPhysicist: Correct! Thank you.

"Specific requirements vary from state to state" -- and some states who did well sued the Federal Government when they discovered that the unfunded "No Child Left behind" mandate would require them to actually decrease the quality of their education. The suit went nowhere.

"Jonathan, I have little doubt it starts in middle school."

This might be true. Right now, I'm invested in getting High School credentials for California, and have to hope that heroes and heroines attack the middle school problem.

"I've picked up a few sections here and there of a 'college' (scare quotes fully justified) math class that is roughly at the 9th grade level. (Linear inequalities, point-slope formula, that sort of thing.)"

The signs became clear to me, which I had ignored before, being from an elite high school and an elite college, when I had some such students. How could they rationally have graduated from high school? This could not have happened in my country by accident.

"It was inevitable that you would get a student dealing with a horrid case of math anxiety."

So I read the literature of Dyscalculia a.k.a. Clinical Math Anxiety. Again, some states don't admit it exists; others have programs to deal with it to some extent. Bottom line: 1/3 of the time the student has some brain structure or brain function abnormality that we don't know how to treat. But 2/3 of the time the student has simply never had a good teacher, and went way off the track, and developed authority and/or peer geroup and/or self-esteem issues.

"Applying a technique picked up from a colleague would just as inevitably turn up the fact that the student did fine in math, even liking it, until middle school. What teachers did to inflict that anxiety was horrifying. (Think about how bad you would have to be for a public school system to fire you within the first week of the semester.)"

That is the most amazing thing. I've discussed this at length with others who have independently discovered it, including Caltech Executive Officer for Math, the brilliant and capable Gary Lorden.

The student, once he or she trusts you and you ask, will almost inevitably say:

"I was doing just fine in Math. I liked Math. Then Miss McGillicuddy (or whomever) in 9th grade did such and such to me, and I've failed math every semster since then."

They know WHERE they went off the track. They know WHEN they went off the track. They are suffering. They have identified a precise problem, which is a huge step to solving the proble. IF the teacher has asked. IF the teacher knows what to do.

I am a good teacher. Not a great teacher. I worked very very hard to figure out each student's learning style. To follow up on their identification with testing instruments to verify or modify their hypothesis. To reward the students for showing me what is going on in their heads.

"If you don't know the equation, draw me a picture. A good picture gets you half credit at least. If you can't draw a picture, write me a paragraph, a narrative, something. Let me know what's in your mind."

I work extra hard to interpret each answer. I spend 10 times as much time as the other teachers in the department, with the homework answers and the exam answers. I literally stay up all night grading sometimes. Other teachers suggest that I use multiple choice, and Scantron, and save time. But I NEED to see how the student grappled with the proble, to see that they got it right up to an addition error, or whatever, and give them partial credit plus show them how to get back on track in that problem.

It has much harder for me because I was not trained in the suite of techniques to maintain proper discipline, so that those who wanted to knock me down ("he's a Rocket Scientist, so if I make him look like a fool, my homies will like me even more") could mess things up for the rest of the class.

Eventually I won over the leaders of the opposition, who were not the fools they pretended to be, but sometimes had the seeds of leadership, albeit misapplied. Won them over, most of them, and got them to act as my assistants in keeping the others in line.

Eventually, I applied the discipline that the principal recommended, which included confiscating iPods and skateboards that got locked in the principal's safe until parents came to school and recovered them

In every single case, except for the student who literally spoke NO English, those who met me halfway did finally learn. Some students got an A from me who hadn't had an A in years. And they actually deserved it. Other students I did have to flunk, if they didn't meet me halfway. "Forgetting" to come to the midterm or final exam in not halfway. Becoming homeless in mid-course because Mom moved away from the abusive boyfriend who was a narcotics dealer, but coming to me about it, was enough for extra effort on both sides.

Students told the principal, and each other, that I "actually EXPLAINED things" to them. That they finally "got it."

But this took, not formal pedagogy training for me, but my love for Math, which I do every day. It took compassion, in a way that I learned from my mother, who went back to school late in life and became a 3rd grade teacher, until she died of cancer.

It took approaches to quality that I learned from my Physics professor wife. Who, by the way, is a great teacher in the Physics lab. It took learning how to LISTEN.

That was the hardest for me, because I do love the sound of my own voice.

I forced myself to learn how to LISTEN by working in offices where I wrote resumes, curriculum vitae, cover letters, gave inbterview training, and the like for over 700 clients, from warehouse workers to chefs to researchers to judges. "What is the story of your life?" I would ask. And then listen, taking notes. Then work with them to find a job, or a better job.

My methods worked, to some extent, for me. They work, quite often, for my students. But I am now going through teacher's college for several reasons.

For one, as a manager and executive, I recognize that depending on heroic managers is a classical management mistake. HERO does not scale up.

We have to make do with whom we have, and can retain; and whom we can quickly recruit; and with the tools we have, where they are needed, right now.

Day to day, I sometimes feel that civilization itself hangs in the balance, at least in this neighborhood, this state, this country.

Sometimes I would come home and cry.

And then the next day, go in and try again.

I know that one can fail. That it's okay to fail. That what matters is how you pick yourself up and try again, in a different way. I show this to my students.

It is too early for me to evaluate teacher's college. I have mixed feelings. I am not a normal student. I am very grateful to my professors. I am very polite to bureaucrats who seems determined to make it all impossible. By being unfailingly polite and attentive to them, they become polite and helpful to me, within their limits.

Thank you, Chad and collagues for giving me chance to be painfully honest, to admit my mistakes, and to express my passion.

It matters so much!

If I may quote an article from my local newspaper, the Pasadena Star-News which gives some insights from the student, teacher, parental, and administrative perspective, and an innovative program to improve the process:

Meeting focuses on middle school transition
By Caroline An, Staff Writer
Article Launched: 12/16/2007 01:26:37 AM PST
http://www.pasadenastarnews.com/news/ci_7734374

ROSEMEAD - Moving from elementary to middle school is an emotionally and academically difficult transition for students.

That's why Muscatel Middle School officials this weekend have been focusing on educating students and parents about what it takes to succeed.

At an informational meeting for parents Saturday at the school, officials were slated to address a number of topics - from the California Standards Test to adjusting to the rigors of the middle-school environment.

Five specific areas are on the agenda: psychological, sociological, physical, environmental, and academic changes.

"This is to help our families understand the difficult times that are the pre-teen years," school counselor Anne Agnant said.

While parent meetings are fairly common affairs, this weekend's meeting is the first at which middle school students and their parents are being targeted. School officials attribute the focus to some unusual behaviors seen on the Muscatel campus.

"There are so many factors that impact the youth, such as media and technology," Agnant said.

Some red flags that have surfaced include peer pressure to experiment with drugs and sex and students having trouble peacefully resolving conflicts with their friends.

Another disturbing trend has been an increase in students inhaling spray deodorant to get high. The school responded by banning spray deodorants, she said.

The focus on the middle school years is a welcome one, said Principal Dean Wharton. Too often, the middle-school years have been ignored, even though the two years sandwiched between elementary and high school are critical and deserve attention, he said.

Academically, students need to adjust to more-demanding homework and more tests. Struggling students need to get help, he said.

Muscatel offers after-school tutoring and intervention programs, which students and parents sometimes are not aware of.

Emotionally, middle-school students are no different today than they were 20 years ago, said Wharton, who has been the school's principal for 23 years. But children these days are exposed more to adult issues. While middle-school girls generally are more focused on academics, boys tend to be "in la-la land, so to speak," he said.

Parents - especially parents experiencing the trials of middle school for the first time - should understand that a middle-school child's first priority is being accepted by peers, not seeking the approval of parents or teachers, he said.

"Being accepted is more important - to the point where they do not make good decisions," Wharton said.

caroline.an@sgvn.com

(626) 578-6300, Ext. 4494

www.insidesocal.com/hallwaymonitor

On Education [NY/Region section]

How a Middle School Can Be 'Dangerous' and Still Get an A
By SAMUEL G. FREEDMAN
December 19, 2007
http://www.nytimes.com/2007/12/19/nyregion/19education.html

When Shawn Carson taught last year at a middle school named the South Bronx Academy for Applied Media, he entered his room on many days to find a message from his students on the blackboard. In graphic and vulgar language, as he recalled in a recent interview, it described him committing a homosexual act.

On one occasion, Mr. Carson said, he caught his female students breaking open lockers in the room. Some of his pupils, known in the school's parlance as "scholars," threw his books and stapler out the window. When he went from desk to desk, offering editing advice on writing assignments, he was often met with profanity.

Mr. Carson was not alone among the school's faculty members who said they endured such episodes. Michelle L'Eplattenier said a digital camera and a cellphone were stolen from her room. A student in Shannon Staples's class routinely overturned desks. Ms. Staples was also punched while trying to separate two pupils trading blows.

Because of their experiences, Mr. Carson, Ms. Staples and Ms. L'Eplattenier have all left the school within the past year, part of an exodus that has claimed roughly half the faculty. And their concerns about the school's climate are echoed by students. In a survey conducted last year by the City Department of Education, 98 percent of Applied Media's students said there was fighting in the school, 94 percent said there was bullying and 67 percent said they were worried about crime and violence in the school.

Reflecting such realities, the New York State Education Department has placed Applied Media on its list of "persistently dangerous" schools, one of 52 in the state. Applied Media earned the designation after its second year of existence.

Yet when the city's Education Department recently released its progress reports about public schools, Applied Media received an A.

There are, of course, firm statistical reasons for the grade. While the overall performance of Applied Media on standardized tests falls well below citywide averages, the school raised the scores of its lowest-performing pupils, as well as those in special education and bilingual tracks, which are indeed sensible criteria for appraising a school.

The A grade, though, may also have something to do with the fact that the progress reports weigh all safety factors as only 2.5 percent of a school's total grade, said James S. Liebman, the Education Department's chief accountability officer. He has said the department decided not to give safety more consideration because statistics on school violence rely on self-reporting and tend to be deceptive.

For a great many children, parents and teachers, however, the order and security inside a school matter for rather more than 2.5 percent. And so the case of Applied Media and its A is a tale of two schools, the one reflected in the Education Department's metrics and the one experienced firsthand by many of the teachers.

"This is a school that's doing remarkably well on the progress side, and 'remarkably' isn't a word I use lightly," said Mr. Liebman, who is also a law professor at Columbia University, where this reporter is on the journalism faculty.

The principal, Roshone Ault, said she supported teachers in disciplinary matters by bringing in experts in "social-emotional learning" to train the faculty and was offering students incentives like pizza parties for good behavior.

"ON discipline we had a system in place," she said. "There was a lot of support around it."

But teachers dispute her description.

"I didn't teach last year," Ms. Staples said. "I was a police officer and a baby sitter. You'd write up kids left and right, and then nothing would happen. No one would help you. And the kids would just come right back. After I got hit, the principal's response was, 'That's what happens in middle schools.'"

Mr. Carson similarly described a lack of administrative support and meaningful discipline. "The administration would be telling you that it would all fall into place if you had a better lesson plan or more student engagement or arranged the desks in a U shape," he said. "But it doesn't matter how good your lesson plan is if the kids can't even stay still long enough to write the 'Aim' and 'Do Now' off the board. There are no repercussions. There is no punishment fitting the infraction."

The woes, Ms. L'Eplattenier said, went beyond discipline. Many classrooms lacked books, a problem also cited in the student survey. A school supposedly oriented to media did not have a student Web site. A closet's worth of canned food, donated by pupils before Thanksgiving 2006, was never given to any charity and eventually spoiled, Ms. L'Eplattenier said.

During the 2006-7 term, 13 of the 16 teachers were in their first year. The principal, Ms. Ault, had never led a school before founding Applied Media in 2005. She previously coordinated special education at a charter school in Harlem that was shut by the state for academic deficiency.

Still, Applied Media showed student progress on its standardized tests.

One reason for the improving scores, Ms. Ault said, was that during the period of test preparation in the late winter and early spring, she removed the "most disruptive" students from their regular classes. Dmitry Terekhov, a teacher, said: "The A we received is a testament to the teachers. We got the job done."

Mr. Liebman advanced another view of Applied Media's identification as "persistently dangerous," saying it actually speaks well for the school. Only a school that keeps track of its disciplinary incidents will compile enough examples to make the state list, he said. Ms. Ault, the principal, offered the same explanation. Some teachers, however, say they were dissuaded from reporting incidents.

As for the high attrition rate among teachers, Ms. Ault called it "commonplace" at new schools. Mr. Liebman said many teachers flee schools that are in the midst of reform and instilling a "culture of accountability." He did not address the roles of theft, violence and insults in persuading teachers to leave.

Even Mr. Terekhov, one of the few teachers striking some optimistic notes about Applied Media, conceded the challenges. "No principals want to be where we are," he said. "No teachers want to be where we are. It's too hard."

Samuel G. Freedman is a professor of journalism at Columbia University. His e-mail is sgfreedman@nytimes.com.

On the last school day of the local school district's schedule, I was a substitute Math teacher all day at a high school whose students fall into these categories:

# Behavior problems at the comprehensive high school
# Attendance problems at the comprehensive high school
# Substance abuse problem at the comprehensive high school
# Parent and or student request
# Students awaiting expulsion procedures

I found it to be a very positive experience. Some students tested me by attempting disruptive behavior, but I was easily able to calm them down, as I was backed up well by the staff on patrol.

I was observed by the regular teacher, who is about to be deployed to Afghanistan. He is recommending that I be hired full-time, at least on a probationary basis.

For some students, whther in middle school, high school, or otherwise, the issue is NOT the Mathematics, as such, but the consequences of having made some very bad decisions in the wider world.

Lessons in Reality
Young idealists arrive to teach at Washington's Coolidge High. And learn how frustrating efforts at reform can be.

Fixing D.C.'s Schools

By Lonnae O'Neal Parker
Washington Post Staff Writer
Sunday, December 23, 2007; Page A01
http://www.washingtonpost.com/wp-dyn/content/story/2007/12/22/ST2007122…

"... Ninth grade is when about 35 percent of the students who don't graduate fall through the cracks. In inner-city schools, 'easily half of the kids who fail to graduate don't make it from ninth to 10th grade,' says Christopher B. Swanson, director of the Editorial Projects in Education Research Center."

"Freshman academies are designed to aid that transition. They limit electives and keep students largely bound to a small group of teachers. There are signs it's working..."

(1) I've been describing my slightly revised philosophy of education at John Scalzi's "Whatever" blog, now that I've recovered enough from major surgery (9 Jan 08) to be back in the classroom. This includes (new to me) the Middle School classroom. Especially the Middle School into which is fed many of the children from group homes, who have no functional families.

(2) As quoted, on the "n-Catgory Cafe" research blog,
March 3, 2008
A Deep Sense of Miserable Ignorance
Posted by David Corfield
On p. 171 of Peirce's lectures, Reasoning and the logic of Things, having favourably compared the universities of Europe to those of America, he explains what is wrong with the latter's pedagogy:

In order that a man's whole heart may be in teaching he must be thoroughly imbued with the vital importance and absolute truth of what he has to teach; while in order that he may have any measure of success in learning he must be penetrated with a sense of the unsatisfactoriness of his present condition of knowledge. The two attitudes are almost irreconcilable. But just as it is not the self-righteous man who brings multitudes to a sense of sin, but the man who is most deeply conscious that he is himself a sinner, and it is only by a sense of sin that men can escape its thraldom; so it is not the man who thinks he knows it all, that can bring other men to feel their need of learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning. That is why, to my very humble apprehension, it cannot but seem that those admirable pedagogical methods for which the American teacher is distinguished are of little more consequence than the cut of his coat, that they surely are as nothing compared with that fever for learning that must consume the soul of the man who is to infect others with the same apparent malady.