Algebra in 2nd Grade?

In February, 2009 a teacher in Montana made EdWeek headlines because she was teaching algebra to second graders and had been doing so for five years. Why all the oohs and aahs?


Elementary math is supposed to prepare students for high-level math classes in middle and high school. Students should not need a dedicated pre-algebra class. When I was a kid, pre-algebra did not exist. Now it is part of every school's math course line-up.

The author of a pre-algebra text wants students to build math reasoning skills. However math reasoning often does not happen. Many teachers treat pre-algebra as a last chance for students to get those blind elementary math procedures down pat. Problem is, a student can be A+ in procedures and still not understand algebra. In fact, students competent with procedure often believe they are good at math. It is not their fault. Our education system has been telling them for years that grades equal understanding. So if they get a good grade in math, naturally they conclude they are good at math.

Math has been misnamed. What passes for math in schools is often non-math. “Carry the one” is not a mathematical explanation for what happens in addition. It is a blind procedure. Students get good grades in non-math believing it is math. No wonder algebra is such a shock. Math reasoning skills actually matter in algebra.

Still a student with a good memory can get by, at least until they meet a new math monster, calculus. However, since middle and high school math also fail to teach math reasoning, now students take pre-calculus, another relatively recent addition to course offerings. Without a major change of emphasis, pre-calculus prepares students no better for calculus than pre-algebra prepared them for algebra.

By now pre-calculus students have so internalized non-math that they complain to the instructor, “Just tell us how to get the answer. We don't want to know why.” Just give us some more blind procedures.

Dissing the Gifted

For too long, the nation’s education system has neglected the needs of its high-potential students.

Ann Robinson, president of the National Association for Gifted Children (NAGC) is right. One indication of the neglect is the lack of monetary investment.

The federal government’s investment in gifted and talented learners now stands at 2 cents of every $100 education dollars...

Another indication is the test scores of gifted students.

Over the past decade, despite impressive gains by students at the low end of the performance spectrum, the scores of students in the top 10 percent have remained largely flat.

Forget the test scores. Of course they are flat. Some of these students are already bumping their heads against the ceiling and ceilings tend to be flat. There is nowhere for their scores to go. Worse, in our society, there is no good reason for the gifted to raise their scores, and lots of reasons to at least look like they are not so smart.

America will pay the price for neglecting its gifted students.

By focusing an outsized amount of attention and resources on helping failing students attain proficiency, our nation has fostered a troublesome underinvestment in the very student population most likely to be its next generation of innovators, discoverers, and pioneers.

The reason our nation “has fostered a troublesome underinvestment” in our gifted kids is because our nation fundamentally does not value what these kids offer. Just check out the comments below the original EdWeek article to see what I mean. Society winks at the dissing of the gifted. Psychologists advise the friendless gifted that they are the ones with the social problems. Psychologists offer to “facilitate” exercises in “self discovery” designed to teach the gifted better “social skills.” I have tried to point out to some of these well-meaning professionals that the gifted are not the ones with the bad attitudes and poor coping skills. I get vacant looks.

The biggest problem our gifted students face everyday is not boring classes. The biggest problem is that our society surrounds the gifted with messages that they are somehow deficient human beings, and then wonders why the gifted have such low self-esteem even as they ace tests.

As “Anna” wrote:

A child with an IQ of 130 is as far from average as a child with an IQ of 70. They both need specialized instruction and guidance that allows them to develop to their full potential. Right now, only the child with the cognitive impairment is entitled by law to this support.

As far as the schools are concerned, no extra money, no extra support.

What about the work world? It will be different there, right? No, we have all seen or lived situations where excellence, initiative and professionalism take a back seat to mediocrity.

Don't Blame the Schools of Education.

They are just doing the best they can with what they've got, says Pedro Noguera. First he grants the schools of education deserve some criticism.

It’s true that many schools of education don’t recruit the best students into the profession... and that too often the research produced in schools of education is of little use to public schools...As is true for American universities generally, there is considerable variability in quality among the nation’s schools of education.

Many graduates of even the best schools of education lack effectiveness in the classroom.

Graduates of teacher-credential programs at my university, for example, and at Teachers College, Columbia University, are highly sought after, even at a time when teaching jobs are scarce. Does this mean that they are highly effective when they enter schools? In many cases, they are not.

The game is rigged against these promising graduates.

But this is not because they lack the intellect or dedication. Rather, it is largely because they are frequently assigned to work in the most dysfunctional schools and are expected to teach the most disadvantaged students. This is precisely what many schools and districts do to new teachers.

I completely agree that many schools essentially sabotage their new teachers.

In fact, there are schools which routinely assign the most difficult students to the most novice teachers. Older teachers believe they have paid their dues and deserve less challenging students even as their competence presumably improves with experience.

Mr. Noguera has four recommendations:

1. Give schools of education a financial reason for establishing lab schools in difficult areas.
2. Provide more debt relief for math and science majors.
3. Incentivize academia to collaborate with classroom teachers in the development arts, humanities, and science curricula.
4. Use work-study to motivate undergraduates to tutor in high-need schools.

I will add a fifth recommendation. Schools should hire the veteran math and science teachers they have pushed away for decades.

schools could also welcome veteran teachers who move into their communities as the valuable assets they are instead of viewing them as budget breakers. State credentialing commissions could remove the arbitrary obstacles that make it difficult for proven out-of-state teachers to get certified in their new state of residence.

I am not talking about alternative certification. I am talking about proven classroom veterans. I also agree with the first comment to Mr. Noguera's article.

Why not establish teacher-training programs with instructors who can show education students how to work effectively and exclusively in dysfunctional schools?

In fact, I did a small study of the curriculum vitae (resume for the uninitiated) of professors of education. The data confirms the common student perception that half of their professors of education do not have genuine teaching experience. It is difficult to find a professor of education with over ten years genuine teaching experience, and exceedingly rare to find one with more than twenty years.

Ironically, at precisely the time when a life-long teacher would be most valuable to the next generation of teachers training in our schools of education, they are at an extreme disadvantage. Anybody with a PhD goes to the head of the applicant line over dedicated teachers who were too busy actually teaching to go to graduate school. If they are hired, they will very likely be relegated to the ranks of the never-eligible-for-tenure. A little budget trouble and they are laid off on a last-in, first-out basis. Schools of education unload their most experienced teachers first. Maybe the schools of education could do with their own alternative certification program.

Selling Grades

Chocolate didn't work. Presumably gift wrap, cookie dough, flower bulbs, and toffee peanuts didn't work either. I would not be surprised. For a while there, almost every day somebody's child knocked at my door selling something. Sooner or later the neighborhood had to be saturated.

According to a November 10, 2009 article in The News and Observer, one school decided to get creative.

A $20 donation to Rosewood Middle School will get a student 20 test points — 10 extra points on two tests of the student's choosing. That could raise a B to an A, or a failing grade to a D.

...snip...

Shepherd, the Rosewood principal, said her school needs more technology. She said any money raised would help buy digital cameras for the school's computer lab and a high-tech blackboard.

First, it should be obvious to anyone that a grade-based fund raiser is a terrible idea. How it ever got out of committee is beyond me. Second, surely there are greater priorities than digital cameras and high-tech blackboards. How is the school fixed for music, art and PE, I wonder.

The reaction was swift and sure, coming the very next day.

However, the fundraiser came to an abrupt halt today (November 11, 2009) after a story in The News & Observer raised concerns about the practice of selling grades.

Wayne County school administrators stopped the fundraiser, issuing a statement this morning.

Yesterday afternoon, the district administration met with [Rosewood Middle School principal] Mrs. Shepherd and directed the the following actions be taken: (1) the fundraiser will be immediately stopped; (2) no extra grade credit will be issued that may have resulted from donations; and (3) beginning November 12, all donations will be returned.

One parent involved in the decision defended it as creative.

Breedlove said teachers dig into their own pockets each year to buy classroom supplies for under-funded schools. She said no one voiced any objections until Tuesday.

When teachers contribute funds from “their own pockets,” the first $250 is an “above the line” deduction on the first page of their Form 1040. The deduction of any remainder is lost unless the teacher is able to surmount two thresholds. One, the contribution, when added to other deductible expenses of being a teacher, exceeds 2% of the teacher's adjusted gross income, and two, the sum of all the itemized deductions exceeds the teacher's standard deduction. Most teachers receive no tax benefit beyond that first $250.

More important is Ms. Breedlove's claim that there were no objections until the November 10 news report. I have a hard time believing the school office received no phone calls from irate parents. On the other hand, maybe most parents simply threw the letter from the school away.

Events happened quickly. By the fourth day after the initial report, the principal had gone on leave with the intention of retiring December 1, a month earlier than she had originally planned.

One parent has a point.

Too much emphasis was put on the fundraiser rather than the reason the school has to raise its own money in the first place, said Jennifer Mercer, mother of two Rosewood students.

When it's the little education guys, heads roll. Big financial guys are “too big to fail” or even suffer consequences. As scandals go, this one is pretty small potatoes, yet generated more outrage and quick, retributive action than scandals involving millions of dollars.

And where is the shame? I do not mean the principal's shame, or the Parent Advisory Board's shame, but the national shame? Schools all over the country do not have enough money. Sure, some priorities are probably misplaced, and sure, there is probably waste everywhere to be curtailed. But when I was a kid, we did not do fund raisers.

The schools had enough money to cover their everyday waste, provide a regular program of art, music and daily physical education, PLUS pay for all kinds of great programs, from violin instruction to fun and exciting summer school offerings to free driver training to special trips to booster buses for away games, to after-school clubs and more. We kids were never burdened with the worry or responsibility of making up shortfalls.

What happened? I have heard that in California, it is all Prop 13's fault. But how does that explain the rest of the country? I really do not know. I was teaching for Department of Defense Dependents Schools (DODDS) overseas when it all gradually went to pieces. When I came back to America, I found the frogs had already been boiled. What happened, and why are we so complacent?

Confounding Teacher Recruitment by Discouraging the Best

"Good teachers matter. The data on that are clear. If we want more talented people in the classroom, a first step toward encouraging them would be to stop discouraging them."

I did not expect to see a piece about education under Yahoo Personal Finance, but there it was. What would an economist, Charles Wheelan PhD, say about education? Usually it is educators (like me) who write about education. The fact he is not an educator may be a point in his favor. At least he will not have an educator's biases. On the other hand, not being an educator, he may not understand the shortcomings of applying a business model to schools.

He implies that “alternative league” players become teachers, and because they are “alternative league” players, they naturally resist the threat that merit pay proposals represent.

The idea of some kind of merit pay has been kicking around for 20 years, if not longer. But this discussion almost always focuses on how compensation practices affect the incentives (and therefore the behavior) of existing teachers.

In fact, too many teachers chose education precisely for the cozy situation of job security with no accountability.

Economists refer to this phenomenon as adverse selection. Individuals use private information (their expected productivity in this case) to sort themselves into a job with a compensation structure that suits them best.  Public education is the equivalent of the alternative league.

His wife is about to make a mid-career change into teaching math, so very soon she will be able to enlighten him about the realities of our education system. Apparently she has already begun.

First, all prospective employees must undertake two years of full-time specialized training, at their own expense, just to be considered for a job. Study after study has shown that this training has zero connection to subsequent performance at the firm, but Company B sticks to this screening mechanism anyway.

… snip...

As you may have guessed, Company B is public education.

I do not know about you, but I can almost hear his wife talking as if I were right there sharing breakfast with them.

Prospective teachers jump through hoops because state law says they have to. If a state requires that all public school teachers take a course on the history of discrimination against left-handed children, then training programs will make a fat living offering courses on the history of discrimination against left-handed children. The state requires the course, education schools offer it, and future teachers must take it. There is nothing in that process to ensure that it actually produces better teachers. 

I agree with something Dr. Wheelan says right now.

Good teachers matter. The data on that are clear. If we want more talented people in the classroom, a first step toward encouraging them would be to stop discouraging them.

He strongly implies that merit pay will attract higher quality aspirants to teaching.

The most pernicious aspect of the public education pay structure is that it discourages motivated, productive, energetic people from entering the profession in the first place.

Between the pay structure and the certification requirements, the situation is well nigh hopeless.

We compound that problem with ridiculous teacher certification laws.  Despite a steady flow of evidence that our current teacher training requirements have essentially no correlation with performance in the classroom, most states continue to mandate that prospective teachers undertake expensive and time-consuming courses. That, too, is a huge deterrent for bright young people who might otherwise be attracted to teaching.

One day his synthesis of education and economics may produce pearls of insight. I look forward to a regular place at his breakfast table.


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Where Professional Development IS an Inside Job

I agree wholeheartedly with Anthony Cody. Professional development should be an inside job. Within the Department of Defense Dependent Schools (DODDS)it is.

Mr. Cody details the advantages to using local teachers to conduct professional development instead of outsiders.

1.The local has credibility. The participants know the presenter has actually taught and understands the challenges they face in their local context.
2.The local is available after the presentation to be an ongoing resource.
3.The local's expertise is recognized and affirmed, as opposed to being ignored.

Outside consultants should be brought in only when their particular knowledge is essential and lacking within the system. And these consultants should seek to collaborate with local teacher leaders so they can connect with existing practices and expertise. Their goal should be to invite the growth of local knowledge and skills so that teachers can lead the work as it develops going forward.

In most cases, however, local teachers should be considered the first and best choice for professional development within a district. If they are not experienced in leading their colleagues, they should receive support and training in this arena. The assumption that “outsiders always know best” should be replaced with the assumption that our teachers are the greatest experts we have available day-in and day-out in teaching our students. Developing their leadership is our best chance to drive sustained improvement in our schools.

I will add one more advantage to using locals for professional development. They are a lot cheaper.

When I was the local presenter, I did it for free---in the sense I was already being paid for the time, just like my audience was being paid to participate.

When I was the outsider, the district paid me transportation, hotel, and presentation fee. One workshop can easily cost a district $1000.

Your district can make it an inside job too. Teachers who would like to present should submit a presentation proposal to the district office. Even better than proposals trickling in one-by-one, a group of teachers in a school could create a package proposal. The only drawback is that some districts have already signed agreements with outside contractors. At least that is how my local district responded to my insider proposal.

But once those contracts expire, districts would be unlikely to renew once they realize the potential right at home, IF they have a sheaf of local proposals in hand. If just one or two teachers submit proposals, the district is likely to renew the outsider's contract. So teachers, get it together, and propose professional development truly relevant to your teaching circumstances. Go for it.

The Difference Between High Expectations and Harsh Mandates

A couple weeks ago, I wrote about my role in raising academic achievement in one school. I had had a discouraging day and I wanted to encourage myself by reliving an accomplishment. So I was gratified to find I had prefigured Joann Yatvin's understanding of the Pygmalion effect. Well said, Ms. Yatvin.

The discrepancy between the Pygmalion researchers’ concept of high expectations and that of today’s reformers stems from the multiple meanings of the word “expectation.” To the researchers, it meant the power of belief to influence the behavior of others. To the reformers, it means the power of authority to exact compliance from underlings.

I did not announce to any of the students, “You WILL be studying algebra in the eighth grade.” Those kinds of so-called high expectations back fire.

What I did everyday is communicate to my students in a myriad of subtle ways that I believed in them, I believed in their abilities and I believed in their worthiness. My entire education philosophy could probably be summed up by a version of the Golden Rule. I thought, “If these were my kids, what would I do?” One parent reported to me that her daughter told her, “My teacher is so smart. If she thinks I'm smart, too, then I must be.”

That said, I raise a hearty amen to this comment:

As a lifelong educator, I am not so starry-eyed as to think that believing in students is all that teachers and schools have to do to enable them to succeed. Every school needs a strong curriculum, high-quality materials, well-planned instruction, extra-help options, and meaningful assessments.

Effective education is about meeting the needs of the students, not the needs of pundits, politicians or even educators.

schools must appeal to and support the strengths of students, not play on their fears and weaknesses.

Schools are meant to be wellsprings of vigor, interest, exploration, growth, and illumination. Rigor, the word so often used by reformers to describe what schools should emphasize, is more properly the companion of harshness, inflexibility, and oppression. It is time to change the current conception of high expectations back to its original meaning.

Any former student of mine who happens to read what Ms. Yatvin says about rigor will chuckle. They will remember the many times I said that rigorous does not mean studying “hard;” it means studying right.