Education Policy Proposal #3: Repeal IDEA

I’ve gone through the low-hanging fruit of my ideas for presidential campaign education policies. Now we’re into the changes that take on laws and Supreme Court decisions.

And so this dive into “special education”, the mother of all ed spending sinkholes.

We’ve been living in the world of IDEA for forty years. IDEA forces the states to provide free and appropriate education to all disabled students in the least restrictive environment.

Special ed is the poster child for primer #5 and the courts’ unthinking disregard for costs. In most special ed cases, the courts read the law in the manner most favorable to the parents, who don’t have to pay court costs if they win, even if the losing school or district operated in good faith.

While IDEA promises that the federal government will pay 40% of sped services, the feds have never coughed up more than 15-20% while always telling the states to pay more. What’s more? Well, in 2013, the federal allocation for special education was $12.8 billion. That’s less than a fifth.

States all have varying percentages of special education students, which suggests that classifications are more opinion than diagnosis. But regardless of the definition, research hasn’t revealed any promising practices to give those with mild learning disabilities higher test scores or better engagement. And that’s just where academic improvement might be possible. In many cases, expensive services are provided with no expectation of academic improvement.

“Special ed” is a huge, complex canvas of services, and definitions invoke thoughts of the five blind guys and a camel so far as the public is concerned, so it may not mean what you think it means. The feds collect data on the following narrow definitions but most general education teachers think in terms of broad categories:

  1. Learning disabilities: ADHD, executive function, auditory processing.

  2. Emotional disturbances/mental illness: See definition
  3. Physical handicaps: wheelchairs, blindness, diabetes, and the ilk. No cognitive issues.
  4. Moderate mental handicaps: The highest of the low IQs, or educable.
  5. Severely handicapped: Eventual institution inhabitants, or assisted living. At best, “trainable”. At worst, this.

The role of special ed teacher varies, but they all have one common role: overseeing compliance. Their jobs have a substantial paperwork burden: producing the Individualized Education Plans in accordance with federal law. They schedule and run the review meetings, deliver IEPs to gen ed teachers.

High school special ed teachers for group 1 can’t be academically knowledgeable in all subjects, so they are basically case managers who run study halls, a full period that designated special ed kids can use to complete tests or do homework (or do nothing, as is often the case). They also do much of the assessment work for initiating IEPs. In this, they are akin to life-coaches or social workers. Since they are working with a lower level of academics, elementary sped teachers are more likely to be instructing students, whether in in self-contained classrooms designing easier lessons for students with mild learning disabilities, or in a pull-out class that would be called “study hall” in high school.

Group 1 sped teachers also manage group 3 student plans (e.g., wheelchair bound, diabetics) with no cognitive disabilities. These students, who don’t usually have study halls, are also more likely to be handled with 504 plans. They need health or access accommodations, often have expensive aides to see to their needs during the day. Other handicaps (visual, auditory) usually require a specialist credentialed in that disability, as well as an IEP.

Mildly retarded and emotionally troubled students (groups 2 and 4) are usually in self-contained classrooms by high school. They have little contact with general ed students on average, and are taught middle school level material by a special education teacher. At the elementary school level, general ed and special ed teachers share these responsibilities (here’s where the inclusion and mainstreaming debates are the sharpest).

Teachers who work with group 5 “students” at any age are providing specialized day care.

All sped teachers work with a wide range of aides, from those who help handicapped kids use the bathrooms, to those who lead blind children around, to those who help relate to the emotionally disturbed kids to those who babysit severely disabled children who can’t walk, talk, or relate on a scale handled by k-12.

I say none of this to be dismissive or cruel. Sped teachers I work with (the case managers with study halls) and their aides are caring and realistic; sped teachers who work with mentally limited students are incredibly gifted and dedicated, in my experience. But a massive chunk of them are not doing what we would normally refer to as teaching, and in another world we’d be able to question whether we are getting our money’s worth generating paperwork for the feds.

I don’t want to make feds the only bogeyman here. States are greedy for federal dollars, and special education spending gets more expensive each year for reasons unknown. Education has been put under tremendous additional constraints over the past 40 years, and the states should be asking why the hell they are forced to pour funds into a service that takes precedence over all the other needs in their district. Why should they be paying for aides to change diapers instead of giving study halls for disadvantaged kids who struggle academically? Why are they spending teacher head count and sections on study halls and case managers—especially since no evidence shows that pull outs and extended time improves academic outcomes of kids with executive function issues?

One (or more!) of the Republican candidates (pretty much has to be Republican) should emblazon “REPEAL IDEA” on his education policy webpage.

He could call it “state choice”.

Sure. Let states decide how to provide education, special or general. All special education services won’t instantly appear on the chopping block. But not having the federal courts hanging over every parent’s demands, cheerfully adding zeros to every expense, they might…well, trim. After a while, even cut.

Remember, many disabled students are still protected with 504 plans, which aren’t part of IDEA. Moreover, there’s this other federal law that doesn’t hesitate to interfere in state and local affairs if judges feel that people with disabilities aren’t getting their due. But allow states to decide if they want to bow to judges wishes in public schools, or provide separate facilities, without the anvils of FAPE and LRE mandates hanging over them.

Let the states and voters decide how to provide services for those students who can’t be educated within the K-12 framework, and how much support to give students with learning disabilities as opposed to disadvantaged students, arts education–or hey, even exceptionally bright students. If these services were left to the states, parents and other disability advocates could duke it out with other parent interests. And if some districts want to cut some special education services to keep the athletic teams, then states can decide based on the PR/Twitter storms, not federal law. (notice the line about “Athletics represent one of the largest costs that the school system carries that isn’t mandated by law.”? Think Fairfax parents would trade in some sped study halls for a football team?)

I make this sound so easy, don’t I? New York City alone has something like 38,000 special ed teachers. The National Association of Special Education Teachers will not be pleased. Nor will the teachers’ unions, I’m thinking.

But actual teachers? the rest of them? Maybe not quite so unhappy. Teachers see lines drawn and services provided to sped kids with no academic issues when gen ed kids who struggle academically get no services because they don’t have a disability, or economically disadvantaged kids who don’t qualify for special education resources, extra time, and study halls but could clearly benefit. Furthermore, elementary teachers are often….unenthused about the required inclusion of moderately to severely disabled students they have to cope with and pretend to educate in addition to their usual rambunctious kids with an already wide range of abilities.

Naturally, any teacher displeasure pales next to the onslaught of sped parental fury at the notion of killing IDEA, the massive anvil they have on the scales when making demands of their schools for their kids.

Kill SPED! doesn’t have the same ring or instant recognition of Ban College Remediation! or Bring Back Tracking!

But special education mandates are not only shockingly pricey straitjackets on schools, but a forcibly applied value system that many Americans don’t entirely share, at least not when it comes to stripping resources from their public schools. Politicians who face down the inevitable shaming attempts that would accompany this proposal could really open up the debate to reveal what Americans really want in their education system, as opposed to services they’ve been forced to pay for.

Education Policy Proposal #2: Stop Kneecapping High Schools

Continuing onto the second of my education policy proposals for the upcoming presidential election, I offer up the one nearest to my heart.

Our national education policy has led to an absurd paradox: colleges charge students full freight tuition for a suite of remedial classes that high schools are effectively banned from offering for free.

The ban is most noticeable in math. Some examples: In 1997, Chicago Public Schools wanted all freshmen to take algebra, so all remedial and pre-algebra classes were dumped., giving students and their counsellors no other options. A decade ago, Madison, Wisconsin did the same thing. California effectively banned pre-algebra in high school by docking test scores of students who weren’t taking algebra in 8th grade (drop one score category) or, god forbid, 9th grade (drop two score categories).

City after city, state by state, schools took away the “easy” math options: business math, consumer math, general math. At the same time math credits required for graduation became more difficult. Many state diploma requirements specify three years of math ending in algebra 2, which means the student must get a passing grade in algebra 1 by sophomore year. Some states just indicate “3 years of math” but a close read of the fine print shows that pre-algebra doesn’t count as a credit, but only as an elective (e.g., NYC, Ohio)

It’s less discussed, but English, history, and science have few differentiators other than Advanced Placement classes, and occasionally honors. This story on Madison’s attempt to detrack their English (and eventually science) classes based on reading scores is so completely typical it’s practically a template of the process of course restriction–just change the locations. All students reading at 9th grade level (which was questionably set at the 40th percentile of 8th grade reading scores) were put in “advanced” classes. Those below the 40th percentile were put in “regular” classes, and 8% of that group were given remedial reading. In other words, all but the genuinely illiterate were expected to understand 9th grade material.

The rationale for this wholesale purging of high school course catalogues is well-documented. States or districts are faced with a dramatic racial gap in test scores, which everyone attributes to the equally dramatic imbalance in high school college track course enrollment. Federal mandates, as well as civil rights organizations armed with class action lawsuits, demand the end to imbalance in enrollment, the better to end the gap in test scores . Unlike other education reforms that take money, training, and buy-in to implement, course catalogs and transcripts are entirely under administrative control. Shazam! The courses many students need disappear, leaving only the college track option.

So students who enter high school with elementary reading skills and no basic math facts are put in exactly the same classes as students with college level reading skills and impatient algebra readiness. Schools are given no ability to offer alternate easier courses except by going the extreme route of declaring the students incapable of participating (that is, putting them in special ed). Students have no choice in their education.

Sadly, the problem was misdiagnosed, in large part because many people want to ignore primer rules 1, 2, and 4. Schools have dramatically increased access to college level courses, but test scores and demonstrated ability have barely budged. The data on this approach shows failure that’s not only discouraging but depressingly consistent: But then, as Tom Loveless has observed, the “push … is based on an argument for equity, not on empirical evidence”.

Most people address this issue from the other end, complaining that inclusion of weak students damages the education of stronger students. I agree, and see the results of this every day. Since I work in a Title I school, the high-ability students I see losing out on more rigor and challenges are also poor students, often Hispanic or black. Teachers can’t adequately challenge strong students while also encouraging weaker students. Maintaining rigor requires failure for those who can’t achieve it.

Unfortunately, failure requires blame these days. To avoid blame, schools and teachers run roughshod over rigor by lowering standards. (Feel free to blame me on this count; I refuse to hold my students to standards they didn’t choose when it’s a choice between failing or graduating.)

Alas, many students still fail these classes, even given our dedication to keeping them on track despite content that is beyond their capabilities and/or interest. But remember, the schools offer no courses to fall back to after failure. Kids just have to take the subject again.  America spends millions teaching the same kids the same course twice, or even three times, both during the school year and in summer school and other credit recovery programs. Many of them don’t learn much the second time or third time through, of course, but teachers and administrators are fully aware of primer rule #3, which is why we pass them anyway, eventually. That way, at least, they can go to college and get the remedial classes we can’t offer, even if the poor kids will have to pay for them.

Those of you who focus on lost opportunities for the high achievers, I ask you to take a moment and ask yourself what it’s like for kids at the other end, to constantly fail courses that they have no choice in taking, no interest in, and no ability to genuinely understand. And to make it worse, once students are identified as strugglers whose test scores will hurt the school, they’re shoved into “support” classes for math and/or English, stuck for twice as long in classes they already despised. Why even try, when they know that if they stick it out eventually they’ll get a passing grade? And who can blame them?

This must change. High schools need to be able to teach all students at the appropriate pace and content level, which for many doesn’t begin to approach the expectations of our absurd national education policies. Pre-algebra, arithmetic and basic math literacy and general purpose reading and composition are necessary to allow students who needs those skills to acquire them without having to go to college to pay for them. Science and history need to be appropriately gauged as well, so that students can learn basic information at the pace they need.

The many students challenged by these simpler topics will be unlikely to progress to college level work. Ever. Algebra during senior year might often be a worthwhile goal. However, all students, regardless of underlying ability and interest, can learn to use the knowledge and skills they have and we can, indeed must, learn to build curriculum to challenge and extend their capacity. But schools can’t do this while lying about student capacity, which is what schools are forced to do when policies prohibit them from offering a full range of courses that meet student interests at the appropriate cognitive level.

So what can a presidential candidate do? Well, since the states have made these changes in response to federal pressure, a good place to start is get rid of the pressure. Praise the new ESEA bill for returning accountability back to the states. Promise to collect data, but accept that student learning is a complex mix and leave it at that.

Then promise to fund efforts to research and develop challenging yet accessible high school curriculum and course sequences to assist in educating the students who weren’t able to absorb the information from the prior eight years of schooling. Everyone fears that putting students into remedial classes will involve thought-obliterating worksheets piled on one after the other. I’ve taught remedial classes, and have been able to develop or borrow engaging curriculum. But the risk is legitimate.

A presidential candidate can also address the most compelling objection to this proposal: fear that schools will just place black and Hispanic kids into the lowest level classes by default. I think that fear is overrated; I once went looking for the bad old days and couldn’t find many (if any) cases of schools deliberately, systematically putting high-scoring black students into low ability classes. Many schools used test scores, which created the imbalance, as test scores by race always will. However, there’s still a messy middle in which white parents and black parents make different demands for kids with identical test scores, or badly behaved low income students who are nonetheless quite bright are failed by teachers who confuse behavior with ability.. Testing and required placement will help mitigate that risk. The federal government can certainly require proof that schools and districts are appropriately placing students with strong test scores, regardless of race. (States, schools, and districts will need that data to avoid lawsuits.)

But here’s the real education policy proposal for the candidates of 2016: Stop pretending education is the answer to poverty. Many kids who don’t care for school are galvanized by the possibility of a job. Stop offloading national responsibilities onto the schools. Schools can’t give students jobs with good wages. The economy can. Stop the flow of cheap labor at all education levels, by squashing requests for more H1B visas, scrutinizing citizen layoffs for cheap Indian labor, and enforcing our immigration laws. You build an economy with the workers you have, not the workers you can import at the price you want.

To say this proposal is at odds with the zeitgeist is to reveal how thoroughly at odds the public is with the “white professional ghetto”, as Harold Myerson describes the intelligentsia. The public doesn’t believe that everyone can achieve equally; that’s a delusion reserved for people who’ve never spent time in the schools they want to “fix”.

Ed Policy Proposal #1: Ban College Level Remediation

So if any presidential candidate is out there looking for ideas–particularly you Republicans–here’s my first proposal:

Colleges and universities have been constantly complaining for 30 years or so that incoming students are in dire need of remediation1. These complaints inevitably lead into a conversation about failing high schools, accompanied by fulminations and fuming.

The correct response: Why are remedial students allowed to matriculate in the first place?

It’s not as if the knowledge deficit comes as a surprise. Most students have taken the SAT or the ACT, which most if not all four-year public institutions use as a first-level remediation indicator–that is, a score of X exempts the student from a placement test. Those who don’t make that cut have to take a placement test. Community colleges usually cut straight to the placement test. The most common placement tests are also developed by the Big Two ((Accuplacer is SAT, Compass is ACT).

So why not just reject all applicants who aren’t college-ready?

Private institutions can do as they like, but our public universities ought to be held responsible for upholding a standard.

Most states (or all?) offer two levels of post-secondary education: college and adult education. As colleges have sought to increase access to everyone who can demonstrate basic literacy (and far too many who can’t even manage that), adult education has withered and nearly died.

Pick a level and split them. My cutoff would be second year algebra and a lexile score of 1000 (that’s about tenth grade, yes?) for college, but we could argue about it. Everyone who can’t manage that standard after twelve years of K-12 school can go to trade school or to adult education, which is not eligible for student loans, but we could probably give some tax credits or something for self-improvement.

Adult education could be strengthened by repurposing the funds we now spend on remedial education. The existing community college system could, for example, be split into two tiers—one for actual college level work or legitimate AA degrees, the other for adult education courses, which are currently a weak sister of K-12.

The federal government could enforce this by refusing to back Pell grants for remedial courses in college, as Michael Petrilli and others have called for. State legislatures could arguably just pick a demonstrated ability level and restrict funding to those public universities that ignore it.

Of course, some argue that college is for everyone, regardless of their abilities. This path leads to a complete devaluation of the college degree, of course, but if that is to be the argument, there’s an easy solution. If no one is too incapable for college, then no education is remedial. So give the students credit for remedial courses, let barely functional students get college degrees after 120 credits of middle school work. No?

Proposal #2: Put Remedial Classes Back in High School


1College remediation in its present form came about during the seventies, when colleges expanded access largely to give opportunities to blacks and other minorities. At the time, remedial education was dubbed “compensatory”. Believing that socio-economic circumstances and poor schools led to a correctable deficit….well, see, I can stop right there. If you want the whole history, check out CUNY’s version of it; similar responses took place in campuses all over the country. But I don’t have to explain why that was a flawed belief. Just see the primer items 1-4.

Five Education Policy Proposals for 2016 Presidential Politics

Every election year, someone bemoans the fact that education is never a major factor in presidential politics. This year might be an exception, because of Common Core. But the reality is, presidential aspirants never talk about the issues that really interest the public at large.

Instead, politicians read from the same Big Book Of Education Shibboleths that pundits do.

To wit: Our public schools are a national disgrace with abysmal international rankings. Our test scores that haven’t budged in 40 years. Unions prevent bad teachers from being fired. Teachers are essential to academic outcomes but they are academically weak and unimpressive, the bottom feeders of college graduates. Administrators are crippled because they can’t fire bad teachers. We know what works in education. Choice will save our country by improving student outcomes. Charters have proven all kids can learn and poverty doesn’t matter. And so on.

All the conventional wisdom I’ve outlined in the previous paragraph is false, or at least complicated by reality. Any education reformer with more than two years experience would certainly agree that the public is mostly unmoved by rhetoric about teacher quality, tenure, curriculum changes, and choice—in fact, when “education reform” is a voting issue, the voters are often going against reform.

Education reformers are very much like Meg Ryan in When Harry Met Sally: All this time I thought he didn’t want to get married. But, the truth is, he didn’t want to marry me.  

Yeah, sorry. Your ideas, reformers, they just don’t do it for the public.

So I put together some policies that a lot of the public would agree with and many would consider important enough to make a voting issue. In each case, the necessary legislation could be introduced at the state or federal level.

There’s a catch, of course. These proposals are nowhere on the horizon. But any serious understanding of these proposals will lead to an understanding of just how very far the acceptable debate is from the reality on the ground.

To understand these proposals, a Reality Primer:

1) Some children cannot learn to the desired standard in an acceptable timeframe or, in the case of high school, in any timeframe.
2) The more rigorous the standard, the greater number of students who will be incapable of learning to that standard.
3) As a result of the first two immutable facts, schools can’t require an unbendable promotion standard.
4) By high school, the range of student understanding in any one classroom is beyond what most outsiders can possibly conceive of.

and somewhat unrelated to the previous four:

5) Education case history suggests that courts care neither about reality or costs.

The primer is important. Read it. Embrace it. In fact, if you read the primer and really get on board, you’ll be able to come up with the proposals all by yourself.

Some additional reading to remind readers of where I’m coming from:

I originally had all the proposals as one huge post, but I’ve been really short on posts lately. Here’s the list as I build it:

  1. Ban College-Level Remediation
  2. Stop Kneecapping High Schools
  3. Repeal IDEA
  4. Make K-12 Education Citizen Only
  5. End ELL Mandates

Handling the Teacher Perks

Before turning teacher, I spent all but five years as a temp worker, self-employed or contract. Unemployment? A hassle I didn’t bother with the few times I was eligible. Retirement? My very own funded SEP_IRA, no employer matching. Paid vacation and sick leave? Outside of those five years, I never had any.

Going from that life to public school teaching was kind of like Neal Stephenson’s description (excerpted from In the Beginning was the Command Line) of the guy who was raised by carpenters from early childhood with only a Hole Hawg as a drill and then meeting up finally with a puny homeowner’s version.

What the hell. With so much free stuff, how can you call this work?

From Veteran’s Day to the first week of the New Year, over three weeks off, the bulk of them from mid-December to early January. Five plus days off at spring break, and two months off in the summer. Eleven days of sick leave that accrue, and two “use it or lose it” days. I get the same amount of pay every single month. Guaranteed pension, already vested comfortably, probably to retire with 30%—not bad for a late entry.

Plus, I hear it’s hard to get fired.

I clearly remember watching the perks of corporate employment slowly be stripped away back in my twenties, perks that few people under 50 can even imagine. So it’s bizarre to have entered a profession where it feels like the 80s again.

Now, I’m wondering if I’m getting used to it.

In the previous five years of teaching, my collective time out of the classroom was 3 sick days and 6 mandated professional development days. This year, I was out of class for nearly 10 days of professional obligations: three days for an honest to god, out of state, education conference, two-plus days for mentoring and induction responsibilities, and 4 days of Common Core testing.

I felt very guilty about all this time off, and without question the absences impacted instruction time and coverage. So much so that when I came down with a really severe case of with food poisoning (you know those rotisserie chickens? Used to love them. Hope I eventually trust them again) during testing week, I came in anyway because I knew it would wreak havoc both on testing schedules for administration and my carefully scheduled coverage plans (I was missing alternate classes during the week). I went four days munching crackers and chugging that weird chalky pink stuff, previously unknown to me.

In retrospect this struck me as idiotic, so I went to the principal’s secretary and asked how to request time off. That’s when I learned formally I had 13 days a year, including two use or lose–which I’ve been losing for the past five years. I took a whole day and a half just for a family graduation 10 hours away, when I normally would have left Friday afternoon and come back Sunday night.

More evidence: for the first time in eight summers, six of them as a teacher, I decided to forego employment (part-time and no benefits, of course) at my favorite hagwon, where I usually act as chief lunatic for book club, PSAT prep, and occasionally geometry.

Why? I wanted more time off.

This wasn’t a sudden decision. Last year it finally sunk in that despite the easy hours and students, the elapsed time of my hagwon day clocked in at 9 hours: three on, three off, three on, for eight weeks. While this hadn’t seemed punitive with a 5 minute commute, the schedule lost much of its charm when I moved 45 minutes away. Meanwhile, the eight week schedule left just eight uninterrupted days off at the end of summer.

Yes. The four weeks I am granted throughout the year is not enough. I want more of the eight uninterrupted weeks. It shames me.

But there’s hope. If eight days seemed too little, two months off seemed….excessive. Years of temp work leaves me never entirely comfortable not knowing where my next dollar would come from. Long vacations make me nervous. Back in my tutor/test prep instructor life, my son and I took a long road trip one summer that culminated in a 6 week stay in another city. I notified a local Kaplan branch, got some SAT classes, put ads in Craigslist and got some private tutoring, making enough to offset the fuel and food expenditures for the trip.

I am not yet ready to abandon summer work altogether. I wanted a summer job. Just a different one, with a shorter work day, a shorter employment term, and higher hourly pay so I’d get more time off but the same dollars’ pay.

Normal people are thinking “Hah! And a pony.” Teachers are thinking “Duh. Just teach summer school.” Public summer school, that is. Six weeks at most in my area, higher hourly pay, out at 1:30.

I have very strong feelings about summer school, none of them positive. But public summer school it is, this summer. More of that later, assuming I can push through and finish this absurdly non-essential piece because family fun time and work are coming perilously close to giving me writer’s block.

As a side note, a transition marked: I’ve now left all three legs of my previous income behind. Private tutoring mostly gone over the past two years, the hagwon this last year, Kaplan since ed school.

A job change to get a longer summer break. Another worrisome trend?

But then, just when I began to worry about having been slowly sucked in, I learned what my preps for the upcoming year would be and nearly had a meltdown.

Every year, teachers are given a form to list their preferences for subject assignments (aka, “preps”). Every year, my form says “I’m happy to teach any academic subject I’ve got a credential for–but please don’t limit me to one prep a semester. Two is better, three is best.” Then I list three classes I haven’t taught in a while, or would like to do a second time. This year, I’d asked to teach at least one session of history, to build on my last year, pre-calc, which I hadn’t taught in a year, and any lower level class, just to keep myself humble. Again, this is in the context of teaching any other class as well.

I went into school after summer started to work on one of the professional obligations above, and as a thank-you, the principal showed us the master schedule board.

Semester One: Algebra 2, Trig. Two blocks of each.
Semester Two: Algebra 2, Trig. Three blocks total, two blocks Trig.

This schedule would be, to most teachers, a perk. Just two preps I’m familiar with. An easy year, after an extraordinarily demanding one in which I had two brand new classes, one of which was in a completely different academic subject for the first time in five years. Some might view the schedule as a form of thank-you, or maybe an acknowledgement that I’ve got more professional responsibilities so require a schedule with less planning or curriculum development.

I looked at the board and thought Christ, I have to quit this school, that’s awful, I love this school, but I have to get out of here. I need some time for job-hunting. I can’t quit summer school, it starts Monday. But I can jobhunt in the afternoons, it’s a Friday so I have some time to update my resume. Maybe I won’t have to leave the district, so I could keep tenure, and maybe I can talk to the administrator at summer school, hey, it’s actually good that I’m not at the hagwon this year, I just need to update my resume….

So not a perk, to me.

I tend towards extreme reactions, as alert readers may have noticed. Self-knowledge has led to compensatory braking systems. In years past, I would have just turned in my resignation on the spot. But my braking system kicked in, I remembered that quitting is just a symptom of my temporary worker mindset. I reminded myself how good it felt to get tenure, that my administration team likes me. Before I quit, I should perhaps consider other alternatives.

I will cover those alternatives, and my fears, in a follow-up post. No really, I promise.

So no, I’m not yet sucked in by the teacher perks. But I do want more free time during my 10 weeks off. Call me ungrateful.


Note: I will always value intellectual challenge over predictability for my own job satisfaction. But many teachers do an outstanding job teaching just one subject or the same two preps for thirty years. Outsiders, particularly well-educated folks with elite pedigrees, champion intellectual curious teachers with cognitive ability to spare as an obvious advancement over what they see as the “factory model” teacher turning out the same widgets ever year. But little evidence suggests that intellectual chops produces better results, much less better teachers. So please don’t interpret my rejection of predictability and routine as evidence of anything other than a fear of boredom.

Math isn’t Aspirin. Neither is Teaching.

First, congrats to Dan Meyer, who finished his doctorate at Stanford and just hired on as CAO for Desmos, a tremendously useful online graphing calculator. He persisted in the face of threatened failure, and didn’t give up even when he had an easy out into a great job. (Presumably Dan and most of the Math Twitter Blogosphere are still annoyed at my jeremiad about the meaning of his meteoric rise, in which Dan played the part of illustration.)

Dan has asked math teachers for ways to create “headaches” for which math can be considered aspirin:


And this interested me because the request completely, perfectly, captures the difference between our two philosophies, which I also wrote about a couple years ago:


The comparison is an instructive one, I think. Both of us find it necessary to build our own curriculum, rejecting the one on offer, and both of us, I think, tremendously enjoy the creation process. Both of us reject the typical didactic contract described by Guy Brouseau, setting expectations very different from those of typical math teachers: explain, work a few examples, assign a set. Both of us largely eschew textbooks for instruction, although I consider them completely unnecessary save as reference books that often provide interesting problems I can steal, while Dan dreams of the perfect digital textbook.

And yet we couldn’t differ more in both teaching philosophy and curriculum approach.

Dan’s still selling curiosity and desire for knowledge, assuming capability will follow. I’m still selling capability because I see confidence follow.

Dan still believes that student engagement captures their curiosity which leads to academic success, that the Holy Grail of academic success in math lies in finding the perfect problems that universally stimulate interest in finding answers, which leads to understanding for all. I hold that student engagement leads to their willingness to attempt what they previously thought was impossible but that the Holy Grail doesn’t exist.

Meyer thinks teachers skeptical of his methods are resistant to change and the best interests of their students. I advise teachers and recommend curriculum; if they find my advice helpful, great. I encourage them to modify or even reject my advice, to continue to see an approach that works for them and their students.

Dan wants to be “less helpful”. I want to teach kids to use their own resources, but given a kid who wants to give up, I’m offering help every time.

Meyer’s methods would probably need tremendous readjustment if he worked in a low-income school with a wide range of abilities. I’d probably be much “less helpful” if I taught at a school with a high-achieving, homogenous population obsessed about grades.

Meyer rose quickly in the rarefied world of rock star teachers. I aspire to the role of and indie with cult status.

Dan’s query: “Why did mathematicians think this skill was worth even a little bit of our time? If the ability to factor that trinomial is aspirin for a mathematician, then how do we create the headache?

My answer: You can’t.

The commenters, mostly teachers, took the question seriously, understanding that it was another way of looking at the students’ demand, “When will we use this?”. Answering this question clearly troubles most of the commenters—or they have an affirmative answer they’re satisfied with.

My answer to the student demand: “Probably never. But the more willing you are to take on challenging tasks you learn from, the more opportunities you’ll have in life, both professional and personal. Call me crazy, but I see this as a good thing.”

Dan Meyer is wrong, I believe, in looking for the Holy Grail that makes math “aspirin”1. But that’s not the point of my running through the Dan vs. Ed showdown.

Instead, consider the comparison yet another data point in my slowly developing thesis that ed schools need more flexibility and even less prescription. Few people understand the vast scale of values, philosophies, management and curriculum found in the teaching population.

Two teachers developing uncommon curriculum who agree on very little—yet both of us are considered successful teachers. (one has much more success selling his ideas to people with money, I grant you.) Take ten more math teachers likewise who build their own curriculum, have their own takes on philosophy, discipline, and even grading and they’re unlikely to change to suit another model. Take 100 more–ditto. Voila! an expanding population of teachers who have successful teaching approaches and curriculum design that they’ve developed and modified. None of them are going to agree on much. They have come to widely varying conclusions that they will continue to develop and enhance on their timeline as they see fit. No one will have anything approaching a convincing argument that could possibly convince them otherwise.

The point: the current push to “fix” ed schools, a fond delusion of reformers, progressives and union leaders alike. People as diverse as Benjamin Riley, Paul Bruno, Rick Hess and others believe we can find (or already have) a teaching knowledge base that can be passed on to novices.

Teachers are never going to agree.

Agreement or even consensus is impossible. Teachers and students form infinite combinations of interests, values, incentives and unlike reformers, teachers are going to value their experience and unique circumstances over anything ed schools tried to pretend was the only way.

Teaching, like math, isn’t aspirin. It’s not medicine. It’s not a cure. It is an art enhanced by skills appropriate to the situation and medium, that will achieve all outcomes including success and failure based on complex interactions between the teachers and their audience. Treat it as a medicine, mandate a particular course of treatment, and hundreds of thousands of teachers will simply refuse to comply because it won’t cure the challenges and opportunities they face.

So when the status quo has prevailed for the next 30 years, don’t say you weren’t warned.

1which isn’t to say I don’t plan on writing up the how and why of my quadratic equations section.

Grant Wiggins

Curriculum is the least understood of the reform efforts, even though parents have more day to day contact with curriculum than choice or accountability. This is in large part because curriculum advocates don’t agree to the degree that accountability and choice reformers do, but also because teachers have far more control over curriculum than most understand. As Larry Cuban explains, curriculum has multiple layers: intended, tested, taught, and learned. Curriculum battles usually involve the intended curriculum, the one designed by the state, which usually creates the tested curriculum as a manageable subset. (Much of the Common Core controversy is caused by the overwhelming difficulty of the tested curriculum, but leave that for another time.)

But intended and tested curriculum are irrelevant once the doors close, and in this essay, I refer to the taught curriculum, the one that we teachers sculpt, whether we use “the book” (actually just pieces of the district approved book), use another book we like better, or build our own.

To the extent most non-educators know anything about curriculum advocacy, it begins and ends with E. D. Hirsch, otherwise known as “the guy who says what my nth grader should know”, author of a book series he eventually transformed into a curriculum for k-6, Core Knowledge. Hirsch offers one Big Idea: improving student background knowledge will improve their reading comprehension, because only with background knowledge can students learn from text. But, the Idea continues, schools ignore content knowledge in favor of teaching students “skills”. To improve reading comprehension and ongoing student academic outcomes, schools must shift from a skills approach to one dedicated to improving knowledge.

Then there’s Grant Wiggins, whose death last week occasioned this essay as an attempt to explain that we’ve lost a giant.

The media proper didn’t give Wiggins’ passing much notice. Valerie Strauss gave his last blog sequence a good sendoff and Edutopia brought back all their interviews with him. Education World and Education Week gave him obits. It doesn’t look as if Real Clear Education noted his passing, which is a bit shocking but perhaps I missed the mention.

Inside education schools, that world reformers hold in considerable contempt, Wiggins’ work is incredibly influential and his death sent off shockwaves. Since 1998, Understanding by Design has been an essential component in preparing teachers for the professional challenge of deciding what to teach and how to deliver the instruction.

Prospective teachers don’t always understand this preparation will have relevance to their lives until their first year in the classroom. Progressive ed schools would never say anything so directly as “You will be faced with 30 kids with an 8 year range in ability and the textbooks won’t work.” Their ideology demands they wrap this message up in hooha on how insensitive textbooks are to the diverse needs of the classroom. Then, their ideology influences the examples and tasks they choose for instruction. Teacher candidates with an instructivist bent thus often tune out curriculum development classes in ed school, rolling their eyes at the absurd examples and thinking keerist, just use the textbook. (Yeah. This was me.)

Usually, they figure out the relevance of curriculum instruction when they get into the classroom, when they realize how laughably inadequate the textbook is for the wide range of abilities and interests of their students. When they realize the book assumes kids will sit patiently and listen, then obediently practice. When they realize that most of the kids won’t bring their books, and that all the well-intended advice about giving consequences for unprepared students will alone result in failing half the class, never mind the problems with their ability. When they realize that many kids have checked out, either actively misbehaving or passively sitting. Worst of all the teachers experience the kids who are eager to learn, try hard, don’t get it, and don’t remember anyway. Then, even after they make a bunch of adjustments, these teachers realize that kids who do seem to be learning don’t remember much—that is, in Cuban’s paradigm, the learned curriculum is wildly different than the one taught (or in the Wiggins universe, “transferred”).

The teachers who don’t quit or move to charters or comprehensives with a higher SES may remember vaguely hey, there was something about this in ed school (hell, maybe that’s just me). So they go dig up their readers and textbooks and suddenly, all the twaddle about diversity and cultural imperialism fades away and the real message becomes legible, like developing invisible ink. How do you create a learning unit? What are your objectives? How will you assess student learning? And at that point, many roads lead to Wiggins.

Grant Wiggins was impossible to pigeonhole in a reform typology. In 1988, he made 10 proposals for high school reform that leaned progressive but that everyone could find some agreement with. He didn’t think much of lecturing, but he wrote a really terrific analysis of lectures that should be required reading for all teachers. (While I also liked Harry Webb’s rejoinder, I reread them in preparation for this essay and Grant’s is far superior.) He approved of Common Core’s ELA standards, but found the math ones weak. In the space of two weeks in 2013, he took on both Diane Ravitch and E. D. Hirsch, and this is after Ravitch flipped on Hirsch and other traditionalists.

Grant Wiggins was more than ready to mix it up. Both his essays on Hirsch and Ravitch might fairly be called broadsides, although backed with research and logic that made both compelling, (perhaps that’s because I largely agreed with them). His last two posts dissected Hirsch supporter Dan Willingham’s op-ed on reading strategies. While he listened and watched teachers intently, he would readily disagree with them and was rarely gentle in pointing it out. I found his insights on curriculum and instruction absolutely fascinating, but rolled my eyes hard at his more excessive plaints on behalf of students, like the nonsense on apartheid bathrooms and the shadowing experience that supposedly revealed the terrible lives of high school students—and if teachers were all denied the right to sarcasm, as he would have it, I’d quit. He didn’t hesitate to say I didn’t understand the lives that students lead, and I told him right back that he was wrong. More troubling to me was his conviction that most teachers were derelict in their duty and his belief that teachers are responsible for low test scores. But what made him so compelling, I think, is that he offered value to all teachers on a wide range of topics near to our needs, whether or not we shared all his opinions.

I knew him slightly. He once linked to my essay on math philosophies as an example of a “learned” teacher, and read my extended response (do I have any other kind?) and took the time to answer. Then, a few months later, I responded to his post on “teacher job descriptions” with a comment he found worthy of pulling out for a post on planning. He then privately emailed to let me know he’d used my comment and asked me to give feedback on his survey. That was a very big day. Like, I told my folks about it.

In the last week of his life, Grant had asked Robert Pondiscio to read his Willingham critique. Pondiscio, a passionate advocate of all things content knowledge, dismissed this overture and declared his posts on both Willingham and Hirsch “intemperate”. Benjamin Riley of Deans for Impact broke in, complimenting Grant and encouraging the idea of debate. The next day, Daniel Willingham responded to Grant on his site (I would be unsurprised to learn that Riley had something to do with that, and kudos to him if so). Grant was clearly pleased to be hashing the issues out directly and they exchanged a series of comments.

I had been retweeting the conversation and adding comments. Grant agreed with my observation that Core Knowledge advocates are (wrongly) treated as neutral experts.

On the last day of his life, Grant favorited a few of these tweets, I think because he realized I understood both his frustration at the silence and his delight at finally engaging Dan in debate.

And then Grant Wiggins died suddenly, shockingly. He’ll will never finish that conversation with Dan Willingham. Death, clearly, has no respect for the demands of social media discourse.

Dan Willingham tweeted his respect. Robert Pondiscio wrote an appreciation, expressing regret for his abruptness. If the general media ignored Grant’s passing, Twitter did not.

I didn’t know Grant well enough to provide personal insights. But I’m an educator, and so I will try to educate people, make them aware of who was lost, and what he had to offer.

Novices can find plenty of vidoes on his “backwards design” with a simple google. But his discussions on learning and assessment are probably more interesting to the general audience and teachers alike—and my favorites as well.

Reformers like Michael Petrilli are experiencing a significant backlash to their causes. Petrilli isn’t wrong about the need for parent buy-in, but as Rick Hess recently wrote, the talkers in education policy are simply uninterested in what the “doers” have to offer the conversation.

Amen to that. The best education policy advocates—Wiggins, Larry Cuban, Tom Loveless–have all spent significant time as teachers. Grant Wiggins set an example reformers could follow as someone who could criticize teachers, rightly or wrongly, and be heard because he listened. If he disagreed, he’d either cite evidence or argue values. So while he genuinely believed that most teachers were inadequate, teachers who engaged with him instantly knew this guy understood their world, and were more likely to listen.

And for the teachers that Grant found inadequate—well, I will always think him in error about the responsibility teachers own for academic outcomes. But teachers should stretch and challenge themselves. I encourage all teachers to look for ways to increase engagement, rigor, and learning, and I can think of no better starting point than Grant Wiggins’ blog.

I will honor his memory by reading his work regularly and looking for new insights to bring to both my teaching and writing.

If there’s an afterlife, I’m sure Grant is currently explaining to God how the world would have turned out better if he’d had started with the assessment and worked backwards. It would have taken longer than seven days, though.

My sincere condolences to his wife, four children, two grandsons, his long-time colleague Jay McTighe, his band the Hazbins, and the many people who were privileged to know him well. But even out here on the outskirts of Grant’s galaxy of influence, he’ll be sorely missed.

Functions vs. Equations: f(x) is y and more

I wanted to talk about function algebra, which naturally would include a reference to function notation.

So here’s the frustrating thing about writing this blog. I try to include links to other sites that explain a concept, so that I don’t have to reinvent the wheel for my reading audience. But a google gives me these results: useless links that do little more than say “f(x) is the same as y”. That’s not math. That’s test prep. And there’s nothing wrong with test prep, but every one of these sites purport to be math teaching sites, and hey, I’m not a mathematician, but shouldn’t we be explaining what f(x) means?

Someone somewhere is saying “See, this is why we need teachers to be math majors, instead of English majors who get 800 on the GRE quant section. You can’t substitute math understanding that comes with the study of these important principles.” That someone somewhere is wrong. I used to think that in my early days, until I had too many conversations like this:

Me, to AP Calculus teacher WHO MAJORED IN MATH: Hey, what do you tell your kids about function notation?

AP Calculus teacher WHO MAJORED IN MATH: f(x) is the same as y.

Me, nonplused: Well. Yeah. But I mean about why we developed function notation, what it serves that can’t be served by….

AP Calculus teacher WHO MAJORED IN MATH: It’s just notation. Don’t be confused.

Me: I’m not confused. But they serve different purposes, and I’m just trying to be sure I accurately capture…

AP Calculus teacher WHO MAJORED IN MATH: They don’t serve different purposes. It’s just notation f(x) is the same as y.

Me: Ok.

In my experience, very few math teachers WHO ACTUALLY MAJORED IN MATH care about these things either. My beer drinking buddy is an exception (and he’s now department head), and he’s the only math teacher I’ve found so far who was interested in my work on this subject.

Textbooks? McDougall Litell, CPM has a lot of those function machines. But no explanation. Holt does a little better but I didn’t understand that until I understood what I was looking for.

So I spend more time looking for a good link. Otherwise, I have to spend a lot of time figuring out how to explain function notation accurately, or at least inoffensively, so that people reading this blog don’t make me remind them that, for chrissakes, I’m an English major not a mathematician! That takes time. It’s not time I wanted to spend. I don’t want to tell you what function notation is, in a way that will pass expert muster. I want to tell how I build on function notation to teach function algebra. But I can’t do that well without explaining function notation, which I didn’t set out to do. This leads to many blog entries taking much more time than they should. The original intent for my function algebra post was to be just a quick little throwaway.

I began writing this post nearly a month ago, and got stalled looking for a way to characterize the explanation. You may be wondering why I would explain something I don’t understand—but that’s not it, really. I just don’t know what to call it. And that’s fine for teaching, not so much for writing, and so I spend hours trying to figure out the correct query. Which took me, literally, up until today.

Just fifteen minutes ago (as I write this sentence) I finally found the kernel in this discussion on function notation before Euler, in which someone writes:

but [Newton] refers to these as equations, not functions, and admittedly (written the way they are) that is exactly what they are. It seems anything that we would today write as a function, Newton described in words, such as:

HA. I learned something I hadn’t quite understood completely before–a function and an equation are not the same thing. Googling “what is the difference between an equation and a function” led me to the right websites. I realize now that I wasn’t just looking for an explanation of function notation, but rather why and when we use functions vs. equations.

Here’s an explanation that covers what I was trying to say.

So my research paid off. In practice, what I’ve been doing in this lesson is introducing function operations and function notation as a way to overcome a constraint in using equations.


Sami needs $15 more to buy the new hoodie that he wants. But if Sami skips the hoodie, he needs just three more dollars to buy a ticket to the pizza feed on Friday. If Sami has x dollars, how much money, in terms of x, does Sami need if he wants both the hoodie and the ticket to the pizza feed?

The first thing the kids think is that Sami needs $18 more.

I say okay, Sami has $20. How much does the hoodie cost? $35. How much does the pizza feed cost? $23. How much ….oh. Huh, say the kids. He needs a lot more than $18.

Depending on how goofy I feel, I might get out some fake money. I count out $20, give it to a quiet student. How much more for the hoodie? Count out another $15. Now how about the…Right about then, a student gets it: you need the $20 twice.

So then we go to the board and model the two different equations for each purchase.


So if we are getting both things, what are we doing? Adding, the class choruses.

Ah, now there’s a new wrinkle. The kids have been adding equations for a while now, in systems. So I say, let’s try to add these equations.


Is that right? We test it with $20 and the kids realize that the right side “works” (that is, we get $68) but the left side says we still need to divide by 2, which would be…wrong.

“So what’s happening is that we are running into the limits of an equation. An equation tells us that two expressions occupy the same point on a number line–that is, after all, what “equal” means.”

“But when we use multiple variables in equations, then the equation becomes a relationship between two variables, an if-then. If y=x + 15, then the point (3, 18) is a solution because setting x=3 and y=18 creates an equation that has both sides occupying the same point on the number line. If 3x + 2y=12, then (2,3) is a solution because setting x=2 and y=3, etc.”

But in an equation, the variables are values. So in the Sami case, we can’t treat y as a collection point. We can’t keep track of the dependent variable because it varies, obviously. The y in the first equation has a different value from the y in the second equation. If we wanted to keep them separate, we could use two different variables, like z = x + 15 and y = x + 3. Or we could number the ys: y1 = x+15, y2 = x+3.

“Using the language of functions makes a lot of these constraints disappear.”

“First, logically. Functions are different in a key way from equations: a function is an output. An equation is a relationship between variables. Yes, y=x+3 and f(x)= x+3 yield the same results, which is why we teachers always tell you to remember that ‘y and f(x) are the same thing’. However f(x) isn’t a variable, but an output. So when we add two functions, we’re adding outputs. Remember, too, that a function doesn’t even have to be an equation, like in the cell phone code example.

Then there’s function notation, invented by Euler. Function notation enables unique names, usually a single letter. But it doesn’t have to be. You can get creative with the letter names and the input values.”

“Function notation is just more elegant and efficient, too. Instead of saying ‘if x=7’ you can just say f(3). Once you define the function named ‘f’, anything can be input, even another expression, like f(a+7). And then, instead of saying ‘y=’ and solving for x, write f(x)= 3.”

“So let’s call Sammy’s cash on hand c, and then create a function h for hoodie, and p for pizza feed.

h(c) = c+15
p(c) = c+3

In both cases, c represents the money Sami has, so the input value is the same. But the output value varies based on the function used.”

“Now, this is a small difference. But how many have you been told that f(x) is the same as y?” Bunch of hands raised.

“Yep. And in a lot of ways, it is. But you have to be wondering why, if they’re the same thing, we bother teaching you about function notation.” Lots of nods.

“So as you move on into advanced math, you’ll start to learn other reasons why we sometimes use functions and other times use equations. For now, it’s enough to know that function notation allows us to keep track of our different outcomes.

“Once we can do this, we can actually create an entire math with functions. They can be added, subtracted, multiplied. They have inverse operations.”

“But then why do we use equations?”

“Well, for one thing, functions don’t do systems well. Remember, when we solve systems, we are expecting both the x and the y (and any other variables) to be equal. Functions don’t handle that well. So you’ll see that we switch back and forth between equations and functions as needed.”

When you need to add expressions, functions are great. So now we can add h(c) and g(c).

h(c) + p(c) = (x + 15) + (x + 3) = 2x + 18

“Because we are adding outcomes, and have a unique way of tracking each outcome, we can add them properly. Remember, too, that since a function doesn’t need to be an equation, I can add or subtract outcomes without even having an equation. If a(x) = 9 and b(y) = 17, then b(y) – a(x) is 8, and I don’t have to care if a(x) and b(y) are generated by an expression or a rule or a code or a random happenstance—provided, of course, that random happenstance is only one per input.”


I know. You’re wondering why I don’t just follow the AP Calculus teacher’s “f(x) is the same as y”. Well, it turns out that function operations are a big part of pre-calc, so they’ll use this later.

In the meantime, I give them some practice with function notation (I stole this at random). Not enough. Kids don’t really know it later. But at least they’re exposed to it.

Then I go on to linear function addition and subtraction. I usually just put problems on the board.

Sample quiz:


Here’s a test question:


And from here I go on to linear function multiplication (aka quadratics) and, eventually, rational expressions (linear function division).

Like teaching congruence with isometries, I can’t argue that using functions to further our work in linear and quadratic equations is better. I find it more…elegant, maybe?

But the execution isn’t quite there. This is the first year I’ve really taught this whole sequence: introducing functions, function addition/subtraction/notation, function multiplication, inverse functions, rational expressions. Writing it up has revealed an obvious improvement. Up to now, my function illustration has been a quick standalone lesson. Then later I introduce the notion of function addition and in doing so, bring up function notation.

This is goofy, now that I look at it. In the future, I’ll introduce functions and then go into function notation. I can spend a day or two on that, quiz that early. Then I can go back into linear equations or inequalities (the placement is flexible) and then bring up function addition and subtraction, with function notation already covered.

You know what’s irritating? The huge effort described at the beginning of this post to figure out how to describe what I was teaching led me to this. The huge effort underwent solely in order to write this post. Which I was griping about. In learning how to describe function notation for my readers, I learned that the proper way to characterize my work is as a difference between functions and equations, and that led to an idea for better sequencing.

This is kind of a placeholder post. Obviously, I’m in flux about this right now. My linear equations unit has been in good shape for a while. This gives me plenty of room to add flourishes, introduce more complicated topics onto a subject the students know well. Meanwhile, linear function multiplication has proven to be a great introduction to quadratics. So now I’m involved in putting it all together.

Next up in this sequence: the post that I really wanted to write, on my quadratics introduction.

Sorry for the slow rate of posts lately. I did five in April, then got lazy.

The Day of Three Miracles

I often hook illustrative anecdotes into essays making a larger point. But this anecdote has so many applications that I’m just going to put it out there in its pure form.

A colleague who I’ll call Chuck is pushing the math department to set a department goal. Chuck is in the process of upgrading our algebra 1 classes, and his efforts were really improving outcomes for mid to high ability levels, although the failure rates were a tad terrifying. He has been worried for a while that the successful algebra kids would be let down by subsequent math teachers who would hold his kids to lower standards.

“If we set ourselves the goal of getting one kid from freshman algebra all the way through to pass AP Calculus, we’ll improve instruction for everyone.” (Note: while the usual school year doesn’t allow enough time, our “4×4 full-metal block” schedule makes it possible for a dedicated kid to take a double year of math if he chooses).

Chuck isn’t pushing this goal for the sake of that one kid, as he pointed out in a recent meeting. “If we are all thinking about the kid who might make it to calculus, we’ll all be focused on keeping standards high, on making sure that we are teaching the class that will prepare that kid–if he exists–to pass AP Calculus.”

I debated internally, then spoke up. “I think the best way to evaluate your proposal is by considering a second, incompatible objective. Instead of trying to prepare every kid who starts out behind as if he can get to calculus, we could try to improve the math outcomes for the maximum number of students.”

“What do you mean?”

“We could look at our historical math completion patterns for entering freshmen algebra students, and try to improve on those outcomes. Suppose that a quarter of our freshmen take algebra. Of those students, 10% make it to pre-calc or higher. 30% make it to trigonometry, 50% make it to algebra 2, and the other 10% make it to geometry or less. And we set ourselves the goal of reducing the percentages of students who get no further than geometry or even, ideally, algebra 2, while increasing the percentages of kids who make it into trigonometry and pre-calc by senior year.”

“That’s what will happen with my proposal, too.”

“No. You want us to set standards higher, to ensure that kids getting through each course are only those qualified enough to go to Calculus and pass the AP test. That’s a small group anyway, and while you’re more sanguine than I am about the efficacy of instruction on academic outcomes, I think you’ll agree that a large chunk of kids simply won’t be the right combination of interested and capable to go all the way through.”

“Yes, exactly. But we can teach our classes as if they are.”

“Which means we’ll lose a whole bunch of kids who might be convinced to try harder to pass advanced math classes that weren’t taught as if the only objective was to pass calculus. Thus those kids won’t try, and our overall failure rate will increase. This will lower math completion outcomes.”

Chuck waved this away. “I don’t think you understand what I’m saying. There’s nothing incompatible about increasing math completion and setting standards high enough to get kids from algebra to calculus. We can do both.”

I opened my mouth…and decided against further discussion. I’d made my point. Half the department probably agreed with me. So I decided not to argue. No, really. It was, like, a miracle.

Chuck asked us all to think about committing to this instruction model.

Later that day, I ran into Chuck in the copyroom, and lo, a second miracle took place.

“Hey,” he said. “I just realized you were right. We can’t have both. If we get the lowest ability kids motivated just to try, we have to have a C to offer them, and that lowers the standard for a C, which ripples on up. We can’t keep kids working for the highest quality of A if we lower the standards for failure.”

Both copiers were working. That’s three.


I do not discuss my colleagues to trash them, and if this story in any way reflects negatively on Chuck it’s not intentional. Quite the contrary, in fact. Chuck took less than a day to grasp my point and realized his goal was impossible. We couldn’t enforce higher standards in advanced math without dooming far more kids to failure, which would never be tolerated.

Thus the two of us collapsed a typical reform cycle to six hours from the ten years our country normally takes to abandon a well-meant but impossible chimera.

Many of my readers will understand the larger point implicitly. For those wondering why I chose to tell this story now, I offer up Marc Tucker, whose twopart epic on American education’s purported failures illustrates everything that’s wrong with educational thinking today. I would have normally gone into greater detail enumerating the flaws in reasoning, facts, and ambition but that’s a lot of work and this is a damn good anecdote.

Some other work of mine that strikes me as related:

I think I’ve written about my suggested solution somewhere, but where…(rummages)….oh, yes. Here it is: Philip Dick, Preschool and Schrödinger’s Cat–the last few paragraphs.

“Reality is that which, when you stop believing in it, doesn’t go away.”

When everyone finally accepts reality, we can start crafting an educational policy that will actually improve on our current system, which does a much better job than most people understand.

But that’s a miracle for another day.

Evaluating the New PSAT: Math

Well, after the high drama of writing, the math section is pretty tame. Except the whole oh, my god, are they serious? part. Caveat: I’m assuming that the SAT is still a harder version of the PSAT, and that this is a representative test.

Metric Old SAT Old PSAT ACT New PSAT
44 MC, 10 grid
28 MC, 10 grid
60 MC 
40 MC, 8 grid

1: 20 q, 25 m 
2: 18 q, 25 m 
3: 16 q, 20 m
1: 20 q, 25 m 
2: 18 q, 25 m
1: 60 q, 60 m 
NC: 17 q, 25 m 
Calc: 31 q, 45 m
1: 1.25 mpq 
2: 1.38 mpq
3: 1.25 mpq
1: 1.25 mpq 
2: 1.38 mpq
1 mpq 
NC: 1.47 mpq 
Calc: 1.45 mpq

Number Operations 
Algebra & Functions
Geometry & Measurement
Data & Statistics


elem & intermed.
coord & plane
1) Heart of Algebra 
2) Passport to
Advanced Math
3) Probability &
4) Data Analysis
Additional Topics
in math

It’s going to take me a while to fully process the math section. For my first go-round, I thought I’d point out the instant takeaways, and then discuss the math questions that are going to make any SAT expert sit up and take notice.

The SAT and PSAT always gave an average of 1.25 minutes for multiple choice question sections. On the 18 question section that has 10 grid-ins, giving 1.25 minutes for the 8 multiple choice questions leaves 1.5 minutes for each grid in.

That same conversion doesn’t work on the new PSAT. However, both sections have exactly 4 grid-ins, which makes a nifty linear system. Here you go, boys and girls, check my work.

The math section that doesn’t allow a calculator has 13 multiple choice questions and 4 grid-ins, and a time limit of 25 minutes. The calculator math section has 27 multiple choice questions and 4 grid-ins, and a time limit of 45 minutes.

13x + 4y = 1500
27x + 4y = 2700

Flip them around and subtract for
14x = 1200
x = 85.714 seconds, or 1.42857 minutes. Let’s round it up to 14.3
y = 96.428 seconds, or 1.607 minutes, which I shall round down to 1.6 minutes.

If–and this is a big if–the test is using a fixed average time for multiple choice and another for grid-ins, then each multiple choice question is getting a 14.4% boost in time, and each grid-in a 7% boost. But the test may be using an entirely different parameter.

Question Organization

In the old SAT and ACT, the questions move from easier to more difficult. The SAT and PSAT difficulty level resets for the grid-in questions. The new PSAT does not organize the problems by difficulty. Easy problems (there are only 4) are more likely to be at the beginning, but they are interlaced with medium difficulty problems. I saw only two Hard problems in the non-calculator section, both near but not at the end. The Hard problems in the calculator section are tossed throughout the second half, with the first one showing up at 15. However, the coding is inexplicable, as I’ll discuss later.

As nearly everyone has mentioned, any evaluation of the questions in the new test doesn’t lead to an easy distinction between “no calc” and “calc”. I didn’t use a calculator more than two or three times at any point in the test. However, the College Board may have knowledge about what questions kids can game with a good calculator. I know that the SAT Math 2c test is a fifteen minute endeavor if you get a series of TI-84 programs. (Note: Not a 15 minute endeavor to get the programs, but a 15 minute endeavor to take the test. And get an 800. Which is my theory as to why the results are so skewed towards 800.) So there may be a good organizing principle behind this breakdown.

That said, I’m doubtful. The only trig question on the test is categorized as “hard”. But the question is simplicity itself if the student knows any right triangle trigonometry, which is taught in geometry. But for students who don’t know any trigonometry, will a calculator help? If the answer is “no”, then why is it in this section? Worse, what if the answer is “yes”? Do not underestimate the ability of people who turned the Math 2c into a 15 minute plug and play to come up with programs to automate checks for this sort of thing.


Geometry has disappeared. Not just from the categories, either. The geometry formula box has been expanded considerably.

There are only three plane geometry questions on the test. One was actually an algebra question using the perimeter formula Another is a variation question using a trapezoid’s area. Interestingly, neither rectangle perimeter nor trapezoid formula were provided. (To reinforce an earlier point, both of these questions were in the calculator section. I don’t know why; they’re both pure algebra.)

The last geometry question really involves ratios; I simply picked the multiple choice answer that had 7 as a factor.

I could only find one coordinate geometry question, barely. Most of the other xy plane questions were analytic geometry, rather than the basic skills that you usually see regarding midpoint and distance–both of which were completely absent. Nothing on the Pythagorean Theorem, either. Freaky deaky weird.

When I wrote about the Common Core math standards, I mentioned that most of geometry had been pushed down into seventh and eighth grade. In theory, anyway. Apparently the College Board thinks that testing geometry will be too basic for a test on college-level math? Don’t know.

Don’t you love the categories? You can see which ones the makers cared about. Heart of Algebra. Passport to Advanced Math! Meanwhile, geometry and the one trig question are stuck under “Additional Topic in Math”. As opposed to the “Additional Topic in History”, I guess.

Degree of Difficulty;

I worked the new PSAT test while sitting at a Starbucks. Missed three on the no-calculator section, but two of them were careless errors due to clatter and haste. In one case I flipped a negative in a problem I didn’t even bother to write down, in the other I missed a unit conversion (have I mentioned before how measurement issues are the obsessions of petty little minds?)

The one I actually missed was a function notation problem. I’m not fully versed in function algebra and I hadn’t really thought this one through. I think I’ve seen it before on the SAT Math 2c test, which I haven’t looked at in years. Takeaway— if I’m weak on that, so are a lot of kids. I didn’t miss any on the calculator section, and I rarely used a calculator.

But oh, my lord, the problems. They aren’t just difficult. The original, pre-2005 SAT had a lot of tough questions. But those questions relied on logic and intelligence—that is, they sought out aptitude. So a classic “diamond in the rough” who hadn’t had access to advanced math could still score quite well. Meanwhile, on both the pre and post 2005 tests, kids who weren’t terribly advanced in either ability or transcript faced a test that had plenty of familiar material, with or without coaching, because the bulk of the test is arithmetic, algebra I, and geometry.

The new PSAT and, presumably, the SAT, is impossible to do unless the student has taken and understood two years of algebra. Some will push back and say oh, don’t be silly, all the linear systems work is covered in algebra I. Yeah, but kids don’t really get it then. Not even many of the top students. You need two years of algebra even as a strong student, to be able to work these problems with the speed and confidence needed to get most of these answers in the time required.

And this is the PSAT, a test that students take at the beginning of their junior year (or sophomore, in many schools), so the College Board has created a test with material that most students won’t have covered by the time they are expected to take the test. As I mentioned earlier, California alone has nearly a quarter of a million sophomores and juniors in algebra and geometry. Will the new PSAT or the SAT be able to accurately assess their actual math knowledge?

Key point: The SAT and the ACT’s ability to reflect a full range of abilities is an unacknowledged attribute of these tests. Many colleges use these tests as placement proxies, including many, if not most or all, of the public university systems.

The difficulty level I see in this new PSAT makes me wonder what the hell the organization is up to. How can the test will reveal anything meaningful about kids who a) haven’t yet taken algebra 2 or b) have taken algebra 2 but didn’t really understand it? And if David Coleman’s answer is “Those testers aren’t ready for college so they shouldn’t be taking the test” then I have deep doubts that David Coleman understands the market for college admissions tests.

Of course, it’s also possible that the SAT will yield the same range of scores and abilities despite being considerably harder. I don’t do psychometrics.



Here’s the function question I missed. I think I get it now. I don’t generally cover this degree of complexity in Precalc, much less algebra 2. I suspect this type of question will be the sort covered in new SAT test prep courses.


These two are fairly complicated quadratic questions. The question on the left reveals that the SAT is moving into new territory; previously, SAT never expected testers to factor a quadratic unless a=1. Notice too how it uses the term “divisible by x” rather than the more common term, “x is a factor”. While all students know that “2 is a factor of 6” is the same as “6 is divisible by 2”, it’s not a completely intuitive leap to think of variable factors in the same way. That’s why we cover the concept–usually in late algebra 2, but much more likely in pre-calc. That’s when synthetic division/substitution is covered–as I write in that piece, I’m considered unusual for introducing “division” of this form so early in the math cycle.

The question on the right is a harder version of an SAT classic misdirection. The test question doesn’t appear to give enough information, until you realize it’s not asking you to identify the equation and solve for a, b, and c–just plug in the point and yield a new relationship between the variables. But these questions always used to show up in linear equations, not quadratics.

That’s the big news: the new PSAT is pushing quadratic fluency in a big way.

Here, the student is expected to find the factors of 1890:


This is a quadratic system. I don’t usually teach these until Pre-Calc, but then my algebra 2 classes are basically algebra one on steroids. I’m not alone in this.

No doubt there’s a way to game this problem with the answer choices that I’m missing, but to solve this in the forward fashion you either have to use the quadratic formula or, as I said, find all the factors of 1890, which is exactly what the answer document suggests. I know of no standardized test that requires knowledge of the quadratic formula. The old school GRE never did; the new one might (I don’t coach it anymore). The GMAT does not require knowledge of the quadratic formula. It’s possible that the CATs push a quadratic formula question to differentiate at the 800 level, but I’ve never heard of it. The ACT has not ever required knowledge of the quadratic formula. I’ve taught for Kaplan and other test prep companies, and the quadratic formula is not covered in most test prep curricula.

Here’s one of the inexplicable difficulty codings I mentioned–this is coded as of Medium difficulty.

As big a deal as that is, this one’s even more of a shock: a quadratic and linear system.


The answer document suggests putting the quadratic into vertex form, then plugging in the point and solving for a. I solved it with a linear system. Either way, after solving the quadratic you find the equation of the line and set them equal to each other to solve. I am….stunned. Notice it’s not a multiple choice question, so no plug and play.

Then, a negative 16 problem–except it uses meters, not feet. That’s just plain mean.

Notice that the problem gives three complicated equations. However, those who know the basic algorithm (h(t)=-4.9t2 + v0 + s0) can completely ignore the equations and solve a fairly easy problem. Those who don’t know the basic algorithm will have to figure out how to coordinate the equations to solve the problem, which is much more difficult. So this problem represents dramatically different levels of difficulty based on whether or not the student has been taught the algorithm. And in that case, the problem is quite straightforward, so should be coded as of Medium difficulty. But no, it’s tagged as Hard. As is this extremely simple graph interpretation problem. I’m confused.

Recall: if the College Board keeps the traditional practice, the SAT will be more difficult.

So this piece is long enough. I have some thoughts–rather, questions–on what on earth the College Board’s intentions are, but that’s for another test.

tl;dr Testers will get a little more time to work much harder problems. Geometry has disappeared almost entirely. Quadratics beefed up to the point of requiring a steroids test. Inexplicable “calc/no calc” categorization. College Board didn’t rip off the ACT math section. If the new PSAT is any indication, I do not see how the SAT can be used by the same population for the same purpose unless the CB does very clever things with the grading scale.


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