kitchen table math, the sequel: 24%

Sunday, November 28, 2010


Recently released data from ACT shows that only 24 percent of high school seniors knew enough in four subjects — math, reading, science and English — to do college-level work.

No More A’s for Good Behavior
by Peg Tyre
Published: November 27, 2010
New York Times


Anonymous said...

To me, the most interesting part of that story was the truth that teachers had no idea who had mastered the material, because they had never tested anyone against what they'd taught.

"A few years ago, teachers at Ellis Middle School in Austin, Minn., might have said that their top students were easy to identify: they completed their homework and handed it in on time; were rarely tardy; sat in the front of the class; wrote legibly; and jumped at the chance to do extra-credit assignments.But after poring over four years of data comparing semester grades with end-of-the-year test scores on state subject exams, the teachers at Ellis began to question whether they really knew who the smartest students were.

About 10 percent of the students who earned A’s and B’s in school stumbled during end-of-the-year exams. By contrast, about 10 percent of students who scraped along with C’s, D’s and even F’s — students who turned in homework late, never raised their hands and generally seemed turned off by school — did better than their eager-to-please B+ classmates....
Over time, we began to realize that many teachers had been grading kids for compliance — not for mastering the course material,” Ms. Berglund said. “A portion of our A and B students were not the ones who were gaining the most knowledge but the ones who had learned to do school the best.”

Last fall, over protests from parents of some of the above-average students, the eighth-grade math teachers at Ellis tried a new, standards-based grading system, and this fall the new system is being used by the entire middle school and in high school for ninth graders."

I'll repeat here what I said elsewhere: I could not believe the number of schools I've visited in the last 2 months that *did not know* what a standards-based school was. (cont)

Anonymous said...


I have visited half a dozen parochial schools, 3 charters, another 4 independent private schools, plus a couple of public ones.

The public schools and the charters are required to be "standards based", so at least their principals knew what standards are.

But of the other privates and parochials, only *1* school was standards based! That means, they a) have a set of standards,
b) teach to that set,
c) assess with a test that maps to the standards,
d) close the loop and address deficiencies in teaching, curriculum, etc. based on those results.

And that 1 school was the only school that even KNEW WHAT I MEANT when I asked if it was standards based. The others couldn't tell me what standards they used, or claimed not to have them. They couldn't tell me how a) they knew what they should be teaching, b) how their curriculum met that need, or c) how they could know if their students had been taught that material.

We're talking not just typical neighborhood Catholic schools, ranging from 3k-8k a year where they have no specialists before 7th grade, or even no specialists at all. This included the 12k a year pre-k through 12th grade school who claims to roll their own curriculum in math for middle school, and even included the 22k a year private schools.

For the two 22k a year privates, they did not have any idea that their lack of standards had been a root cause of their huge disparity in mathematics skill by 5th grade--because they had no idea how to even begin to address how different teachers of 4th grade taught "the same material" differently. What assessment mechanisms they did have did not match their curriculum, so they were not measuring anything relevant anyway.

Yes, there are caveats--of course a standards-based school need not succeed either; standards can be too weak; assessments can be too weak to properly test mastery of standards, etc. etc. etc. but I am not surprised to hear that if you have no standards, and your assessments don't measure against your curriculum, then no one has any clue who has mastered the material.

Hainish said...

To what extent can grading policies in K-12 be thought of as a status-grab by the mediocre? (I mean, why else would a parent complain about grades being based on understanding instead of compliance?)

I blog about this here.

- Hainish

lgm said...

I found it interesting to look at the NYS school report card for my district and compare the number acheiving a '4' in math with the number admitted to middle school accel math. About half did not acheive a '4', and of course several boys who did acheive a '4' serveral years in a row were not admitted due to the nonteacher pleasing behavior. No surprise, we parents have always been told it's all about the WHOLE child, not just academics.

Glen said...

Near monopolies often forget who works for whom. It's easy for teachers to start thinking of themselves as bosses and the kids as employees. Bosses usually "grade" employees based on how much their behaviors and attitudes benefit the boss and "the team".

Of course, if students aren't employees, then grades shouldn't be employee evaluations.

Anonymous said...

I totally agree with the idea that a student's grade should be comprised of assessments that are based on subject matter only and not compliance. I currently give daily quizzes that are correlated to the several preliminary exams leading up to the final exam for the course. I also assign projects that are completed individually and are closely related to the material on the quizzes and tests. So, I am all for assigning student's grades based on mastery of the course material BUT


be very careful when you hear "standards based grading." I have seen some blog posts and descriptions of this idea that curl my hair (and my hair is normally straight). The issue I have with standards based grading is that, from what I have seen, the assessments will only assess one standard in each question. I really think that this is a major mistake and will actually harm students in the long run. The analogy I always use in my classes is that there is a big difference between learning to drive a nail and learning to cut with a saw versus learning to build a house. It is vital that students learn to use their skills in problem solving situations which means they have to make decisions about what to do and when. I sometimes talk in my classes about "obstacle course problems." These are problems that assess several skills at once. A simple example is instead:

Solve using the quadratic formula:


Solve for x:


The projects I assign are also like this. I was grading some over the holiday that required the students to graph three lines using graphing software, find the points of intersection of the three lines and then find the area of the triangle. Finding the area of the triangle can be done using Heron's Formula, which only requires the students to find the lengths of the three sides of the triangle. I also ask that they find the area using .5b*h. To do this, they must pick a base for the triangle and find the equation of a line that is perpendicular to the base and passes through the opposite vertex. Then find the intersection of the base and the perpendicular and find the height and the base. I don't lay all this out for them - I just mention that the base and height must be perpendicular. I really believe that this is where I see what the students understand. Can they fit it all together?

Sometimes yes, sometimes no, but even the students who struggle with these projects have at least been exposed to this type of multi-step problem solving situation. This is my biggest problem with standards based grading - the lack of multi-step problem solving that is essential for success in mathematics (and in my opinion any endeavor).

Anonymous said...

The students have two weeks to complete these projects and they're typed up with explanations for each portion of the solution and the connections between the different ideas...

Anonymous said...

But that isn't a problem with "standards based grading". It's a problem with bad standards and bad assessments of those standards.

There is no reason that standards can't demand mastery of complex problems and multi step problems, or that assessments require sufficient mastery of material to demonstrate the standards have been met.

The SAT math is, as noted elsewhere, a very good example of an assessment that assesses mastery of concepts, procedural fluency, and multi-step logic all at the same time. Lack any element and you'll get the problem wrong.

Anonymous said...

Allison, I agree with that this isn't necessarily a problem with "standards based grading." If this is really about assessment of standards that includes complex problem solving - then I'm all for it.

I'm just saying - be careful when people come selling it. Make sure that it really does assess student understanding.

I'm involved in the adoption of a adaptive software package for our students which I think can really help them. But, tagging along came all of these methods approaches that I don't believe serve the students in the long run - and they were presented in a very aggressive and deceptive way.

But, again, this is just my experience, your mileage may vary...

SteveH said...

Unfortunately, I could never talk about standards based anything in our area because it usually means low standards and some sort of authentic grading. In education, words and terms get gobbled up. I still can't believe they took over the meanings of "understanding" and "problem solving" in math. Either they are completely clueless, or it's a cover. Both, probably.

The state tests only give feedback in a general way, so the information is not very helpful. They see lower scores in "Problem Solving" and they tell teachers to come up with ways to add in more problem solving. They actually have meetings where they do this. This is the level of feedback they work on.

They have a hard enough time trying to differentiate teaching and learning. They can't possibly figure out and implement ways to correct mastery issues for kids at multiple levels. You have to have a low or vague definition of education to think that this is OK.

Throughout my son's lower school education, there has always been a fundamental gap between what my wife and I expected and what the schools expected. This hasn't been simply a matter of us wanting a Core Knowledge approach versus their thematic discovery approach. It has to do with low versus high expectations. It's not simply that they know what a rigorous education is, but just don't want to push. They just don't know what a good education is. They would only define it in the vaguest sorts of terms, like "lifelong learning". Many don't have a clue what is needed for a proper STEM degree in college, but that doesn't stop them from coming up with silly solutions.

I would be interested in Allison's reaction after all of her school visits. My reaction with our schools could be described as dumbstruck; unable to figure out any way to solve the problem because they are on another planet, not just pedagogically, but education-wise. They don't know enough to understand the problem.

FedUpMom said...

@Glen -- I liked your comment so much that I featured it on my blog:

Grading for Learning

Jen said...

Have to agree with anonymous above that it's all about the quality of the assessment(s). Too many standards-based programs/curricula have really awful assessments.

They test in ways that weren't taught, they don't combine standards in ways that are useful to students, etc.

Even back at the original article quoted, I'd guess of the 10% on either end of that spectrum there are maybe 5% on each end that are truly assessed poorly -- on the top end that would exclude kids that panic for high stakes testing and the odd situation that pops up and is never reflected in "data" (a student that missed three weeks of school before the state testing, say, or the student that was sick and had to be woken up regularly during testing).

On the other end, sure, you've got some kids who can pick things up without doing the work in class (just like some of the high scorers likely would score just as high without doing the work -- they want the grade too!) You also may have some that just are lucky, that day, that test and it hits on the things that they did pick up, they make some lucky guesses, etc.

Honestly? 5% top and bottom isn't all that bad -- if it's a class of 100 kids, you'll have 5 kids that seem to have gotten a higher grade than their one-time high stakes test score indicates they should have and 5 kids whose grades are lower than their test indicates. Then you have 80-90 kids whose grades accurately predicted results. Is that so unexpected?

Hainish said...

Serendipitously, as I was reorganizing some of my parents' stuff today, I came across my grade 5 report card. It was stapled to a printout of my scores for a standardized test I took at the end of that year, branded Testcorp (this was before NCLB state test craze).

With a grading scheme of NI, S (satisfactory), G, and Ex, I got almost all S's, in all subjects, each quarter that year. Maybe there were a few G's thrown in for good measure, but that thing was like a sea of S's. My grades were literally middling.

The test scores, OTOH, were between the 76th and 99th percentiles (with an outlier at the 27th percentile for computation...I guess I did sloppy work.) This report sheet told the story in grade equivalents, percentiles, stanines, and a normed curve equivalent. My GE's were mostly 11+. I was in the 8th or 9th stanine for all but a couple of the subtests.

I'm trying really hard to come to terms with this discrepancy, I really am. I'd always thought of myself as a bright underachiever. I went on to ace AP calculus, even though I wasn't "on track" for it. So what was my grade 5 teacher seeing?

Jen, it's never that bad until it's you that's affected.

Anonymous said...

-- Too many standards-based programs/curricula have really awful assessments.

I'm not defending bad assessments. But what is the alternative to standards-based schools--where that means that they actually close the loop with a feedback mechanism that shows them if they have successfully taught their students what their standards say all of the students will learn?

Standards as inputs aren't enough.

Consider a big company that builds something complicated, like a car. Consider that they have "standards" for engineering, but only as inputs. Then, a defect is found only after a customer has the product. Now what? How can the company fix the defect? How can they even find out the cause of the defect to fix it? How can they tell how many other cars have the same defect? And above all, how in the world will they ensure it doesn't happen again, if they have no idea where their standards weren't met?

You must close the loop. You must have mechanisms for assessing whether or not your process in controlled, and you must be able to ensure your process is repeatable, and be able to then fix where the system is deficient. Then, you can use what you know from your assessments to improve your process.

People grouse about the processes put in place to ensure quality control over the life of the whole system. Whether it's 6 Sigma, or CMMI, or any other process, sure there can be issues, but the alternative isn't "let's throw out process control and engineering assessments."

In a school, input standards aren't enough. How do you *KNOW* that n different 5th grade teachers are teaching against the same standards? How do you know they've done so effectively? How can you be sure that all 6th graders will meet the minimum knowledge they need to move forward? How can you be sure your students made a year's progress in a year's time? If you aren't assessing against the standards, and using that to FIX what's taught, it's impossible to know.

Just like the process of building a specific instance of a car, it's extremely difficult to observe in real time any errors in the education process for a given child. The only possible way for a school or parent to be able to observe any such errors is if the observable they are given--GRADES--match the standards.

This doesn't imply there aren't additional grades for conduct, or ways of grading above minimums in standards.

But it says that teachers and schools can't hide behind differentiated instruction and only move children epsilon ahead in a year.

PhysicistDave said...


My grades in elementary school were similar, at least in the lower grades - perhaps equal numbers of A, B, and Cs. However, I was valedictorian in high school (A+ average), had near-perfect SAT scores, and went on to Caltech and Stanford.

I remember pretty clearly why.

I was bored to tears in grade school -- I would read all the textbooks in the first month or so, and then stare out the window and day-dream the rest of the year (it was relaxing!). I usually did not know where the teacher was when she was going through a book, since, after all, I had long since gone through the whole book. Like most little boys, I did not much care whether my name was in the upper left or upper right of the paper, above or below the date.

They started tracking us in junior high. I was still the top student in the class, but at least the class moved at a fast enough pace that I thought it was worth paying attention.

Frankly, I think I behaved wisely: why should I have taken grade school seriously?


PhysicistDave said...


I see three major problems with standards:

1) The standards just cannot be placed at a level where it really will be totally impossible for two-thirds of the students to meet the standards. It is one thing to have “demanding” standards that push the students, but if you know that most of the students have no hope of even coming close… well, realistically teachers cannot teach a class that way. They have to deal with the students they actually have and try to teach at a level those kids have some chance of grasping.

But, if the standards are appropriate for the kids in the middle, the top kids are going to just be wasting their time. I know that tracking can ameliorate this, although it does not eliminate the problem. However, if you are serious about standards and about tracking, then you need different standards for the different tracks.

And, then you also face the problem of kids who are borderline between the tracks.

No matter how you cut it, an administrative nightmare.

2) Whom do you trust to set, implement, administer, and test the standards?

The problem, after all, is not that, in the USA, we generally have truly brilliant principals, involved and supportive parents, and great state educational bureaucracies, but, for some reason, our classroom teachers are just not measuring up.

The whole system is broken. Any attempt to fix it assumes that at least some parts of it more or less function. And they don’t.

It’s one thing to deal with a termite infestation if it is localized to a few sections of the house. But, if the little fellows are already into every cubic inch of wood in the whole structure, it’s too late.

3) Teaching is not like manufacturing. If it were, we could use those little boxes (“teaching machines”) B. F. Skinner invented for programmed instruction and drop the teachers altogether (admittedly, I think that might work better than current schools!). A good teacher works at personalizing her instruction to the particular student, she tries to work with the student to understand what particular roadblocks the student faces in moving forward faster, and she tries to figure out how to remove those roadblocks.

But, of course, a teacher who does that actually does know how the student is doing. So, good teachers would not make the misjudgments mentioned in the story you quote. I have had some teachers like that, as well as a lot like those in the story you quote.

The good teachers will be pretty good without standards (again, I can think of some I have had); the bad will still be bad even with standards.

Standards might help a little bit if the whole system were more or less functioning. But in the current system, it seems to me they basically do nothing much but offer full employment for a “standards” bureaucracy.


Rocky said...

Does showing your work count as compliance or understanding?