kitchen table math, the sequel: Are standards requirements? Are curricula products?

Thursday, April 29, 2010

Are standards requirements? Are curricula products?

The push for standards is everywhere. But what are standards?

In engineering disciplines, engineers build products based on *requirements*.

Requirements are specifications of a problem to solve in order to build a product, or system or process. Requirements are NOT a design--they are not a solution. They specify key elements that a solution must have, should have, and would like to have, but properly written, they leave open what the actual solution is.

Examples of requirements are:
device must weigh less than 2.2 ounces;
device must operate properly during and afterw a fall from 8 inches into a bath of 110 degree liquid for not less than 6 seconds duration
device user input method must support touch typing at not less than 20 wpm

system performance requirements are things like:
system must detect intrusion within N seconds with probability of detection >=80% in noisy/cluttered environment

system must locate target within accuracy of 3 sq feet at range of 1.5 miles with false positive rate of no more than 1%

Excellent requirements are difficult to write. The best ones are (at least) unambiguous, concise, testable and/or measurable, and finite. Unambiguous requirements leave little room for confusion (and seldom have compound requirements in them.) Measurable requirements give you a way to tell performance; testable ones allow you a method to demonstrate you've met the requirement.

Requirements define inputs and outputs as well as what happens in between.

Given good requirements, a good design will meet them, and even more, will trace how they are met (if possible, every design choice points to a set of requirements, and on design choice exists without such requirements backing it up.) Every choice at every stage would be traceable to the requirements.

Among the stakeholders looking for a product/process/system, most aren't skilled at requirements writing. Explicit requirements are few and far between, and most must be teased out, so that derived requirements (that do meet the above criteria) can be created.

Given that, what in the world are standards in education? Are they supposed to be requirements? Of WHAT system/process/product? A classroom's learning? A classroom's teaching? Are they requirements from which one defines curricula? Is the curricula the product that meets the standards? Are students the product that are supposed to meet standards?

Reading the Common Core standards, they don't come close to meeting the criteria of requirements.
Here's an example:

1. Understand that multiplication of whole numbers is repeated addition. For example, 5  7 means 7 added to itself 5 times. Products can be represented by rectangular arrays, with one factor the number of rows and the other the number of columns.
2. Understand the properties of multiplication.
a. Multiplication is commutative. For example, the total number in 3 groups with 6 things each is the same as the total number in 6 groups with 3 things each, that is, 3  6 = 6  3.
b. Multiplication is associative. For example, 4  3  2 can be calculated by first calculating 4  3 = 12 then calculating 12  2 = 24, or by first calculating 3  2 = 6 then calculating 4  6 = 24.
c. 1 is the multiplicative identity.
d. Multiplication distributes over addition (the distributive property). For example, 5  (3 + 4) = (5  3) + (5  4).

So, apparently, these are *student* requirements.
They mean to be saying
"THE STUDENT SHALL understand that"

But what student? All students? A typical student? A student who passed the prior year's standards?

What does it mean to understand that 1 is the multiplicative identity? Does it mean to be able to recite that phrase? use that fact in a problem? use that fact in N problems, and get the answer right M times out of N problems? does it mean being able to cite the use of the multiplicative identity in order to solve the problem?

These standards aren't finite, concise, unambiguous, and without guidance, certainly aren't testable.

Where does that leave curricula? Since the standards are "THE STUDENT SHALL" rather than "the system shall", how can any curricula meet the requirements of what a student is required to learn?

If curricula aren't solutions to the problem defined by the standards requirements, then what are curricula? And what are teachers or students or schools? Stakeholders ? Or something else?


Boe said...

Education standards are nothing like product or system standards. As far as I can tell, education standards simply identify topics to be addressed. You can have identical standards year after year: third grade, fourth grade, fifth...

The curriculum is the what and the how, what are we going to teach and how are we going to teach it. Text books and the like--things that I would have called curriculum--are really 'materials.' They are part of curriculum, but not the whole thing.

The closest education equivalent of a business requirement is 'outcomes.' That's the part where we define what students should know and be able to do as a result of the curriculum. So the logical order of planning would be: standards, outcomes, curriculum, materials. I think. :-)

Allison said...

I should add that sometimes people complain about standards by saying "platinum rulers don't make you taller", which is a claim that the standards are actually standards in a weights and measures sense: this 1 kg weight is the standard by which all others are compared, and yours may be off in some way, but ours define what a kilogram is.

The Common Core standards aren't standards in this sense at all. In as much as they are in this sense, they claim to define a first grader--so that's nonsensical. Any attempt to interpet it as a statement of curricula or a req for an exit exam fails because of its ambiguity. The 1 kg weight at NIST is not ambiguous.

Laura M. said...

What's missing, I think, is something like concrete, specific, objectively measurable goals, graduated benchmarks, and a plan for meeting the benchmarks and goals (and for addressing failure to meet benchmarks on time or for adjusting goals when benchmarks are met more quickly than planned).

This is what we are hammering out for my son's IEP. You are only supposed to put in short-term benchmarks for kids who have to take alternative assessments, so I'm trying to come up with a less formal plan to make sure we are measuring progress in short enough increments that there is time to meet and change strategy before wasting too much of the school year.

Also, have you looked at the Core Knowledge sequence?

Allison said...

Goals are targets for solutions to some problem. That is, your solution is supposed to reach goals. They are desinations.

But solutions are jumping the gun.

What problem is the one to be solved?

Goals aren't meaningful until you've defined a problem.

Standards--in the weights and measures sense--aren't solutions or goals. Stanadidards in the requirements senses aren't goals either.

And IEP assumes the problem is what, precisely?

That the child cannot learn in the traditional classroom? That the child cannot learn the way "everyone else" can? That the teacher can't teach this child?

Yes, I know all about CK. My point was to start a discussion about what CC standards are trying to achieve, and how people don't seem to be able to even define the problem, so no wonder they can't agree on if the CC standards will solve it.

Linda said...

Your insights on standards are precisely why public school teachers spend so much time scrutinizing the state tests. The REAL standards are the information on the tests. The *students* are whatever percentage it takes to make AYP. If the test asks kids only to identify an example of the multiplicative identity, then that is the default standard. If the test asks kids in an open-ended question to use it in problem solving, then that is the standard. In PA, the PSSA asks kids to use three different models for fractions (part of a whole, part of a set, number line); therefore, I make sure our fourth graders have seen all 3 even though Singapore doesn't show them the number line model by that point. Of course we are teaching to the test; that is what they were designed for Unfortunately they are terrible tests.

Laura M. said...

Goals aren't meaningful until you've defined a problem.

Maybe a potential problem. For instance, I don't think "needing to learn to decode" is a problem if we're talking about a toddler who hasn't yet learned to speak in full sentences. If we're talking about an 8 year old, it's a problem.

A non problem-focused goal might look something like: By the end of the year, given 5 non-fiction paragraphs written at their reading level, the student will be able to paraphrase two of the facts described.

A graduated benchmark might look something like: given the same conditions described above, student will be able to tell the teacher one fact orally, by October.

Yes, I know all about CK.

O.k., I haven't had a chance to look thoroughly at the sequence (which I only just realized had been released for free), so I was wondering what your opinion was about it.

Also, I'm not sure the goal of standards is to fix a problem, so much as to minimize the creation of problems.

Not that I think standards alone are going to accomplish that.

Laura M. said...

I wonder why my posts aren't showing up in the "recent comments" section.

Anonymous said...


They seem to show up later at times. It's kind of odd.


Allison said...

--I don't think "needing to learn to decode" is a problem if we're talking about a toddler..

It's not a problem for a toddler because most people don't consider toddlers as children who should be reading in the first place--so for them, that a toddler isn't decoding isn't a problem. Since it's not a problem, in what sense is it a goal at all?

My point of talking about problems is to ask what lack/deficiency needs to be met by schools, because when people talk about standards, they refer to schools. And people talk about problems of schools all the time: "fix the darn schools" means people say the schools have problems. What problems? Some people claim the main problem is the achievement gap. Other problems include: our students are falling in achievement compared to other nations; the majority of our students enter college needing remediation; a large percentage of children are innumerate after 12 years of school; a large percentage can't write a coherent essay; a large percentage can't tell you when the US Civil war took place.

Pushing harder, some people see the above problems as symptoms of bigger problems, such as: teachers don't know material they purport to teach, schools promote socially regardless of skills, schools have a full inclusion model and use differentiated instruction, schools don't meet the students at their skill level and accelerate them up, schools don't respond to parent desires, etc. There's a hundred more answers here, but hardly any consensus on whether these are actually the problems, the causes of those other stated problems, etc.

When you can't define the problem, you won't be able to solve it.

Laura M. said...

Thanks, Susan--I guess I need to be more patient about it. :-)

When you can't define the problem, you won't be able to solve it.

True, but

a)defining the problem in a way that satisfies most Americans or even most people in one school district may prove more "costly" than other approaches--or perhaps, not. I'm not sure at this point.


b) If we want to point education in a particular direction, it's going to be hard to do that if we spend all of our energy putting out fires rather than some significant amount of that energy figuring out what direction we want to take. What direction will help avoid new problems that we have not yet imagined?

Since it's not a problem, in what sense is it a goal at all?

In the sense that eventually you want the toddler to grow up into a preschooler or Kindergartner or at least 1st grader who can decode.

And if the toddler is having trouble learning to talk (compared to the norm), that's a potential flag to keep in mind on the way toward the goal of having them decode by age 4-7. If they are already recognizing letters it's worth keeping in mind that by K, they're probably going to be ready for more than basic decoding, and so we may we wish to revise the implicit goals we have in mind for them for K.

Allison said...

So then the toddler goal is "learn letters and numbers". And that has nothing to do with the schools, because standards for schools don't involve toddlers.

To your other point, "but if they can do something... then we'll need to revise"

well, yes, that's the problem with a standard for the typical student. What about the atypical? How in the world will a national standard meet the needs of millions who are distributed in background, skill, and ability?

Laura M. said...

And that has nothing to do with the schools, because standards for schools don't involve toddlers.

It was meant simply as an example of a long-term goal (decoding) with short-term benchmarks (learning to talk on schedule)that is not focused on solving pre-existing problems.

But even taking that specific example at face value, what do you think Early Intervention (for babies and toddlers) is about? It is meant to catch problems that might at a later age affect school performance.

By the way, I agree with you that national standards are insufficient--I'm interested in a conversation about what we can imagine (since we are not empowered to do anything directly) adding to or how we can imagine supplementing or revising the standards in a way that would make them sufficient.

Allison said...

--What do you think Early Intervention (for babies and toddlers) is about?

I don't know specifically what you mean. Here in St. Paul, Early Intervention means hearing tests, developmental test for coordination, speech etc, and the like to determine if kindergarten readiness is being met. Is that what you mean? In that case, the issue is again: is there a problem; if yes, then we do X.

Or do you mean the Head Start like claims that if we take disadvantaged children and put them in pseudo school run by disadvantaged adults, somehow something magic will happen?

We--our society, whether academics, wonks, or anyone else you want to name-- do not know how to raise the achievement scores of those below average once they reach school. We've no data that it's ever been done by anything but one classroom teacher. It's not been repeated, and every other study has shown the gains don't last.

Allison said...

See, I can't see how adding to or supplementing or revising standards makes them sufficient because they are not solving the right problem.

But could requirements help solve the problem of teachers who don't know material? yes. Could requirements help the problem of curricula that are weak on content? Yes.

Requirements--the school shall employ teachers whose content knowledge is sufficient, as deemed so by X score on Y test; the school group by ability, as assessed every semester by ..., etc. would be much better than a set of standards in my book.

Laura M. said...

Ok, I can agree with that--requirements rather than standards. I like that.

is there a problem; if yes, then we do X.

It's not necessarily that strictly defined, though (at least not here in Westchester County)--for some areas, at least (like, say, the way you hold a pencil) it's more like if you are 2 standard deviations from the norm in a particular behavior, you get therapy meant to bring you up to the norm by Kindergarten.

So, it's not necessarily a problem itself (is a 4 year old not being able to hold a pencil correctly inherently a problem, for example?), but an indicator that a problem might crop up when it matters.

But again, I like the idea of requirements, because it means not having to wait until there is a hard-to-fix problem to start assessing and changing tactics until we hit upon a successful strategy.

How to make that strategy "generalize" past the point that you are employing it? That is a big question . . . how would we assess that before having to observe kids go through a whole program? That's a key concern.

Laura M. said...

Ok, I just re-read your post, and I don't know why the word "requirement" didn't stick out for me when I read it the first time (for some reason, "problem" was what I fixed on").

It might be because I was just having a conversation with my husband about goals and benchmarks, and he used the word "requirement," so maybe that's why it's making more sense now.

So, apologies for that . . .

I actually agree with you.

SteveH said...

Lots of things fall apart in education when you look at the details. That's because they don't believe in quantifying anything. That's too rote. Education is more mystical. Did you ever notice that when they use "authentic", they mean less well-defined? It also, quite conveniently, means that you can't quantify whether they are doing a good job or not. Ever since my son started school, I've been looking for specific details and educational goals. I haven't found any.

"then what are curricula?"

Generalized high level fluff to keep everyone happy while they continue to do whatever it is that they do. I've always wanted to go into my son's schools and start digging and asking many specific questions. I might as well tell them that I don't think they know what they are doing.

Laura M. said...

So, what do you all think of this:

From Driven By Data:

"Standards are meaningless until you define how you will assess them."

"The level of mastery that will be reached by a given class is determined entirely by what sort of questions students are expected to answer. This turns conventional wisdom on its head: instead of standards defining the sort of assessments used, the assessments used define the standard that will be reached."

Lisa said...

As I see it, the problem with standards is they soon quit being a baseline and become an endpoint. An example, the standard for 3rd graders is something like 'will know 2,5 and 10 multiplication tables.' The teachers have quit teaching all the multiplication tables because they don't NEED to know them.

Laura M. said...

they soon quit being a baseline and become an endpoint.

So, isn't the solution then to either raise the standard for each grade, and/or build in a way for raising the standard individually as it is met by each child?

Anonymous said...

I've seen lots of similar discussions in software development, and a similar set of issues around defining goals and measurement.

In particular, when generating numbers to measure progress towards a (desired) goal, very often the (achieved) goal ends up being "make the measured number better". For example, measuring code-writing ability as "lines of code checked in" leads to lots and lots lines being checked in - even if they are not actual useful code (comments, blank lines, etc).

The equivalent in education would be that the NCLB goal of "teach all the children" was filtered through the measurement of "percent getting above the threshold on the test", a common reaction was to either change the test or change the threshold to pass, rather than change the way the children are taught.

Good requirements are a huge amount of work to do correctly - where I mean "correctly" to mean "encourage [people] to make progress to the actual intended goal" - but without requirements or measurements it is impossible to tell if you're making any progress.

Laura M. said...

Good requirements are a huge amount of work to do correctly - where I mean "correctly" to mean "encourage [people] to make progress to the actual intended goal" - but without requirements or measurements it is impossible to tell if you're making any progress.

Would you have any suggestions for writing education requirements correctly?

Jonathan Crabtree said...

Hi Catherine

5 x 7 does NOT mean 7 added to itself 5 times.

7 added to itself 5 times is 42 because 7 added to itself once (7 + 7) is 14.

5 x 7 DOES mean 7 added to ZERO 5 times in succession or 5 added to ZERO 7 times in succession depending on which convention is followed.

The Common Core editors have since dropped this problematic definition.

For this history of this error goto

Best wishes
Jonathan Crabtree
Mathematics Researcher
Melbourne Australia