A couple of weeks ago, I was watching a dad teach his son how to ride a bike. The son had a helmet on, elbow pads, and training wheels on the bike. As the dad put his son on the bike, he walked behind his son as the son rode the bike in circles in the parking lot.
Just recently, I witnessed the same father and son in the school’s parking lot and this time the training wheels were off. The dad continued to walk behind the son and the son completed the same circles. At one point the son fell over and the dad quickly picked him up and put him back on the bike immediately. After about 10 minutes, where the son did not fall once, the dad stopped walking behind the child and the child started to do more complex paths on his bike.
This is how assessment should be!
It would be ridiculous to mandate that all fathers must spend exactly 10 minutes of time with their child until they stop walking behind them; as each child will require a different amount of time to learn the skill.
It would be ludicrous to allow a son to write a multiple choice test where, if he scored over 50% (even though he wrote it is ok to play in traffic on a bicycle), the father would let him ride alone as the son “passed the test”, since the son doesn’t understand all the safety issues of riding a bike.
It would be unfortunate if all fathers were required to purchase the same bicycle since not every child is the same height, or has the lower body lengths.
Yet all of these ideas are allowed in schools, why is that?
I wonder what school would look like if instead of holding teachers accountable with mandated common assessment we instead allowed teachers to teach students “how to ride a bike”?
I believe, students would learn the skills at a deeper level before moving on, they could learn at their own pace, and each “test” would be different for each student.
Still not convinced? Reflect on this picture as it represents the traditional testing model of students.
In an ideal world, this would be great! However, I'm not sure how this could be accomplished with a student load of more than 175 students each day. Anyone have ideas?
ReplyDeleteThe purpose of assessments - okay, tests - is to provide 'proof' to students and parents of what students have learned. Sometimes it's for teachers, too. But we could find out what students truly know through other formative assessments.
I'm willing to hear any suggestions.....
I have been a big advocate of parent involvement. There is only so much that a teacher with 20 to 30 students in a class can do compared to what a parent can do one-on-one. In fact, in the TIMSS assessment, parent involvement outranked all other factors, including socio-economic, as being correlated to success. I would venture to say that after quality teacher time and quality parental involvement, all other factors (i.e. books, technology, etc.) are so trivial they are not even worth debating.
ReplyDeleteHonestly, where I teach the parents all say they never got to Algebra, so they can't help their kids, thereby absolving themselves of any and all accountability.
ReplyDeleteHere is something for you Dave that you might like. My 3rd grade son is deep into multiplication right now and our discussion about groups of things and multiplication eventually led to factors. And while he was pondering how many numbers can be multiplied together to get 12 or 16, he asked a very good question. He asked me "How come there isn't a division table?" and he went on to say "We could make a division table and sell it!"
ReplyDeleteI explained to him that division tables do not exist because once you put the numbers down the sides, the majority of the inside is empty because most numbers are not (evenly) divisible by the other numbers. I told him that when we do division mentally we actually use the multiplication facts in reverse, as we did with addition. But I could see in his eyes that my explanation didn't phase him much and he was still dreaming of selling millions of division tables to other 3rd graders. So I said "Let's make a division table!" Big smile.
So I opened a spreadsheet and we started making our table. I said to him "let's just go up to 20 for now and we can expand it later", otherwise we would be there for hours if we went all the way to 144 on both edges. So I numbered the rows and columns from 1 to 20 and then like a game of battleship I started calling off the rows and columns and waiting on him for the quotient, or as is the case in the majority of cells, his response "it doesn't divide".
It took less time than I imagined before he saw the light as to why it is difficult to make a good division table. Maybe it was all the dead ends with him responding "it doesn't divide", but he realized that most of the cells are empty and when you are talking about "whole" division you are actually talking about knowing which combinations of numbers are divisible in the first place which is essentially the multiplication table. But something neat happened. He noticed the diagonal of 1's (you can't really miss that) but then he spotted the 2's, so we studied that for a bit and I started coloring the 1's, then the 2's and then the 3's and so forth so that he could see how they each repeat and form a line. And then I pointed out that there were some numbers with no quotients at all, except for 1 and themselves. I colored those red and pointed out that every now and then those patterns of 2's and 3's and 4's line up in such a fashion that they skip a number entirely, we call those primes. They aren't divisible by any number, except 1 and themselves.
In the end (actually there is no end to this) I told him that what we are doing is turning the multiplication table inside out and if we go in and count all of the filled in cells there will be 144 of them (assuming we did the whole table), one for every entry in the multiplication table. You will find all of the 2's and 3's and 4's and so forth but spread out in a 144x144 table, instead of a 12x12 table.
Our division table is here...
http://dl.dropbox.com/u/39455389/DivisionTable.pdf
It was a very productive evening to say the least.
While we all agree this analogy would be nice in a perfect world, there just isn't time in a day. The father spent 10 minutes with one child. What if he had 30 children to teach? 300 minutes is 5 hours. I think dad would find another way, because in just 1 hour another 30 children are coming to learn to ride a bike.
ReplyDeleteThis is great when working one on one, as with the one child on the bike. What if the father had 25 children all the same age and all wanting to learn to ride a bike at the same time? How would he "walk behind" each child at the same time? Or would he take turns teaching each child, and then how long would each session with his 25 children take? What you propose would certainly work in a class of 5 to 10, but it requires tremendous time and effort to achieve it in a class of 30 students. There are some teachers out there that are willing and passionate enough to spend the time required, but it takes a toll and I speak from experience. If parents (and the students themselves) took on more of a responsibilty for their own education, we would have much more success. Perhaps parents shouldbe required to attend the Math class with their child so then they can continue the lesson at home!!!!
ReplyDeleteJust my 2 cents worth...:-)))
I agree wholeheartedly with the previous 2 posts.
ReplyDeleteIn response to your comic: I don't see what's wrong with that. If the goal of the assessment is to see how well each animal can climb the tree, then it works. Through this simple test, I can see that the monkey is most qualified/capable to climb a tree. What's wrong with that? I'm not saying the fish is "worse" than the monkey. He just isn't good at climbing trees. If the penguin can draw a picture of the tree, who cares? That's not what I'm interested in. If the dog can create a clever video about trees, so what? If the elephant can tell me about photosythesis and name the different parts of the tree.... I want to know who can climb a tree, and this assessment gives me the answer to it.
I have done this in a class of 44 students and I am currently doing this in a class of 25.
ReplyDeleteI do agree with that it is more work than sliding a scantron through a machine, but I can offer guidance and assistance there.
What I will NOT even discuess is that the multiple choice exam is a higher caliber of assessment and that is what we should be aspiring to.
For those who want to try but believe it is a lot of work, I challenge you to try this on a smaller assessment first. Maybe instead of giving a traditional quiz, give 1 single question that is open ended and allow this assessment to turn into formative assessement. Give feedback, allow for collaboration and then evaluate the product.
The excuse of "There is not enough time" is getting old. If there is not enough time to do what we should be doing in school, then let's change the schedule and/or the expectations!
ReplyDeleteHow rational is it to expect all students to learn a certain amount of material (for lack of a better word) when experience tells us that most students will not be able to master it in the given time?
Settling on poor assessment methods because we don't have time to do a better job is barking up the wrong tree.
As for the comic, the point is that in school we ARE assessing how good a student is by how well they do in tests. That is one reason why so many young people give up on math. They think "I was never good at it", when they should say "I could not master the tests they gave us".
"As for the comic, the point is that in school we ARE assessing how good a student is by how well they do in tests."
ReplyDeleteWell, that is a very poor example of a comic to indicate that point. It says "climb that tree", how more applicable can that be to tree climbing? Music is tested the same way, the student is given music to play. Why is it so ludicrous to test a student in math by giving them math problems to solve? How can math even exist, devoid of the problems it applies to? That would be like music that cannot be played.
I am not trying to put words in anyone's mouth, but the anti-test faction here is not explaining a critical piece of this puzzle, how do you have math yet fail on these tests? Unless you can show that, your debate is over. If you can't give a sensible explanation of how students could be doing well in math yet at the same time be unable to solve the same types of problems that any one of us could solve in our sleep then you have a huge contradiction. Did it ever occur to you that the reason math tests suck to some kids is that math itself sucks to some kids? Essentially, when you throw dirt at math tests yet don't provide a reasonable explanation of why math tests are not math, you throw dirt on math.
There are two questions here. The first is do mid course assessments and grades help teachers do their jobs (which is teaching). Most teachers swear by that method, Dave is trying alternatives, all the power to him.
The second question is can you have students succeeding in math but fail exams? That is like asking if students can be musical yet unable to make music? It makes no sense.
Throwing dirt at math tests is throwing dirt at math? Don't agree...as well that I don't agree that I am alone thinking that tests are the ONLY way to evaluate learning of math.
ReplyDeleteHere is my statement: ALL (that is right every single one) tests do not allow for any (again all) student to demonstrate all (another universal quantifier) knowledge about a course.
To disprove me, please provide me with a test which does allow this. I would like to see an assessment which you are happy with. Can you provide this to me so I can offer feedback?
Roberto, do you teach? It doesn't sound like it. Education is all about time constraints. End of the unit, end of the quarter, end of the semester, end of the year, move on to the next grade. People act like teachers think that our school schedule works the best. Of course we don't. I often tell students that I'd like to teach math like the ancient Greeks. Just gather 'round each day and let me tell you what I know. But I can't do that since the federal/district mandated end of semester exam is coming soon. It is unfortunate that we try to put all the different size square students through the same square hole.
ReplyDelete@Tim:
ReplyDeleteYes he does teach, and so do I, and I do agree with the time constraints, but I agree with Roberto that too many teachers use this as a defense for poor (and even malpractice) assessment techniques.
Teachers complete homework checks (I would say this is malpractice) and justify it with "not enough time to check all the homework".
I understand the problem with time, but I fear that we use it too often to get away with things we shouldn't be doing at all, whether there was less or even more time.
Tim I challenge you try my approach, and I guarantee you will see that:
a) It doesn't take any more class time than it would preparing students to write a test (a block of review), a class to write the test, and a half of block to go over the test.
b) Students will be forced to learn the material at a higher standard as no one will be able to get a 40% and end the assessement
c) You will witness how learning and assessment can coexist.
Too many times I see teachers argue that assessment and learning cannot occur at the same time, and I would argue they can but we need to have different assessment techniques.
How come in the real world we call collaboration a great technique, but in classrooms we call this cheating?
"Here is my statement: ALL (that is right every single one) tests do not allow for any (again all) student to demonstrate all (another universal quantifier) knowledge about a course."
ReplyDeleteLet me see if I understand your statement correctly. You seem to be saying that no test can be comprehensive enough to assess everything a student learns in a course. I would agree with that. Who wouldn't agree with that? And what does that have to do with anything we have talked about here?
My statement is that it is not difficult at all to construct a comprehensive test for a course in mathematics that determines with a high degree of accuracy if the student was successful or not in owning the body of work that was covered in the course. This is not a revolutionary idea, it is done by teachers every day.
"To disprove me, please provide me with a test which does allow this. I would like to see an assessment which you are happy with. Can you provide this to me so I can offer feedback?"
I can't provide you with a test that tests all math because as I have agreed, no such test exists. And you really need to explain the relevance of that to this discussion. But I can provide you with a pair of tests that are deadly accurate in their assessment of how well math took generally for a student in their first 11 years of school, public or any form. The SAT and ACT. I have compared the results on these two tests, the SAT most of all, and they hit the sweet spot of mathematical awareness for the average high school student planning on going further. They are well placed at the intersection of number sense, algebra and geometry and how well you do on them does very much indicate your current prospects in this subject, in a general sense, in schools or in life. And I base that also on my interaction with 100's of engineers, accountants, financial analysts and any of a number of other professions that count math as part of their draw.
I have answered your question, now answer mine. Are you suggesting that there are a significant number of students that fail these exams yet are actually good in math? I mean, are you saying that after a year of algebra, there are a significant number of students that fail the final exam, but are actually good in algebra?
Consider that "evaluation", "test" and "assessment" are not synonyms. Allow, at least for a moment, that each has a completely distinctive meaning.
ReplyDeleteEvaluation literally means to place a value upon something. We use this word to mean exactly that in our math classes all the time. When we evaluate students, it means we give them a grade.
Tests are events which attempt to determine whether or not a conjecture is true. We use this definition of test in our statistical applications (and our colleagues in the sciences use it the same way, but much more often). When we test our students, we begin with the conjecture, "I think that my students know how to answer this question", and then we seek to find out if that's true. (Problematically, because learning and knowledge are non-linear, it may be true today, and not true tomorrow, for any given student. If we're honest about that, then our conjecture ought to be, "I think that my students know how to answer this question, TODAY...")
To assess a thing is to attempt to discover it properties, characteristics and/or value. This is distinct from evaluation, in that evaluation involves *placing* value on things, and assessment involves *discovering* values and other characteristics and properties. We seldom use this definition, instead considering assessment to be synonymous with testing (which is, I admit, closely related), but actuaries (for example) use this definition routinely. When we assess our students, we seek to learn what it is that they know, and don't know.
Often, we tie the process of evaluation to assessment-- sometimes this is called summative assessment (because the grade, once given, presumably won't be changed). It should be clear that this is still a two-step process: learn what the student knows, and then assign a grade based thereupon.
In the bike-riding analogy, the father *never* appears to explicitly evaluate the son's growth: at no point does he say, "And now, son, you can ride a bike." He doesn't NEED to do that: it's clear to the son, who is perfectly capable of self-evaluation.
As for the time spent by the father, we ought to note that there's exactly one interaction during which the father actively participates in the son's growth as a bike-rider: when the son falls down, the father immediately helps him, and puts him back on the bike. There's essentially no reason why that father couldn't be supervising a whole room full of cyclists, barring the unlikely possibility that several emerging riders might fall down at the same time (which would be a challenge, though presumably not an insurmountable one). That's because it's the son doing the growing.
Among the ideas being discussed here is the purpose of education, in the first place. Are we, as teachers of mathematics, here to serve as a kind of sorting machine which evaluates the specific abilities of individual students? Or are we, as teachers of mathematics, here to expand the knowledge and abilities of our students. Many teachers seek to strike a balance between these. Personally, I have no tolerance in my soul for the sorting machine (I think it's discriminatory and undemocratic, a la John Dewey). But, I'm not trying to convert anyone to that way of thinking. Rather, I'll be happy if we're all simply thinking more clearly about what assessment, testing and evaluation all mean, and how they relate, and what they really say about our students, and what our role is and should be in shaping that.
Dave, I have no problem trying some new ideas. I looked at a few of the things you do on this website and will try to implement something similar. True, we can utilize time better, but unfortunately we still have time constraints. I'm not talking about assessment time, just time in general.
ReplyDelete@Robert
ReplyDeleteI hope you are not using the SAT as an example of a good assessment. There are so many problems with standardized exams, illustrated here: http://www.alfiekohn.org/teaching/edweek/staiv.htm
@Tim
Glad to hear, let me know if you need any help!
"I hope you are not using the SAT as an example of a good assessment."
ReplyDeleteI think that is exactly what I said I was doing Dave. You asked for an example and I gave you an example, and a question. I have reviewed Alfie's arguments before (when you brought up the homework thing on APCalc) and they are not direct arguments, they are collateral, if that is a way to say it. In other words, he (and you) make tangental statements about tests being unfair or that they cannot test everything to imply that tests do not work. But the intended goal of tests is not to be fair or to test everything. The intended goal is simply to give an accurate picture of achievement by the student in a body of work. If you want to make an argument that tests do not work then that is where you have to start. But you can't make that argument because it doesn't make any sense. Why even teach a subject if you can't test it? Another reason you can't make that argument is that out here, after school, those test scores correlate pretty damn well. I mean we all work with many people in many professions and walks of life. It is no mystery whatsoever to any of us who is good at math and who isn't. And you know what else, it's no big deal.
There are many problems with taxes but we still use them to finance government. There are many problems with our legal system but we still use it.
"The intended goal [of testing] is simply to give an accurate picture of achievement by the student in a body of work."
ReplyDeleteSo, it seems that we at least all agree that tests have nothing to do with the learning *process*...
Tim, for the last 23 years I have been paid good money by a post-secondary institution (and more before that) to take care of first year University math courses. I am not sure if that counts as teaching (I am not being sarcastic, I really don't), but it certainly gives me full awareness of the limitations within which those who lay claim to the title of "teacher" work. And I am subject to those same limitations, so that what I can do in class is very far from what I would like to do.
ReplyDeleteBut should I feel that just because I see some limitations in the system, I must agree with the current way to work around them? Well, I don't! Instead I look at each aspect of my work and try to understand what is its purpose, why it is done the way it is and what alternatives exist. When I see a practice based on no good reason, I try to dump it. When I find an alternative I try it, if I can, and I keep the ones that work and/or make sense (we don't always have the resources to conduct systematic and believable research on these issues).
I lecture, I give assignments and traditional tests and I complete the course on time, because I realize that those constraints exist and must be considered. BUT, I also try to move in what I see as the right direction as much as the system allows and I share my ideas in the hope that someone smarter than me will find a way to refine them and implement them, or shoot them down convincingly.
What I can definitely NOT agree on is that "education is all about time constraints". I suspect that you overly emphasized an important concern, and that you agree that education is all about the intellectual growth of our students. It is for me, anyway.
On a different note, I think that James has highlighted a key aspect of the discussion. The educational process is a complex one and tests are only one part of it, and a part with many interactions with others. Are non-traditional assessment and evaluation methods suitable for all teachers? I don't think so. Are they suitable for all students when properly done? I don't think so either. Reaching overarching conclusions about any of the topics we are touching on is dangerous.
ReplyDeleteI think we can all benefit more from the discussion if we step back in our roles of advocates of our respective positions, and try a little more to share our experiences, our successes, our failures, our doubts, our limitations etc. I see teaching as an art, where pinnacles and disaster can be achieved in different ways. If we learn from each other's perspectives we can only grow in our own practice.
"So, it seems that we at least all agree that tests have nothing to do with the learning *process*..."
ReplyDeleteI can agree with that, somewhat, technically. The learning process is what goes on before the test. But I use the test results and grades my son brings home to help me monitor his progress and identify those areas he needs more work on, so they are a diagnostic tool and affect what I teach. And when I test him at home we end up with a score but we never talk about like a grade. What's the point? I am not going anywhere till he gets 90% or better anyways.:) So I actually do follow that philosophy of Dave's, and in my instance, there is little need for a "grade" but the tests are crucial, as are my eyes when I work him. And, in the fashion of a thought experiment, I could make an almost identical statement and say that getting paid has nothing to do with work. But that seems to defy human nature. So in human terms, I think achievement does have much to do with learning.
Let us define "learning" as the growth or development of a student, through a series of activities (some of which may be purely mental exercises!) In that case, I posit that no single test can describe any student's *learning*, inasmuch as a single test provides only a single data point, and thus cannot describe growth over time or across multiple activities of learning...
ReplyDeleteBut, I fear that I might be starting to fall into "just being difficult..." :)
"Let us define "learning" as the growth or development of a student."
ReplyDeletePeriod, no need to define how.:)
Since we have established that tests have nothing to do with learning then they cannot hurt learning either, which frees us to use them to determining if we have been successful.:)
At least in the specific cases, like in a class that teaches "algebra", or a class that teaches "piano" or a class that teaches "tree climbing".
It seems that no matter how you slice it, testing itself really isn't a key component of the "learning process". Testing can help one determine if they have been successful but it doesn't cause that success or failure. Testing can be used diagnostically to find gaps in the student's understanding and mastery, but it can't fill those gaps. This makes one (well me at least) wonder why is testing even part of a discussion about learning, let alone such a big part of this one?
Robert,
ReplyDeleteI don't get your logic. Who decided that tests have nothing to do with learning? Saying that the two are not the same thing is a long way from saying that they are not related. The presence and structure of tests have a great effect on the learning process. Not sure where you are going with this.
Well it is refreshing to see so many people passionate about education to discuss it!! AWESOME!
ReplyDeleteNow my turn..:)
@James fully agree with you and you are not being difficult.
@Roberto and Robert: I think the point is that the day of the exam is where the least amount of learning occurs. Students are only reguritating the information and not learning anything. I have never heard of a student leaving a traditional exam and having more knowledge than before.
You made a comment that "Since we have established that tests have nothing to do with learning then they cannot hurt learning either"...This is where you are wrong and why I dispise these...Two words "TEST PREP". You have no idea of the amount of test prep that occurs in schools to prepare students for the exam. Robert I could train students to write exams and work the system without really understanding the material. I do not do this! BUt you have no idea the amount of teachers which use exams as a justification to horrible practice and just say "this will help them on the test".
Make no mistake, the misuse of exams have a horrible impact on learning
Agreed! Moreover tests are the main external motivator for students, therefore how we structure and administer them has a tremendous impact on how students spend their learning time. They are not the destination, nor the engine, but they are the steering wheel.
ReplyDeleteRoberto wrote...
ReplyDelete“I don't get your logic. Who decided that tests have nothing to do with learning?”
Hold on, I was agreeing with James technically. For example, if I were teaching a class all semester and neither the students nor I were aware of any test and then on the last day of the semester someone walks in and gives a test (to the class) then there is no way that test could affect any attribute of the class prior to that day (i.e. the learning process). It is the anticipation of the test that is the factor here, not the act of giving a test. How this anticipation is handled is up to the teacher. Surely they must teach this in teacher school, no? If they don’t then they should.
Roberto wrote...
“Moreover tests are the main external motivator for students, therefore how we structure and administer them has a tremendous impact on how students spend their learning time.”
I get what you are saying, but part of being a good teacher is to insure that tests are not the main motivator, at least not the majority of the time. Obviously I disagree strongly with the idea that you accomplish this by not having tests. You accomplish this by how you run your classroom and how you focus your students (assuming your students can be focused). In the beginning you focus on skills and understanding just for the sake of the math before you. As you go along you assess with quizzes, questions and interactive dialog (interactive meaning you and the student, not the student and a toy). Eventually you reach the stage of review and then it is only natural to become aware of the nature of the exam. And the nature of the exam is very important. It should have a general personality, like word problems, that requires you to put that term’s worth of math together and use it. If the exam is like this you cannot fall into the trap of teaching to it. If you do all this will build towards the exam and it will be a valid accomplishment for the students.
Dave wrote...
ReplyDelete“Robert I could train students to write exams and work the system without really understanding the material.”
No Dave, you cannot do this. This is a myth. I mean, you cannot take a random selection of students and prep them all to score above 700 on a test like the SAT. Not in one year, not in five years. I can’t do it, you can’t do it, no one can do it. And I know this FACT in a very simple way, it has NEVER been done before. Do you know how many schools and teachers have been spending years trying to do exactly what you suggest? Trying to “prep” students doing poorly in math for the SAT. And in all that activity there has been no success. In fact, if such a notion was true, even just a little bit true, wouldn’t we notice it in SAT scores rising? We would be scratching our heads and wondering why SAT scores are going up. It isn’t that people are not trying to do exactly what you suggest, just like they try to beat the house in Vegas with surefire schemes. It is that it just does not work. You are correct, teaching that reduces to prepping for a test is wrong. It is wrong pedagogically and it is also wrong because it doesn’t work, especially for exams like the SAT.
You said that when students take a test they are simply regurgitating information and not learning anything new. Well, what do you call it when we teach a student to play a musical instrument and we eventually set a piece of music in front of them, a piece that they have never seen but is within their technical ability? When they play that music are they regurgitating? This is what I compare the SAT to, a recital. It is the type of test that you cannot prep for because it relies on an actual fluency and proficiency that takes years to mature, not months, and it is well within the technical range of any student that has been successful with math through algebra and geometry.
As far as learning goes, no, taking the test doesn’t teach new skills. But it does teach you what you are capable of and it is only then when you fully realize it. Just like the music student, the math student needs that recital. Something that they have never played before. To see if they really have arrived and that they really can play, like the others that can play.
I make a lot of analogies to music because I find the pedagogy and progression of both arts to be very similar They both rely on a personal sense that must be developed and refined by the teacher and the student. It helps me at times to step away from one and look at the other and music hasn't gathered the social baggage that math has in recent times, so it offers a clearer example at times.
The original discussion is based on the quality of tests being used. I've worked hard over these past 8 years of teaching to refine the questions offered on tests, but also to look at how the questions relate to each other on the tests. In other words, though I use tests as one form of "evaluation", I make sure that the test is built in a way to allow students to see the correlation between the material that we have been talking about during the last week/month/semester/year.
ReplyDeleteIs it possible to create a test that covers everything discussed over the course of the year? Yes, but the time it would take to construct and take that test is too much. Instead, we whittle down the essential elements of what we taught to the end of year Final - and most of the information I write questions on have some correlation to almost everything we discussed throughout the year.
Now, when we discuss Standardized Testing, that presents us with different issues. I have heard very few people say the AP math exams are not good tests. That is because a great deal of the material that they test is the material that we would teach anyway (not 100%, but close enough). When we talk about the SAT, though, the testing pool is too big for that to be an accurate test. That is, it asks all students to be at a certain level when not all students can reach that level by the time they are graduating high school. That doesn't mean they aren't good at the math they CAN do, just that they haven't mastered it fast enough to get to the SAT level of math. State Tests are just as bad.
The issue is, the Standardized Test scores are what determine whether a school is doing its job well. Thus we get teachers "teaching to the test" instead of teaching the material. That is, the focus of the class from start to finish is the test, not the material and THAT is what affects the learning process.