One third of students end up in remedial math in college and “the level of interest in the subject is at an all-time low,” writes Jo Boaler, a Stanford math education professor, in Ed Week. She blames timed math tests — solve 50 multiplication problems in three minutes — for causing math anxiety that cripples learning

Math has become a performance subject. Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest. The damage starts early in this country, with school districts requiring young children to take timed math tests from the age of 5.

Common Core State Standards, which call for math “fluency,” may encourage timed testing, Boaler worries.

Stress caused by timed testing can lead to changes in the brain, permanently hurting children’s ability to learn math, she writes.

There are many good teaching strategies for encouraging fluency in math, but the ones that are effective are those that simultaneously develop number sense—the flexible use and understanding of numbers and quantities—without instilling fear and anxiety. Strategies that involve reasoning about numbers and operations, such as the pedagogical approach called “number talks,” are ideal for developing fluency with understanding.

Beyond the fear and anxiety, timed tests also convey strong and negative messages about math, suggesting that math ability is measured by working quickly, rather than thinking deeply and carefully—the hallmark of high-level mathematical thinking.

Children can learn math skills *and* concepts in tandem, writes Barry Garelick on Education News.

Reformers criticize traditional math instruction as “skills-based,” implying “students who may have mastered their math courses in K-12 were missing the conceptual basis of mathematics and were taught the subject as a means to do computation, rather than explore the wonders of mathematics for its own sake.”

Students have struggled with math for a long time: *If one dinosaur eats two cavemen per hour, how many cavemen can four dinosaurs eat in 30 minutes?* When I was in elementary school in the ’50s, before calculators or timed tests of math facts, many kids were anxious about math because there were right and wrong answers. We didn’t tackle the lowest common denominator to appreciate math’s beauty or explore its wonders. We though the point was to “get it.”

“New math” came in a few years later, when my brother was in first grade. In trying to teach concepts, it made kids even more anxious.

My daughter did timed tests of addition and subtraction problems in first grade — 25 years ago! They probably did multiplication in second grade. She thought the tests were fun. Of course, she was good at it. But Boaler says math anxiety is worst for high-ability students.

All of this seems like a pretty deliberate (and fraudulent, IMHO) attempt to move math away from being a skill aimed at finding an answer towards an activity where all that matters is how you feel about it, because then there is no right or wrong answer and therefore no onus on the teacher to actually teach anything. In other words, it’s just another part of the decline of the US educational system over the last 30 years.

Postmodernism is harmless when applied to literary theory or philosophy and so the camel’s nose crept into the tent when no one was paying particular attention. Now, however, we’ve got the whole camel and there’s no room left for rigorous thought.

By the way, it’s stupid to talk of “understanding the beauty of mathematics” if you don’t actually understand the mathematics (which you demonstrate to your teacher by solving problems). It’s like a blind man saying he appreciates the beauty of a painting.

Rob,

I very much appreciate your writing skill. It was enjoyable to read your comment. And though I didn’t really like the flow of “understanding the beauty of mathematics”, I’d like to offer a couple of rebuttals.

The author supports moving away from timed tests because of the effects of anxiety. There is a decent body of consistent research literature, over a couple/few decades, indicating that this math or text anxiety acts as a secondary task, which hinders the child’s ability to use their full math ability. If we expect them to “get over it”, guess what, many won’t. And they grow up dodging math.

Also, the idea that a kid would “demonstrate to your teacher by solving problems” seems reasonable, the idea that this is the only way to demonstrate understanding of concepts is (respectfully) short sighted.

We, as a society, have been “brain-washed” (and I use that term loosely) into thinking that performance is the only way to show understanding, and that there is only one way of doing the problem. 119 X 3 = 357. You could do this the “traditional” way. OR you could do 3 X 100 added to 3 X 20 then subtract 3 X 1. More steps? No kidding, this is how I do problems, and I don’t need a pencil and paper.

The idea of the touchy feeley “ain’t math beautiful” is to allow for exploration of the subject and different ways of doing it. Critical thinking requires approaching things in different directions, not just the “this is the right and only way to do it”.

Doing this breeds robots of dependence on authority figures (like teachers) into a mass of “did I do it right?” instead of independent thinkers of “I can figure this out, myself”.

We’ve amassed a good number of research papers on the website linked to the name above about math anxiety. Enjoy and thanks for your comment.

I’ve reached the point at which my default reaction to anything said/done/recommended by the math ed world is not no, but @#** no. I was one of the first trial balloons of the algebra I version of New Math, taught by a teacher who had had exactly one month’s summer school experience with it and I’ve watched all of the subsequent math contortions, now at the spiral curricula (Everyday Math, TERC etc) stage. The current aim seems to be the pretense that ALL are learning, since mastery of anything is not required – at least, not before pre-algebra arrives. I remember a comment, on another website, from a SAT tutor. In her 5+ years of experience, she has just encountered the first and only student who does poorly on practice SAT tests because of test anxiety. ALL of her other students, past and present, do not do as well as they/their parents think they should because they do not know the material well enough to do better. Unlike the personal essay, math actually has right and wrong answers.

I remember disliking timed multiplication tests when we first started doing them, but once I was forced to learn the tables I go them all right. When I encountered algebra and higher math, though, it was great to have one less thing to think about. It’s hard to learn algebra when you’re having to think consciously about arithmetic.

As far as seeing the beauty of the subject…I think that biology is a beautiful subject. My students don’t believe me, but halfway through the semester, once they know something, I start to hear comments about how cool or amazing some parts are. Competence does wonders for both opening eyes to the beauty and eliminating anxiety.

Timed tests cause anxiety. Next headline: Take-home tests cause anxiety. Or perhaps “untimed tests”, although I’m not sure what that would mean – if a test is untimed would you actually have to turn in your answers?

In terms of some testing, drills and the like that are supposed to help kids master and build upon basic skills, there are probably techniques that can be used to a similar effect without timed tests – the “solve 50 multiplication problems in three minutes”-type testing mentioned above. Which isn’t to say that the best alternatives would be cheap, or easier for the teacher to administer. Computerized drills, for example, could be designed to facilitate learning and overlearning, while providing tracking of progress that should exceed that obtained through drills, but now you need to get each child enough time in front of a computer to make that meaningful.

I guess the thesis here is that test anxiety, worst with some “high-ability students”, turns kids off of math? Well, maybe, but I can’t say that I saw any shortage of test anxiety among high performing students in graduate school. Perhaps, just as high self esteem is on the whole negatively correlated with academic performance, it is the absence of anxiety that causes some students to be lax about their studies rather than working hard enough to achieve high ability.

Not that anxiety and low self-esteem should be goals, or that we can assume that raising anxiety or lowering self esteem will improve academic performance, but the world is more complicated than “test anxiety = bad”.

I used to enjoy coming here and participating in lively debates with all of the traditional teachers who love to drone on incessantly against anything new and progressive. Although I still enjoy Joanne’s posts, the commentary has become tiresome.

It’s clear that you folks are entrenched in your old-school beliefs and will never consider anything different from your sit-still-be-quiet-be-bored approach to learning — no matter how much practical experience or research is shared.

Mark:

We’ve used roughly the same methods for teaching math since Leonardo of Pisa wrote his famous book on arithmetic in 1205 or so. Before we chuck out eight centuries of experience, I think those who claim they have a bold new plan need to prove that the plan works by running at least one large cohort through it from K-12. If the product of that experiment is successful, then you scale up slowly, always on the lookout for problems of scale. This is how you overturn any well-accepted practice.

What you don’t do is say, “Oh, shiny new way to do things, me want!”

That’s hardly fair. Mark doesn’t just like new things… he likes the things he believes to be efficacious.

(And which sell him books, maybe.)

He is a revolutionary at heart. Caution isn’t their strong suit. But it’s not as if he’s advocating change for change’s sake. He has a vision that he thinks should be made reality.

Let’s give him a little credit.

Among the things he rejects in favor of a “new way” that sells books, perhaps, logic? If he wants to convince me that he has a point – that he has any interest in evidence – the best way to do that would be to argue his point and present his evidence, rather than lazy resorts to circumstantial ad hominem.

I have a little different take on this in that because anxiety of timed tests and actual math ability are two separate issues, by evaluating so much of math ability with very short timed tests, a kid can be mistaken to be weak in math when it is really that they are weak on timed tests or have anxiety.

I say this because I had almost forgotten this was me. I mistakenly got put in the lowest tier in second grade at the very beginning because I did so poorly on timed tests, all subjects, just not math. It was anxiety in that I just had no clue how to handle short timed tests. I wasted a lot of time not understanding what to do. Eventually the teacher and assistants figured out that I knew the actual material, I had just tested poorly. A key factor is that they then worked with me on how to do short timed tests. A few months later they had me redo the timed tests and I went from the lowest tier to the top tier.

I think the way to deal with anxiety of timed tests is not to get rid of them, but to help kids be able to take short timed tests. It is a different skill set from the mastery of the material. It takes practice to be able to do well on timed tests. The other thing to remember is a poor result on a short timed test may not mean the kid doesn’t know the actual material, but does poorly on that type of test.

This also reminds me of when I took the GRE the first time. I really could do every math problem on the GRE test, but doing it within the time frame was the problem. For the GRE, we also had to do an experimental section, and I got an experimental math section. The experimental math section was the second to the last section and it was throwing out all these bizarre math problems that freaked me out. Then the very last section was the real math section for the GRE, but by that time I was freaked out and exhausted. I was feeling math test anxiety and I usually love math. I did alright, but since I am actually strong in math, I wanted to redo the GRE. So I went back and practiced the math section based on time limits and I redid the GRE with a much better math score.

Recognizing that math anxiety is a separate issue from math ability would help kids and even adults not to be scared of math itself and therefore that would be helpful.

This happened to me, too! Except it didn’t screw up my math score (I got an 800) but my verbal. I got a 780 because I was annoyed at what I thought was going to be my poor math score and I was applying to Stanford as a math teacher with an English degree and no math classes on my transcript. And I teach GRE prep, so I knew the math test practically by heart. I didn’t even think about the possibility of it being experimental until the real math section came up. I did the verbal in about 12 minutes, fussing about why the heck there hadn’t been any geometry questions on the test, and why did the questions take so long, and there were two reading questions that I should have taken time to think through but I just clicked on what was probably the right answer, stewing about the math test.

Oh, by the way: this has nothing to do with test anxiety. It’s just sheer stupidity, and an inability to focus on the moment.

Math anxiety is quite different from test anxiety. It exists, but it’s not why students don’t like timed tests, which is an issue with memorization.

“Math anxiety is quite different from test anxiety. It exists, but it’s not why students don’t like timed tests, which is an issue with memorization.”

On what do you base that?

I’m not taking a substantive position about math anxiety or test anxiety or anything like that, except to say the following:

If you can’t perform when it’s crunch time, if deadlines and high-pressure situations freak you out… that is a flaw. A failing.

And it needs to be either fixed, or flagged so we can make sure that you’re never given anything really important to do.

So. If you can’t do it, you’re a loser. You failed. And we should never give you anything important to do.

Gee, thanks. Anxiety is a flaw and a failing, and the solution is to “fix it or flag it,” but you have no suggestions for how to do that…

I thought “getting poor scores on timed tests” pretty well covered that… Especially times tests like the SAT and GRE.

Like most people, Michael confuses what he finds important with what is actually important. That there are millions of important jobs that don’t involve crunch time abilities is utterly unimportant, so long as he can pronounce and FEEL important.

And of course, he pretends that he’s not trying to take a substantive opinion when, in fact, that’s exactly what he thinks his post is. He’s wrong on that, too.

I pretend nothing.

I didn’t say I wasn’t taking a substantive position, simpliciter. I said I wasn’t taking a substantive position

, and even then the refraining was operative EXCEPT to make my point about the general inutility of those with eggshell psyches.about math anxiety or test anxietyNeat word, “except”. It means

.exceptBut, as it happens, I said nothing about the relation between timed tests and math anxiety, nothing about the utility of timed tests in terms of teaching math, and nothing about whether the ability to perform on a timed test is indicative of having learned math.

These are, I take it, the main issues under consideration, and I wanted to be clear that I wasn’t taking sides on them.

My point was solely limited to the fact that if timed, high-pressure situations cause you to wilt, you’ve got a fairly serious problem that ideally should be fixed, but at least shouldn’t be allowed to interfere with “really important” (note the intensifier, which you dropped in your retort) occupations and projects.

So I wasn’t, in fact, taking a substantive position as to the ongoing conversations about math anxiety and test anxiety… EXCEPT that I was making general remarks about the ability to control and/or surmount anxiety in general, which touches generally (though tangentially) on the underlying subject matter.

(Deep breath, long sigh.)

Which is pretty much what I said.

And like many (though perhaps not most) people, Cal likes to invoke the profusion of examples supporting her position without bothering to identify a single one.

Math is about problem solving. ‘Getting the answer’ is just one way to motivate kids to develop their thinking.

BTW, as far as the “one third of students end up in remedial math in college” goes, it’s likely that one third of students don’t belong in college at all (percentages vary among colleges, of course) and that there’s likely to be significant overlap between that group and the remedial math group. It’s also useful to remember that some colleges require no math at all (I know a new grad from an Ivy that requires no math or science ) and that some kids (like mine) use AP calc to meet general-ed requirements in non-math majors. I am also familiar with schools which require no math or science, in certain majors (including el ed).

On a related note, there’s some pretty decent work showing that these short timed tests, while useful for assessing knowledge of basic facts aren’t necessarily very good for teaching and learning basic facts, and we could certainly do better on that score. I recommend Ed Rathmell’s discussion on this if you’re interested in more detail:

http://thinkingwithnumbers.com/QuestionsAnswers/index.html

50 problems in 3 minutes. You know, the kids aren’t being asked to “solve math problems” when they do Mad Minutes. They’re supposed to be quickly recalling memorized facts, such as 7 x 8 = 56. They should not be counting on their fingers, nor drawing little pictures, on a timed test of quick recall.

Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest.It’d be great if children appreciated the beauty of many things in life. Math is a beautiful subject. I think it’s more likely to “pique their interest” if they understand it. I would certainly hope a functional school would place math achievement over math appreciation. I would also expect a student to find it very stressful to not understand a math lesson, day-in and day-out.

I’ve taught mathematical aspects of computer science to college students for decades, and I’ve met very many students who are very bad at math, but I’ve never met anyone who had “math anxiety”. I understand “math anxiety” to mean that someone is basically good at math, but has trouble performing in certain pressure situations. Furthermore, whenever I’ve read about “math anxiety”, I’ve never seen a good example of it described.

Now I’m sure that math anxiety really does exist. But I believe it is extremely rare, and not a big problem for society.

Much more common is the opposite of math anxiety: students who think they are competent at math (perhaps because they can calculate the derivative of a polynomial) but really are totally hopeless.

No one who can calculate the derivative of a polynomial is

totallyhopeless.@LTEC, I have to disagree with you. I have found it to be rather common. People may not come out at first and say that they have math anxiety, it may be more so at first that they say they hate math or they were told growing up that they were not good at math by someone else, however, talking or working with them, I find out it comes down to math anxiety. It is possible for someone to have both weak math skills and math anxiety, but the ability to learn math is there once the fear of math is overcome. I really have met quite a few people that were quite good at math or did not realize how much that they were using math in their everyday lives, but yet tested poorly because they freaked out over the math.

It has been a while, but I actually wound up for tutoring several people that had math and science anxiety. It tended to be smart teenage girls who thought math was pointless or middle aged women wanting a promotion at work that required more math, but I had a few guys as well with math anxiety. It is real, but it also can be overcome.

“

Postmodernism is harmless when applied to literary theory or philosophy…”Well, not really.

Timed math tests do not test math knowledge alone. They also test ability to write numbers quickly. In other words, they are pedagogically invalid. They would be valid if given as oral tests, but you can’t do that in a class of 25 students. Having students recite multiplication (and addition, etc.) tables works better.

The ability to write numbers – and words – rapidly is a useful academic skill. Unless you are limiting your comment to very young kids (k-1) who are still learning to write, I see no problem in helping them acquire this skill – which takes many years of practice to do well. Being able to take notes, either mathematical or verbal, quickly, accurately and completely is valuable not only in HS and college, but in the real world in many different occupations.

I would agree with you if the test were designed to assess whether a student could write numbers quickly. It’s not. It’s designed to test mathematical knowledge alone. It doesn’t.

If a teacher suspects that inability to write quickly is a problem for a particular student, she could test that student verbally. If it’s a problem for all, then the whole situation needs to be re-evaluated. Perhaps the class needs more writing practice.

Let me repeat: it is intended to test mathematical knowledge alone. It does not. It is fatally flawed. Period. Reciting multiplication tables worked. This doesn’t.

Then there’s an easy solution: just hire a telepath.

Because what REALLY matters is just what’s in your head, what’s abstractly possessed as knowledge by the Platonic-Cartesian homunculus.

What you can actually do with it is, apparently, completely irrelevant.

I have to take very difficult exams from cisco to mantain several certifications that I have, and the exams are times, and do NOT allow one to skip a question and come back to it later (though this should be allowed if time is remaining on the exam in question). The average is about 60 questions in 75 minutes, but in life, one is always tested (and that if you’re prepared, and know how to solve the problem and have mastered that skill, it shouldn’t be a problem).

Here’s a larger question, what happens when these students have to pass the ASVAB (which is a timed test) to see if they can enter the military, or the ACT or SAT (which are also timed), etc?

Easily resolved. For the ACT or SAT, you — or your parents — pay for a psychologist to diagnose you as ADD. Then you take it untimed. I hope it doesn’t work this way for the ASVAB, but I won’t bet on it.

Yes, because taking an SAT is just like churning out 50 facts in 3 minutes.

Look, I agree with those of you who say these are math facts that should be memorized. I just think all of your extrapolations from that point are pure idiocy. As are Boalers. It’s not about the ability to work quickly, or about math anxiety, but about memorization.

Therefore, any handwringing about SAT or ACT or ASVAB or OH MY GOD THEY’LL NEVER BE ABLE TO DO ANYTHING IMPORTANT AT ALL or social promotions is just insanely, shoot yourself in the head silly.The only thing lost are math facts for some, not all, of the students. Many of them will memorize anyway. Some will never be able to memorize, no matter how many tests they take. The small percentage of students who are hurt are the ones who would actually be able to memorize with the practice they won’t get if they don’t have the timed test. Yes, I’d rather they get that practice. Yes, memorization is good. It’s just not anything you all seem to think it is.

I refer you to a previous discussion in which the same suspects were declaiming at the top of their voices that students who can’t add fractions can never learn algebra. Of course, it’s not like any of them ever taught algebra but when did ignorance ever stop folks?