OK, I admit that's provocative. After all, lots of people take math and experience anxiety, so how can it make sense to say that there's no such thing as math anxiety? What I question is Boaler's (and others') claim that there are lots of students who are highly proficient in math who experience a mysterious surge in anxiety when they are in a testing situation, and as a result can't function properly. In my experience, this never happens. Instead, when a student comes to me and explains that they "really understand the concepts" but when the test came along they experienced some sort of "math anxiety", I inevitably find with a few simple questions that in reality they don't understand the material and can't solve the problems, even in a low-stress environment. Instead, they vastly overestimate their competence (see Dunning-Kruger).
A lot of math education in the US is based on collaboration and group work. Also, many instructors are less concerned with getting the correct answer, and will grade charitably if the student can somehow display some form of "conceptual" understanding. Whatever the merits of this approach, it allows weak students to drift along, delusional in their belief that they are developing strong math skills. Once they get into a test however, they can't rely on the group to carry them through, and the test is marked so that they really do have to get the right answers.
So, sure, students experience anxiety on math tests. Even I concede that. But that anxiety isn't some mysterious psychological affliction that descends on talented students with strong math skills. Rather, the anxiety is caused because it's only on the test that students are confronted with the fact that they don't really understand the material. To be honest, I've been there myself, and I know firsthand that it's a very unpleasant experience -- after all, you can fake your way through an English exam, but if you can't solve a problem it's difficult to hide that fact.
Here's my cool innovative idea for resolving math anxiety: explicitly teach students methods for solving problems, and then give them lots of hands-on practice to develop procedural fluency. I do, we do, you do.
We hopefully 'test' for different reasons. Hopefully, if we add a timed component on a test, there is a reason: e.g., The tested construct includes processing or motor speed and it makes sense to give the tt. a finite amount of time to work on the items. But it does not sound as if Dr. Boaler is looking at that. Which leaves me thinking she is referring to classrooms where students are required to 'do' things fast. The only (good) reason I can think of doing that is because building fluency leads to automaticity which then, as you well know (I bought both your books) leads to reducing cognitive load. I used Precision Teaching as a classroom teacher as well as an educational diagnostician. I never used timings until I had taught the skill/content to mastery (at least 80% accuracy). Don't believe in testing what hasn't been learned/taught (lack of proficiency AND speed really makes for a stressful experience!) Anyway, I did no-stress timings and kept things low-key. I also had my kids self-chart which they really liked (no public posting, or competitions etc) They liked that kind of time
test. It's been a while so if you want references you will have to wait a bit. I have my own reference list going. I recently included two really good ones.
My long-time pal Charlie's observations are excellent. There are times for timed tests, especially when students know _how_ to do things (e.g., say names for numerals, compute simple "facts," perform more complex computations).
Teachers should provide students with assessmemt opportunities on which they can demonstrate their achievements. "Last week, I got 43 with two mistakes. This week I got 50 with only one mistake! GOAL!"
To condemn assessments that are timed and that allow students to demonstrate their skill is to dismiss their opportunity to show their competence. Why would one want to thwart children's opportunities to show how capable they are?
Personally, I don't think we will ever get concrete evidence on this, not least because 'timed test' could encompass such a wide range of possibilities - low or high stakes, math fact recall or problem solving etc. To me, this is an issue of craft knowledge. If Boaler had simply stated her opinion, rather than suggest hers was an opinion based on research, that would have been fine. I would still probably have disagreed, but we wouldn't have all gone on this hunt for papers.
Kumon the largest after school math program in the world uses timed tests to measure progress. The solution isn't to get rid of timed tests. It would be beneficial to all students learn breathe work and relaxation techniques so they will be in a relaxed state before any test, timed or otherwise. It wouldn't hurt if the understood the power of sleep as it relates to learning and the issues around caffeines consumption. I am looking forward to reading Boaler's research citation.
It somewhat reminds me of some research/experimentation of the Rapid Assessment Test (RAT) whererin skipping steps, and time efficiency, was used as a surrogate measure of long term memory. RAT was based on assessing which parts of math were in long term memory and which parts were not. The assumption was where writing or slow down began, a gap in long term memory existed. There is some problems but it is interesting.
Bringing myself back to this subject of test and anxiety - isnt testing history (and understanding strategies within a testing environment) a potential mediating factor here? Those who study for timed tests may have less anxiety as they have better strategy, understanding, and overall preparation (therefore attention is not on lack of time, but on options remaining).
"The WWC and the expert panel assigned a strong level of evidence to this recommendation based on 27 studies of the effectiveness of activities to support automatic retrieval of basic facts
and fluid performance of other tasks involved in solving complex problems.131 Twenty-one of
the studies meet WWC group design standards without reservations,132 and six studies meet WWC group design standards with reservations" p. 51
I’d like to second one commenter’s remarks about the impact group-working/pair-working can potentially have on a student’s self-assessment of their facility with the material. The are only 2 times I’ve had a student specifically approach me after an exam to say they felt something had gone wrong during the exam and many of the types of problems they’d thought they knew how to do suddenly seemed impossible. In both cases, that student always did homework paired with a much higher-scoring student (in one case the highest-scoring student on the exam by far, for that section).
Fortunately in both of these cases this was only a first exam of 4, so I spoke with them about adapting how they worked in pairs, for example doing the problems independently before checking with their partner, and if they ended up relying on their partner to explain a problem, then finding another similar problem to do on their own before moving on, to make sure they really understood how to do that problem on their own. Both students did much better on the remaining exams.
There's no such thing as math anxiety.
OK, I admit that's provocative. After all, lots of people take math and experience anxiety, so how can it make sense to say that there's no such thing as math anxiety? What I question is Boaler's (and others') claim that there are lots of students who are highly proficient in math who experience a mysterious surge in anxiety when they are in a testing situation, and as a result can't function properly. In my experience, this never happens. Instead, when a student comes to me and explains that they "really understand the concepts" but when the test came along they experienced some sort of "math anxiety", I inevitably find with a few simple questions that in reality they don't understand the material and can't solve the problems, even in a low-stress environment. Instead, they vastly overestimate their competence (see Dunning-Kruger).
A lot of math education in the US is based on collaboration and group work. Also, many instructors are less concerned with getting the correct answer, and will grade charitably if the student can somehow display some form of "conceptual" understanding. Whatever the merits of this approach, it allows weak students to drift along, delusional in their belief that they are developing strong math skills. Once they get into a test however, they can't rely on the group to carry them through, and the test is marked so that they really do have to get the right answers.
So, sure, students experience anxiety on math tests. Even I concede that. But that anxiety isn't some mysterious psychological affliction that descends on talented students with strong math skills. Rather, the anxiety is caused because it's only on the test that students are confronted with the fact that they don't really understand the material. To be honest, I've been there myself, and I know firsthand that it's a very unpleasant experience -- after all, you can fake your way through an English exam, but if you can't solve a problem it's difficult to hide that fact.
Here's my cool innovative idea for resolving math anxiety: explicitly teach students methods for solving problems, and then give them lots of hands-on practice to develop procedural fluency. I do, we do, you do.
Interesting insight to U.S. education and your conclusion makes a lot of sense.
Common sense, rare yet not valued like it.
From my experience a lot of anxiety students have about high stakes testing comes from teachers themselves.
Absolutely. There is evidence that maths anxiety in teachers is liked to maths anxiety in their students.
https://psycnet.apa.org/fulltext/2023-52163-001.html
We hopefully 'test' for different reasons. Hopefully, if we add a timed component on a test, there is a reason: e.g., The tested construct includes processing or motor speed and it makes sense to give the tt. a finite amount of time to work on the items. But it does not sound as if Dr. Boaler is looking at that. Which leaves me thinking she is referring to classrooms where students are required to 'do' things fast. The only (good) reason I can think of doing that is because building fluency leads to automaticity which then, as you well know (I bought both your books) leads to reducing cognitive load. I used Precision Teaching as a classroom teacher as well as an educational diagnostician. I never used timings until I had taught the skill/content to mastery (at least 80% accuracy). Don't believe in testing what hasn't been learned/taught (lack of proficiency AND speed really makes for a stressful experience!) Anyway, I did no-stress timings and kept things low-key. I also had my kids self-chart which they really liked (no public posting, or competitions etc) They liked that kind of time
test. It's been a while so if you want references you will have to wait a bit. I have my own reference list going. I recently included two really good ones.
My long-time pal Charlie's observations are excellent. There are times for timed tests, especially when students know _how_ to do things (e.g., say names for numerals, compute simple "facts," perform more complex computations).
Teachers should provide students with assessmemt opportunities on which they can demonstrate their achievements. "Last week, I got 43 with two mistakes. This week I got 50 with only one mistake! GOAL!"
To condemn assessments that are timed and that allow students to demonstrate their skill is to dismiss their opportunity to show their competence. Why would one want to thwart children's opportunities to show how capable they are?
Personally, I don't think we will ever get concrete evidence on this, not least because 'timed test' could encompass such a wide range of possibilities - low or high stakes, math fact recall or problem solving etc. To me, this is an issue of craft knowledge. If Boaler had simply stated her opinion, rather than suggest hers was an opinion based on research, that would have been fine. I would still probably have disagreed, but we wouldn't have all gone on this hunt for papers.
Kumon the largest after school math program in the world uses timed tests to measure progress. The solution isn't to get rid of timed tests. It would be beneficial to all students learn breathe work and relaxation techniques so they will be in a relaxed state before any test, timed or otherwise. It wouldn't hurt if the understood the power of sleep as it relates to learning and the issues around caffeines consumption. I am looking forward to reading Boaler's research citation.
Timed tests is an interesting concept.
It somewhat reminds me of some research/experimentation of the Rapid Assessment Test (RAT) whererin skipping steps, and time efficiency, was used as a surrogate measure of long term memory. RAT was based on assessing which parts of math were in long term memory and which parts were not. The assumption was where writing or slow down began, a gap in long term memory existed. There is some problems but it is interesting.
Bringing myself back to this subject of test and anxiety - isnt testing history (and understanding strategies within a testing environment) a potential mediating factor here? Those who study for timed tests may have less anxiety as they have better strategy, understanding, and overall preparation (therefore attention is not on lack of time, but on options remaining).
100% agreed. Especially regarding your position on personal attacks.
My experience with “low stakes” and 13-14 yr olds is “low stakes”=low effort.
I time-test students weekly; if I want their best effort, it has to count, and count somewhat significantly.
Yes, I think this will depend a lot on context and on, say, whether you have Grade 1 or Grade 8 students.
The WWC from IES suggests timed "activities" as an intervention strategy for fluency. https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/WWC2021006-Math-PG.pdf
"The WWC and the expert panel assigned a strong level of evidence to this recommendation based on 27 studies of the effectiveness of activities to support automatic retrieval of basic facts
and fluid performance of other tasks involved in solving complex problems.131 Twenty-one of
the studies meet WWC group design standards without reservations,132 and six studies meet WWC group design standards with reservations" p. 51
I’d like to second one commenter’s remarks about the impact group-working/pair-working can potentially have on a student’s self-assessment of their facility with the material. The are only 2 times I’ve had a student specifically approach me after an exam to say they felt something had gone wrong during the exam and many of the types of problems they’d thought they knew how to do suddenly seemed impossible. In both cases, that student always did homework paired with a much higher-scoring student (in one case the highest-scoring student on the exam by far, for that section).
Fortunately in both of these cases this was only a first exam of 4, so I spoke with them about adapting how they worked in pairs, for example doing the problems independently before checking with their partner, and if they ended up relying on their partner to explain a problem, then finding another similar problem to do on their own before moving on, to make sure they really understood how to do that problem on their own. Both students did much better on the remaining exams.