
Report examines origins and nature of 'math anxiety' - dnetesn
https://medicalxpress.com/news/2019-03-nature-math-anxiety.html
======
pflats
In my experience as a math teacher, there's a lot of sources of math anxiety.
There are a few I see the most:

* Stereotype threat.

* High school students thinking "I was good at math in 3rd grade, so I need to be good at math now."/"I was bad at math in 3rd grade, so I will be bad at math now." while not taking into account the differences in the subject and themselves over that time.

* Students never being told that math is actually difficult and requires perseverance, encountering a struggle for the first time in math, and taking it as a personal failing rather than the expected order of things.

~~~
japhyr
I've been a middle and high school math teacher for 25 years, mostly to at-
risk students. Almost all of them have what we call "math anxiety".

By far, the most common reason I see it is how they were treated by math
teachers. One student had a teacher who made students go up to the board and
write their incorrect solutions on the board, and they had to stay there until
they "figured it out". Many have been told they were stupid, or told they
would just never be able to learn. That experience is way more common than
many teachers and administrators want to admit.

There's also the pacing issue. Many students get lost in a math class at some
point in their early learning career, and then there's no real way to get
caught back up. This compounds with teachers who don't really understand math,
who are just teaching algorithms and rules and don't know what to do with
students who are lost.

I've had good success just by meeting each student where they're at, and
letting each student progress from where they are. I always look for what
students do understand, and build on that understanding. It typically takes
students one or two classes being treated well to start really recovering from
that earlier anxiety.

~~~
liveoneggs
does "new math" help or hurt this?

~~~
japhyr
I'm not quite sure what you mean by "new math".

~~~
klyrs
Look up the Tom Lehrer song with that name. I'm a mathematician who followed a
long and nonstandard path into the field and I agree with 100% of what you've
said. In my experience, it's "cool" to be bad at math -- typified by that Tom
Lehrer bit

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iandanforth
The problem is with mathematical notation, not the students. If you step back
and look at mathematics from a product perspective, from a tool designers
perspective, it's pretty clear that the user experience is awful. Generation
after generation of students encounter this tool and say repeatedly,
emphatically, "I hate math." and yet we seem blind to the possibility that the
tool itself could be improved.

It's like we're forcing children to learn how to use an astrolabe and then
blaming them for finding it complex and inapplicable to their daily lives.
Google maps provides the answers they want with a better user experience. I
would have astrolabe anxiety, I don't have Google maps anxiety.

Unfortunately there is a pseudo-religious connotation to mathematics. It is
"pure", "beautiful", etc. Teachers rarely encourage students to change,
improve, disrupt, or invent math.

Mathematical notation and pedagogy is continuously evolving and to think that
we're at the global optimum right now both ignores the negative reviews users
are constantly providing and ignores the history of math itself.

~~~
antidesitter
Do you have an example?

~~~
tomatotomato37
Skipping all the way to college level, but the notation of quantum physics can
get absolutely ridiculous. It's the only system that I can think of which will
use both the upper and lower case symbol of a Greek symbol in the same
handwritten equation while meaning different things; phi, psi, and theta being
the most notorious.

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ppseafield
I used to tutor folks in basic math classes at a small community college,
mostly classes leading up to college algebra (Math 097, 098). Varied
backgrounds, ages 18-50s.

There was a common theme to some of the problems these students had: if you
didn't quickly grasp a concept in the specific way that particular teacher
taught it, the class would soon move on to the next topic anyways. And
sometimes teachers would not teach one particular thing very well, but it was
something the rest of the class's instruction depended on. This left people
adrift for the rest of the curriculum. If they took the class over again, they
could get stuck at the same point because the class moved at the same pace,
often with the same instructor. That's both incredibly frustrating and a huge
waste of time and money!

~~~
CalRobert
Seriously! I took trig and nobody ever said "Here's a picture of a circle.
Here's what cosine, sine, and tangent are".

I had no clue what those concepts were for at least a year, but I managed
because I always knew I could take both sine and cosine and say "well I need
the bigger number in this scenario ∂or the smaller one in that one, so it must
be (cos or sin)"

When I saw a picture of a circle and an angle that basically said "Cosine is
how far you are horizontally and sine is how far you are vertically" it was so
damned simple I hated that I hadn't learned sooner. How did I miss it? Was I
sick that day?

~~~
jononor
Maybe we should have 'intuition checks'? A kind of test (not graded) that
regularly checks that key intuitive concept have been learned? Like show a
circle and ask to place the sin,cos..

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sethammons
> Students often discussed the role that their teachers and parents played in
> their development of maths anxiety. Primary-aged children referred to
> instances where they had been confused by different teaching methods, while
> secondary students commented on poor interpersonal relations.

For the teaching methods, I'll defer to A Mathematician's Lament by Lockhart.
Kids are taught to memorize and often by teachers (esp in grade school) who
don't understand the math. When I got my teaching credentials in secondary
mathematics, one of the points driven home was that a large factor that led
many grade school teachers to avoid secondary (high school) was fear of the
math.

Case: my daughter's 7th grade teacher taught the rules of exponents. Part of
it, he said anything to the zeroth power is 1 and anything to the oneth power
is itself and nobody knows why, it is just one of those things. Fast forward a
year or two, and kids are lucky to remember a factiod right. A simple pattern
matching exercise would have helped kids rediscover the rule if needed.

~~~
bitwize
> Kids are taught to memorize and often by teachers (esp in grade school) who
> don't understand the math.

On the flip side, if you _don 't_ know e.g. your times tables by heart, you
are in for a shitton of trouble when it comes to doing the higher level stuff.
The best way to achieve the arithmetical competence it takes to successfully
do math at secondary levels and above is drilling. Educational history is
littered with the wreckage of alternative attempts: New Math, some of the
approaches derided as "Common Core", etc.

~~~
natestemen
As someone who majored in math/physics I'm going to heavily disagree. I was
quite poor when it came to multiplication tables, and monsters like long
division, but was a pretty good student through university. I never felt like
I needed any of those things through any higher level maths, and making those
a requirement to learn (or at least drill as much as they do) seems counter
productive.

~~~
pflats
The basic times tables are a big sticking point in secondary mathematics.
Because polynomial work depends heavily on factorization, students who cannot
readily see that 56 = 7 * 8, and then apply their elementary operations skills
to say 7 * 8 = (2 _7)_ (8/2) = (4 _7)_ (8/4) will struggle more than those
that can.

You can develop skills to compensate (e.g., starting with small primes and
working up instead) but it's still an extra step in the process.

This does not necessarily affect a student's overall understanding of
polynomial functions, but can hang over their head in the actual work with
them.

~~~
asark
I've observed factoring generally to be a big problem. I also recall the
official introduction of factoring in our curriculum (9th grade?[0]) to be
when they lost an _awful_ lot of people. Perhaps not coincidentally, it's also
where things took a big swerve from straight application of memorized facts
and the correct algorithms into lateral thinking and intuitive guesswork, and
no-one bothered to make that clear at the time. Lots of very angry,
discouraged students resulted, all wanting to know exactly WTF they were being
asked to do and getting, from their perspective, no straight answer.

Mathematics from there on continued to mostly be the memorizy-algorithmy kind,
but with enough of the intuitiony-thinky kind sprinkled in and no clear guide
to which was which or even that the teachers were asking us to do something
fundamentally different that anyone who hit a big speed-bump at factoring
didn't have a hope of keeping up.

[0, EDIT] Maybe 7th or 8th? It's been too long, IDK.

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japhyr
Here's an interesting question: How far should we require students to get in
math for a high school diploma?

School districts in the US answer this in a couple different ways. Many define
the number of credits you need to earn, and many define the level you need to
reach. But that's compounded by all the issues in math education that occur
before high school. How do you hold everyone to the same bar if some are
coming in with elementary skills and some are coming in already beyond high
school? Many systems don't serve either group well, and the effects can be
devastating to people in both groups. How many of us on HN had high-level math
skills and had to endure years of boring required math classes?

I had an interesting exchange with another math teacher once. My school
requires everyone to move forward from where they're at, and to reach a skill
level appropriate to your post-high school goals. Many students end up just
becoming well-grounded in Algebra 1, which is great. Another school in my
district requires students to get through Algebra 2. We were discussing this
discrepancy at a district meeting, and I was being looked down upon for "only"
bringing some students to Algebra 1 level skills. I looked this teacher in the
eye and asked, "How does a D- in your Algebra 2 class compare to a B- in my
Algebra 1 class?" (They have to reach B level work to earn credit, which is
why we are okay with them staying in Algebra 1 work if they need to.)

His response? "Well, at least they've seen Algebra 2 level work before they
leave high school." The arrogance and uselessness of that statement echoed
through the room that day. I would love to see this conversation play out more
around the country.

------
rahimnathwani
This topic is addressed nicely in section 1.6 of "How I wish I'd taught
maths", by Craig Barton, a famous maths teacher in the UK.

His book covers what he used to think and do in his earlier years as a
(successful) teacher, what he has learned since then from academic studies and
other teachers, and how applying these principles and techniques has improved
his students' learning.

"How children fail" is another excellent book on how not to teach maths.

~~~
pcmaffey
Also, Seymour Papert's Mindstorms.

------
renholder
My first experience with maths anxiety was when going from degrees to
radians[0]. Memorising/Remembering the conversions was, for some reason, my
fucking kryptonite and, feck me, if I didn't feel like I was falling behind
because of it (hint: I was).

[0] -
[https://en.wikipedia.org/wiki/Radian#Conversions](https://en.wikipedia.org/wiki/Radian#Conversions)

------
rlanday
Why does “math anxiety” get such special attention? What about “foreign
language class anxiety” or “essay-writing anxiety” or “being forced to read
old books I don’t care about” anxiety? Is it because journalists tend to like
those activities and be scared of math?

~~~
wyattpeak
Pure anecdote, but maths seems to me to be in a class of its own when it comes
to people _feeling_ incapable of solving problems. People may not know much of
a foreign language, and they may not enjoy speaking it, but they will rarely
look at a sentence in another language and think "Nope, can't work out what
that means" when in fact they can.

I noticed a particularly odd example of it with my mother, who "hates maths"
but has worked with finances all her life. If you ask her what 10% of 200,000
is, she'll say she doesn't know. If you ask her what sort of return she'd
expect on a $200k investment she'll say, no shit, "you'd want 10% per year,
so... $20,000.".

It's not that she's incapable of doing it. Her mind just shuts down when faced
with the question.

~~~
paultopia
This part does seem like the notation is responsible to at least some extent.
I definitely have that experience myself when I read things like econometrics
and machine learning papers. I know the concepts and could probably handle the
words, but the pages full of bizarre elongated Greek letters that has to be
translated with some kind of nonexistent Rosetta Stone just induces a bit of
panic.

------
subless
I have math anxiety. I've been bad at math since I was a child. Mainly because
I was hyper and had short attention span and neither of my parents were good
at math, nor did we have money to get a tutor so my basic mathematical
foundation has always been weak.

I'm 31 years old now with my BA in Computer Information Systems and I still
don't know all of my multiplication problems from 1's to 12's, and have
difficulty solving basic algebra problems.

I've always stated that I hated math, and that schools are always forcing
students to learn certain types of math just to pass/graduate. Instead I think
the schools should focus on math that the students can immediately start
applying to their daily lives and jobs; no child working at a fast-food chain
is going to even try to apply calculus to their job.

My issue is that not everyone learns or interprets the language the same. Some
like myself take longer to process a problem to form a solution, but in school
you're on a timed schedule so people like me struggle.

Also, some teachers only teach the way they learned and understood the
language and don't really care or think that other students may learn from
different ways/perspectives.

I know I can learn any type of math, I just need it explained and demonstrated
to me in simple english that even a 5th grader could understand and not with
college words that I need a dictionary to comprehend.

I secretly deep down want to be great at math and to learn and master,
algebra, trigonometry, geometry, calculus, etc. so that I feel competent in
the computer industry to solve basic and more advanced problems. But instead,
I am reclusive and feel dumb and that I will never be great at any type of
math discipline.

------
itchyjunk
I have hard time studying in general, especially math. It's hard to sit down
and focus for any significant amount of time. But friends and family noticing
the anxiety would do very little for me. Then again, I am a grown man and
maybe understanding the plight of the kids will help us not put pressure on
them.

But people could also be experiencing this for any subject. I don't see why
this is limited to math.

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danharaj
I have math anxiety and I have a BS in it ._.

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JimBrimble35
I have a recurring nightmare that the semester is almost over and I haven't
been to a single one of the math classes that I need to graduate because I
keep forgetting about it and I know I'm too far behind to ever catch up. I've
been out of college for _years_.

I think my math anxiety started in high school as a result of teachers moving
through material too quickly in a learning style that didn't match up with how
I learn. Once you get a little bit behind it can be really hard to find your
way back in.

------
ptah
i think western culture's disdain for people good at maths and stem in general
is being ignored

~~~
cafard
Which western culture?

~~~
Nasrudith
The anglosphere at very least but there is a long history of "practical" and
mathematical being the proverbial red-headed stepchild of social classes in
spite of wealth. And that isn't limited to the anglosphere.

Millers were commonly demonized and scalegoated for neither doing honest work
with the rest of the peasants and instead maintaining "strange" machinery that
did the work for them and they worked with knowledge but neither as a part of
clergy nor nobility. Worse yet knowledge outside of known and respected
sources.

Merchants, owing to astoundingly bad economic theories were considered to have
to be engaging in fraud because the idea of the value of a fur coat being
higher in the mountains than the desert never occured to those not dealing
with the bleeding obvious of the profession. They were also widely considered
"non-productive" \- without irony given nobility.

Impetus theory is another sign of the disdain for the practical - how long
upperclass and "learned" men would use a theory of projectiles in triangular
motions that any artilleryman or archer would burst out laughing at from how
obviously wrong it is.

One common factor in even more modern times is ignorance and its self-
perpetuation. People fear what they don't understand and avoid it leading to
not understanding and more fear.

It probably isn't just from this feudal history and the causal link may be
tenuous but the tendencies have been around for a long time.

------
keithpeter
Quote from OA

 _" The UK is facing a maths crisis: according to a 2014 report from National
Numeracy, four out of five adults have low functional mathematics skills
compared to fewer than half of UK adults having low functional literacy
levels."_

And yet the pass rate at GCSE and previously GCE O Level has been fairly
stable at roughly two thirds passing give or take a couple of percent for 60
years...

Downloading report now.

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zachguo
Is it just exam anxiety? Or STEM anxiety? It seems to have the same root cause
as STEM supremacy, or some bias opinions towards liberal art majors.

------
ivan_ah
Direct link to report:
[https://www.repository.cam.ac.uk/bitstream/handle/1810/29051...](https://www.repository.cam.ac.uk/bitstream/handle/1810/290514/Szucs%2041179%20-%20Main%20Public%20Output%208%20March%202019.pdf?sequence=1&isAllowed=y)

=== Summary of Key Findings ===

o We conducted a literature review into the long-established relationship
between maths anxiety and performance (those with higher maths anxiety tend to
have poorer maths performance). We conclude that this is likely because
anxiety interferes with performance and poorer performance increases anxiety,
acting as a vicious circle.

o In our large sample of British children, we investigated the relationship
between maths anxiety and developmental dyscalculia. We found that whilst more
dyscalculics than typical children met criteria for maths anxiety, the
majority of those with maths anxiety had normal performanc.

o In a separate group of Italian children, we participated in research looking
at developmental change, gender differences and specificity of maths anxiety.
We found that unlike general anxiety, maths anxiety increases with age. The
relationship between maths anxiety and performance becomes more specific with
age – in younger, but not older, children, this relationship disappears after
accounting for general anxiety. See Maths anxiety: Gender differences,
developmental change and anxiety specificity for more details.

o We have identified, in our large British sample, anxiety subgroups. These
may increase in complexity with age. In our secondary school students, we
found that those with anxiety specific to academia (high maths and test
anxiety) had poorer performance than those with higher, but less specific,
anxiety. We conclude that this may reflect a dual path in anxiety development
and maintenance.

o In our smaller subsample of British students, with whom we conducted further
testing, we looked at the relationship between various cognitive variables and
maths performance. It seems that a myriad of factors are associated with maths
performance, but that basic numerical processing is not (unpublished data).

o In another Italian sample, we investigated specific memory subtypes and
their relationship with maths anxiety and dyscalculia. Whereas maths anxiety
appears to be associated with a deficit in verbal working memory and perhaps
also visuospatial working memory, dyscalculia is associated with deficits in
visuospatial memory; both short-term and working memory are affected.

o Our qualitative research has shown that children of 9-10 years are able to
discuss their experiences and origins of mathematics anxiety. Mathematically
anxious children seemed to describe negative events with less
contextualisation. They were also more likely to discuss physical sensations
in their maths classes and clearly articulated some of the negative
consequences of maths anxiety.

=== Conclusions ===

Each of the completed projects within our study further reveals the complex,
multifaceted nature of mathematics anxiety. It is likely that mathematics
anxiety is not a simple construct with only one cause – rather, it can emerge
as a result of multiple predisposing factors including gender, cognitive
abilities and general predisposition towards anxiety, rumination or panicking
under pressure. This helps to explain why mathematics anxiety is robustly
correlated to a small degree with many constructs (e.g. test anxiety, general
anxiety and mathematics ability). We have clearly shown that emotional and
cognitive mathematics problems dissociate and therefore require different
intervention strategies. Our qualitative analysis of structured interviews
suggests that children as young as 9 are experts in their own experiences in
mathematics and this can be harnessed to further understand the thought
processes underlying maths anxiety. This brings us closer to design effective
prevention and remediation programs for mathematics anxiety.

=== Recommendations ===

o The 9-item modified Abbreviated Mathematics Anxiety (mAMAS) scale developed
by this project proved to be a reliable tool for investigating math anxiety in
school context. o Teachers need to be conscious that individuals' maths
anxiety likely affects their mathematics performance. o Teachers and parents
need to be conscious of the fact that their own mathematics anxiety might
influence student mathematics anxiety and that gendered stereotypes about
mathematics suitability and ability might drive to some degree the gender gap
in maths performance. o Hence, for parents and teachers, tackling their own
anxieties and belief systems in mathematics might be the first step to helping
their children or students. o With our research showing that maths anxiety is
present from a young age and goes through significant developmental change, we
suggest focusing further research on how maths anxiety can be best remediated
before any strong link with performance begins to emerge. o The qualitative
part of our research shows that children are able to verbalise the suffering
that mathematics anxiety causes them. Our qualitative research also points to
several potential causes of maths anxiety that could be focused upon by
further research. o Teacher training should clearly highlight the role of both
cognitive and affective factors behind maths learning in schools. o Policy
makers should be conscious that emotional blocks can have substantial impact
on learning potential. o Emotional and cognitive problems require completely
different interventions.

I like the part about "for parents and teachers, tackling their own anxieties
and belief systems in mathematics might be the first step to helping their
children or students," which I think is super important.

