A couple days ago there was an article in the SMH, titled,
Bad with numbers? You might have maths anxiety
Yeah, maybe. Or maybe you just suck at maths. It’s a conundrum.
The SMH article, by education reporter Christopher Harris, is adorned with a photo of a beaming Eddie Woo trying to look smart, and begins with a dire warning:
Eddie Woo says it only takes nine words from a parent to make a student struggle with numbers for the rest of their 13 years of schooling: “Don’t worry, I was never any good at maths. … It is a well-meaning statement, but it has disastrous effects,”
“Disastrous”. A couple stray words and little Johnny is doomed. Eddie continues:
“It is meant to reassure a kid and say don’t stress; the irony is, it has the opposite effect … it reinforces mathematics anxiety.”
And we’re on our way with “maths anxiety“. Harris tries to explain:
Mathematics anxiety is the name given to the feeling of being overwhelmed and confused when faced with a mathematical problem.
Heaven forbid one should ever risk tackling a problem that might be overwhelming, or even confusing.
Researchers in 1972 defined it as the feeling of tension and anxiety that interferes with the solving of mathematical problems in both ordinary life and academic situations.
Yes, the difficulty of a problem can interfere with thinking clearly about solving the difficult problem. Welcome to life.
None of this is anything, of course, beyond the issue of accepting the reality of obstacles and learning how to manage them. Which is part and parcel of learning. And none of it has anything to do with Eddie’s fantasy disasters, which Harris finally gets around to noting:
Unlike generalised anxiety, [maths anxiety] is not an official psychiatric disorder,
So, not an official psychiatric disorder. Or much of anything. Which doesn’t stop education academics acting as if it were:
… but academics have been studying [maths anxiety] in some form for more than 60 years.
Well, fifty years from 1972, not sixty. But it’s not that Harris is bad with numbers. He probably just has maths anxiety.
From there, Harris’s article degenerates into the standard, aimless discussion of bad maths vibes, and what to do about it. Harris quotes Eddie and others, about the importance of having a “positive mindset” or whatnot. It is all nonsense.
More than anything kids, and adults, fear what they do not know or do not understand. In particular, if kids are confused by, have a disliking of, are nervous about, or are even made anxious by some aspect of mathematics, it is almost certainly in large part because they are being presented with ideas or tasks that they do not understand. The solution, then, is obvious: give the kids clear information and clearly defined techniques to master, to be done by the completion of carefully chosen and clearly expressed exercises, with and without teacher direction as appropriate.
In brief, the solution to bad maths vibes is not to fetishise these vibes into a fake syndrome. The solution is to get the kids to not suck at maths. The first step of which is to admit that the kids might, as it stands, suck at maths.
But of course truth is a terrible idea for kids, isn’t it? Better to smile like Eddie and think nice thoughts. There’s no way that that could end disastrously.
So I do not disagree with EW about parents passing in a dislike of maths. I agree that good teaching is a solution. But we need to make it unacceptable to say “I am no good at maths” or “I am not a maths person”. I once told an art teacher that I was no good at art and did not enjoy it as a subject. She was really insulted. But she had just told me that she hated maths. Apparently that was ok to say?!?
The “I am no good at maths” thing is of course lazy and stupid and unhelpful. But it’s not by a country mile the main point, and it has nothing to do with the grab bag of nothings that is maths anxiety.
Ah yes. The solution is obvious. Or is it?
I remember clearly a discussion I had with a colleague about an aspect of a first year (university) mathematics subject. Some students were confused about vectors and matrices. They specifically didn’t know what they were and when given exercises didn’t know what to do. I suggested cleaning up the notation, the definition, and formatting the strategy as an algorithm (at that time there was a definition by picture, three different notations for vectors, and the strategy in question was explained in a paragraph of text). I was met with fierce opposition and that shocked me. That would make the problem much worse, I was told. Ah well. What do I know?
Somehow university stuff seems a small point in comparison to primary and secondary. My reason for mentioning the story is just the following: if obvious solutions are to gain any traction, it is by continual advocation. If colleagues can’t see it, then what chance is there. Sorry, this turned out to be a more depressing comment than I intended.
Maybe performance measures or something (that isn’t a thing really at uni) will be the difference maker. I don’t want to completely give up hope.
‘The solution is to get the kids to not suck at maths’ is somewhat radical, Marty. It means that teachers and kids have to work without excuses 🙂 That is unheard of and especially when ‘The first step of which is to admit that the kids might, as it stands, suck at maths.’. What’s next, then? Learning timetables by heart and doing homework?
Pardon my sarcasm; certainly, I 100% support what you are saying.
I have don’t like to write English papers anxiety. It gets me really strong on the night before a big assignment is due. When I have (as always) not done any work on it and have to just jam it out under pressure. Can I please get out of turning the papers in? I’m anxious.
No!? OK, I’m coming down with a cold. Probably need to stay home tomorrow and write my paper. I mean get well from my cold.
Do not be alarmed.
Now that “ChatGPT got its “Wolfram superpowers”!”, all anxiety will soon cease.
If I know that I will be anxious about doing X, then I just do it. Eventually my X-anxiety disappears.
How many therapy sessions do you require between getting anxious about X and doing X?
I have just learned this from experience.
I think there are a lot of concessions made when kids are told by their parents ‘oh it’s ok, I was never good at maths’. Students just throw their hands up in the air when it all gets a bit too hard.
However, as a high school teacher, I am finding students’ level and understanding of maths as they transition to us rapidly decaying over the last 15 plus years. Many primary school teachers are not confident with maths and avoid it. Also the amount of ‘maths tricks’ and techniques they teach in primary school puzzles me as many of them take longer to complete than just standard processes. Students go home and get stuck on their maths homework, and their parents can’t help them as they don’t know the strange method the student is using and when they try and show the kid the method they know, the student refuses as it isn’t the same as their teacher.
Also many junior high school maths teachers are not maths trained, some have not even done any maths subjects at uni but schools are struggling to find teachers with actual qualifications in the subject. I work in a senior school and the partnership junior schools all use ‘Maths Pathways’ which is a computer program designed to teach at the student’s level. It is absolute crap and students just say that they figured out how to ‘clock it’. I have Year 11 Maths Methods students who claim they did not sketch quadratics in year 10, or learn how to factorise etc who used this program.
I think a good start is ensuring all primary teachers are confident in teaching maths and all maths high school teachers have some maths or science in their tertiary education. However considering we have had a VCE maths position available for nearly 2 years now and we can’t fill it, I doubt any of my wishes are possible.
It is getting more and more difficult teaching maths as students’ start with so many gaps in their understanding.
Maths Pathways is utter poison.
Yes the place to start is in Primary. Maybe it is time to have specialist teachers at Primary level. So many primary teachers i have talked to admit that maths is not their stron subject and that they themselves do not really understand what they are teaching. I have seen some excellent primary maths lessons and some really, really bad ones. I once saw a teacher stop the students doing an English activity and say “ok, we need to do maths now. I know it is not so much fun, I hate maths too, but we need to do it”!
Yes, once I did a Primary school placement in a grade 3/4 class for 2 weeks and by Wednesday I asked my supervising teacher, “why have you not taught any maths this week?”
She said, “oh I just don’t really like teaching it”
(meanwhile, there had been a religion lesson every day….)
I asked if she would like me to teach it, and she was happy about that. I took the maths classes for the remainder of the 2 weeks. I planned a daily lesson. The kids were fine.
This was a long time ago now and I can only imagine it has got worse.
The point you raise about students feeling they have to solve a problem in exactly the same way as their teacher does is a very valid, and not often enough acknowledged point.
Heaven forbid a student may have to decide something for themselves…
The discussion on this thread started to go in circles.
I could see that some participants claim that math is hard. Math isn’t more hard than any other subject. Saying that math is harder than, let’s English language is just outright wrong. Percentage of people knowing how to write isn’t higher than percentage of those who know how to count. Stop spreading misconceptions. Number of people knowing grammar properly isn’t higher than number of those who can solve quadratic equation or prove Pythagoras theorem. Doing things right is hard no matter what they are.
Am I spreading a misconception, or is your comment directed at this post in general?
A minor point, but on this comment from the maths ed professor Ben Zunica:
“the phenomenon of maths anxiety did not occur in other subjects like reading and writing because answers to basic maths sums were either right or wrong.
” “The teacher will say, ‘sorry, that’s not the right answer’,” he said.
“In English you don’t have such a black and white answer; with maths you do, especially with younger kids.” ”
In one sense this is obviously true: of course maths anxiety (if it exists) would not occur in English. But that aside, where is the evidence that tasks with right/wrong answers are more anxiety inducing than tasks with degrees-of-rightness answers? I’ve met many students who find the right/wrong answer aspect of maths comforting, because they know that if they use an appropriate method correctly, they will get the answer right – there’s no “maybe my teacher won’t like the way I’ve phrased this, or maybe I didn’t use enough quotes, or …”
Very good point. But I’ll bet another aspect now is that maths, which *should* basically have a right or wrong answer, is full of fake meaning and fake explanation. My primary-age daughters continually get this “explain” instruction, and never know what the hell it means, typically because there is no meaning to be had.
If “anxiety” or whatever is increasing in maths, it is undoubtedly due to the de-concretisation of maths, the “problematising” of maths for no purpose.
In VCE, I’ve found that “maths anxiety” (or anxiety about an upcoming maths task) reaches its peak when students need to do these “application task” or “modelling task” SACs. Even otherwise strong, confident maths students get very nervous about what they might be asked to do because it’s all so wishy-washy.
Exactly. Because they have no damn clue what is expected.
Hey Marty/everyone,
Has anyone got a link to any articles criticising the maths anxiety stuff?
How do you criticise a non-thing?
I think people can be proficient at mathematics AND have anxiety about it. Anxiety affects your ability to think properly, so students may not be as good as they would be otherwise, but that doesn’t mean they suck at mathematics. They may perform well enough but still be anxious.
I feel a bit uncomfortable with the way you’re conflating mathematics anxiety (claims of it anyway) with sucking at maths. One source of anxiety could be the fear of being judged if they make a mistake. I can’t see how it would help to have that compounded by the fear that if you admit to being anxious, then teachers will take that as an indication that you “suck at maths.”
In the article, they say “teachers asking questions of pupils in front of the whole class could unintentionally worsen it” and Eddie Woo is quoted talking about that. I don’t think this means that you shouldn’t ask students questions (and he didn’t say that either). But I think it can be very helpful once you start asking a student a question to not leave them with a sense of failing to answer it in the end. For instance, if they give the wrong answer or say they don’t know, then try to work out why, explain the error, and finally have them work it out by the end. I think you can be positive about the process in a way that makes it less embarrassing (and check they understand the main ideas one on one first so there is not too lengthy a process). I read this idea in a teaching textbook (Teach Like a Champion by Doug Lemov). So, I wonder if Eddie Woo made a more nuanced point but it was lost.
Jesus, wst. I’m not conflating anything.
But you say “the solution to bad maths vibes is not to fetishise these vibes into a fake syndrome. The solution is to get the kids to not suck at maths.” Getting kids to not suck at maths seems like a solution to a different problem, that is, sucking at maths.
Bad maths vibes is not a problem. It is a symptom. And it’s not maths anxiety. Which is not a thing.
What is it a symptom of?
A lack of understanding of what should be known and what should be done and how.
Just reading this passage made me anxious!: “A lack of understanding of what should be known and what should be done and how.” 🙂
I experienced math anxiety when I got to differential equations. It had the ingredients of (1) requiring a fundamental skill that was not utterly mastered, Calculus, and (2) involving step after step without feedback, so who knew if I was on the right track? I did OK in the end, but I remember the cold sweats half way through a full page solution.
Meanwhile, no kid experiences anxiety when starting a new video game, although they will fail every time until they complete every level — and put the game away! And struggle? They love it! Games that are too easy to beat are panned. The difference is they get constant feedback, and see steady improvement even while failing steadily.
I remember a computer math tutorial that provided the answer after three failures, because they did not want students to get frustrated. Oh, my.
I’m being quick and broad brush here. But seriously, wst, this anxiety stuff is 99% bullshit. It is not the goddam problem, and the fact that Eddie uses his stature to argue this shit, rather than addressing the systemic problems of curriculum and teaching, particularly in primary school, is obscene.
I recall teaching a student about swimming. I was told that he was very anxious about even being in the water. This was an understatement. I walked him across a shallow pool so that he could hang on to the side at all times. He was terrified! It was good that I had been warned that he was anxious. Even though a formal definition of anxiety was not offered, I got the drift of the warning. The warning helped me to help the student.
Keep at it Marty!
One can add the word “anxiety” to anything one finds difficult.
But giving one’s pain a silly name doesn’t make it a “thing”.
(I am 75. If any of you have parents(!), you should realise that *everything* they once did without thinking eventually begins to fall apart. It is a horrible process. But please don’t just give it a name! Learn to offer solidarity: we are unlikely to improve; but we can learn to “manage” with what we’ve got. We geriatrics, we have no choice but to “suck it up”. Solidarity is the only softener – and exercising it may even teach you younger folks a thing or two.)
Liberal democracy is on its knees precisely because, having created sufficient well-being and mental space for its citizens to flourish, those citizens have instead chosen to contemplate their self-indulgent navels. It is no longer just the Poms who “whinge”.
There is no need for kids (or adults) to “suck at maths”, or to invent false syndromes. There are systems that show us how to give everyone a chance at getting their heads around this stuff (mathematics is a *mental universe*) – even if, in the end, maths remains hard.
Maths has given us unimaginable benefits: modern society is rooted in maths (which makes the challenge of helping everyone to learn its basic language even more important). But it does not come for free: in particular, *failure* is part of the package (the best mathematicians “fail” much more often and much more painfully than ordinary mortals).
If kids or adults are encouraged to see their own feelings as the ultimate yardstick by which to measure the worth of something, then maths is going to get a bad press. The response should not be to pillory maths, but to realise the folly of our slavish self-indulgence in elevating personal feelings.
Education has no value unless its message is that the universe (and its sometimes painful reality) is more interesting than my personal feelings – which I should (and can) transcend. Maths is one of the best vehicles for achieving this experience of “transcendence” – even at school level.
The failure of large numbers to master basic mathematics is an educational challenge – which has a partial “solution” that we can all work on. Noone has the breadth of experience to be sure, but in my experience, those who respond by struggling relentlessly to help more students achieve a degree of mastery are a separate breed from those who invent syndromes to make excuses. We don’t need excuses (or celebrities taking sides in an opportunistic fashion). We need effort – and support for ordinary teachers.
Let my son read your post, Tony. Now he has a new game. He is adding word anxiety to everything 🤣
That’s hilarious!
TG ,
Your comments on ageing “use it or lose it” is often said applies to most people
I note RD the well known evolutionary biologist is still using it !
touring down under at 82 and he speaks as logically as ever IMO
Regards
Steve R
Off topic, and asked fearfully (like Oliver Twist wanting more gruel) but what are math methods and math specialist? In USian?
Is one honors and the other normal track? Or is one taken the year before the other? I checked the Victoria site but it kind of waffled.
Also, can you roughly translate what age the students are? Trying to equate to US grades. I get the impression your kids are actually more accelerated than our kids are. So, good for you.
Also, the math methods description sounds strange since it is calculus but then it says it is also algebra? And even probes and stats? And then the special just says its deeper but a lot of overlap? I guess I’m trying to correlate to a stereotypical US curriculum (and it is probably based off of the Brits instead, so I know it’s not exact, but approximately?)
I had something like this for honors track in the US at a public school:
[1 year accelerated start]
7th, 12yo: prealgebra (mostly solving 2x-5=12-7x type problems)
8th, 13yo: algebra 1 (mostly y=mx+b, but finish with cts and quadratic equation)
9th, 14yo: geometry (Euclidean geometry proofs, mostly in the plane)
10th, 15yo: algebra 2 (logs, exponents, etc.)
10th, 15yo: trig (plane of course). Nominally algebra 2 is a year and trig is a half year, but the honors accelerates an extra half year, by throwing in trig)
11th, 16yo, semester 1: “functions” (domain, range, how to handle inequalities and very simple calculus)
11th, 16yo, semester 2: analytic geometry (I remember rotating axes was a pain in the ass)
12th, 17yo, AP Calculus BC (covers the first two semesters of US college calculus…has a small ODE primer and a bit on series convergence at the end as this is traditional to prime the pump)
——————-
Uni freshman, 18yo, semester 1: calc 3 (multivariable calc)
Uni freshman, 18yo, semester 2: diffyQs (mostly or all ordinary)
The regular track is similar but doesn’t have the year acceleration at the start and doesn’t double up trig with algebra 2. Kids are still set to take a standard calc 1/2 US university class freshman year (I’m aware that UK and Germany typically see calculus as a high school class but in the US, it has traditionally been a freshman uni class.)
[Of course there can be variations with different counties and the like. In particular “precalculus” has the most variability. (I probably went to a more traditional/hard one where they wanted a bunch of stuff done ahead of calculus…some schools in the rush to calculus, will just consider an algebra 2/trig class to be precalculus and blow off theory of functions and analytic geometry.]
But I guess I’m trying to understand if Methods sort of equates to precalc and maybe AP Calculus AB (about 60% of a US freshman year calc class). And then does Specialty equate to AP Calculus BC (essentially first year US calculus from college but done with high schoolers)?
P.s. I don’t remember any prob/stats in this math sequence, although I believe it has snuck in a bit now (gotta train these kids to be little Goldman McKinsey quants, don’t we?). I did somehow learn what averages and medians and the like were, but it may have been mostly in middle school math (or even science) classes. I don’t remember it being belabored.
There are two year levels for VCE, (units) 1/2, and 3/4. You’re supposed to take them in year 11 and 12 respectively, but some people take methods accelerated (so they take 1/2 in year 10, and 3/4 in year 11.)
Specialist 3/4 is a watered down version of Calculus 1, and at most universities you can skip Calculus 1 if you do Specialist 3/4. Methods 3/4 is really just a watered down version of Specialist 3/4; there’s not too much difference between the two in terms of what they teach, and Specialist is just a strict subset of Methods, with a few more things you study like complex numbers. There’s also a bunch of random stuff like statistics and calculator proficiency thrown in to all the subjects as well.
About a quarter of people do methods 3/4, and maybe about 6-7% of people do specialist mathematics. The most popular mathematics subject by far is further mathematics 3/4, which about half of the cohort do, but I don’t much about it.
The 1/2 subjects are just watered down versions of the 3/4 subjects; they cover roughly the same content, just less of it. 1/2 subjects are a lot less formal as there’s no exams and they don’t matter for your final results as long as you pass. Passing in VCE is very different from that in America, it’s very, very difficult to fail. Even if you get a 0 you can technically pass as long as you show up to classes and show that you understand the content in some capacity. It’s also normal for about 30-50% of people to get below 50% in their final exams, which you can see from the graded distributions, e.g. https://www.vcaa.vic.edu.au/Documents/statistics/2021/section3/vce_mathematical_methods_ga21.pdf
There’s also UMEP (and formerly MUEP) which are the level 1 university subjects linear algebra and calculus 2, but very few people do them and very few schools offer them.
Generally year 11 students are 16-17 years old and year 12 students are 17-18, so the same as in America.
I don’t really think precalc exists as a subject as it does in America, in Australia, students (at least hopefully) just gradually learn more and more concepts, until they eventually start calculus in Methods 1/2.
Mathematical gripe: how can something be a “strict subset” if it has “a few more things”?
Not relevant to the core of the argument, I know, but I strongly believe that Specialist as a subject makes some sense. Methods (as someone who has taught it for 20-ish years) does not.
Meant a strict superset.
The International Classification of Diseases describes anxiety as follows.
“Anxiety and fear-related disorders are characterised by excessive fear and anxiety and related behavioural disturbances, with symptoms that are severe enough to result in significant distress or significant impairment in personal, family, social, educational, occupational, or other important areas of functioning. Fear and anxiety are closely related phenomena; fear represents a reaction to perceived imminent threat in the present, whereas anxiety is more future-oriented, referring to perceived anticipated threat. A key differentiating feature among the Anxiety and fear-related disorders are disorder-specific foci of apprehension, that is, the stimulus or situation that triggers the fear or anxiety. The clinical presentation of Anxiety and fear-related disorders typically includes specific associated cognitions that can assist in differentiating among the disorders by clarifying the focus of apprehension.”
https://icd.who.int/browse11/l-m/en#/http://id.who.int/icd/entity/1336943699
Thanks, Terry. Entirely irrelevant.
I thought that this description of anxiety in general from the International Classification of Diseases (ICD-11) would be a good starting point for discussing maths anxiety in particular, In this case, the focus of apprehension would be mathematical problems. Maths anxiety could come under the heading of “Generalized Anxiety Disorder” or “Social Anxiety Disorder”.
No. It’s not a good starting point. It’s entirely irrelevant. Maths anxiety is not a thing.
Here is a description.
“Mathematics anxiety involves feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations.”
Reference
Richardson F. C., Suinn R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554.
Big fat hairy deal. Maths anxiety is still not a thing. Christ, Terry. Give it up.
What is with “numeracy”? (A Google shows the word is older than I, but I don’t remember ever using it before in conversation.) Does it refer to math learning in general (algebra+) or is it essentially arithmetic skills? Is it just edspeak wanting to sound fancy and 21st century, not 19th century by saying numeracy instead of arithmetic ability. Or is it really a good word, simpler/shorter than the alternative.
Also, I’m not sure that using a word that is so similar to literacy makes sense. There is a very powerful decoding that happens in reading. Yes, it gets better with practice and kids go on to deeper texts. But it seems “more digital” (can you read or not). Of course it’s not fully digital. But it just seems different than math, where there’s kind of a long pyramid of new skills (counting, adding, subtracting, multiplying, dividing, long multiplication, long division, decimals, percents, ratios, pre-algeba, algebra 1, etc.)
Like reading is like learning to bicycle. You might get stronger/better. But it’s not really a new skill. Whereas math is like gymnastics, with harder and harder tricks, sometimes with some similarities to old ones, sometimes rather new.
To convert a recipe for 6 people from an American cook book that uses American units to a recipe for 4 people that uses metric units requires numeracy.
To understand inflation requires numeracy.
To understand the trajectory of a tennis ball requires numeracy.
To understand how votes for the Senate elections in Australia are counted requires numeracy.
“Numeracy” = “Applied mathematics”.
I think we used to call that checkbook math (and kitchen chemistry). The high school I went to had three tracks (honors, regular, and vocational). The vocational track still had to take some math and chemistry, but the math was more oriented to balancing your checkbook and other practical aspects of life. I think the chemistry, was a real course, but just a bit easier and with textbooks at a lower reading level (nothing wrong with that). I think they had real names, the courses, but everyone used the nicknames colloquially. It wasn’t even politically incorrect.
[There was no lower track for English. And for history, there was a lower track for world history but not for American history or civics. And no lower track physics or biology. All of those just had regular and honors.]
Let me give another example that requires numeracy.
We are told that the five-year survival rate for women diagnosed with breast cancer is 91.8%. What does that mean?
One might think that it means that for every 100 women diagnosed with breast cancer, on average, 91.8 of them will still be alive 5 years later.
But it doesn’t. To work out what it means requires numeracy.
It demands mathematics, for Christ’s sake.
That sounds more like a finer point of health statistics, not basic numeracy. Like do women that get hit by cars count against the death rate? (Obviously some would have lived on, some would have expired of cancer.) I don’t think I need “numeracy” to figure that out. I need to ask for the exact definition of how they are tracking things. It may not even be clear unless I really read the paper and the methods SI. I put that more in the “stats can be complicated, get a full description” bucket, not the arithmetic skill bucket. Really it’s more of a “watch out” than anything else. Converting the recipe is a more reasonable every day task.
I think the reason why literacy and numeracy are named similarly is that they concern similar things. Literacy is the ability to read and write in order to communicate and perform necessary things in order to function in society effectively. Similarly, numeracy is the ability to do whatever mathematical things are necessary in order to function in society effectively. What this means exactly is subjective and depends on what you think of as necessary to succeed in life. But in both cases, I think it is to do with how it affects your ability to succeed in your life and work, and engage as an effective member of society. That’s my explanation for why descriptions are vague – everyone has a different opinion about what the world needs and what is important for it.
Numeracy is not a thing.
I’m still working my way from back to front. Sorry about not commenting on all the posts; some of them have too high a math/drama ratio.
Don’t ruin the suspense and tell me if Sauron won the ACARA war. Still got 2022 to process.
Yep, maths is hard. Just spent 4 hours over the weekend trying to solve a Specialist Maths problem, until it dawned on me I had the wrong approach (was trying to use a force diagram, but this wont work).
But then I tried the right approach, and got bogged down for hours and still couldn’t quite get the numbers right.
Maths is hard, hard, hard. Much harder than any other subject. Fundamentally, conceptually really hard.
And we shouldn’t hide from this.
Math is not harder than any other subject, especially when it comes to science. Math isn’t harder than English (or any other language). Number of people knowing how to use grammar properly isn’t greater than number of people capable of proving Pythagoras theorem. The number of great writers isn’t greater than number of great mathematicians. There are good teachers and there are bad teachers. I experienced both. There are families where education valued and efforts made and there are families where parents don’t give a toss.
I think it is harder.
Firstly, I’m not talking about basic mathematics, ie counting and arithmetic, but what comes after that, notably algebra and calculus.
I think there are two elements to math’s hardness:
1. The concepts themselves are really hard to understand.
2. And then the work you have to do to get problems right (after you learn those concepts) is extremely detailed and rigorous
And grammar doesn’t require rigid rules? Writing good essay isn’t easier than solving pde. In general doing things on a certain level of quality is difficult no matter what those things are.
Harry here. I wanted to get my comment back on topic- I think maths is incredibly hard, but I dont believe in maths anxiety. Its just that maths is really difficult to do. There is no shortcut that if you overcome your anxiety etc etc you’ll get better at it, this just sets you up for more frustration when you still can’t bloody do it.
I think you’re back on track. Comparisons are off the point.
The wonderful advantage of this blog is that it gives us the opportunity to explore ideas about teaching mathematics with colleagues in a safe environment. For this, we are all grateful to Marty to starting the blog and the work involved in continuing it. Thank you Marty.
This section started with the question about maths anxiety. Does it even exist? Here I want to summarise my own conclusions after thinking about it for a little while.
There is a medical condition known as “anxiety”. For details see International Classification of Diseases (ICD-11). This authoritative source describes various disorders known collectively as anxiety. It makes a distinction between “anxiety and fear-related disorders”.
It does not describe maths anxiety specifically; nor does it mention other specific types of anxiety; rather, it describes broad characteristics of anxiety. For maths anxiety, the “stimulus” could be a mathematical task presented to a student that “triggers” the anxiety. A mathematical task would be “the focus of apprehension” for a student.
However, to fit the definition in ICD-11, the reaction of the student should be “excessive” or “significant”, not simply a dislike of mathematics.
It seems to me that, with a bit of work, maths anxiety might well be covered by the umbrella term “anxiety” as used in ICD-11.
Thanks to Marty and other contributors above for prompting me to think more about this.
Thanks, Terry. I’m not sure everybody regards this blog as “safe”: plenty of Nice People regard it as The Dark Side. But I appreciate the thought.
Yes, “maths anxiety” is a thing in the sense you describe, and as wst described it in the top comments on this post. But the point is, as you say (now), “maths anxiety” as anxiety triggered by maths has to have some level of extremeness and stubbornness, some independent existence. But the percentage of kids for whom this is the case is obviously small, and probably tiny. And it is in that much more important sense, as a question for general maths ed, that “maths anxiety” is not a thing.
Every second article on maths ed mentions “maths anxiety”, as it were the plague, this disease inflicting overwhelming numbers of students. But all they’re really referring to is bad maths vibes. It is all bullshit, and it is critically distracting bullshit. Eddie Woo is currently doing way more harm than good. Except for himself.
For teachers, uncommon problems can be pervasive. What I mean is – even if a problem affects only a small minority of people, then as a teacher teaching over a hundred students it’s likely that you deal with it in at least one student every school year. And anxiety is hard to deal with, especially if you are naturally empathetic. So, it’s an ongoing issue for teachers even if it affects only a small minority of students.
Sure. But that is not what Harris and Smilin’ Eddie and all the other clowns are talking about. I’m just gonna keep saying it: maths anxiety is not a thing.
To me it seems like the target audience of the article is well-meaning parents who want to help their kids succeed at maths. It ends on a long series of quotes from a teacher and students at an private all-girls school advertising the merits of all-girls schools in combatting maths anxiety. If I try to find an underlying intention in the article, it is to advertise that school. Maths anxiety is just an issue that they can say they do well with.
Agghh!!! wst, of course these people are “well meaning”. That doesn’t preclude them from being deluded and damaging. If parents and/or teachers want their kids to succeed at maths then they get their kids to do some goddam maths. Done.
Christ, why is this so hard?
On some level, I think most people don’t care much about mathematics or how well their kids do at it. They just want to be good parents and do what’s expected of them. There is still a belief that most of whether kids do well at mathematics is down to natural talent and they don’t have much control over it.
Also, the value of everyone doing well at mathematics as a whole to society is not seen – schools are largely used as a sorting tool for deciding what people are “good at”. That is, schools are not just teaching knowledge or skills, but helping young people find their path in life. Then mathematics class is just seen as a way of testing whether it’s something the students like. If they don’t, then people think “oh, well – something else then…”
“they just want to be good parents and do what’s expected of them”.
I guess what I’m saying is – what Eddie Woo is choosing as his message does make some sense. There’s always a mixture of nature and nurture in determining how well students like and succeed at school maths, and he seems to be encouraging people to recognise the effect of nurture.
The fact that “succeeding at maths” is a moving target because it depends on what is in the curriculum and what is valued is an issue that most parents probably don’t feel they have much sway in.
I know what you’re saying. What you’re saying is wrong.
Which part?
You said: “If parents and/or teachers want their kids to succeed at maths then they get their kids to do some goddam maths. Done.”
Okay, but I think there’s a lot in the “If” here. I think the core of the problem is in the “If”. What if they don’t care?* Why should they? What difference does it make? Is it fair to try to convince them? I’m not even sure on the reasons why myself.
* here I mean about the kind of mathematics that I care about, and perhaps you do. Perhaps they care about mathematising and stuff like that.
Christ.
By “succeed at maths” we’re talking, first of all, about young primary kids having a basic functioning sense of and facility with arithmetic. Are there parents who argue against that as a concern for their kids? If so, do you want to defend them? Or, is it more the fact that the parents care about this but are absolutely clueless about what to do about it, and are often even unaware there is a problem to be dealt with until the poor kid gets to fractions and algebra and is thoroughly screwed, because the parents are being poisoned by idiotic articles about “maths anxiety”?
This debate is insane.
By “succeed at maths” we’re talking, first of all, about young primary kids having a basic functioning sense of and facility with arithmetic.
There’s some ambiguity here. When I said parents want their kids to succeed at maths, what I was thinking of as success was not that. People are social animals. When we think of “success”, especially at an institution like school, we mostly think of recognition from others – being told we did a good job, getting a good mark, succeeding at whatever tasks are given to us. If those tasks are arithmetic tasks, then succeeding at arithmetic is called success. If instead, they get tasks asking them to explain three different ways to explain how to do an arithmetic problem, then doing that is called success.
People do make the case that arithmetic is not important anymore. That calculators can do it so why should we? That algebra is not for everyone, and it doesn’t matter. That calculus is too abstract. That a solution to having students not understand things is simply to remove them from the curriculum. Then everyone can succeed.
But I also meant succeed as in learn actual mathematics. I can see I was using it ambiguously, sorry.
I don’t want to defend them. But I don’t know how to convince them otherwise either. I like arithmetic. Sometimes I think maybe you take my comments as making an argument, when I’m not. Here I was asking the questions about how to convince people to care. They weren’t rhetorical.
My God.
I posted on a thoroughly idiotic article, with a thoroughly idiotic take on a thoroughly made up and seriously damaging cultural panic. No one has made more than a token effort to defend the article, to counter my criticism. Why? Because they cannot. It is all bullshit, and very damagingly distracting bullshit. And you goddam know it.
Now, you want to drive us down some other crazy roads, concerning parents who just want “to be good parents and do what’s expected of them”. You want me to consider the “ambiguity” of “succeed at mathematics”.
Here’s the reality. Last year my Year 5 daughter was asked, on paper, to answer 3 x 7, and then “explain” how she got her answer. That kind of insanity is endemic in primary schools.
You want me to debate the “ambiguity” of “succeed in maths”? Forget it. I’ll stay in the Real World, where “mathematics” means something, where “success” means something, and where “utter pedagogical madness” means something.
Getting children to memorise a table of multiplication products is a relic of the Dark Ages™ and is never coming back. It’s over.
Seriously though, do the people making these “explain 3 x 7” really think that the point of learning (obviously not memorising) times tables is a way to “think mathematically”? I thought the point of them was to do as little thinking as possible.
Maybe all this “anxiety” (frustration) comes from kids trying to come up with answers for your daughter’s explain problem.
Have you heard this podcast? https://podcasts.apple.com/au/podcast/math-teacher-lounge/id1617133517?i=1000607053813
I don’t do podcasts. Can you summarise?
With quotes like ‘ there is a fairly immediate psychological effect on someone when you say they’re wrong’ and ‘In English you don’t have such a black and white answer; with maths you do, especially with younger kids’, even the article itself hints that ‘maths anxiety’ is just the fear of being told that you’re wrong. Which is a reasonable fear, but the way to overcome it is to face it and learn that being wrong is not the end of the world!
But the way this article is written just reinforces that being wrong, especially in front of other people, is something students should be afraid of. The maths ed guy that’s quoted says ‘The teacher will say, ‘sorry, that’s not the right answer’’ as if it’s some kind of horror story. Students have to be ok with being corrected, or else how are they supposed to improve?
After reading the article, you’re left wondering what exactly the problem is. Is it that teachers are too mean about wrong answers? No, even this hypothetical boogieman teacher is perfectly civil. Is it that students aren’t good enough at maths? Not according to the article… Is it that maths is too objective? Subtly (or not), this does seem to be the point of the article; I sincerely hope our journalists don’t really take issue with things that are ‘too objective’. Is it that Harris wanted to get plenty of clicks from people who are insecure about their maths skills by absolving them of responsibility in a clickbait-y title? Hmmm…
Harris doesn’t think anything coherent at all. Like all education reporters, he works under the assumption that maths ed makes some fundamental sense, and thus the people he interviews are talking some fundamental sense. He pieces together what he’s told as best he can, and of course the result is something that makes no sense whatsoever.
Huh, that is true… explains why he keeps contradicting himself as well. On a second reading I notice: ‘The kids these days have been told, if they’re going to make something of themselves, maths is something they have to be really good at’; then, almost immediately afterward: ‘A lot of people will wear a badge saying ‘I’m not good at maths’ but would not wear a badge saying, ‘I can’t read’. So, the problem is that kids are under too much pressure to be good at maths, but also that it’s too societally acceptable to be bad at maths… surely we can’t err too far in both directions at once?
And of course my favourite line is ‘they know what to do – but when they’re asked to do it, they can’t recall the information’. Maybe I’ve taken it unfairly out of context (kids are too stressed to do maths if they’re ever asked to). And sure, it could be true to a degree for some students with anxiety problems. But as an assessment of why so many students score badly in maths? ‘They do all know the maths, except for when you ask them to do it’… I mean, that’s pretty funny!
That’s a fairly common sentiment in general, and it is for me equally annoying when applied to english, physics, math or whatever. The idea that students “know” things but can’t produce them in response to assessments. That’s perfectly normal! The solution is to keep learning. This may be difficult and time-consuming. With more knowledge comes more confidence and they will eventually be able to — relatively stress-free — complete assessments. Just like Marty, I’d suggest that they don’t “know all the maths”. They know a little bit of maths, and they need to learn more before being expected to do well on assessments.
One of the ways not to worry
@Marty: On asking students to explain their working.
Recently I asked my Year 9 students to explain their working for a question on a test. One student wrote “I used my brain”. Made me laugh.
Pretty funny. Note that I’m not against “explain” questions. I’m against insane “explain” questions.
UKMT Olympiad questions require ‘insane’ level of explanation. Obviously explanations might be very subjective and it creates certain difficulties.
A couple of things.
Providing reasoning is a key to better understanding and remembering things learnt. It is rare.
How many of maths teachers require this? Or at least a statement what the solution is at the conclusion of the solving process? How many such teachers do you know?
I read somewhere that in US number alone, where there in a context, without a unit , is considered incorrect. I try to push with this, having frequently asked: 12 what? And hearing, e.g. “seconds” when it is about distance.
My old school required a full sentence as well as the units included in the response. If my memory does not fail me, one could lose half of the marks for missing it.
How many of you, how frequently did you run intermediate olympiad? Is reasoning required? What is your experience with this competition?
Now, back to anxiety. What about teachers’ anxiety? As a retired now, relief teacher, I looked recently on the screen of a student. One of the educational programs, let’s call it RollyPolly,heavily promoted for use in schools. It read: “The trapezium is a quadrilateral that has (now the emphasis in blue) two parellel and two opposite sides”.
So I experienced some anxiety. Who is doing it? Does anybody care?
Thanks PollyMaths. Leaving “3 x 7” aside, I think asking “why” can be a reasonable part of a question. Most of the time, it is not.
Why don’t you name “RollyPolly”?
I’m going to echo one of the commenters and tell you that you *are* conflating math anxiety with sucking at math (which, to your credit, is often the source of math anxiety).
I see there’s a lively discussion going on here, and many make good points. But I see where you are coming from.
You don’t like how the word “math anxiety” has been used by ed school idealogues.
On that point, I totally agree with you. When we designate something as an “X-anxiety,” we medicalize it, and it gives us a veneer that this anxiety is its own thing, separate from the common source of said anxiety. It allows the Education “experts” to claim, “she isn’t struggling in class because she *sucks*. Oh no, (gasps), you can’t say that. She is struggling because she has *math anxiety*, and we have to treat that anxiety.” It can be and often are used as a deflection from the real problem – that many suck at math because schools don’t properly teach them. And it often can be used to put false blame on more surface level traits like parents’ attitudes (though, they do matter a lot).
Hell, I’ve seen this in my own life, too. I knew someone who was struggling in an honors college level course (very tough for a first year class, I’d say) make excuses for her bad grades, saying she has “text anxiety,” when she was also struggling with homework sets.
But despite all these I mentioned, I still think math anxiety, is very real. Many people do dread having to solve math problems. And it can cause poor performance *beyond* what you may predict from their abilities alone. It *changes* people’s behavior. It IS real.
See, you’re right that sucking at math is often the biggest source of math anxiety (coupled with the fact that they’re forced to do that thing they suck at for a grade, etc.). If you talk to any respectable psychologist/therapist, one of the first things they’ll tell you is that *anxiety* can be “normal” – especially if it reflects legitimate concern out in the real world (e.g. in this case, sucking at math). I’ve watched a video by Dr. K (on Youtube) interviewing someone who suffers from social anxiety, and one of the things brought was how the interviewee was bullied as a kid. Dr K. tells him, how, when he (the interviewee) is having anxiety when receiving any sort of attention, it’s his brain correctly functioning because when as a kid, he received those attention, he was being physically bullied. It’s his brain’s way of alerting him to the danger – it’s a normal reaction.
But despite being a “normal reaction,” if it is currently not helping you – e.g. in the case of math anxiety, preventing you from further developing math skills, then that should be addressed. I do think in addition to properly teaching mathematics, we *should* address people’s emotional reactions and attitudes as they related to math. They do matter. I totally see when you criticize the Math Ed creatures for *only* addressing the attitudes and emotions and identities or whatnot without proper training. It’s a parody of treating math anxiety because the *real* treatment of math anxiety also addresses one of the most common sources of it – their lack of skills! But at the same time, you *should* address the attitudes, emotions, identities or whatnot.
Sheesh. Would it do any good to repeat that I’m *not* conflating “maths anxiety” with sucking at maths?
I’m flat out today but I’ll respond properly tomorrow-ish.
Johnald, I knew plenty of kids who were ‘sucking at math’ and never had any anxiety about it. You are conflating things.
Am I the one conflating things?
Which two+ things am I conflating?
I guess some people “suck at math” and never cared enough to have anxiety, but I don’t think it’s controversial to say that sucking at math is a common source of math anxiety among math anxious people…
I think it could benefit you if you read the whole thread. Everything is well explained above. I can understand you are coming late to the party however, it is all there.
Aight, I’ll be honest with you. At the time I wrote my comment, I only skimmed through the comments. There’s no way I could read through 80+ comments.
I did read through the whole thread after posting it, but I still maintain this. I get that math anxiety, used by Boaleresque clowns and ed school goons, are not real. But I think that anxiety – no matter where they come from, whether it be due to a genuine lack of skill or due to other “irrational” reasons, should be addressed. And the label “math anxiety” can be helpful the way that “social anxiety” label can be helpful. Yes, that label can be harmful as well, the way the ed school ideologues use them, but that can apply to a whole bunch of other things as well.
You know, this reminds me of that time when, on Twitter, Abigail Thorn tweeted claiming that Gender Dysphoria is not real. Of course, it’s real. But what she (probably) meant was that Gender Dysphoria, the way it was appropriated by the transphobic entities and medical institutions, and the way it was used to gatekeep people from transitioning, is not real.
Rene Descartes once said: “Before we start the discussion let’s agree on the meaning of words”. Even if you believe that ‘wrong’ definition might help the ‘good cause’ it is still a wrong definition. Nature has enough of entropy for all of us, there is no need to multiply it.
So, what makes my definition of “Math Anxiety,” which you and Marty seem to agree are real, the “wrong” definition?
If anything, it’s the ed schooler’s definition of “Math Anxiety” that seems to be wrong.
It’s funny how both you and the ed school goons agree on the definition of “Math Anxiety,” one side, to argue against objective reality and against proper standards for the sake of equity, and the other side, to knock down the dumb Jo Bailer-esque clowns as much as possible.
I’m reading this exchange, but have had no time to think to respond carefully. Soon …
With a quick reading, Johnald, I don’t think you’re raising anything that hasn’t already been addressed thoroughly, and repeatedly, in the comments.
I’m pretty sure there’s one aspect that I *did* address which hasn’t been addressed in the comments. But yes, much of what I said was in some ways, addressed in the comments, though perhaps not to my complete satisfaction.
Yeah, take your time with your response. I’ll be curious to hear it.
I’ll look at all your comments carefully, but feel free to specify/clarify the particular aspect you’re thinking of.
Hi, I’m replying here because there’re no more reply buttons on your response.
So, we both agree on a few things: 1) Math Anxiety, as defined by “people have anxiety about math” is real, and 2) It is not typically a phenomenon independent of their lack of skills (which is what the ed schoolers insinuate while also subtlely or not so subtlely hinting at the idea that skills don’t even make sense, and objective reality don’t even make sense).
I maintain that Math Anxiety, as understood by psychologists (as far as I can tell) is still a useful concept and is in line with definition 1) and is very real. On top of that, that should be addressed *in addition* to addressing the lack of skill that is usually the cause of the Math Anxiety, and it’s in that sense, Math Anxiety is real. Maybe you really did address this part above, but I think you may be underestimating the role anxiety, the emotion, plays into math achievement, in addition to the teaching.
I notice that you, understandably so, have a quite a bit of distrust towards “research.” But the thing is, if you look closely at the Boaler-esque types, what you find is that psychologists don’t really agree with her either, at least ones (in the majority) who are grounded in reality. This, I think, is one of the many examples.
Still too busy to reply, but no, I don’t accept maths anxiety is real. At least not any more real than, for example, child predators are real.
There’s nothing unusual in two sides of a debate agreeing on the definition of the thing at the centre of it all.
Indeed
Yes, but I do think it’s a problem when both agree on the *strawman* version of the definition, which is what I think it is.
OK, I’ve finally had a chance to read Johnald’s comments, and this is a brief (re-)reply. I don’t think there is much to say, but if I have not properly addressed anything, feel free to point it out and we can go from there.
Johnald wrote:
“I do think in addition to properly teaching mathematics, we *should* address people’s emotional reactions and attitudes as they related to math.”
To which the answer is, of course we should. And, it is the answer I had already given to Johnald’s comment on a previous post:
“In particular, kids can have all manner of negative emotions towards maths: stress, distaste, fear and so on. These emotions are of course always worth addressing, specifically with each kid and as general cultural phenomena.”
But that is pretty much it. The fact that there is a genuine clinical condition referred to as “anxiety”, and the fact that this condition may manifest as “maths anxiety”, are almost entirely irrelevant to teachers’ general and reasonable and necessary concern with their students’ feelings about mathematics and its learning.
There is a clear political purpose to labelling a broad range of emotions and reactions with a profound clinical title. Here, it is exactly to shift the focus from the teaching of mathematics to instead shooting at the flames of feelings. This clinical fetishisation of student feelings comes at the expense of dealing with mathematical deficiencies, and it has been disastrous.
This is a general cultural phenomenon now. The pathological is taken to be much more common that it is, and evidence for this commonness is then manufactured by labelling fundamentally mild and rational behaviour in pathological terms. It encourages, and too often rewards, the very pathology that is supposedly of such great concern. It is madness, and it is poisonous.
There is more I could respond to in Johnald’s comments, and I’m really, really tempted to troll myself by doing so. But I’ll leave it there.
Real math anxiety comes from reading a Soviet era math book 🙂