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Think you're bad at math? You may suffer from 'math trauma'
I teach people how to teach math, and I've been working in this field for 30 years. Across those decades, I've met many people who suffer from varying degrees of math trauma – a form of debilitating mental shutdown when it comes to doing mathematics.
When people share their stories with me, there are common themes. These include someone telling them they were "not good at math," panicking over timed math tests, or getting stuck on some math topic and struggling to move past it. The topics can be as broad as fractions or an entire class, such as Algebra or Geometry.
[...] One of the biggest challenges U.S. math educators face is helping the large number of elementary teachers who are dealing with math trauma. Imagine being tasked with teaching children mathematics when it is one of your greatest personal fears.
(Score: 2) by Snotnose on Monday November 05 2018, @02:10AM (15 children)
Math? Remember 1-3 formula a week and learn how to use them. Stuff you learned last week you'll use this week and will be on the final, albeit as step 2 of a 4 step solution.
History? Learn 10-15 dates a week and memorize them. No date has any correlation to any other, except Columbus discovered the New World sometime after he was born.
Social studies? Fine art? English? These all fall somewhere between these two, with the emphasis on "x + y = z" being T, instead of "if x, and maybe y, but only if y is $SpecialCase, then there is a chance z will be satisfied.
My memory sucked ass, still does, so the whole "1-3 formula a week" has worked for me for years.
Relationship status: Available for curbside pickup.
(Score: 2) by MichaelDavidCrawford on Monday November 05 2018, @02:21AM (14 children)
Still haven't.
Instead I count by N's: 3-6-9-12-15.
Yes I Have No Bananas. [gofundme.com]
(Score: 2, Touché) by Anonymous Coward on Monday November 05 2018, @02:52AM (13 children)
You're clearly American, because nobody else would be proud of such ignorance.
If you haven't memorized at least the 10x10 table, your ability to do any math at all in a reasonable time frame is more or less zero. It also puts you into a place where you can easily be taken advantage of because being able to multiple those numbers helps to greatly improve your estimation of how much things should cost and how long they should take. rounding things to just one or two actual digits each and multiplying them together before adding an appropriate number of zeros at the end will always get you within an order of magnitude of what you're dealing with. But, it definitely doesn't work if you don't know your times tables.
I honestly, don't get why people seem to think that this level of ignorance is acceptable. This isn't even math, this is basic arithmetic that a typical 3rd grader should be able to do.
(Score: 2) by MichaelDavidCrawford on Monday November 05 2018, @03:03AM (5 children)
Test?
I regard reasoning as far more important than memorization
Yes I Have No Bananas. [gofundme.com]
(Score: 4, Insightful) by Anonymous Coward on Monday November 05 2018, @03:21AM (4 children)
You can't properly reason, if you haven't memorized the basic facts relevant to the task at hand.
I see people make that assertion all the time and they're never people that should be looked up to. They're people that are too lazy to put in the work necessary to get good at the task at hand and generally refuse to learn from their mistakes.
I'm capable of improvisation and expansion _only_ because I have an ever increasing library of solutions and techniques with which to work with. It doesn't matter how good you are at reasoning, you're still going to get your ass whipped every time by people who have bothered to memorize the relevant facts related to the areas. It's just not practical to take everything back to first principles every time. At some point, you have to actually get things done.
(Score: 2, Insightful) by Anonymous Coward on Monday November 05 2018, @07:23AM (3 children)
You assert that people are lazy and are making mistakes if they think differently than you or mentally process math differently than you do? Why limit this condescending and judgmental behavior to people's memorization of basic math or ability to calculate equations in their head in a fraction of a second rather than taking a second or two? All those seconds will add up to several hours a year that could be spent doing something else (like learning math).
I think everyone should be judged by their abilities in algebra, chemistry and physics, too. Those basics involve memorization and some simple formulas as well. Binary math only involves 0's and 1's yet over 99% of people just don't get it! And don't get me started on the plebes who haven't memorized, or can even recognize, classic literary passages. People who lack basic computer skills? They should be tarred and feathered.
Or, and hear me out on this, let someone with superior intellect - such as yourself - invent something that does simple math for the inferior humans. We can send you back in time and we can call it an "abacus". Or, if someone like you hasn't invented a time machine yet, we can invent this device more recently and call it a "calculator". We shall build it small enough that it will fit on a desktop ... or in a desk drawer ... or in a pocket ... or in a phone ... or even in a watch. We can even let it perform more complicated tasks than basic multiplication tables.
Ironically, you being a condescending jerk because you can do something better or differently than others is why people look down you. You see, the most important skills in life are people skills. My people skills are much, much weaker than my abilities in all the sciences but I try to improve them everyday. These are much harder than memorization, at least for me. But most people seem to have them almost naturally, like they don't have to even think about them. And get this, they are so good at these people skills that they don't tout their abilities over others.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @02:29PM (2 children)
This has nothing to do with "superior" intellect. I've got multiple disabilities that make things like reading and writing very hard for me and I have a tendency to read and write things that are incorrect. Most of what I've accomplished in math is the result of just working at it long after other people would have given up.
People shouldn't be permitted to refuse to learn from experience. Yes, there are people out there that have intellectual or learning disabilities that may not be able to manage, even without help, but those individuals are relatively few and far between. For the vast majority of people, what you're talking about is ridiculous. Just sitting down with the table and even without mnemonics the thing should be memorized within a few weeks tops.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @04:44PM (1 child)
I'll check the medical journals, but I don't think douchebaggery is considered a disability.
Are you saying that memorization is a tool that you use in order to make up for other issues? If so, then it is much more important to you than to most other people.
Oh well, back to the douchebaggery. People aren't refusing to learn. They have already learned at least one way to do it and that way meets their needs. But you, you take learning as a severe point of pride. And then you project your "I did it and it is very hard for me to have accomplished it, so others should do it too!" attitude upon others in a measurably condescending way.
Which part?
My expectations of myself a pretty high, but I don't have high expectations for others, and I certainly don't think they should be able to do what I can do. People are different, and that's good. If everyone was like me the world would be a dreadfully boring place.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @05:36PM
Nice string of ad hominems you've got there. God forbid you actually make a valid point.
And yes, people are refusing to learn their times tables. There's only 144 entries in the 12x12 times table and 100 in the 10x10 table. If you literally learn one per day and don't take advantage of the commutative property of multiplication it would literally take less than a school year. That's a school year, it's not even a calendar year. Are you seriously telling me that there's this epidemic of people who can't learn through some method 1 of these facts a day who isn't profoundly disabled?
This is basic arithmetic here, it's something that people should be using on a more or less daily basis. It's not a high standard to meet and people in countries not called the USA are just expected to be able to do it because it's not acceptable to not be able to manage it. This is a bar that's only somewhat higher than what other animal species can achieve.
(Score: 2) by RandomFactor on Monday November 05 2018, @03:36AM (1 child)
OK Google, what is the square root of 372...Approximately 19.287
Now sure, I can just look at it and know it is a little less than 20. But any 3rd grader with their phone has the exact answer in the time to ask the question.
They even use calculators on math tests and SATs these days. It is pure craziness.
В «Правде» нет известий, в «Известиях» нет правды
(Score: 4, Insightful) by Anonymous Coward on Monday November 05 2018, @03:43AM
Calculators are dangerous. This is a really good example of something you shouldn't be doing without having the ability to estimate an approximate result. If you can't estimate an approximate result, how do you know the result is correct? You could have entered a wrong number. On rare occasions I've had my TI calculator give me wrong answers due to memory corruption. And the problem wouldn't go away until I reset the calculator. If I didn't have a roughly back of a napkin estimate for what a reasonable answer would be, I'd have no idea that it was off.
Calculators more generally speed complex calculations up, but they don't care about what the result is and if you're not there to sanity check the inputs, then you have no way of knowing if the result is correct.
I'm not personally completely against the use of calculators, I'm against the use of calculators without having a basic grounding in whatever you're using it for.
(Score: 2) by ledow on Monday November 05 2018, @02:09PM (4 children)
I'm not the OP.
However, it's people like you - that don't actually UNDERSTAND maths - that think that maths is anything to do with arithmetic at all, whatsoever in any way. It's like saying that you need to know how to operate a mouse in order to get a computer science degree. Go on, laugh at people for that. Funny, isn't it? How long were computers around before mice? How many mice do you think the average touchscreen-tapping-toddler is going to touch in their life? How many of the CS greats were qualified before mice even existed or, indeed, INVENTED the mouse?
And the part you really miss - studying mathematics is like studying computer science - NOTHING WHATSOEVER TO DO with actually using a computer. You're studying the science of them. How they operate, are constructed, designed and operate. What you are inferring (poor knowledge of arithmetic being associated with poor knowledge of mathematics) is no different to the computing/computer science equivalent (because I don't know how to use a Mac, I must be an idiot who knows nothing about computers, etc.). Even USE OF computers doesn't require USE OF a mouse.
You know why you hold that prejudice? Because you had a BAD maths teacher, who gave you maths trauma, and drummed into you that memorising a list of random facts is somehow useful to you beyond a quick reference - just like this discussion is hinting at - and that arithmetic is maths and maths is arithmetic. I have literally never spent any significant amount of my life worrying about or working out arithmetic problems.
If you ask me to calculate or derive a third-order differential of a curved 3D surface, I can do it for you from first principles. If you ask me 7 x 8, I may well double-check either in my head (long-wise and manually) or on a device. You know why? It's trivia. It doesn't matter. That's not maths. You stop plugging numbers in to equations at age 11/12 if you've been educated properly. And only for the CALCULATION, not for the derivation or understanding or the provision of a correct answer (you literally need to plug numbers in ONLY once you have done all the hard work and just need an answer directly applicable to real-life).
And you know the bigger problem? I can calculate 7 x 8 in my head faster than you can remember it. There's no need to memorise it. None whatsoever. No need to recite it in boring, difficult-to-remember lists (you know them NOW, but you spent years getting that data into your head, and it's a complete waste of a young mind). You know how I know that it's pointless and off-putting? I had a maths teacher throughout primary school who thought I was nothing special, because I couldn't memorise their silly lists of numbers.
In actual fact, it was nothing to do with that. My memory is *FABULOUS* for random data (I once wrote a computer program age 11 to calculate pi using a Taylor-series expansion and memorised the first 32 digits in order to verify their accuracy - which is pretty good considering I wrote that program on an Amstrad PCW512 with CP/M which doesn't even have 32-decimal-digit accuracy. I did that for my own interest, by the way. But I didn't want the embarrassment of being made to stand up and reciting times-tables out loud. I even didn't want to show everyone else up because if I'd done it, but all my mates couldn't, I'd feel bad for them and they'd probably mock me. I also didn't see the point, as I was actually CALCULATING THEM (I didn't realise my peers were memorising them until later on, I thought they were working them out as they went!). I also got bored because we used to do them for hours on end, and you'd fail for making the slightest slip up, and it had to literally be recited - one times twelve is twelve, two times twelve is twenty-four, .... up to 12 x 12. Perfectly. Without a stutter or a pause. What kind of sadist...?
My primary maths teacher didn't think much of me. I wasn't classed as particularly good at maths, and left that school still never having done a complete run of 1 x 1 up to 12 x 12 over 8 years of full-time education.
When I went to secondary school interviews, a maths teacher who knew my brother (also a mathematician, and a teacher) took one look at my name and INSISTED I join his top-set class based on nothing else. He instantly dismissed all my primary-school reports which showed no particular skill for maths (I still have them all!).
He was my maths teacher from 11 until I was 18. He was also my computer science teacher. He couldn't care less that I couldn't do the primary school stuff, he recognised in the first few lessons that I was good at mathematics (not arithmetic). The same as he recognised people good at sports (but maybe not hockey, for instance). He single-handedly taught me maths for 8 years, and I immediately went and got a maths (and computer science) degree straight after - Bachelor's degree, with honours.
I still struggle on my times-tables, because I still can't be arsed to memorise them, and still just work them out in my head if they are vital and I don't have a calculator or similar nearby. I still struggle a bit to get a graph going in Excel or doing a Word mail-merge. It doesn't make me a computer-science idiot. However what I can do is run rings around you in dozens of mathematical areas that actually matter, which feature almost zero arithmetic, work out anything necessary in Maple (or MathCAD or similar), or on paper (if you give me long enough), program any application you can imagine (given enough time) and teach even maths teachers things they didn't know about maths and CS teachers things they didn't know about CS.
It's EXACTLY this attitude that we're talking about here.
And I have no idea why people like yourself - ignorant about maths vs arithmetic, "computing" versus computer science - think that this level of ignorance is acceptable or, worse, something to propagate unto the next generation.
I was wiring up circuits using binary, BCD and hexadecimal, and creating adders, counters and multiplication/division circuits from first-principles (I didn't have the luxury of Internet access to Google it, or even parents/teachers available to me who knew that stuff in-depth enough to help... even my brother was strictly astrophysics and applied maths, and we differ almost polar-oppositely in our preferences for maths) etc. long before I'd ever bothered to complete your chore of what you think maths involves.
Honestly, if you even use the "x" as a multiplication symbol, you haven't studied maths to any depth yourself.
P.S. I do expect *everyone* to be exposed to a core of arithmetic, language and basic science. I don't expect them to all excel at it. However, I expect someone who does excel at mathematics to study mathematics and I couldn't care less if they can't do arithmetic. And I would never expect a random joe with no interest in mathematics to do anything about/beyond basic arithmetic. They are entirely different disciplines with entirely different applications. Mathematics is academic. Arithmetic is "life-skill". Hell, I know professors with multiple PhD's to their name who can't tie their shoes in the morning. Who cares?
(Score: 0) by Anonymous Coward on Monday November 05 2018, @02:43PM (3 children)
You're completely full of shit. If you can calculate 8x7 faster than remember that it's 56, then you're doing something very wrong. You might be fast at calculating it, but you're certainly not faster than I am at just remembering that 8x7 is 56, that happens completely instantaneously. If it takes any time at all, then it's not properly memorized. I'm capable of multiplying 2 and 3 digit numbers in my head and generally getting them right because I have my 12x12 table memorized, which is good if you're in the US where we still use inches and feet, and use them to generate the needed values.
As for your assertion that I don't really understand math, that's a load of bullshit right there. You shouldn't need to be taught how to use a mouse because it's bloody fucking obvious. The thing has like 2 buttons, a scroll wheel and you roll it around. Chances are a toddler would accidentally discover most of the functions without being taught. Basic arithmetic and number theory are incredibly important to learning and using math.
It's ignorant people like you that clearly have no clue as to what you're doing that damage people more than anything else. Being able to do arithmetic is absolutely essential to doing any sort of meaningful math as it's the basis for things like number sense and determining whether the answer you've got makes sense. Good luck dealing with more complicated math if you can't estimate whether a result is within the realm of possibility.
As far as the use of x as a multiplication symbol goes, nice strawman. Considering the complete lack of any evidence of mathematical literacy on your part, you just assume that I shouldn't have done that and the reality is that there's nothing at all wrong with it. I just don't have a fancy font to use. Using an x is more or less what's done up until algebra and we only stop doing it then because we start using it as a variable name. And we then get back to it sometime either in pre-calculus or calculus when we learn about dot products and cross products.
But, you're claim that it's wrong to do it is complete bullshit. It just takes somebody who isn't a freaking moron to understand the notation. Literally and 3rd grader should be able to read it properly.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @10:42PM (2 children)
Get over yourself.
There are life skills: Tying your shoes, adding money to your checking account, having friends, and evening having a conversation.
There are deep thought skills... mathematics in one of them.
You can be ass and not get it.
I meet a college professor. many, many years ago at party... He had friends that would help get him dressed, made sure he ate, drove him to school, appointments and events... He was basically a non-functional human. Now they would take him parties, put him in corner, put a drink in hand and then seed the party with questions about CHAOS THEORY. That was the "coin" that brought out this man, this mind. He would light up and talk theory and patterns, problems left unsolved and go and go. He got me to think about the math world is left behind for computers. and actually write some fractal programs for the IBM PC (8086) in BASIC, taking an hour or so to graph the image on the green screens.
YES, their are people that do basic math all the time in their with LARGE and small number of digits. Just because you assume others have the only skill you have for basic numbers is a DIV-0 eror on your part.
(Score: 0) by Anonymous Coward on Tuesday November 06 2018, @05:34AM (1 child)
Knowing your 10x10 times table isn't a deep skill it's routinely done by grade school students. If you haven't done it by 4th grade there's something wrong. People all over the world routinely learn and use basic arithmetic on a daily basis.
I'm sorry that you're suffering from such an obvious intellectual disability, but that doesn't change the fact that this is a necessary life skill.
(Score: 0) by Anonymous Coward on Tuesday November 06 2018, @04:38PM
Go and look up school house rock and why it came to exist
Mean sit down and shut up
(Score: 2, Interesting) by Anonymous Coward on Monday November 05 2018, @02:20AM (1 child)
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Primary-Krypto/ [nctm.org] Play Krypto. fun game and gets you out of math issues. Played with my daughters starting at age of 4, using dice to limit numbers. Mode rule slightly... I had to come up with 3 solutions before they came up with one.
Really helps to get fluid with math and numbers.
PS: Daughters got degrees in Math, in 3 years of college. Now, where are those STEM jobs?
(Score: 0, Flamebait) by Anonymous Coward on Monday November 05 2018, @02:56AM
When I was a kid, I used to love playing Number Crunchers on the school's Apple ][ computers. It was fun, but it also helped a lot with number sense and basic calculations.
It's a shame that educational software is nowhere near as engaging as it was in the '80s and early '90s.
https://www.youtube.com/watch?v=brvLpircQe4 [youtube.com]
(Score: 4, Insightful) by looorg on Monday November 05 2018, @02:29AM (14 children)
You may suffer from 'Math Trauma'? Can't you just be bad at math? Is that somehow not an option any longer? Does everyone have to be good at everything? There is some urge to label everything and failure is apparently not an option, cause someone might get their feelz hurt? Considering that most people don't need much more then basic math skills anyway this shouldn't really be as much of an issue.
I recall a professor I had calling Mathematics a contact sport -- you work with the numbers and the problems, you just don't read books and think that you will somehow understand or get things. You get in there and you solve problems over and over and over again until you know what you are doing.
I do believe this is one of the main issues here. They think it's supposed to be easy, something that everyone should understand. Anything beyond basic arithmetic can be quite abstract and require a certain mindset to understand. Some people might never be able to grasp it, just like some people might never be able to play an instrument or speak many languages. Practice and training will only take you so far.
(Score: 5, Interesting) by Anonymous Coward on Monday November 05 2018, @02:45AM (13 children)
Not really. As somebody who has been a math tutor for years and is currently working on a masters in teaching math, there's limited evidence to suggest that there are people out there that are "bad at math." There are some who have learning disorders or intellectual disabilities that negatively impact their math ability, but those individuals are much smaller in number than the people who are "bad at math." And they usually can learn it, if the material is properly presented and they're given adequate support. There is a point where some people just can't keep up without a lot of extra help and effort, but you're talking about something beyond calculus. And at that point, there's no reason for most students to study it as it's just not relevant for most people.
Most of the people who are bad at math, aren't, they've been on the receiving end of poor quality instruction or have been victimized by improperly trained and generally inept teaching.
An individual of typical intelligence or even somewhat low intelligence without an LD shouldn't have any issues getting through at least algebra and the pieces of pre-calculus relevant to every day living. Or should be able to do so with some extra assistance.
I've worked with people that are "bad at math" and only rarely have I had a student that might be bad at math. Most of the time there's an obvious explanation that comes back to either an LD or poor quality of instruction. Rarely, is it the case where I can't identify the likely presence of some sort of impairment that is more appropriately dealt with by a special ed professional.
(Score: 3, Interesting) by Gaaark on Monday November 05 2018, @03:02AM (8 children)
When learning difficult fractions, I struggled: unfortunately I had a male teacher who spent his time looking down the tops of the girls who'd developed early and I got ignored.
Then I got to learning X over y when I couldn't do 1 over 2? With a teacher who just said "Ask your neighbour for help" because he was almost retired and couldn't be bothered teaching....
I had some good teachers and some crap teachers. For math, I had too many crap teachers.
Trauma? Yup. But a good tutor helped me some: enough to get me by.
A good teacher makes all the difference, but to me schools should go back to teaching math and reading above all (with reading the most important...too many kids are going to French class who can't fecking read. Stupid.
If you can read, you can teach yourself history, languages, science, even math. If you can't read, why are they teaching you French? So you can speak it but not read it? Stupid.
Too much stupidity in the people running the school system.
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 0) by Anonymous Coward on Monday November 05 2018, @05:25AM
Keep thinking about it. You'll figure it out.
(Score: 4, Insightful) by cubancigar11 on Monday November 05 2018, @06:13AM (5 children)
I had the shittiest female teacher who just couldn't be bothered with teaching boys, so she would routinely make all the 'trouble-makers' i.e. all the boys stand outside for the whole class. I never noticed that gender side of it, and so I never complained about it, and my parents readily believed that I was just a bad student. Fortunately I had dedicated mother so I never flunked, like a lot of the other boys. When I reached 16, my father told me something that made me actually like math and I ended up being an engineer. He said, "Math is not a different thing, it is just a language in which God has explained about the universe."
It is so important to have good parents. I, of course, still suck at probability, but it is because I have realized that learning math is a process - you have to solve and solve and you will keep solving but since I haven't solved a math problem in decades, I suck at it. But I still love it. It is how universe is.
(Score: 2, Touché) by Azuma Hazuki on Monday November 05 2018, @04:32PM
Wait, is *this* where your disdain of women comes from? Yer Freudian slip is falling off...!
I am "that girl" your mother warned you about...
(Score: 1) by kurenai.tsubasa on Monday November 05 2018, @07:44PM (3 children)
You too with the group punishments? Anybody else here? What time period was it?
For me it was during the late 80s, when I was in elementary school. They made the boys sit with our heads down on our desks during recess instead of standing in the hall during class.
Azuma's response to your comment is hilarious. She will never admit that anti-democratic evil lurks in feminism outside of her Emmanuel Goldstein-like "TERFs."
(Score: 0) by Anonymous Coward on Monday November 05 2018, @10:53PM (1 child)
It called Military Training, or Football (or other team sports). If one makes a mistake all are punished (and some time praised). The goal is to get the team to control selves and work together, supporting the "weakest" to improve. Generally it works well, but sometimes its just makes it worst. se: "You cannont handle the truth!"
(Score: 0) by Anonymous Coward on Tuesday November 06 2018, @04:03PM
Yes, military training for boys and perks and privileges for girls. Sports team mentality for boys during math class. Maybe we need to implement group punishments for girls and treat them like they're on a sports team and prepare them for the military instead if we want cisfemale programmers. You just keep sowing the wind, feminist; the whirlwind is coming. You are nothing more than a transparent bigot. Roe v. Wade is going away, and you have nobody except your own self and 53% of white women to blame. You will understand this after you discorporate and spend some time in hell preparing to come back as a black boy in Africa, South America, or the Middle East, probably destined to be killed when he reaches "military age" for no other reason than being assigned the male at birth.
(Score: 2) by cubancigar11 on Tuesday November 06 2018, @05:21AM
I ignore her. She is like a leaking trumpet.
(Score: 1, Interesting) by Anonymous Coward on Monday November 05 2018, @10:13AM
I went to a high ranked private school and that is what they mostly taught - reading and writing. Even the non reading and writing classes, you were expected to read books outside the textbooks, many primary texts. Eg., reading On the Origin of Species for biology class, then write a term paper comparing it with Lamarckism in the context of scientific thought of the time.
(Score: 4, Interesting) by Whoever on Monday November 05 2018, @04:04AM (3 children)
So, let's start with the assertion that the plural of "anecdote" is not "data".
In my personal experience, what made the difference was not the quality of teaching, but the attitude of the teachers. I started doing well in school when I dropped many subjects (as was normal in the UK) and I found myself with a set of teachers who didn't care whether you played rugby or not. When teachers tell you that you are smart and can achieve good results, you are more likely to succeed.
Being told by teachers (mainly a couple of teachers) for several years that we (my class group) were a bunch of poor students did not help academic performance. I think that my later success at math was due to my personal belief in my abilities. Having achieved very mediocre results at "O" level (national exams taken at around age 16 in the UK), I surprised many teachers by achieving the highest overall results of my year at "A" level (national exams taken at around age 18, just before leaving high school). Those teachers still didn't acknowledge my success because I didn't play rugby.
(Score: 1, Insightful) by Anonymous Coward on Monday November 05 2018, @04:31AM
The teacher's attitude is a part of the quality of teaching that the teacher provides the students. I can't remember who said it, but it really is true that people don't care how much you know until they know how much you care. It doesn't matter how much you know and how good your methods are if the students get turned off by a shitty attitude. It's actively demotivating. Now, having a good attitude isn't necessarily enough, but if you've got a good attitude, the students are more likely to seek out additional resource and ask questions to try and bridge the gap.
(Score: 2, Funny) by Anonymous Coward on Monday November 05 2018, @10:19AM
I had a university math professor ask me "Are you retarded?" while handing back calculus tests.
He was a really good teacher. I thought it was funny.
(Score: 2) by loonycyborg on Monday November 05 2018, @02:33PM
There is no such thing as "being smart". Any sort of intellectual achievement requires a lot of work, and you won't find enough time to master everything. So it's worthwhile to focus on things that really interest you. But if teacher is being a jerk who is convinced that math is some sort of magic inaccessible to mere mortals you'll never learn anything from him without suffering a disproportionate amount of stress.
(Score: 5, Insightful) by Anonymous Coward on Monday November 05 2018, @02:36AM (15 children)
When I used to tutor students in math, I ran into people who were convinced that they "just didn't get it" or "were just bad at math". While it's possible that I was just a better teacher, most of them actually already knew what to do but were paralyzed by low confidence and frustration would make them give up.
Something like:
Me: Alright, what's the problem?
Them: I don't know what to do.
Me: What did you think you should do?
Them: Isolate the variable?
Me: Why don't you try that?
Them: Oh, now this kinda looks like that other problem I solved. What do I do now?
Me: What did you do for that other problem?
Them: Cancel things out and simplify. But that problem was different?
Me: Do you have any better ideas to try?
Them: No.
Me: Then why don't you try simplifying and see what happens.
(Score: 2, Insightful) by Anonymous Coward on Monday November 05 2018, @02:49AM (4 children)
In my experience, there's a number of things that happen. But, this is one of the big ones. A refusal to try unless absolutely certain that you're on the right track. It's very, very difficult to learn anything if you refuse to try unless you've already got the answer.
This is one of the reasons why I advocate against having too many tutors available for the students. If they don't try before getting help, then there's no way of knowing if they could do it on their own. And there's no way of developing any sort of self-confidence as you only build that via either succeeding or handling failure gracefully. Neither of which happen if you've got support right there immediately on demand.
I'm not sure who it is that gives students the idea that it's possible to advance in math without making any mistakes. Sometimes you can't reasonably determine the appropriate method without first trying a few things because either the rule that would tell you what to do doesn't exist, or more commonly, is more complicated than just taking a few educated stabs.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @03:26AM (2 children)
Idiot parents who themselves have math trauma and think rote memorization can get one through algebra.
It can't.
And I wish somebody would tell the people always going "I wanna be a programmer" that if you barely passed algebra, chances are that you will never be a programmer, no matter how much you blame half the planet's population. In the next life you'll realize how much of a childish jackass you were being with that approach.
(Score: 2) by hendrikboom on Monday November 05 2018, @03:18PM
Except that the procedural intuition you build up doing things in the real world can carry you far enough to gain confidence and bypass the blocks you set yourself up with in algebra.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @11:00PM
Can you cook? You can be a programmer. What else a recipe?
Do you knit? You can be a programmer. What else is pattern?
Remember the first programs where punched metal plates, strung together in a loop for the loom.
Now, will write code in less than 2k and use it pilot a spaceship to moon? Maybe not. But just like math, there are many different skill levels that required for the many facets of the business.
Go watch "Hidden Figures".
(Score: 0) by Anonymous Coward on Monday November 05 2018, @10:22AM
This applies to much more than math.
(Score: 3, Interesting) by BsAtHome on Monday November 05 2018, @07:03AM (1 child)
This is how you go from a "closed mindset" to an "open mindset". Many pupils and students have had bad experiences, which causes them to lock-up (mindset: "I think it is hard, so I rather not try as to prevent another bad experience").
The trick is to get the student into an open mindset as in "lets try, it can't ever get any worse and only better" and in "I don't know it yet, but I might in a moment". This is where the quality and experience of the teacher comes into play...
(Score: 0) by Anonymous Coward on Monday November 05 2018, @07:50AM
I feel like pointing out that that's most common with computers. People cannot figure things out because they are afraid to do anything wrong, and thus never manage to use a computer unassisted.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @12:19PM (6 children)
I have tutored also...
Most do not understand or "get" (came to realize) the fundamentals of math...
1) Addition is just counting up the number line (ruler)
2) subtraction is just down counting the number line (ruler)... or Addition with a counting sign (-)
3) Multiplication doing Addition repetitively.
4) Division doing Subtraction repetitively.
5) ... and so on
It is taught to slow and disjointed... it was assumed *ALL* will see the patterns. Yup, math is about patterns.
So in our language:
1) X + Y
2) X - Y --> X + -Y
3) X * Y --> S=0 : c=0 : while c D=0 : R=X : while R >= Y : R = R - Y : D++ : loop : print D, R
5) ...
Don't you see math as computer program too?
(Score: 1, Insightful) by Anonymous Coward on Monday November 05 2018, @02:56PM (1 child)
I never really realized this until more than ten years after I took multivariable calculus. I knew it in theory, but I never applied it to common mental math problems:
5%: take 10%, then divide by 2.
12%: take 10%, then add 1% two times.
142-59: subtract 60, then add 1; add 1 and subtract 1 from the initial problem (142-59 = 143-60).
39*39: 40*40 (forty, forty times), then subtract 40 (forty, thirty-nine times or thirty-nine, forty times), then subtract 39 (thirty-nine, thirty-nine times), which is also 40*40 -80 +1.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @03:27PM
You are VERY right... It is one of those things in early programming to find the fastest way to do something.
Had two programmer working on 80186 trying to figure out how to quickly (fewest clock steps) to calculate the the position of the curosr on a 24x80 screen.
So they where going to use MULT instruction to multiply by 80, and could not see how to speed it up. I looked a the Assemebler book (I was Z-80 ASM and IBM mini ASM knowledgeable.
80 is 16 (2^4) * 5 (2^2 + 1)...
Save ACC
Shift left twice (x 4)
Add saved back to ACC (+ 1)
shift left 4 tiems (x 16)
If i remember right 12 clocks total. The MULT function 5 to setup and 2 per 1, so X * 80 = 165 clocks.
(Score: 2) by hendrikboom on Monday November 05 2018, @03:22PM (2 children)
I've always seen mathematical induction over the integers as being a for-loop in a proof.
There's a remarkable correspondence between proofs and programs.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @04:35PM (1 child)
And there should be a lot of similarity, proofs are what you do if you need to know that the program is correct over whatever set of inputs you need to run it on. For many programs that's overkill, but if you're wanting to make sure that your plane doesn't kill people from above, that's the kind of thing you do.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @11:03PM
And even if you do!! Military need those.
(Score: 2) by acid andy on Tuesday November 06 2018, @04:56PM
That's not the problem for me.
More or less, yes.
The problem for me is when the teachers get lazy / sloppy and start skipping over steps in those patterns. Disjointed? Yep. Assume? Yep. I don't know about "too slow" though. I think part of the reason they skip over steps is to save time and go faster.
Master of the science of the art of the science of art.
(Score: 2) by tangomargarine on Monday November 05 2018, @05:27PM
Sounds about right. I had to retake pretty much all my advanced math courses in college twice (should've gone to a tutor way earlier).
My problem was that, the book would explain some way to solve for whatever/simplify whatever, and it would make sense. Couple example problems, okay I think I get it.
Then the assignment/test problems would be 3 times as complicated to solve, and half the time my efforts at simplification wouldn't actually get anywhere. Sometimes you can't tell if the simplification will actually work until you get to the last step and everything collapses and cancels out.
--
That, plus fairly frequently I wouldn't "get" the crucial logical step of how you connected one concept to the next. "Okay, so we do blah blah blah...but why?" And the teacher would give you an explanation that made sense to them, of course, because they know how the entire puzzle fits together. But they teach you one concept at a time, which literally involves lying to the student a lot of the time to keep the complexity down for the moment, then they yank the rug out from under you later "well actually that assumption you've been working on so far is something you have to work out for yourself each time."
And yes, fortunately programming has very little to do with advanced math unless you're writing a graphics engine or some other from-scratch project. Libraries--and not having too much pride to use them--are great.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 4, Funny) by BK on Monday November 05 2018, @02:41AM (5 children)
Teacher n., 1. Person who is not good at math. 2. Person who, based on experience, trains others to not be good at math.
...but you HAVE heard of me.
(Score: 1, Interesting) by Anonymous Coward on Monday November 05 2018, @02:59AM (4 children)
This really shouldn't be modded funny, it's unfortunately all too true.
Typical elementary school teachers are not taught how to properly teach basic arithmetic and it gets worse when students advance to middle school. The stuff being taught at those levels is mostly not that hard, but if teachers don't properly cover things, it can leave the students in a position where they're traumatized and convinced that they can't do it.
(Score: 4, Interesting) by Whoever on Monday November 05 2018, @04:09AM (3 children)
The above comment is simply ignorant. In California, teachers who go through the teacher credentialing courses are definitely taught how to teach arithmetic.
Whether they are taught the best method is open to discussion.
On the other hand, private (especially religious) schools don't employ credentialed teachers. As for public schools in the state in which AC lives: they may have poor or no teacher credentialing.
(Score: 1, Insightful) by Anonymous Coward on Monday November 05 2018, @04:29AM (2 children)
And yet, virtually every day I wind up undoing the damage that dates back to elementary school teachers teaching arithmetic incorrectly. If they're being trained in how to teach arithmetic at all, they should sue the colleges and get their money back, because it isn't working.
Basic arithmetic like you see in the elementary school isn't hard to get right, you just have to actually understand that students that age are typically dealing with the concrete and you have to actually understand where the arithmetic is going. I see no evidence to support the notion that it's common for those conditions to be taking place.
(Score: 1, Interesting) by Anonymous Coward on Monday November 05 2018, @08:49AM (1 child)
Education research is at the epicenter of all that is wrong with academia. It was EF Lindquist (developer of the ACT exam) who first published a stats 101 book for educators in which significance and hypothesis testing got confused and merged into one nonsensical procedure now referred to as NHST.[1] This efficient method for producing sciency sounding bs has since spread like wildfire throughout the academic community, gradually destroying every field it touches. Feynman even used education research as one of the prime examples of cargo cult science back in the 1970s.[2]
[1] https://web.archive.org/web/20150213231408/http://www.jameslindlibrary.org/illustrating/records/statistical-analysis-in-educational-research/title_pages [archive.org]
[2] http://calteches.library.caltech.edu/51/2/CargoCult.htm [caltech.edu]
(Score: 0) by Anonymous Coward on Monday November 05 2018, @02:59PM
I can't argue with that. My experience has been that the key to teaching math effectively is to make what you're doing clear and meaningful. If you make the material meaningful you're less likely to deal with unmotivated students. And if you make the material clear, then the students are more likely to be able to make their own meaningful connections to between the things that are going on and identify their own patterns.
I've been an English teacher and I'm personally convinced that the students I work with in math are mostly suffering from a lack of literacy. Being able to read the symbols and understand them is a huge component of being able to learn the material. Krashen has a huge point with regards to students having to comprehend what they're being presented with. I like Vygotsky was well, there's something inherently social about learning and you have to keep things in the Zone of Proximal Development to have the best chance of getting the material to stick with the students long enough for the students to own the material.
(Score: 3, Interesting) by Phoenix666 on Monday November 05 2018, @01:31PM (2 children)
I do think that they've gotten better at teaching basic math to kids. I help my kids with their homework and the books are teaching the right strategies to break problems down into easier steps. They have also introduced a weird element of vocabulary tests into the math books, which feels a little bit like English majors trying ton invade the math territory and render math, not-math. But let's be charitable and say they did studies and figured out that kids' inability to understand math ability was getting in the way of understanding the numbers.
As adults who learned math the old-fashioned way, it's understandable why they might fear numbers. Math and numbers are used to control them and steal from them everyday. They don't know enough math to be able to figure out exactly how, but they feel it in their gut.
Washington DC delenda est.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @02:55PM (1 child)
It's a mixed bag. There's too much emphasis on understanding and not enough emphasis on doing. The result is that the students might understand, but if they can do it at all, they're very slow at things that become important as time goes by.
There's also goofiness like repeat addition. There's that viral problem from a while ago that was something like 3x5=? and having to do 5+5+5 and not 3+3+3+3+3 or perhaps it was the other way around. This is wrong. Both of them are legitimate ways of thinking about the problem, even if it's better to think of the 3 units being stretched by a factor of 5 or 5 being stretched by a factor of 3.
(Score: 2) by hendrikboom on Tuesday November 06 2018, @03:15PM
No point learning to do if you don't understand -- you'll never know in real life when to do it.
Doing with understanding is a powerful combination.
(Score: 2) by All Your Lawn Are Belong To Us on Monday November 05 2018, @03:29PM
It is a stressor to have to not only learn facts and rules, but also reasoning which allows you to apply those facts and rules to problems you will never be given in school. Learning anything is traumatic to some degree because it does require the learner to change.
You're told, "you're wrong, you're wrong, you're wrong," and many times "you're right" is ignored because that is what is expected. Beg and plead, "why do I have to learn this?" I did with the multiplication tables. Fortunately I had parents who were very sympathetic and understanding.... and absolutely insisted I memorize them, because they knew I was capable of doing so.
Can it be unnecessarily traumatic, or additional trauma be applied by a teacher? Yep. I wouldn't doubt that this occurs and then makes it harder the next time around if there is one.
But on the other hand I've seen others who simply will not accept and cope with the stress that comes along with learning. They don't give up because a teacher has traumatized them, they give up because they do not want to expend the effort it takes to memorize, learn, and then adapt that knowledge. There is no perceived benefit to the learning, or the perceived benefits are outweighed by the estimated effort to get there. What I'm saying is that there are student who do indeed refuse to learn.
Either can happen. An excellent teacher is one who has learned to analyze the student and decide where the problem is and offer remediation consistent with that. Should the student not want to proceed after that point, a teacher is better off using their resources to assist those that do want to succeed and will make the effort necessary. I've had not-so-good teacher and extremely excellent ones. Another mark of an excellent teacher: If the student is interested that teacher tends to commit everything possible to enabling the learning to occur.
This sig for rent.
(Score: 2) by donkeyhotay on Monday November 05 2018, @03:55PM (2 children)
I think math "trauma" might be a bit excessive as a term, but I have long suffered a sort of math "recoil".
When I was a kid I was always good at basic math. I even did well at beginning algebra. Then I hit freshman algebra. The teacher of that class had, straight up, the worst halitosis I have ever encountered. He was a poor teacher and I learned early on never to ask him for personal help because his bad breath would make me physically ill. Of course, if you get a little behind in algebra, the game is up. I barely passed.
In subsequent years I found that I did great in geometry and even did all right in college algebra, but still had an aversion to higher math. Every time I see an advanced math problem, I can almost smell Mr. Black's rancid breath in my face.
Fortunately, coding is more a matter of logic than pure mathematics and I've made a good career at it, despite being poor at math.
(Score: 1, Insightful) by Anonymous Coward on Monday November 05 2018, @04:38PM (1 child)
Trauma probably isn't hyperbole. I've dealt with students that are every bit as traumatized by their experiences with math as people who have been sexually assaulted or been in combat.
It's not something that makes rational sense, but if emotions were rational, we'd live in a very different place. And over the years of having the same negative reaction to the idea that it's scary, it can become a rather large bogeyman to fight with just on the off chance that you can do it. Usually, those kinds of students can do it, they just need enough psychological help to see some success. Once they connect the idea that they can do the work with success they tend to do just fine.
(Score: 2) by acid andy on Tuesday November 06 2018, @05:12PM
It does make rational sense when you remember that the conditioning in schools is fear based. Fear of punishment, fear of ridicule and the fear of future economic destitution (never mind the fact that may or may not come regardless of your education--that's not what they're taught). The regime of fear is designed to try to tame even the most unruly pupils, so some are bound to wind up with some kind of PTSD in later life. But hey, work ethic, amirite? Gotta keep feeding fresh drones to that corporate hive.
Master of the science of the art of the science of art.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @04:51PM
I don't know about you, but every time I see those zeros in my bank account I experience math trauma and reality shock.
Is Post Trauma Math Disorder a thing?
(Score: 1) by CheesyMoo on Monday November 05 2018, @10:55PM
"Think you're bad at math?"
No.
(Score: 2) by acid andy on Tuesday November 06 2018, @03:01PM
Whilst it's true I'm not the fastest ever at mental arithmetic and my memory's not the strongest, having to often stop to re-look up mathematical methods and formulae, none of that has really held me back too far in mathematics.
What I struggle with is when a lecturer or teacher is explaining a very advanced topic and they start to skip out steps in the explanation. I think usually it's because they assume a certain grounding in their students' prior mathematical knowledge of the simpler topics, so presumably they would feel the bits glossed over are obvious. That's not a good teacher though. The best teacher takes the time to state the obvious because when a problem is broken down such that every part of the explanation is obvious, the whole thing becomes easy to grasp. Pretty much all operations in physics and mathematics can be understood in terms of basic arithmetic--addition, subtraction, multiplication (and a few look up tables like trig. functions and square root)--if only someone bothers to be thorough in their explanation of them. To put it another way, don't be too quick to dismiss the "Dummies" books--they were onto something!
Master of the science of the art of the science of art.