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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, 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