Admit your Brain lock

[IanB]

I find it amusing when younger people say this. When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently. 70% would get you an A, as the questions were tough enough that this restricted those As to less than 10% of students. I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.

I think this shows how many people have a brain lock with mathematics, and how mathematics is "hard". For example, in the O-level test paper where I was able to answer all the questions correctly, most of my classmates were marked below 70% and only one or two above that. So, statistically, it was not an easy test for the population as a whole.

[Siwastaja]

I find it amusing when younger people say this. When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently.

I think this just represents small implementation differences between countries. Here, the scoring system usually required around 40-50% score to pass, then linearly the best grade for 100% correct answers, without such weird 7% deadzone on the top. With finite resolution and usual rounding rules, the best possible exam score could be had even with one or two small mistakes.

Maybe it was easier for us here.

[tggzzz]

I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.

My father was once given 96% on an exam (probably maths) on the principal that nobody should be able to get 100%

My second year undergraduate elwctronics degree was given by someone from the maths faculty. We showed our notes to a friend doing that course, and he was flabberghasted - saying that the content was most of his course. The end-of-year exam rubric memorably stated "full marks may be obtained for answers to about 6 questions". One other person on this forum might remember that

[IanB]

It's odd (what coppice said). Mathematics does not have fuzzy marking like, say, a language exam. If you get all answers correct, you would get 100%. There is a marking scheme with marks allocated to each question according to each part of the answer that needs to be provided to obtain the marks. For someone to get 93% that means that marks were dropped somewhere, probably due to not providing some expected element of some answers, or maybe by being incorrect in some answers that were given.

[coppice]

I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.

My father was once given 96% on an exam (probably maths) on the principal that nobody should be able to get 100%

Our maths teachers said 100% was unreasonable, as if they gave someone 100% and the next paper in the pile used some great insight the previous paper had taken a longer way around, they would have no room to complement that insight. Why 93% seemed to be that cap below 100% I don't really know. They were awfully vague about that.

[coppice]

It's odd (what coppice said). Mathematics does not have fuzzy marking like, say, a language exam. If you get all answers correct, you would get 100%.

When I was at school if you wrote all the correct answers in a maths paper without any workings you wouldn't get more than maybe 60%.

[Zero999]

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

I just see letter and numbers. I read ϵ and e and t and τ the same. Then there's the nonsense of having lower and upper case in the same formula. It's even worse when I write it down because my handwriting is very slow and scruffy. My hand doesn't do as it's told and sometimes I just randomly write the wrong letter for no reason. I was diagnosed with dyslexia, but probably have dyspraxia, as my reading is fine.

Mathematics is great in that it's either right or wrong, which isn't the case with other softer subjects, but that means there's less room for error. I can misspell words and the sentence still makes sense, but miswriting a symbol or number would lose me more marks.

[Circlotron]

It's odd (what coppice said). Mathematics does not have fuzzy marking like, say, a language exam. If you get all answers correct, you would get 100%. There is a marking scheme with marks allocated to each question according to each part of the answer that needs to be provided to obtain the marks. For someone to get 93% that means that marks were dropped somewhere, probably due to not providing some expected element of some answers, or maybe by being incorrect in some answers that were given.

Unfortunately, mathematics is not what is used to be in the minds of some people. Get a load of this nonsense.

[tggzzz]

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

I just see letter and numbers. I read ϵ and e and t and τ the same. Then there's the nonsense of having lower and upper case in the same formula.

OK, so you literally can't comprehend the formula. Shame, but that the "fault" lies with you, not with maths or the notation.

Frequently lower/upper case is used to convey information, by conventions. For example, in my first week at university my "Senturia and Wedlock" textbook section 2.3.4 is "Notation Conventions" indicates these conventions are in widespread use...
General network variable: v_A, i_C
DC component of a waveform: V_CC, I_B
Peak amplitude of a sinusoid: V_a, I_c
Incremental component of a waveform: v_a, i_c

It's even worse when I write it down because my handwriting is very slow and scruffy. My hand doesn't do as it's told and sometimes I just randomly write the wrong letter for no reason. I was diagnosed with dyslexia, but probably have dyspraxia, as my reading is fine.

Mathematics is great in that it's either right or wrong, which isn't the case with other softer subjects, but that means there's less room for error. I can misspell words and the sentence still makes sense, but miswriting a symbol or number would lose me more marks.

My handwriting is becoming appalling Age and keyboard use are the main points, but a traumatic biceps injury didn't help.

[CatalinaWOW]

It's odd (what coppice said). Mathematics does not have fuzzy marking like, say, a language exam. If you get all answers correct, you would get 100%. There is a marking scheme with marks allocated to each question according to each part of the answer that needs to be provided to obtain the marks. For someone to get 93% that means that marks were dropped somewhere, probably due to not providing some expected element of some answers, or maybe by being incorrect in some answers that were given.

Unfortunately, mathematics is not what is used to be in the minds of some people. Get a load of this nonsense.

WOW.  In these four pages there is a small amount of truth and potential added value.  Buried among a lot of trash, and wit much opportunity to misunderstand the little that is useful.

[Zero999]

It's odd (what coppice said). Mathematics does not have fuzzy marking like, say, a language exam. If you get all answers correct, you would get 100%. There is a marking scheme with marks allocated to each question according to each part of the answer that needs to be provided to obtain the marks. For someone to get 93% that means that marks were dropped somewhere, probably due to not providing some expected element of some answers, or maybe by being incorrect in some answers that were given.

Unfortunately, mathematics is not what is used to be in the minds of some people. Get a load of this nonsense.

WOW.  In these four pages there is a small amount of truth and potential added value.  Buried among a lot of trash, and wit much opportunity to misunderstand the little that is useful.

Unfortunately this thread has become full of boastfulness and overinflated egos, rather than attempts at providing useful information.

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

I just see letter and numbers. I read ϵ and e and t and τ the same. Then there's the nonsense of having lower and upper case in the same formula.

OK, so you literally can't comprehend the formula. Shame, but that the "fault" lies with you, not with maths or the notation.

Oh course I understand the formula. I just read it as numbers and letters. The notation is at fault because it would be easier to learn, if it didn't use similar letters. 

[elektryk]

Maths... How about https://en.wikipedia.org/wiki/Classical_field_theory ?

[m k]

When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently. 70% would get you an A

Here completion of 12 years, the second level, theoretical side, has a final exam where each subject has two hours.
(pre requirement for university, from that route)
All results are gaussian, or at least used to be.
If memory serves 5% will fail.

Second level of practical side, maybe a career college, had 5 to 9 scoring.
Full scale was 4 to 10, but school was paid by graduates, so nobody was perfect and practically all graduated.
Employers had also plenty of levels to choose.
Now it's three levels.
3 is for those who know what they should.
2 is for those who at least tried hard.
1 is for do not hire.

Practical side is also reformed from earlier decades.
Old career college time was stretched so that it got a higher EU level status.
Level of education practically remained.
New career college was also created and its level was lowered.

Now all reformed old career college graduates get a title engineer.
The problem is that current graduates are still using the old title scale.
Practical result is that construction foremen are no more, everybody are construction engineers.

For some reason construction foreman education is restarting.

[tggzzz]

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

I just see letter and numbers. I read ϵ and e and t and τ the same. Then there's the nonsense of having lower and upper case in the same formula.

OK, so you literally can't comprehend the formula. Shame, but that the "fault" lies with you, not with maths or the notation.

Oh course I understand the formula. I just read it as numbers and letters. The notation is at fault because it would be easier to learn, if it didn't use similar letters. 

Well, that is a clearer statement. Because you have difficulty distinguishing between different letters, the notation everybody uses is wrong.

Provided the semantics of the equation and variables is adequately described/understood, I don't see any strong cause for complaint.

[IanB]

This thread has been a bit of a revelation to me.

Previously, I would not have imagined that there are people who might have trouble seeing the difference between \$t\$ and \$\tau\$ in a formula. Or who might not make the immediate mental association that \$t\$ = "time" and that \$\tau\$ = "time constant".

Or that it is natural that both symbols are different forms of "t", since both symbols represent time and correspondingly have the same dimensions. It is thus a deliberate choice to have things this way, and the association of "t" with time would be lost if different symbols were used.

[nctnico]

I was straight-A full scores in mathematics in high school

I find it amusing when younger people say this. When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently. 70% would get you an A, as the questions were tough enough that this restricted those As to less than 10% of students. I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.

I find this an odd reasoning. If you have all the answers correct, you should get a 100% score. I'm not opposed to including more complicated questions to get from 70% to 100% though.

Then again I have had my fair share of inconsistent teachers. Like one who taught digital logic design and made tests where you could score 110%. And at one point I fail a math test while having all answers correct. I missed a few classes due to illness so my father (who is rather math savvy) helped me to catch up with math but made me use me the wrong (according to the teacher) method to get to the right answer 

[Zero999]

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

I just see letter and numbers. I read ϵ and e and t and τ the same. Then there's the nonsense of having lower and upper case in the same formula.

OK, so you literally can't comprehend the formula. Shame, but that the "fault" lies with you, not with maths or the notation.

Oh course I understand the formula. I just read it as numbers and letters. The notation is at fault because it would be easier to learn, if it didn't use similar letters. 

Well, that is a clearer statement. Because you have difficulty distinguishing between different letters, the notation everybody uses is wrong.

Provided the semantics of the equation and variables is adequately described/understood, I don't see any strong cause for complaint.

It isn't just me who has this issue.

There are 26 letters in the alphabet, which should be more than enough.

Not using weird symbols and upper lower case v and V would greatly improve the accessibility of mathematics.

This thread has been a bit of a revelation to me.

Previously, I would not have imagined that there are people who might have trouble seeing the difference between \$t\$ and \$\tau\$ in a formula. Or who might not make the immediate mental association that \$t\$ = "time" and that \$\tau\$ = "time constant".

Or that it is natural that both symbols are different forms of "t", since both symbols represent time and correspondingly have the same dimensions. It is thus a deliberate choice to have things this way, and the association of "t" with time would be lost if different symbols were used.

It's a bit confusing, when printed, although I can normally handle it, but I don't stand a chance of being able to write it down, without making an error.

I was straight-A full scores in mathematics in high school

I find it amusing when younger people say this. When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently. 70% would get you an A, as the questions were tough enough that this restricted those As to less than 10% of students. I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.

I find this an odd reasoning. If you have all the answers correct, you should get a 100% score. Then again I have had my fair share of inconsistent teachers. Like one who taught digital logic design and made tests where you could score 110%. And at one point I fail a math test while having all answers correct. I missed a few classes due to illness so my father (who is rather math savvy) helped me to catch up with math but made me use me the wrong (according to the teacher) method to get to the right answer 

If a maths teacher only gives 93% or over 100%, when all the answers are correct, complete with working, then he or she doesn't deserve their job, because they clearly don't understand percentages.

If you showed your method and arrived at the answer using logic, not just guesswork, then your method is the right one. The exception being the exam question specified which method to use, i.e. use mesh analysis to calculated the voltages in a resistor network and you used a different one.

[IanB]

If a maths teacher only gives 93% or over 100%, when all the answers are correct, complete with working, then he or she doesn't deserve their job, because they clearly don't understand percentages.

As I observed above, there is typically, in fairness to all candidates, a defined marking scheme for exams. For each question, there are certain elements that have to be provided to get the marks. If you correctly provide all the elements required for a question, you get all the marks. If you do this for all questions, you should get full marks.

[tggzzz]

Previously, I would not have imagined that there are people who might have trouble seeing the difference between \$t\$ and \$\tau\$ in a formula. Or who might not make the immediate mental association that  = "time" and that \$\tau\$ = "time constant".

Or that it is natural that both symbols are different forms of "t", since both symbols represent time and correspondingly have the same dimensions. It is thus a deliberate choice to have things this way, and the association of "t" with time would be lost if different symbols were used.

Agreed.

It would not, however, be wrong to use a different symbol for time and \$t\$ for something else - provided it was clearly stated. Nonetheless, that would be bad taste since avoiding following a "design pattern" would violate "the principle of least surprise".

Unfortunately too many schematics ignore design patterns

[tggzzz]

I missed a few classes due to illness so my father (who is rather math savvy) helped me to catch up with math but made me use me the wrong (according to the teacher) method to get to the right answer 

In the UK I was impressed about how teaching arithmetic to 7-11 year olds had improved.

In my day it was "follow the algorithm" - which was admittedly useful when I've had to implement floating point arithmetic! Nowadays they are taught that you can get the right answer by several different "successive approximations", e.g. 99y is easily calculated as 100y-y. That encourages a much better "feel" for the "shape" of numbers and arithmetic.

[IanB]

In my day it was "follow the algorithm" - which was admittedly useful when I've had to implement floating point arithmetic! Nowadays they are taught that you can get the right answer by several different "successive approximations", e.g. 99y is easily calculated as 100y-y. That encourages a much better "feel" for the "shape" of numbers and arithmetic.

On a related note, when I watch (the UK quiz show) Countdown, I am always impressed at how adept Rachel Riley is with her mental arithmetic. She can, in the moment, multiply say 47 by 83 and write down the answer while speaking to camera. I think she must dream numbers in her sleep.

[nctnico]

There are 26 letters in the alphabet, which should be more than enough.

But who says the alphabet you are using is THE alphabet to use for math? There are so many different sets of symbols in use across the globe. Think about Arabic, Cyrillic, Greek to name only a few. Unicode defines about 150000 different characters for a good reason. In math and science quite a few Greek characters have a special meaning like lowercase tau, upper case delta and last but not least, lower case pi. You really have to consider math a language in itself.

[Zero999]

There are 26 letters in the alphabet, which should be more than enough.

But who says the alphabet you are using is THE alphabet to use for math? There are so many different sets of symbols in use across the globe. Think about Arabic, Cyrillic, Greek to name only a few. Unicode defines about 150000 different characters. In math and science quite a few Greek characters have a special meaning like lowercase tau, upper case delta and last but not least, lower case pi. You really have to consider math a language in itself.

The Latin alphabet is used over much of the globe, for the purposes of information exchange. Until fairly recently, virtually all text was ASCII. A good number of those Unicode symbols look virtually identical, which is also a security vulnerability: look up homoglyph attack. There's no need for that crap in the field of mathematics. It's pure obfuscation.

[CatalinaWOW]

Absolutely not intentional obfuscation.  There are more than 26 unique concepts/entities in math and physics.  The people who started the use of these "special" characters did it to provide shorthand and avoid confusion with other entities.  The usage was productive and therefore adopted by others, eventually becoming widespread, used by people whose written language did not involve those characters. 

In today's world of ubiquitous data processors there is an argument that multi-character identifiers could be used, and commonly is for some symbols like pi.  But this all started when you had to write your ideas on paper with a pencil or pen and a terse notation is a benefit to avoid getting bogged down in the mechanics of writing equations.  Having a different notation for notebooks/scratch pads and publication made (and makes) no sense so it stuck.

I am unconvinced that long variable names would be an improvement.

Area_of_Circle Is_Identically_Equal_To Distance_Around_The_Rim Times The_Square_Of(Distance_From_Rim_To_Center) Times The_Ratio_Of_Circumference_To_Diameter

This expression still requires prior knowledge of terms like Equal, Identially, Rim, Square, Center, Ratio, Circumference and Diameter and is horribly unwieldy.  Imagine the fun for a truly complex expression.

Finally, as a native speaker of English, I will point out the 26 characters is not enough even to encode the languages common in Europe.  Even leaving the Greeks and Slavs out there are enough umlauts and tildes and diacritical marks to exhaust that limited set.  Unicode may go too far, but was done in a time when it had been found that even the expanded 255 characters in a byte weren't really enough and the obvious idea is to dedicate two bytes. 

[coppice]

If a maths teacher only gives 93% or over 100%, when all the answers are correct, complete with working, then he or she doesn't deserve their job, because they clearly don't understand percentages.

There can ALWAYS be greater clarity in the workings. There is ALWAYS the possibility of an insightful way to speed up the derivation of an answer that would deserve an extra mark or two. 100% says nothing could be better. I award you 0%, must try harder.