[Blindmath] Math in your head (was: alternative methods of learning college algebra)

Mon Dec 14 23:44:11 UTC 2015

> I just realized that I said that the integral of 1/(1 + X2) dX...

Do you mean 1/(1 + X^2)? The caret '^' means raised to. X with a 2
after it and no symbol in between doesn't mean anything.

Amanda

On 12/14/15, David Moore via Blindmath <blindmath at nfbnet.org> wrote:
> Hi again,
> I am sorry. I just realized that I said that the integral of 1/(1 + X2) dX
> is arcsine X. actually, it = arctangent X. The integral of 1/(1 - X^2) =
> arcsine X. Please read what I had to say in my last post and really think
> about what I am trying to say. Take care all.
>
>
> -----Original Message-----
> From: John G Heim via Blindmath
> Sent: Monday, December 14, 2015 11:45 AM
> To: Jeremy ; 'Blind Math list for those interested in mathematics'
> Cc: John G Heim
> Subject: [Blindmath] Math in your head (was: alternative methods of learning
>
> college algebra)
>
> Maybe I'm getting my responders mixed up but weren't you the one
> originally advocating doing everything in your head?
>
> You're totally wrong about what you say below though. Arithmetic is only
> a very small part of mathematics and you can do the vast majority of the
> arithmetic in your head faster than you can with a calculator.  No exam
> is going to ask a student to calculate the cosign of a 45 degree angle
> by whipping out their calculator.
>
> But I'm not even talking about doing arithmetic. I'm saying that most
> math students, if asked to calculate the cosign of a 45 degree angle
> would have to take out a paper and pencil, draw the unit circle, write
> down the Pythagorean theorum, and  work it out on paper. If you can
> develop an ability to do all that in your head, you're way better off.
>
> I pretty regularly come across students who have told me that they have
> been told they can't be mathematicians because math is essentially a
> visual thing. Quite honestly, I think not only is that wrong, it's
> backward. Relying on vision to do mathematics is a drawback.
>
> On 12/14/2015 09:14 AM, Jeremy wrote:
>> Though I can understand your perspective as a blind person, just about
>> every
>> human being in the modern world carries a cell phone, and all cell phones
>> have calculators. Why trust or tax your memory when a device which can
>> compute far, far more than your brain will ever be able to calculate is
>> right in your pocket. Why walk across the country when a technological
>> advancement such as an airplane will take you to your destination in
>> hours
>> with no effort on your part.
>>
>> Those who know math well such as professors and opt to make calculations
>> using paper and pencil are probably doing so because they have long
>> become
>> aware of the human brain's computational weaknesses and simply solve
>> problems in this way to eliminate the possibility of error.
>>
>> The reason we as humans have seen an incredible jump in our technological
>> advancements is due to computers. If we didn't invent computing machines
>> we
>> would be stuck using slide rulers and taking all day to compute
>> relatively
>> simple calculations which would overall hinder technological
>> advancements.
>>
>> I can imagine making calculations in your head gets some "wows" from
>> others,
>> but it is not reliable if your goal is accuracy. One will have to weigh
>> the
>> pros and cons of learning and practicing mental math over the amount of
>> time
>> necessary to learn such a skill.
>>
>> If you want to see some amazing stuff, look up videos with Asians
>> competing
>> against one another using the abacus. These guys are multiplying and
>> dividing 6-digit numbers in seconds, which would not normally be possible
>> without such an instrument.
>>
>> -----Original Message-----
>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of John G
>> Heim via Blindmath
>> Sent: Monday, December 14, 2015 6:25 AM
>> To: Blind Math list for those interested in mathematics
>> Cc: John G Heim
>> Subject: Re: [Blindmath] alternative methods of learning college algebra
>>
>> I would hesitate to say that you absolutely have to learn braille math.
>> But I'd be even more hesitant to say you don't need it either and I would
>> put a different spin on doing everything in your head. Being able to do
>> math
>> in your head is an extremely valuable skill to have -- if you can develop
>> it. That's actually true for any math student. Personally, it amazes me
>> how
>> some really good mathematicians have to write everything down. It strikes
>>
>> me
>> as primitive. But I'm sure humans vary greatly on their ability to do
>> math
>> in their head and some people are going to have a greater need to write
>> things down than others. It strikes me as bad advice to tell someone to
>> forget about writing stuff down.
>>
>> I do like the advice someone gave to learn latex. A knowledge of latex is
>> considered so basic here at the Department of Mathematics at the
>> University
>> of Wisconsin that we don't even teach a mini-course in it any more.  We
>> don't teach the alphabet either. If you are going to major in math,
>> you're
>> expected to know latex.
>>
>>
>> On 12/14/2015 01:51 AM, Jeremy via Blindmath wrote:
>>> Post the faculty website listing you as "college mathematics professor
>>> at a community college." If this is not the case, I think it may not
>>> be legal for someone to walk around playing pretend in regards to
>>> professional academic credentials.
>>>
>>> Though you think you may have excelled at mathematics using your
>>> technique, it is probably very likely that an objective comparison of
>>> methods and outcomes may not be as generous to your self-assessment of
>>> your mathematic ability.
>>>
>>> If you have truly worked with as many individuals as you claim, it is
>>> likely you would know by now that people learn in very different ways,
>>> and not everyone will be as fluent with mathematics as another, so
>>> claiming no one needs braille and alike to complete math assignments
>>> is the type of comment coming from an amateur and not a professional.
>>> Surely you've heard of the normal distribution, if so, why would you
>>> dare
>> make such a comment?
>>> -----Original Message-----
>>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
>>> David Moore via Blindmath
>>> Sent: Sunday, December 13, 2015 10:36 PM
>>> To: Blind Math list for those interested in mathematics
>>> Cc: David Moore
>>> Subject: Re: [Blindmath] alternative methods of learning college
>>> algebra
>>>
>>> Hi Laura,
>>> I had sight until I was 15. By the way, my name is David Moore. After
>>> I lost my sight, I learned how to do all the math I had done up
>>> through high school algebra in my head the way that I had seen it with
>>> my eyes. You can learn how to concentrate so well, that you could be
>>> able to see the algebra in your head just how you would see it written
>>> and do all of the steps in your head and obtain the answer by seeing
>>> every step just like it is in front of your eyes. I Majored in math by
>>> using this method. If someone reads you a problem, you can learn how
>>> to keep every step straight in your head. If you need some braille to
>>> write down, just make up any code you want. No one else reads the
>>> Braille anyway, so as long as you know what it means, you can just
>>> make up your code. Please email me, Laura. Braille is not needed to do
>>> math and do not let these Braille crazy people tell you that. If I do
>>> write math down in Braille, I use some made up code, because I am the
>>> only one who reads Braille. I will share my experience with you and
>>> teach you tricks of doing all math in your head. Have a great one,
>>> can't wait to talk to you. I will help you get an A in that class. I
>>> have tutored sighted and blind alike just for fun. You will be fine
>>> and you can do it. I am a college mathematics professor at a community
>> college. I am also totally blind. You can do it, I am proof. Take care.
>>>
>>> -----Original Message-----
>>> From: Louis Maher via Blindmath
>>> Sent: Sunday, December 13, 2015 10:11 PM
>>> To: 'Blind Math list for those interested in mathematics'
>>> Cc: Louis Maher
>>> Subject: Re: [Blindmath] alternative methods of learning college
>>> algebra
>>>
>>> You must learn Braille and Nemeth Code which is the Braille
>>> mathematics code.
>>>
>>>
>>> Regards
>>> Louis Maher
>>> Phone 713-444-7838
>>> E-mail ljmaher at swbell.net
>>>
>>> -----Original Message-----
>>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
>>> Laura Etori via Blindmath
>>> Sent: Sunday, December 13, 2015 7:34 PM
>>> To: Blindmath at nfbnet.org
>>> Cc: Laura Etori <letori.etori6 at gmail.com>
>>> Subject: [Blindmath] alternative methods of learning college algebra
>>>
>>> greetings everyone
>>>
>>> I am a college student and i am not proficient in braille. that is
>>> because i lost my sight recently.
>>>
>>> for my core curricular courses i am expected to take college algebra
>>> and since i do not know math braille i would love to get suggestions
>>> from all of you on how i can be able to go through my course using
>> alternative methods.
>>> i am totally blind and eager to take up any suggestions.
>>>
>>> your input is highly appreciated and thanks a lot.
>>>
>>>
>>>
>>> --
>>> for it is Him who works in us, and works through us, and makes
>>> everything beautiful and marvelous in His time and splendour.
>>> Kind regards
>>> Laura Etori
>>>
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>
>
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