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

Mon Dec 14 22:00:26 UTC 2015

Hi,
I am the one who began talking about doing math in your head. People took 
off with this and got off track. Just like you said. There are advantages if 
you do not have to write everything down. The sine, cosine, and tangent of 
the angles like 30, 45, and 60 are so easy to understand if you can memorize 
the values for these. I want to make one thing straight. I am not talking 
about just memorizing values that you do not understand how to calculate 
with Math Type or LeTeX. It is just as important to understand how numbers 
work and to know how you obtained the answer than getting the answer itself. 
So many students believe their technology without even guessing what the 
answer should be approximately. What if you press the wrong button? What if 
you forget a decimal point? So many people punch in numbers into a 
calculator or computer program and believe without a doubt the answer that 
the technology gives. They cannot even approximate what the answer should be 
in their heads before punching the buttons. What really bothers me is that 
students cannot understand how an answer is obtained. They just believe 
their calculator. I tutor many people, and they get out the calculator to 
figure out something like 2/5 to get a decimal. This is so sad. Number 
theory is just as important as it always was. When you do math, it is much 
easier to work from left to right just like you read. You see, let us 
consider the number 527. This means: 5 groups of a hundred, 2 groups of 10, 
and one 7. You can think of numbers like this, because of our base 10 
system. You can easily add hundreds, then the tens, and then the ones. Now, 
for advanced math. Let us consider integrals. Integrals of many functions 
have to be memorized. for example, the integral of 1/(1+X2) dX = arcsine X. 
When I tutor people, they get stuck on a calculus problem, because that 
integral has to be memorized. It is so much faster and more efficient to do 
complex mathematics if you use all tools offered to you. Your head is just 
one tool, but it is an important tool, because it makes you so much more 
efficient. The next tool that is very important is screen readers. Next, MS 
office. Next, Math Type. Next, LaTeX. Next, a scanning software like infty 
reader. which will allow all math material to be scanned and OCR  can be 
done on the text just like regular documents. You see, every tool is 
important to be a successful mathematician. Using the technology as a crutch 
without understanding how the technology is getting the answer is so wrong, 
in my openion. Technology should be used as a way to solve very complex 
problems much faster instead of depending on the technology with out 
understanding how the technology is obtaining the answer. One should have 
some kind of idea what the answer should be by understanding the concepts so 
well, that they can approximate the answer. Again, to be a true 
mathematician, one should understand every step to how the answer is 
obtained as well as the answer itself. Engineers do not care how you get the 
answer, they just want the answer. This is the difference between applied 
math and math theory. I come from the place of loving mathematics for it's 
own sake as a beautiful art. If you just want an answer to plug into a 
formula, I guess that is what engineers care about. That is why I do not 
like to apply mathematics in a lab. I love math for it's own sake, and maybe 
that is why I am coming across like this. For me, understanding all of the 
concepts and understanding how you arrive at an answer is actually more 
important than the answer itself. The head is just one tool, but if you use 
the power of your brain along with the technology, I think that you have one 
beautiful picture. There has been talk about memory based on psychology. it 
is important to note that no human has used more than 15 to 25 percent of 
the power of their brain. We are truly and wonderfully created. The brain 
can do more than people think. However, I want to settle this once and for 
all. I am just saying that doing something in your head to approximate the 
answer is good to do before you press the buttons on the calculator. People 
I have tutored get out their calculator to find what 5 * 6 equals. I am not 
lying, I wish I was. Let us put all tools together including our minds. I 
hope this clears some ideas up. Take care all, and have a wonderful day.

-----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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