[Blindmath] Looking for a particular type of person to ask questions

Sat Feb 7 17:05:09 UTC 2015

I’m no expert, but….

	Sabra, I see your frustrations and I think a piece of it is derived from the idea that Mathematical information is knowledge. I refute this and teach math as a skill personally. It must be practiced, and practiced well. Poor or wandering practice does not develop the skill. For myself in my undergraduate studies I lost my ability to keep up in mathematics courses around the high 300’s and all 400’s. I could follow proofs in class and take meticulous notes, but not do them myself and hardly make sense of what my notes taught me. I was looking for an algorithm and had not realized that I was being taught a method of problem solving. 
	The greatest challenge in math using braille is the presentation of material. Followed quickly by the time to perceive material. Equations used in class must be acquired before the day of the lecture, so you can read them, and potentially rewrite in a way that works for you. It is not valuable to do this on the fly in class, and takes some of your attention away from the lecture. For a sighted student this same ‘distraction’ occurs, but the amount of time to align and copy an equation is far less and they have the added benefit of seeing steps unfold even as they are looking one line away. Their eyes catch this and make it easier to understand when they get there. 
	The challenge in math is that the language has been designed and refined for efficiency in visual presentation and organization. Although functional when read tactually, it does lose some of its efficiency and support for learning.

Sean

> On Feb 6, 2015, at 11:52 AM, Amanda Lacy via Blindmath <blindmath at nfbnet.org> wrote:
> 
> Hi Tim,
> 
> I just wanted to add that I found your last message interesting for
> two reasons: First, I've always found programming easy to understand
> while mathematical proofs often remind me of extremely long run-on
> sentences. If my fingers lose their place in that equation that spans
> 7 lines, I'm finished. Second, this is the first semester where I'm
> required to program with a partner, and I'm struggling to wrap my mind
> around how we will communicate. I think your comments were useful.
> 
> Amanda
> 
> On 2/6/15, Tim in 't Veld via Blindmath <blindmath at nfbnet.org <mailto:blindmath at nfbnet.org>> wrote:
>> Hi Sabra,
>> Yes I agree, tutoring works much better for me than traditional
>> lectures. That's also why an interactive lecturing style (where I answer
>> a lecturer's questions and then we effectively engage in a discussion)
>> works that well for me I think.
>> 
>> If someone tells you "the airplane makes a triangle", he forces you to
>> visualize that triangle (unless he gives you a tactile image). I can
>> visualize a triangle to some extent, but just explaining the visuals
>> probably won't make a blind student understand the issue better. It's a
>> whole different way of thinking about a problem, I might understand the
>> problem if the person explaining to me was taking the effort to really
>> put what is happening in words rather than using the graphical metaphor.
>> So like "the plane's lift counteracts the gravity and this keeps it in
>> the air" rather than "there's an arrow under the plane and an arrow
>> above the plane; the arrows have equal length and direction" (that
>> latter statement is already more verbal than the way many sighted
>> physicians would view this issue).
>> 
>> You seem to be saying you can grasp programming more easily than
>> mathematics. That also applies to me. I think that's because programming
>> can be viewed as a "conceptual linguistic" exercise where as mathematics
>> is a symbolic exercise which requires me to have at least a two
>> dimensional overview of the text. A programming language is linear and
>> quite abstract by definition and doesn't involve 'strange symbols'. That
>> goes much better with a linear working style than mathematical formulae.
>> If I translate a mathematical formula into an imperative programming
>> language, I'm essentially describing the problem in words or
>> instructions if you will. The program tells me exactly what I need to do
>> in a textual manner.
>> 
>> A good chess player has a mental image of his board and can essentially
>> play blind. The only successful blind mathematicians are those whose
>> skills are so good that they can work out problems in their head and
>> have the motivation to put inordinate amounts of time into grasping a
>> formula. I'm quite an effective programmer because I have a mental
>> overview of my program. When something goes wrong, I can quickly recall
>> the bits of code which could cause the issue and do a focused
>> investigation. In general I quickly link issues to one another, an
>> essential skill when debugging code (but maybe also keeping me from
>> having the necessary focus to solve a complicated equation).
>> 
>> In (IT) consultancy assignments, there's a tendency to draw fancy
>> diagrams and say "it works like that". How it actually works remains
>> unspoken. The assumption that the other party understands the whole
>> situation based on the diagram might be flawed. When I'm involved in an
>> assignment, I force people to put matters into words by asking questions
>> until I have a high level mental overview of the matter under
>> investigation. During this "forced interview" (which does take more time
>> than sketching a diagram) I can often infer things about the world that
>> would probably not pop up if we just sketch a diagram. That has the
>> advantage of bringing up unspoken issues and assumptions  which would
>> remain unspoken if the problem is discussed visually, this can result in
>> a more effective consultancy process and a better outcome.
>> 
>> Tim
>> On 2/6/2015 4:46 AM, Sabra Ewing wrote:
>>> Another reason I was curious about this is because in my last programming
>>> class, I learned a lot from being in the class. Of course, I still had to
>>> learn things at home, but I got a lot out of being in class as well. I
>>> knew what things I should study in more detail once I was at home.and the
>>> programming class I am currently in no, I don't get anything out of being
>>> there just like for math.no that situation is a little bit different,
>>> because for some reason I am able to learn program by studying myself so I
>>> can still keep up and do my labs and things even know I don't get anything
>>> out of the lectures.The reasons behind things have always interested me,
>>> so I wanted to know why I would've gotten so much out of my last class,
>>> but not as much out of this class.if I could figure out the difference, I
>>> could figure out what helps me learn things the best. Even if I still
>>> can't ever get things out of the class,this knowledge might help me in
>>> tutoring or it might help me find books and materials that I could more
>>> easily understand. I could know what to look for to know which things
>>> would work for me better.if I could find a patternconcerning what
>>> information I am missing for each one of my math classes that makes it
>>> hard for me to learn the material in class, I could know better what types
>>> of questions to ask.also, if I knew what the exact problem was, I could be
>>> on the lookout and know exactly when it starts to happen so it doesn't
>>> feel like I just sit down and then I am lost somehow. Maybe even if you
>>> had a bad presenter, you could ask questions that would force that person
>>> to give you the information that you need. I'm not trying to suggest that
>>> anyone is intentionally withholding information, but even if they are
>>> presenting things unconsciously in a way that makes it difficult to get
>>> the information, you could ask something so that they would have to give
>>> the information more clearly. HoweverI don't know how this would be
>>> done.for example, I tried to ask a question in my class about a homework
>>> problem that involved a plane flying in the air. Now it understand it
>>> because I went to tutoring, but back then, all I knew was that this plane
>>> flying was supposed to make a triangle, but I didn't know how.I asked my
>>> professor how it was supposed to make a triangle and I got an answer to my
>>> question, but I still didn't know how it makes a triangle.
>>> 
>>> Sabra Ewing
>>> 
>>>> On Feb 5, 2015, at 9:34 PM, Sabra Ewing <sabra1023 at gmail.com> wrote:
>>>> 
>>>> So it might not be possible for me to get very much out of a lecture
>>>> then.i'm not actually looking for details. I was just looking for basic
>>>> big picture outlines of topics. But I feel like when I go to class the
>>>> other students get those things and I don't.I probably can't ask my
>>>> professor to go slower.maybe it might help if we actually did work on
>>>> problems in class. I had a teacher last semester where for part of the
>>>> class we worked on problems in groups to see if he understood it and that
>>>> was helping until he kept pairing me with someone who couldn't speak any
>>>> English.well, she could speak some English, but not well enough for me to
>>>> understand.but most professors don't do that. They are convinced that the
>>>> traditional lecture style is the most helpful and they are going to stay
>>>> with that.I do wish I could get more out of my class while I'm actually
>>>> in class, but I guess that won't be possible unless the structure of the
>>>> class inherently changes, and that won't happen.I am glad that I have
>>>> tutoring to help me learn the concepts so I can still take the course
>>>> without getting things from the class, but I do think it's sad.honestly,
>>>> I get so little out of my class that if I missed it, it wouldn't really
>>>> affect me much, but if I missed tutoring, it would set me back a lot.
>>>> 
>>>> Sabra Ewing
>>>> 
>>>>> On Feb 5, 2015, at 9:19 PM, Tim in 't Veld <tim at dvlop.nl> wrote:
>>>>> 
>>>>> Hi Sabra,
>>>>> Might you not getting anything out of lectures be due to (over)reliance
>>>>> on slides / the blackboard?
>>>>> Many presenters, especially on mathematical or technical topics, will
>>>>> say things like "now, we have this formula here... then we subtract that
>>>>> variable to get that formula there ..."
>>>>> A bad presentation style. Not just because you exclude blind
>>>>> participants, but mainly because you go over the material way too fast
>>>>> and are bound to  lose your sighted audience as well (if they fall
>>>>> asleep they will close their eyes, then we at least have a level playing
>>>>> field in the lecture room).
>>>>> But that sighted audience could read your slides and get a grasp of what
>>>>> you're saying no matter how bad your presentation style or mastery of
>>>>> English actually is.
>>>>> 
>>>>> Good presenters don't need slides or notes. They interact with their
>>>>> audience. Just as Jonathan (one of the best presenters I know)
>>>>> commented. A presentation is for the high level overview, it is not
>>>>> suited to fully cover all the detail which is in the lecture notes /
>>>>> book.
>>>>> 
>>>>> In mathematics lectures you do need a blackboard sometimes, so it is
>>>>> incredibly hard for blind students or professors to be effective in
>>>>> mathematical group lectures. Still having a good presenter does make a
>>>>> huge difference.
>>>>> 
>>>>> I'm not yet a very experienced presenter, but when I present I
>>>>> preferably present slideless (I sometimes make slides because people
>>>>> demand that, but never more than 4 - 5 short phrases per slide and never
>>>>> more than one slide per 2 - 3 minutes). I know my material so well that
>>>>> I can present it from memory (in a more or less improvised style based
>>>>> on a rough planning I have for the presentation). If I don't know the
>>>>> topic I'm presenting inside out, I have no right to bother people with
>>>>> my words.
>>>>> 
>>>>> Another important point is to avoid monologues. Always open your
>>>>> presentation with a question, and ask the audience for input at several
>>>>> points during the presentation (just saying 'you can ask questions at
>>>>> any time' will not do). I guess many people hate this, I usually have
>>>>> the front row of any lecture room to myself. For some reason most
>>>>> students prefer withdrawing to the backmost row and focusing on their
>>>>> smartphone in devote silence. Regrettably, some professors (and most
>>>>> student presenters) accommodate them by rushing through 2 overfilled
>>>>> slides per minute in broken English. Fortunately most professors in my
>>>>> master program are good lecturers, and being part of the very small
>>>>> group which actually responds when they involve their audience really
>>>>> helps me grasp the material.
>>>>> 
>>>>> Tim
>>>>> 
>>>>>> On 2/6/2015 1:55 AM, Sabra Ewing via Blindmath wrote:
>>>>>> I'm not expecting a 100% grass. I'm expecting a good enough grass
>>>>>> though to get started learning outside of class. Sometimes I leave
>>>>>> class with a 0% grasp on the material. Somehow, I was paying attention,
>>>>>> but I didn't learn anything.this even happens when I ask questions.
>>>>>> Even though I remember the answers to my questions,and I remember what
>>>>>> went on in the class, I can't do the problems. I don't know why this is
>>>>>> though. I can literally played back the entire class in my head.I even
>>>>>> tried recording a class before and listening again, but it didn't help
>>>>>> because I already remembered everything that happened anyways. I didn't
>>>>>> get anything off of the recording that I didn't remember.so if I pay
>>>>>> attention, remember everything that happens, and ask questions, why
>>>>>> can't I do the problems until I go to tutoring?it would be good if in
>>>>>> tutoring I could ask questions about what I already learned instead of
>>>>>> having to learn everything from scratch.
>>>>>> 
>>>>>> Sabra Ewing
>>>>>> 
>>>>>>> On Feb 5, 2015, at 6:45 PM, Sean Whalen <nabs.president at gmail.com>
>>>>>>> wrote:
>>>>>>> 
>>>>>>> In my experience, and I think this is broadly true, much of the
>>>>>>> learning of
>>>>>>> these concepts comes with practice and discussion outside of class. I
>>>>>>> view
>>>>>>> the class as a first pass at the information, but I don't think most
>>>>>>> sighted
>>>>>>> students are walking out of the classroom with a 100% grasp on the
>>>>>>> material.
>>>>>>> In various economics and statistics classes that I have taken, when
>>>>>>> the
>>>>>>> professor has done well to read the board and describe key graphical
>>>>>>> concepts, I have left the room understanding the material better than
>>>>>>> many
>>>>>>> of the other students in the class. I haven't used tutors, but sitting
>>>>>>> down
>>>>>>> with classmates to work through problem sets has been when I really
>>>>>>> felt
>>>>>>> that I was gaining a firm handle on the content.
>>>>>>> 
>>>>>>> Sean
>>>>>>> 
>>>>>>> -----Original Message-----
>>>>>>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
>>>>>>> Sabra
>>>>>>> Ewing via Blindmath
>>>>>>> Sent: Thursday, February 05, 2015 7:40 PM
>>>>>>> To: Blind Math list for those interested in mathematics
>>>>>>> Subject: Re: [Blindmath] Looking for a particular type of person to
>>>>>>> ask
>>>>>>> questions
>>>>>>> 
>>>>>>> When I say benefit fully, I mean you as a blind student got at least
>>>>>>> what
>>>>>>> one average cited student would get out of the class. If you were in
>>>>>>> a
>>>>>>> higher level math course, for example algebra two and beyond or
>>>>>>> college
>>>>>>> algebra and beyond, with other blind students,I would also be curious
>>>>>>> to
>>>>>>> know what the format of those classes are and how they work. What do
>>>>>>> they do
>>>>>>> instead of just making everybody look at a board because they can't.or
>>>>>>> if
>>>>>>> you were a teacher and you would be expected to teach a higher level
>>>>>>> math
>>>>>>> course two blind students, how would you do it or how did you do it in
>>>>>>> the
>>>>>>> past?I am curious because when I work one-on-one with a tutor, I can
>>>>>>> learn a
>>>>>>> lot, but in the class, I can't, and I really want to learn more from
>>>>>>> being
>>>>>>> in a classroom setting.I have had teachers verbalize what is on the
>>>>>>> board
>>>>>>> and give me problems and graphs to look at in class, but it hasn't
>>>>>>> helped
>>>>>>> and I don't know why.I know it is not a problem with my learning
>>>>>>> because I
>>>>>>> can learn it if someone teaches it to me outside of class.I want to
>>>>>>> actually
>>>>>>> learn from being inside my classroom instead of wishing it would be
>>>>>>> over and
>>>>>>> just learning everything outside of class at tutoring. I know this is
>>>>>>> possible, but I don't know what it would take for it to happen. So I
>>>>>>> have to
>>>>>>> figure out what it would take, and then how that could work within
>>>>>>> the
>>>>>>> confines of the educational system that my college has.
>>>>>>> 
>>>>>>> Sabra Ewing
>>>>>>> 
>>>>>>>> On Feb 5, 2015, at 5:26 PM, Sabra Ewing <sabra1023 at gmail.com> wrote:
>>>>>>>> 
>>>>>>>> I am looking for someone who was successful at learning higher level
>>>>>>>> math
>>>>>>> courses in a high school or college settingwith in the confines of
>>>>>>> the
>>>>>>> class. If you got tutoring outside of class, that is fine, but I am
>>>>>>> looking
>>>>>>> for someone who actually went to a math class and benefited fully from
>>>>>>> it
>>>>>>> rather than solely relying on outside help.if you taught a blind
>>>>>>> student who
>>>>>>> you felt benefited fully from your class, I am interested in hearing
>>>>>>> from
>>>>>>> you as well.I want to know what happened inside the class to make you
>>>>>>> benefit from it. What strategies did you use as the teacher for the
>>>>>>> teacher
>>>>>>> use that you found effective as the student?did the structure of the
>>>>>>> class
>>>>>>> change to be more interactive for all of the students? If so, how? Is
>>>>>>> it
>>>>>>> possible for a blind student to fully benefit from a math class the
>>>>>>> way
>>>>>>> decided student would without changing the inherent structure of the
>>>>>>> way the
>>>>>>> school teaches?let's assume a traditional lecture teaching style
>>>>>>> here.also,
>>>>>>> what is it about a math class that makes it hard for you to get things
>>>>>>> from
>>>>>>> it?apart from verbalizing things on the boardis there anything you ask
>>>>>>> a
>>>>>>> teacher to do when you weren't getting something out of a class that
>>>>>>> was
>>>>>>> successful?also, could you please provide specific concrete examples
>>>>>>> rather
>>>>>>> then abstract statements? Thank you.
>>>>>>>> Sabra Ewing
>>>>>>> _______________________________________________
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>>>>> 
>> 
>> 
>> 
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