[Blindmath] [Blind math] Spatial Abilities

Fri Jun 6 01:31:14 UTC 2014

Here's what I think. Though blindness may not cause it, it does place a person at a greater risk for developing spatial disorientation. The first aspect of this is that sighted people learn spatial skills from their community, but they learn those skills visually, so blind people are excluded. Sighted people are so convinced that spatial concepts have to be visual that they refuse to find nonvisual ways to teach it. Another aspect is that sighted people don't think it's as important for blind people to get the opportunities they need to develop spatially. Things like participating in sports, traveling independently, and doing other things like cooking are great ways to develop your spatial orientation, they're all things that blind people can and should have the opportunity to do. However, people act out of ignorance and sink in the short-term. Counter to actual research, they say that blind people are more likely to get hurt then sighted people and a lot of other stupid things. So, I know this is harsh, but a lot of parents don't want to give their blind child as much of a chance to learn as their sighted children. I know that they may think of it in a different way, but essentially that's what's happening. For instance, let's say a blind child doesn't know the layout of the grocery store. A parent teaches the sighted children in the family the layout of the grocery store and has them go get groceries, but doesn't teach the blind child because they don't want to go through the hands-on approach required, and because they feel it will take more time and they are into much of a hurry. Even though they haven't thought of it this way, they have reinforced the concept that it's important for their sighted children to learn, but that the learning of their blind child is secondary. Children pick up on this and it further depletes their confidence. For instance, you might start feeling stupid that you have to go to therapy to learn how to tie your shoes and cut your food when everyone else can learn from their parents. Now, back to spatial orientation. As the blind child grows, they keep missing the developmental deadlines for the spatial skills they should have. Many orientation and mobility instructors don't seem to be trained in teaching people who have spatial disorientation. I know that in my case, when I started missing the informal deadlines, my orientation and mobility teachers started to perceive me more and more as an unteachable person. They believed that genetically I was not meant to travel and that the only thing I would be able to do is memorizer route and do it over and over until I could travel it. I started to believe them too, but when I got out of school and got more training, I met an instructor who believed that spatial orientation was more a product of exposure than genetics. Once I was able to get training from her and learn spatial concepts non-visually, my spatial disorientation started going away. At first, I had to process information cognitively, and still due to a certain extent, but I am starting to be able to into it more and more spatial information the more exposure I get to it. Also, having more body awareness has helped. I have developed strategies to know if I'm walking in a straight line or if I'm turning, so now the environment is much more consistent and much easier to make sense of. It doesn't seem like things move around all the time anymore. I have been talking about traveling, but it does relate to matth. I've noticed that the better I've gotten at traveling, the better I can process spatial information and math. It's true that the information is on a smaller scale, but the same skills are involved. Now, let's talk about the thing with the three-dimensional objects. I don't think you can say that a person has low spatial ability if they can't interpret tactile representations of three-dimensional objects, especially if they're blind from birth. I believe that there is a conversion process where you would've had to have vision at one time, or had some vision currently for your brain to produce it. In other areas, we don't say that a person has little ability because a representation doesn't work for them. For instance, when writing an essay, one student might outline it using a flowchart, one student might make a linear outline, and one student might not make an outline it all. When looking at the ability of these three students, we don't evaluate the way they chose to represent their work at the beginning. We evaluate the finished product. If someone is able to work well with the real world objects and has high spatial ability, you can't say that they have low spatial ability because the way you choose to represent the information doesn't work for them. That's what you need to remember. Your two dimensional representation of a box is in a box. It's a representation of a box that doesn't work for everybody. I believe that even if a person blind from birth could learn to interpret these representations, the interpretation process would be so distracting that it would be difficult to learn the concepts related to the objects. For instance, interpreting the shape of the box would be so distracting that you can't actually learn how to find its volume. It would make much more sense and be much more practical to use the three-dimensional box. Just because the blind person doesn't interpret information the way a sighted  person things they should doesn't necessarily mean they have low spatial ability, so it's important to make that distinction when doing research.

> On Jun 5, 2014, at 7:47 PM, Sean Tikkun via Blindmath <blindmath at nfbnet.org> wrote:
> 
> Hello All
> 
> My hope is to delve into this, but the cognitive psychological groundwork is a little thin at this point.  I'm starting with two-step algebra problems as a first foray into cognitive challenge of tasks.  Ideally after my dissertation I will be able to replicate the study for this sort of spatial situations moving both up and down the math curricular spectrum.
> 
> The dilemma is that many of the psychological studies center on media interference and not differences in perception without sight.  If people find related research please post it here as I'm sure I'm not the only one interested.
> 
> Sean
> 
> 
>> On Jun 5, 2014, at 6:10 PM, Susan Osterhaus via Blindmath <blindmath at nfbnet.org> wrote:
>> 
>> No, she has been a braille reader all her life, but she is not totally
>> blind. She never had enough vision to read print though. It is my
>> understanding that Abe Nemeth was blind from birth, and I think he had no
>> difficulty with this type of spatial ability. He could even write print on
>> a blackboard and easily teach sighted students. This is just a fascinating
>> topic, and we really need to get a doctoral student to latch onto this.
>> 
>> Susan
>> 
>> -----Original Message-----
>> From: Amanda Lacy [mailto:lacy925 at gmail.com]
>> Sent: Thursday, June 05, 2014 5:05 PM
>> To: Susan Osterhaus; Blind Math list for those interested in mathematics
>> Subject: Re: [Blindmath] [Blind math] Spatial Abilities
>> 
>> Ms. O, Your blind friend who can interpret drawings of 3D objects, is she
>> blind from birth? My hypothesis is that visual experience is required to
>> interpret most of these kinds of drawings since the only blind people I've
>> ever heard of who could do this once had vision.
>> 
>> Amanda Lacy
>> 
>> 
>>> On 6/5/2014 4:54 PM, Susan Osterhaus via Blindmath wrote:
>>> I am one of those sighted individuals who has always had difficulty
>>> transforming a 2-dimensional drawing of a 3-dimensional object into
>>> the 3-D object in my mind. I prefer making the 3-D object. I have a
>>> blind friend who has no difficulties conceptualizing a 3-dimensional
>>> object from a tactile 2-dimensional drawing. Her husband, who is
>>> blind, is more like me - has difficulties. They have two sighted
>>> children. One can do it easily; one has great difficulty.
>>> 
>>> When I was doing my student teaching in mathematics to sighted
>>> students years ago, I taught geometry, and I was affectionately known
>>> as the "tinker toy lady" because I always created the 3-D objects
>>> which I thought were necessary for understanding the day's concept.
>>> The majority of my students actually thought this was pretty cool and
>>> paid attention!! Of course, now I have a much better collection of 3-D
>>> math toys that I use to teach all students - blind or sighted. I still
>>> get sighted observers who exclaim that they finally understood a
>>> particular concept when they watched me use my various manipulatives.
>>> They demand to know why their sighted math teachers didn't "do it" that
>> way.
>>> 
>>> A possibly related story: When asked, most people will say that they
>>> are better at either algebra or geometry but not both. The "geometry"
>>> lovers are usually quite good with this whole spatial thing, while the
>> "algebra"
>>> lovers are not. Of course I am the algebra-type, and I always wondered
>>> why they decided I should teach geometry for my student teaching. It
>>> didn't stop there. I have had to teach geometry (as well as all the
>>> other math
>>> subjects) all my life, and believe it or not, most people seem to
>>> think I'm very good at it. I also have more geometry math toys than
>>> anything else. It just shows what the right accommodations can do for
>> someone.
>>> 
>>> Bottom Line: I think someone needs to do some research to find out
>>> about this "spatial" thing. Anyone looking for a good dissertation
>> topic?
>>> 
>>> Best wishes,
>>> Susan O
>>> 
>>> Susan A Osterhaus
>>> Statewide Mathematics Consultant
>>> Outreach Programs
>>> Texas School for the Blind
>>>  And Visually Impaired
>>> 1100 West 45th Street
>>> Austin, TX 78756
>>> Email: susanosterhaus at tsbvi.edu
>>> Phone: 512-206-9305
>>> Website: www.tsbvi.edu/math
>>> Distance Learning: http://distance.tsbvi.edu/osterhaus_math_intro.html
>>> Media Library: http://library.tsbvi.edu/
>>> 
>>> 
>>> 
>>> -----Original Message-----
>>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
>>> Mike Jolls via Blindmath
>>> Sent: Thursday, June 05, 2014 1:39 PM
>>> To: blindmath at nfbnet.org
>>> Subject: Re: [Blindmath] [Blind math] Spatial Abilities
>>> 
>>> I find your comment very interesting ... that some blind people (and
>>> perhaps some not) can pack a pack a paper bag without having vision.
>>> I ought to show this email to my daughter in-law to see what she has
>>> to say ... who once told me when I told her I was interested in
>>> developing a computer pgoram that would allow blind people to
>>> interactively work with math equations in Braille ...
>>> "how could a blind person do math when they can't see?".    I don't need
>>> to say that when she made that comment, I got just slightly irritated.
>>> I've seen this bias many times in my lifetime.  They need to be shown
>>> that we just have difficult seeing ... we're not stupid.
>>> 
>>>> To: arielle71 at gmail.com; blindmath at nfbnet.org
>>>> Date: Fri, 30 May 2014 08:03:29 -0400
>>>> Subject: Re: [Blindmath] [Blind math] Spatial Abilities
>>>> From: blindmath at nfbnet.org
>>>> 
>>>> I am not sure this is a blind thing.  When I was sighted back in the
>>>> day we used paper bags at the grocery.  I used to train baggers.  I
>>>> would say it was almost a 50 50 shot that the people I trained could
>>>> look at what was on the counter and be able to quickly and easily
>>>> pack groceries in the least amount of bags, taking into account
>>>> shape, and type of groceries.  TI have found over the years that the
>>>> same people that couldn't pack a paper bag correctly also couldn't
>>>> look at a pile of luggage and figure out how to fit it in the trunk
>>>> without trying 15 times.  Now that I am blind and have been for the
>>>> last 20 years I haven't found it any harder.  I do have my previous
>>>> sighted experience and training but I have met as many blind people
>>>> that understand special areas as well as me.  As I have met that are
>>>> totally unable to walk through a building that they have worked in
>>>> for over 2 years.  So in my experience and just in my humble opinion
>>>> I think it has more to do with how your experiences growing up
>>>> allowed you to learn and maybe
>>> how your brain is genetically wired than anything to do with site.
>>>> It would be interesting to do a study with the old square paper bags
>>>> and a table full of stuff.  To see how different blind people could
>>>> look over a table of objects and be able to pack them verses a  group
>>>> of
>>> sighted folks.
>>>> 
>>>> Ken
>>>> 
>>>> -----Original Message-----
>>>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
>>>> Arielle Silverman via Blindmath
>>>> Sent: Wednesday, May 28, 2014 7:48 PM
>>>> To: sabra1023; Blind Math list for those interested in mathematics
>>>> Subject: Re: [Blindmath] Spatial Abilities
>>>> 
>>>> This is a really interesting question. I have been blind since birth
>>>> and have always had excellent verbal and quantitative skills, and
>>>> reasonable grasp of cardinal directions, but my spatial sense is very
>>>> poor. For example, when moving furniture or packing a moving truck, I
>>>> have no idea how things should be arranged. I feel I am at a
>>>> disadvantage because I can only touch or explore a large space a
>>>> little at a time, whereas a sighted person can see the whole thing at
>>>> once. This is a bit of a different problem from the 2 vs.
>>>> 3-dimensional issue (although I also have trouble decoding raised
>>>> diagrams especially those with complex shapes). I can mental-map a
>>>> space easily if it's a standard square or rectangular block, but have
>>>> a lot of trouble mental-mapping a room or building that's irregularly
>>>> shaped in any way. I have met several blind people who don't have the
>>>> same degree of difficulty as I do, however, so I am hesitant to blame
>>>> it wholly on blindness. That's why I am curious to hear what other
>>>> congenitally blind people experience. I do think growing up I was
>>>> never expected to engage spatially with the world and I wasn't as
>>>> tactually inquisitive as some blind kids, so my spatial development
>>>> might have been hampered. For me there's little connection between
>>>> mathematical relationships between numbers and their graphical
>>>> analogs, which is why my math ability doesn't suffer from my spatial
>>>> impairment.
>>>> 
>>>> Arielle
>>>> 
>>>>> On 5/28/14, sabra1023 via Blindmath <blindmath at nfbnet.org> wrote:
>>>>> Just because someone uses three-dimensional objects doesn't mean
>>>>> that
>>>> they
>>>>> have a low spatial intelligence necessarily. I believe that for
>>>>> spatial
>>>> IQ
>>>>> tests for the blind, it is best practice to use three-dimensional
>>>> objects.
>>>>>> On May 28, 2014, at 1:13 PM, Amanda Lacy <lacy925 at gmail.com> wrote:
>>>>>> 
>>>>>> I think it has to do with the fact that those of us who are blind
>>>>>> from birth don't experience the world as being flat. Sight involves
>>>>>> the projection of light onto a flat retina, so for sighted people
>>>>>> it seems natural to go from there to representing real things on
>>>>>> flat
>>> surfaces.
>>>>>> Flat pictures are everywhere for them since birth, but I can't
>>>>>> think of one single example of anything in the real world that's
>>>>>> flat. Our hands are designed to grasp and rotate and examine real
>>>>>> objects, and then we come to school and have to learn what seems
>>>>>> like a new language. So when people say that my hands are like
>>>>>> their eyes, I have to disagree. I'm speculating as someone who has
>>>>>> never been sighted, so any of you can
>>>> feel
>>>>>> free to correct me with more accurate information.
>>>>>> 
>>>>>> Amanda
>>>>>>> On 5/28/2014 12:46 PM, sabra1023 via Blindmath wrote:
>>>>>>> I wonder if being blind from birth has to do with it. If I'm
>>>> remembering
>>>>>>> how to get somewhere, I just imagine myself walking there. A map
>>>> doesn't
>>>>>>> help. I can imagine three-dimensional things very well and make
>>>>>>> them
>>>> out
>>>>>>> of clay. Also, I can remember a two dimensional shape like a
>>>>>>> circle or square. However, it's difficult for me to imagine and
>>>>>>> manipulate graphs in my head.
>>>>>>> 
>>>>>>>> On May 28, 2014, at 12:07 PM, Susan Jolly via Blindmath
>>>>>>>> <blindmath at nfbnet.org> wrote:
>>>>>>>> 
>>>>>>>> There have been a large number of conferences about and studies
>>>>>>>> of the use of tactile maps and diagrams by blind persons.  This
>>>>>>>> has been
>>>> going
>>>>>>>> on for more than 40 years.  What I got out of reading many of the
>>>>>>>> studies is that different people are different.
>>>>>>>> 
>>>>>>>> There is, however, a lot of evidence that men have better spatial
>>>>>>>> abilities than women.  I know this is controversial but I think
>>>>>>>> there
>>>> is
>>>>>>>> some truth to it.  I can see the sun come up east of my house and
>>>>>>>> go down west of my house.  Nonetheless, no matter how hard I try,
>>>>>>>> I
>>>> cannot
>>>>>>>> imagine that my son who lives 1000 miles west of me lives in the
>>>>>>>> direction where the sun goes down.  I know that it is true
>>>>>>>> logically
>>>> but
>>>>>>>> when I think about him, he's always somewhere off to the east in
>>>>>>>> my mind.
>>>>>>>> 
>>>>>>>> As for graphs, it took me years to understand why it is not
>>>>>>>> necessary when laying out a two-dimensional graph to use the same
>>>>>>>> spacing for
>>>> both
>>>>>>>> axes.  I mention this here for two reasons.  First, it is an
>>>>>>>> example
>>>> of
>>>>>>>> different people being different.  Second, it points out that the
>>>> shape
>>>>>>>> of a graph is to some extent arbitrary.  Of course, the general
>>>>>>>> shape
>>>> is
>>>>>>>> independent of the exact choice of layout. (I'm talking about
>>>>>>>> linear axes; you can dramatically change the shape if you use
>>>>>>>> non-linear axes such as logarithmic ones.)
>>>>>>>> 
>>>>>>>> SusanJ
>>>>>>>> 
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