Blind and Visually Impaired Community
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3-D Graphing help (self.Blind)
submitted by HeftyCryptographer21
I am a blind grade 12 student, and I was wondering if any of you had any suggestions for 3d graphing? I can get images made tactile (IDK what it is called, but on the special paper, that puffs up the lines so you can feel them). I can't get a picture in my head of what the graph should look like. I do have some vision, so if no one knows how to make 3D graphs make sense tactually, does anyone have any thoughts about how to make them very easy to see, with large print? I am Deaf to, so audio wouldn't work for me.
thanks for any suggestions.
thanks for any suggestions.
TheBlindCreative 3 points 2y ago
Hi. I am assuming that you are using thermoform images to view graphs. What part of the tactile graph is hard to interpret? Is the graph too small leaving the grid, marked points, and lines squished together? If yes, you need to ask the person producing the image to enlarge it before creating the tactile image. Are you a visual learner transitioning to tactile learning tools? If yes, it can take time to train your brain to learn using tactile means. Similar to my previous advice, ask the person making the tactile graphs to enlarge it before printing it in order to have visual and tactile input. Let me know if you have any questions.
HeftyCryptographer21 [OP] 2 points 2y ago
the pictures are already enlarged, but I still struggle to understand what is going on. The 2D graphs are fine, but when that third axis comes into play, it really throws me for a loop. Now that I am typing this out, practice seems like it might be useful. I was kind of hoping for a "magic bullet" that could solve all of my problems, but it seems like that won't be happening.
Thanks a lot for your response.
Thanks a lot for your response.
TheBlindCreative 4 points 2y ago
When you mentioned 3D graphs, I thought that you were talking about tactile graphs. I strongly disliked graphs with a 3rd axis. It honestly comes down to practice. This concept is rough sighted and blind alike. If you are having issues with distinguishing between the 2D lines from the 3rd axis, ask the person making the graphs to make the 3rd line using a different appearance like a dashed line. As far as envisioning it, hold a ruler at the (0, 0) point as if it were another axis to give yourself a more tangible way to see the 3rd axis. This will allow you to roughly determine where that point will land. While you might feel a little odd at first, make a fist and place it approximately where that point would land using your ruler as the 3rd axis guide.
HeftyCryptographer21 [OP] 1 points 2y ago
Sorry, I should have clarified. I know a lot of sighted people in class were struggling to interpret the graphs anyway, so I know it isn't just me.
wheresmyglasses12 2 points 2y ago
I use large print and I have to break the parts of the graphs into 2D portions (set one of the axes to 0 and examine how the graph looks on the other two axes). I had to take the class with 3D graphs twice because I needed a professor that took the class more slowly and explained less theory, because that was where I would get the most confused.
texanpanda 2 points 2y ago
I’d love to try to help brainstorm. Is this for a math class? Just making sure I’m on the same page as you as far as what kind of graphics you need. What size font do you prefer? The graphics you’re getting now, do you know if they’re Thermoform or PIAF? Thermoform is a plastic paper and PIAF has raised parts in black ink. (Not trying to be condescending if you know both of these terms. Just explaining in case you don’t.) It sounds like PIAF would be a great option. I’ve created tactile graphics for a student who had needs similar to yours, it sounds like. I’d love to offer my help as much as I can to either of you. If your TVI wants to reach out, I’d love to help her brainstorm or give her ideas of what I’ve done before.
TheBlindCreative 4 points 2y ago
To add extra context provided by OP in response to my comment and other comments, OP is using 3D graphs featuring 3 axises. In other words, there is an x, y, and z. It sounds like OP is in a higher level math class also.
HeftyCryptographer21 [OP] 1 points 2y ago
It seems like the graphics I get are PIAF, from your description. I have a good understanding of how to read normal, 2D tactile graphs, but I am just really struggling with the third z axis.
texanpanda 2 points 2y ago
Okay, I understand now! I was never smart enough to take a math class so difficult, so I did some googling. I can definitely understand how these graphics are hard to understand. I may have the beginning of an idea. Do you think you’d need a 3D item each time, or do you think you might just need it once to understand the concept? Or are you unsure?
Rethunker 1 points 2y ago
u/texanpanda, if you're thinking of using a 3D printer to create a representation of the data, then I'd say that's a fine idea. I'm not trying to answer in u/HeftyCryptographer21's stead, but I'll offer a few ideas related to more general math education using 3D objects.
A 3D printed object would be good in that you could have multiple copies for many students to study. Preferably, the 3D printed object would represent some instance of math applied to an important problem in some other subject the student is studying, such as physics. In a number of subjects there is one key concept that all students must learn, and in many cases that key concept is represented by an inaccessible printed graphic. If many students with visual impairments could have some standardized tactile 3D object representing the concept, then they can develop a common understanding, have a reference to understanding future problems for which there may not be a 3D model, and so on.
In addition there's a need to build up models from scratch. That's where building kits like Legos, Zometool, Technix, and others are useful because they can be taken apart and reassembled.
A 3D printed object would be good in that you could have multiple copies for many students to study. Preferably, the 3D printed object would represent some instance of math applied to an important problem in some other subject the student is studying, such as physics. In a number of subjects there is one key concept that all students must learn, and in many cases that key concept is represented by an inaccessible printed graphic. If many students with visual impairments could have some standardized tactile 3D object representing the concept, then they can develop a common understanding, have a reference to understanding future problems for which there may not be a 3D model, and so on.
In addition there's a need to build up models from scratch. That's where building kits like Legos, Zometool, Technix, and others are useful because they can be taken apart and reassembled.
HeftyCryptographer21 [OP] 1 points 2y ago
Each one would need to be 3D, as each one is a little bit different, and I need the information that each graph has.
niamhweking 2 points 2y ago
Do you have a visiting teacher for the blind? They should have experience in this. There is a software called www.highcharts.com created specifically for blind users. My daughters school books all come in large print, large enough for her to see. If you don't could your teacher, staff,friend have them enlarged from a4 to a4 paper or something similar? Not sure if that helps you exactly
HeftyCryptographer21 [OP] 2 points 2y ago
I do have a vision teacher, but she doesn't have much experience with higher level math and graphing.
As for the large print, I don't really have enough vision to read standard large print textbooks, which are normally about 16-20 font. Even if they could, I would still have the same problem of only being able to see a small part of the graph at a time. Thanks for your response though, I really appreciate it, and I will check out that software you mentioned.
As for the large print, I don't really have enough vision to read standard large print textbooks, which are normally about 16-20 font. Even if they could, I would still have the same problem of only being able to see a small part of the graph at a time. Thanks for your response though, I really appreciate it, and I will check out that software you mentioned.
Rethunker 1 points 2y ago
u/HeftyCryptographer21, I'm reading this reply of yours after I posted my response. Being able to see only a small part of the graph at a time suggests a few things to me:
1. Each part of the graph must be highly distinct so that you can build up a mental model more easily.
2. A 3D tactile representation matching the graphic could be useful, especially in these early days.
3. Practice and repetition can be taken as a prompt to work on one data set after the other, but can also mean studying multiple representations of the same data. One representation can help you make sense of another representation in the same way that we learn that some visual cues are associated with certain tactile cues. Engaging more senses makes it easier to develop a deeper understanding.
This may be a weird analogy, but think of it this way: a great way to learn about poetry is to study one or two tough poems in depth. It's nice to put these in context of other poems, but studying one problem in depth helps to make it stick. These are poems you'll think back to often. You can understand new poems in the context of the ones you know inside and out.
Learning 3D geometry you'll be presented with textbook problems, but consider whether you could gather 3D data of interest to you. With textbook problems we're presented both with new math and unfamiliar data. Sometimes starting with familiar data is helpful.
1. Each part of the graph must be highly distinct so that you can build up a mental model more easily.
2. A 3D tactile representation matching the graphic could be useful, especially in these early days.
3. Practice and repetition can be taken as a prompt to work on one data set after the other, but can also mean studying multiple representations of the same data. One representation can help you make sense of another representation in the same way that we learn that some visual cues are associated with certain tactile cues. Engaging more senses makes it easier to develop a deeper understanding.
This may be a weird analogy, but think of it this way: a great way to learn about poetry is to study one or two tough poems in depth. It's nice to put these in context of other poems, but studying one problem in depth helps to make it stick. These are poems you'll think back to often. You can understand new poems in the context of the ones you know inside and out.
Learning 3D geometry you'll be presented with textbook problems, but consider whether you could gather 3D data of interest to you. With textbook problems we're presented both with new math and unfamiliar data. Sometimes starting with familiar data is helpful.
SirJektive 1 points 2y ago
Hi, seniour university student in math here. Unfortunately there's no one way that works well in general, because there are a lot of different geometric ideas that a 3d graph might be trying to communicate. If you like, feel free to message me about what particular graphs/questions you're having trouble with, and I can try to help you visualize them. It's a lot easier once you have a general idea of the different kinds of shapes you can get.
Rethunker 1 points 2y ago
Could you describe a particular math problem or set of 3D data you'd like represented?
I’ll address your specific question, but other info I provide may be helpful. As a student you have the right to learn mathematical concepts, and other representations could prove more useful to you and to other students. To my knowledge there are no national or international standards for creating accessible representations for 3D data. As an adjunct to my work in assistive technology I'm hoping to help develop and promote such standards.
For large print and/or larger graphics, a few tricks can help reinforce the perception of three dimensions for those with at least some vision. Whether these tricks work will depend on how much vision the student has.
* Print near objects with darker and/or thicker lines than distant objects.
* For near objects, add a reddish tint. For far objects, add a bluish tint.
* For near objects, use saturated colors. For far objects, use less saturated, lighter colors.
* For near objects use solid lines. For far objects use textured lines that may appear ever so slightly blurry.
* For angled lines representing axes into or out of the plane of the paper, always use the same angle.
* Represent each axis of a 3D chart differently: the x-axis as a green dotted line, The y-axis as a red line of X's, and the z-axis as a blue squiggly line. Or the like.
* Use a tactile graphics line slate from APH to create tactile representations matching the graphical representation. Thus the x-axis can be a tactile dotted line.
Here's a link for the tactile graphics line slate:
$1
The 3D graphic should be a hyper-realistic, exaggerated representation. The bland black-and-white graphics in many math textbooks present a barrier to learning, and the barrier is unrelated to the math being taught.
Have **multiple** representations of the same 3D data, at least for the first few problems. One representation could be a large print 3D chart. A second representation could be a tactile 3D model of exactly the same data. A third representation could be a recorded audio description of the data that touches on points of interest. A fourth representation could duplicate an earlier representation, but with less detail for quick reference. And so on. All these representations serve to reinforce the concept they represent.
But there’s a fundamental problem: sighted bias in mathematics education. These visual representations can be misconstrued as being the representations necessary to learn geometry. Presenting 3D objects on 2D paper is an inexpensive means of presenting abstractions that make sense to some fraction of sighted students.
We all live in a 3D world, but we don’t all see that world the same way, assuming we see it at all. People who can find their way through a 3D world can be presented with 3D math in a way that makes sense to them.
Some alternative method to present 3D data.
* Legos can be used to represent 3D objects, including 3D charts. A Lego base plate can represent a mathematical plane, and blocks stacked vertically can represent points in the third dimension. A friend of mine uses Lego models to understand the layouts of rock climbing walls.
* Ball-and-stick kits used for chemistry and the Zometool kit can also be used to present some kinds of 3D data.
* Paper is great for creating 3D solid figures. The work to make the figure reinforces one's understanding.
* 3D graphic programs allow you to build up figures, set colors, and zoom in and out. CAD (computer-aided drafting) software originally meant for engineers can be used create 3D graphics of unlimited flexibility.
* Within 5 - 10 years, reasonably priced force feedback gloves may be available for use in the classroom. Force feedback gloves allow you to "feel" a virtual object in space. Most 3D charts are data representations rather than real objects, but with force feedback we could present the data as a tactile object.
Having a thorough understanding of just ONE reasonably detailed 3D graph can make it easier to understand other graphs.
Some 3D data can make sense as a “heat map” in which colors represent the third dimension. In that case I would recommend red for high points and blue for low points.
As a rule it's hard to choose just the right representation for data. This is one reason I think a mailing group, conference, or other broad standardization effort is necessary: educators, designers, and students need to come together in larger numbers.
For those with the interest and patience to have read this far, here are some of the relevant academic papers on blind students learning STEM subjects.
**“Making Physics Courses Accessible for Blind Students:** **strategies for course administration, class meetings and course materials”** by Holt et al. Authors include a blind graduate with a B.S. in physics and a blind PhD chemist. The papers mentions Braille note takers, embossers, etc., but does not highlight their high cost. The section about tactile graphics does not describe the non-intuitiveness of tactile graphics.
$1
**“Advice from Blind Teachers on How to Teach Statistics to Blind Students”** by Godfrey and Loots (2015)
$1
**“Teaching Mathematics to a Blind Student – a Case Study”** by Tanti
$1
**“Teaching STEM subjects to blind and partially sighted learners”** by Cryer (2013)
$1
**“STEM Access for the Blind and Visually Impaired”** by Sawhney
$1
**“Accessible Physics Concepts for Blind Students”** (web page) by Dick Baldwin
$1
**“Teaching College Physics to a Blind Student”** by Parry et al. (1997)
$1
“We emphasize the necessity of a one-on-one tutorial as the primary mechanism for learning \[for a blind student\].”
\[Some advice may be outdated\]
**“Report on the Science, Technology, Engineering, and Math 2017 NFB National Convention Tutorial”** by Louis Maher
$1
I’ll address your specific question, but other info I provide may be helpful. As a student you have the right to learn mathematical concepts, and other representations could prove more useful to you and to other students. To my knowledge there are no national or international standards for creating accessible representations for 3D data. As an adjunct to my work in assistive technology I'm hoping to help develop and promote such standards.
For large print and/or larger graphics, a few tricks can help reinforce the perception of three dimensions for those with at least some vision. Whether these tricks work will depend on how much vision the student has.
* Print near objects with darker and/or thicker lines than distant objects.
* For near objects, add a reddish tint. For far objects, add a bluish tint.
* For near objects, use saturated colors. For far objects, use less saturated, lighter colors.
* For near objects use solid lines. For far objects use textured lines that may appear ever so slightly blurry.
* For angled lines representing axes into or out of the plane of the paper, always use the same angle.
* Represent each axis of a 3D chart differently: the x-axis as a green dotted line, The y-axis as a red line of X's, and the z-axis as a blue squiggly line. Or the like.
* Use a tactile graphics line slate from APH to create tactile representations matching the graphical representation. Thus the x-axis can be a tactile dotted line.
Here's a link for the tactile graphics line slate:
$1
The 3D graphic should be a hyper-realistic, exaggerated representation. The bland black-and-white graphics in many math textbooks present a barrier to learning, and the barrier is unrelated to the math being taught.
Have **multiple** representations of the same 3D data, at least for the first few problems. One representation could be a large print 3D chart. A second representation could be a tactile 3D model of exactly the same data. A third representation could be a recorded audio description of the data that touches on points of interest. A fourth representation could duplicate an earlier representation, but with less detail for quick reference. And so on. All these representations serve to reinforce the concept they represent.
But there’s a fundamental problem: sighted bias in mathematics education. These visual representations can be misconstrued as being the representations necessary to learn geometry. Presenting 3D objects on 2D paper is an inexpensive means of presenting abstractions that make sense to some fraction of sighted students.
We all live in a 3D world, but we don’t all see that world the same way, assuming we see it at all. People who can find their way through a 3D world can be presented with 3D math in a way that makes sense to them.
Some alternative method to present 3D data.
* Legos can be used to represent 3D objects, including 3D charts. A Lego base plate can represent a mathematical plane, and blocks stacked vertically can represent points in the third dimension. A friend of mine uses Lego models to understand the layouts of rock climbing walls.
* Ball-and-stick kits used for chemistry and the Zometool kit can also be used to present some kinds of 3D data.
* Paper is great for creating 3D solid figures. The work to make the figure reinforces one's understanding.
* 3D graphic programs allow you to build up figures, set colors, and zoom in and out. CAD (computer-aided drafting) software originally meant for engineers can be used create 3D graphics of unlimited flexibility.
* Within 5 - 10 years, reasonably priced force feedback gloves may be available for use in the classroom. Force feedback gloves allow you to "feel" a virtual object in space. Most 3D charts are data representations rather than real objects, but with force feedback we could present the data as a tactile object.
Having a thorough understanding of just ONE reasonably detailed 3D graph can make it easier to understand other graphs.
Some 3D data can make sense as a “heat map” in which colors represent the third dimension. In that case I would recommend red for high points and blue for low points.
As a rule it's hard to choose just the right representation for data. This is one reason I think a mailing group, conference, or other broad standardization effort is necessary: educators, designers, and students need to come together in larger numbers.
For those with the interest and patience to have read this far, here are some of the relevant academic papers on blind students learning STEM subjects.
**“Making Physics Courses Accessible for Blind Students:** **strategies for course administration, class meetings and course materials”** by Holt et al. Authors include a blind graduate with a B.S. in physics and a blind PhD chemist. The papers mentions Braille note takers, embossers, etc., but does not highlight their high cost. The section about tactile graphics does not describe the non-intuitiveness of tactile graphics.
$1
**“Advice from Blind Teachers on How to Teach Statistics to Blind Students”** by Godfrey and Loots (2015)
$1
**“Teaching Mathematics to a Blind Student – a Case Study”** by Tanti
$1
**“Teaching STEM subjects to blind and partially sighted learners”** by Cryer (2013)
$1
**“STEM Access for the Blind and Visually Impaired”** by Sawhney
$1
**“Accessible Physics Concepts for Blind Students”** (web page) by Dick Baldwin
$1
**“Teaching College Physics to a Blind Student”** by Parry et al. (1997)
$1
“We emphasize the necessity of a one-on-one tutorial as the primary mechanism for learning \[for a blind student\].”
\[Some advice may be outdated\]
**“Report on the Science, Technology, Engineering, and Math 2017 NFB National Convention Tutorial”** by Louis Maher
$1
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