What equation(s) did you graph? Describe your experience exploring zooming, panning, and navigating graphs.
I graphed the example equations in the Math tutorial in the Hive course because it’s been a long time since I’ve been in a math class so my memory of these concepts is pretty fuzzy. I did it with just the Monarch first and quickly discovered that having the grid lines on the graph made it more confusing to me, so I changed that setting and with the point and click, it was easier to interpret. I had no problems zooming or panning.
How did the exported graph appear in the Word Processor?
Again, I followed the Hive course tutorial, so the process went very smoothly. I used an external monitor so I could see what a math teacher would see if my student used KeyMath in class, and it looked great!
What challenges did you encounter while transferring and viewing the graph?
None, really.
How do you see the Monarch’s graphing tools benefiting students or clients in CIE settings?
I think it would be useful for college students pursuing a STEM career, and it would be useful for anyone working in a STEM field requiring graphs.
If you’ve used other accessible graphing tools, how does the Monarch compare?
I was doing handmade tactile graphs for one of my students to read and create, because that was his preference, and while it worked well enough, it used so much paper, bump dots, wiki stix, etc… and it was extremely time consuming. The Monarch would have been ideal for that class 3 years ago!
Just did y=sin(x)+1
Little blockier than I thought
Not useful for my Veterans
Only used the Orbit audio addition to the TI-84 so this is easy.
Full disclosure: I am terrible at math and may verl well have an undiagnosed math disability. My struggles in math, I feel, were simply attributed to blindness and ignored, which meant that, though my Braille teachers tried, I was often not given the right support.
I gave this activity the old college try, but I have no idea if I made the graph right, as I didn’t find this tutorial video very helpful. I have definitely become better able to understand the D-Pad’s benefits and zooming, though mostly with Tactile Viewer and less so with graphing. I was able to copy-paste into the wordprocessor fine.
I am definitely not a STEM person and graphing equations will not support me in my job. However, I continue to feel hopeful that the Monarch will support things such as more text-based graphs, spreadsheets, charts with columns, etc., as my colleagues often use these and I have difficulty understanding them when only using my screenreader’s voice output. Being able to use Braille, and to pan/zoom a graph or spreadsheet as necessary, would be extremely beneficial, and would aid my productivity and access to shared data significantly.
I must admit, this is not my strong suit. I am not a graphing person. I tried something very simple and did alright, but this is not an area I will be using much for work, and I do not teach students. I love the technology, however, and wished it was around when I had to try and survive Algebra II and preCalculus.
I graphed all the equations that were listed in the lesson and played with a couple others as well. I loved the ability to zoom in and out and easily find out approximately where different graphs intersected each other the the x and y axis.
I was impressed with how simple it was to export the graphs to a word document and then even print it off! This will be a game changer for sure for my high school students! In the past, graphs in math were the absolute worst, which is a bummer because I personally love them.
When you point and click it tells you where your finger is and it is difficult to get exact intersections. At the same time, it is still so helpful to have an apporximate answer.
My students are senior and headed to college next year. This tool is a blessing for the math applications alone.
My students and I have used online “accessible” graphing tools and my students loath them so much that their teacher lets them describe what graphs would look like; also not optimal.
I don’t use graphing at all for my full-time work. I have one student as a TVI who will probably begin to use these functions in the next few years. So in all honesty, it made the most sense for me to follow along with the very helpful step-by-step Youtube video of graphing the expression. I tried out an inverse of the example expression, 2x-4 = y and felt the downward facing parabola. The whole video was useful, but the most important part for me was the demonstration of the way the minus button could show more detail from a graphing perspective. The exported graph worked well in the word processor, but I’m still nervous about trying this free-form! This process will be a huge boost for students who are blind or who have low vision, because they can graph exactly the way their peers are graphing, and the results can come out in real time. The challenges that come with this method are similar challenges to other students who use more modern methods. If the graph occurs automatically, the proof of understanding is a bit different than it used to be. But that’s a larger challenge that everyone is facing right now! Embossed tactile graphs can have the advantage of different textures for different lines or parts of the line. I think the Monarch attempts to achieve this a little bit with the shading, but the variation of textures is not quite the same. Hopefully this will be updated in future iterations of the product. Not just for graphing but for all kinds of tactile experiences.
I first graphed y = x+2 and y = x-1 and compared the graphs of both expressions. When I opened the graph, only part of the axes were shown, so I pressed - to zoom out until the full graph was visible. From the zoomed out view, I could clearly tell there were two lines representing the two different expressions: one with a y-intercept below 0 (for y = x-1) and one with a y-intercept above 0 (for y = x+2). Zooming and panning worked well. My initial impression was that the lines were quite thick. I then used point and click to get the exact values of the y-intercepts. I ran into an issue where multiple y-values could be reported for the x = 0 value, depending on how precise I placed my finger. For example, when I used point and click on the y-intercept for the y = x-1 line, I received the below values: 0.0, -1.5 on the first attempt, 0.0, 1.0 on the second attempt (which is the correct intercept), and 0.0, -0.9 on the third attempt. This is not counting the times where I was slightly off and didn’t get exactly 0 on the x-axis. This happened at different zoom levels. This could be an issue for students or professionals who need to provide a precise answer from reading a graph. This will also be an issue when trying to identify the values of points at other parts of the graph besides axes intercepts.
I then deleted the first two expressions and graphed y = x^2 + 1. This resulted in the expected parabola with a y-intercept above 0 (exact value should be y = 1). However, I again encountered the issue with getting multiple values for the y-intercept when using point and click, including x=0 y=0.84 and x=0 y=0.56. I also found the graph of the parabola to be very discrete and resembling more of a step function.
I next copied and pasted the y = x^2 + 1 graph into Key Word. This process was straightforward after viewing the instructions on the Mastering the Monarch HIVE video on this topic. In Key Word, the graph was represented as the math expression used to generate the graph (y = x^2 + 1), and the expression was surrounded by the braille symbols edims and edime. When viewing the document in print preview, the graph was represented as the expression followed by the word “graphic”; the edims and edims symbols were not present in print preview. From what I understand, the graphic itself would show up on an external visual display, but not on the braille display. It would be nice to have the option to show the graphic directly in the key word document or in print preview. Alternatively, it would be nice to be able to click on the expression in key word and have it open in key math automatically.
When performing the above tasks, a few things I thought of were:
It would be nice for expressions to be read when arrowing through without having to press space with c. Maybe this feature could be turned on or off by the user for those that don’t want it?
2. I didn’t initially realize that every time a graphable expression is entered, this new expression is added to the graph the next time you view the graph. I figured out that backspace with l can be used to remove expressions from the graph. Therefore, this didn’t take long to get used to, but the way I initially thought it would work is that pressing enter with g would just plot the most recent expression and then additional expressions would have to be added specifically.
3. It is possible to paste expressions from key math into key word. However, is it possible to paste expressions from key word into key math? I could not get this to work.
Currently, I can see how Key Math would be very useful to students in k-12 math and maybe a first-year college student. It would also be very useful for blind teachers who are teaching these math courses. However, I am unsure if Key Math is advanced enough, and if the graphs are high resolution enough, for use in more complicated math settings, such as by professional engineers or mathematicians.
The other accessible graphing tools I use are sonification based, not tactile based. Sonification has the benefit of higher resolution (more data points) than the tactile display on the monarch. However, the monarch’s tactile views can sometimes give better overviews of graphs.
If made by an experienced professional (which often is not an option), physical tactile graphics are more detailed than the monarch. However, the monarch’s feature to zoom and pan replaces the need for multiple sheets of paper. Physical tactile graphs are probably still more precise for identifying intercepts and braille text can be added more easily to physical graphs.
I think the graphing capabilities are comparable to a graphing calculator. For students, I think this is a HUGE improvement over the TI product with the talking hat (which was of course a huge improvement over only visual displays). I didn’t hear graph sonification along with the tactile graphic, and I think for many learners that would be a helpful pairing for multisensory learning. As an employed person, this level of graphing is not helpful to me. I use rStudio and ggplot2 (grammar of graphics) to produce visuals, and would like to see how to view THOSE visuals on the Monarch, as in a terminal mode serving as a braille display with a desktop or laptop computer runing rStudio.
I graphed a simple linear equation, y = 2x + 3, and at first I only saw the equation appear in KeyWord with question marks on either side. It took a minute to get my brain around the workflow, but once I realized that the tactile exploration happens in KeyMath and the visual graph shows up in KeyWord’s print preview, it made sense. Zooming and panning in KeyMath helped me trace the slope and intercept, and then exporting and pasting into KeyWord worked once I used Backspace + E and Backspace + V. When I checked print preview (Enter + V), I could confirm the graph was embedded for sighted readers. The challenge was keeping straight what shows up tactually versus visually, but now that I’ve done it once, I see how this can really benefit students and clients in CIE settings by letting them explore graphs independently and then share the same content with teachers or coworkers.
Paul, I get that. Graphing is not really my strong suit either, but I also found it impressive to see how the Monarch handled even simple equations. Like you, I kept thinking how much easier Algebra and higher-level math would have been if this technology was available back then. Even if we do not use graphing much in our daily work, I think students today will benefit a lot from having this kind of access.
Sarahelizabeth, I agree with you that this feels like a huge step forward from the TI with the talking hat, especially for students who need direct tactile access. I also think your point about sonification is important since pairing sound with the tactile display could really help some learners pick up patterns more quickly. I have not tried rStudio or ggplot2 myself, but I like the idea of exploring how the Monarch could eventually handle those visuals through a terminal mode connection. That kind of integration would open up a lot of possibilities for professionals who already use advanced data tools.
I really like math, so I was excited about graphing expressions. I used the ones from guided notes document first. Then I decided to graph a very simple equation (y=x+2) and explore it. I attempted to point and double click in order to find the x- and y-intercept. I got close the first couple of times, but I think I will need more practice to find the precise intercept. I am not sure what I did the last time because I got (-2.1, 0) instead of (-2,0). When I attempted to export the graph, I inadvertently exported the expressions instead!! There is definitely a learning curve for me! 
I used Desmos quite a bit last year when tutoring. One of the students is proficient with JAWS and found it helpful to listen to graphs. I could also emboss graphics they created. It is amazing to think they might have instant access to graphs they create on a Monarch.
Like Matthew J said, I tried it also and found this to be the toughest part. I transitioned from the Georgia Academy for the Blind to public high school and back in 1988, having access to braille was just a wish, not reality. It took three years before I could get my books in braille, so our limited resources did not help me at all learning higher skills with mathematics.
Wow! I think I need to go back to elementary school now! LOL!
Now that you have graphed an equation, inserted it into a document, and previewed it in print mode, reflect on the experience and share your insights.
Discussion Prompt:
What equation(s) did you graph? Describe your experience exploring zooming, panning, and navigating graphs.
I graphed an easy one! y = 3x-3. I was just trying to get my feet wet, but I can see where more involved equations would work. I want to explore more with Parabolas and pivot tables first though. I experienced no issues graphing an equation.
How did the exported graph appear in the Word Processor?
There was spaces on the graph that made it easy to read.
What challenges did you encounter while transferring and viewing the graph?
None.
How do you see the Monarch’s graphing tools benefiting students or clients in CIE settings?
I think it could replacing T-I 84 calculator’s graphs and also work great when accompanying each other.
If you’ve used other accessible graphing tools, how does the Monarch compare?
It is super easy to read and use with navigation buttons.
Optional Extension:
If you have experience with embossed tactile graphs, how does digital graphing on the Monarch compare? What are the advantages and challenges of each?
Some of my students are in higher ed level math. Most times, their graphs could not be made with an embosser since they go beyond 40 characters. I would have to manually makes these graphs with a braille writer and different textures and then piece the pages together. I know this could have been done with an embosser but it was always easier for me to just make them since I was going to piece them together regardless of which method. I can definitely see where the navigation keys will help with this since the students will just have to navigate over instead of having tons of braille pages to unfold.
Hi William,
I didn’t think it was the toughest part, but I was nervous to approach it lol. I did the lessons, but I found it less nerve wracking to freestyle. It made it more fun for me, but I also realize my students will not always have time to freestyle like I did.
Hi Sarah,
I thought the same thing! That the graphing capabilities were comparable to the TI 84 graphic calculator. I do like the kinesthetic approach that Monarch offers over the calculator though. The calculator is still great, but I like having the ability to differentiate my instruction approaches.
I too had the same level of inaccuracy using point-and-click to find intercepts and intersections. With improvements over time, the idea of pointing-and-clicking could be powerful for teaching math and science.
My experience, too. It’s very powerful to be able to easily export Nemeth expressions into a widely-available word processor. Certainly with support for terminal mode this could be a very powerful tool in CEI, including STEM, settings.
I graphed linear functions (y = 2X+1), a parabola, and a circle. Panning and zooming in and out are powerful tools, and unlike the tactile viewer (at least currently) it is helpful to have several levels of zooming. Functions had lines and arcs that were thicker than I would have liked (at least 2 dots), and the point-and-click to get a location of an intercept was close but not accurate.
The graph that I exported to the Word Processor was useful (I used AIRA Access, an AI tool, to describe it and confirm that it came out usably).
The graphing tools have potential, with improvement, to be even more powerful for students. I look forward to seeing how this can be used in CEI settings, including STEM settings. I find it more useful, at least for me, than audio graphing tools.
Finally, hard copy tactile graphics currently have more resolution, I’ve found. However, the quick availability and ability to export into commercially available platforms such as Microsoft Word is much, much more versatile.
For me, this was the most difficult exercise out of all of them so far. I kept getting an “error” message as my equation was not solvable. I finally went with something easy like y= 3x +3 and 4x = 2. I am not good at equations outside of the Monarch so that is what was giving me the most trouble. I wish the video had given us the equation to work with and gone into a little more detail of step by step directions. Maybe I missed something in the training. I was able to export a graph. I have not previously worked with electronic graphing tools so I can not make a comparison. Comparing it to embossed tactile graphs is like comparing a black and white TV to a color tv. The ability to pane in and out of the graphic is amazing. The ability to get an error as many times as I did and know that your equation is not solvable is instant feed back.