PART 1:
My tech pieces are all about the same topic (circumference). I thought this would help me learn how to better evaluate which method to use (or not) to teach a particular concept.
This cartoon video at http://www.youtube.com/watch?v=eiHWHT_8WrE features a song describing radius, diameter, and circumference. Learning a song might be a good way for students to remember the information, especially for auditory learners (which includes students with visual disabilities).
This video about circumference is the same one I used from week 5: http://teachertube.com/viewVideo.php?video_id=270115. I think it would be good for teaching math because the visuals are easy to understand and the video gives a detailed explanation of symbols/concepts.
My last video is at https://www.khanacademy.org/math/trigonometry/basic-trigonometry/long_live_tau/v/pi-is--still--wrong, and was originally posted in the Week 5 forum by Dr. Droujkova. It is "a video manifesto for abolishing Pi. It has to do with the question of radius vs. diameter". I love the video because it recognizes and addresses the reasons why students new to Pi and circles might have trouble with the 'traditional' Pi-based formulas/concepts; it encourages alternative thinking by exposing students to the idea of using the character Tau in circle equations (the video explains it much better than I do - watch it it's awesome!)
Also a big thanks to Dr. Droujkova for sharing this video; I too struggled with this concept for the same reasons that the video discusses.
PART 2:
Song Video Barriers:
(1) The song appeals to auditory learners (and provides a song to remember information with), but doesn't give many geometric examples; this could pose a barrier to students who are primarily visual learners.
(2) Most of the cartoon figures are white; there is a lack of diversity, which creates a cultural barrier (students are exposed to too many as it is).
(3) The song is in English, creating a language barrier for students who aren't proficient
(4) Some students might just think the song is hokey (for want of a better word) or that the musicians are subpar, or just hate the music genre; music could create a barrier
(5) The video's use of sound to communicate information will create a barrier to students who have hearing or audio-processing disabilities
Circumference Video Barriers:
(1) The video appeals primarily to visual learners, which might create a barrier to those who learn most effectively by 'doing'
(2) Language barrier for students who aren't proficient in English
(3) The length of the video might pose a barrier to those with trouble focusing (not sure how to say this exactly)
(4) Students with hearing or audio-processing disabilities might not benefit fully from the video, as the visual depictions aren't always as thorough as the audio explanations; audio creates a barrier.
(5) The video's reliance upon visuals creates a barrier to students with visual or visual-processing disabilities
Pi/Pie Video Barriers:
The barriers are pretty much the same as above, though it's important to note that this video is intended for students who are already familiar with radians. Also, I think the overall production of this video (animated vocal style, visuals switching between handwriting and pie-making) might be a bit more appealing to students with attention/focusing problems (though that's just a guess).
PART 3:
The Texas School for the Blind and Visually Impaired has an informative website that offers teaching advice geared specificially toward mathematics. It's hard for me to choose what to include in my summary, there is so much useful and thought-provoking information here. I'm going to summarize the collaborative/inclusive strategies found at http://www.tsbvi.edu/resources-math/3237-teaching-strategies#Geometric.
This section of the website addresses specific teacher responsibilities, such as: ensuring that tech resources that provide thorough and precise verbal instruction, having adequate training to ensure mastery of the accessibility tech used, and being aware of limitations of certain tech. For example, as of 2012, commercially available graphing calculators developed for visually-impaired students did not match the capabilities of graphing calculators for sighted students (such as the TI series). Specifically, the specially-designed calculators can't "graph multiple functions at the same time nor work with matrices". Teachers are reminded of the importance of tactile expression, whether by reminding the students to sense hot or cold, how they feel when they are diving into a pool (parabola), as well as providing students with tactile-based teaching materials (such as a braillewriter). Links to suppliers of these resources are provided on the site.
PART 4:
Keeping with the subject of visually impaired students, I would try to use tactile objects to make the concept of circumference more accessible. Please keep in mind that I don't have a special ed background.
Tech (in the form of audio) could be used to explain items that only sighted students see (such as the pies in the last video). This could be done either by headphones or be made available to the entire class - sighted students who respond best to auditory learning would benefit from this as well, and students who aren't proficient in English might also benefit from the extra exposure.
Voice-recognition software is also promising tech for being a calculator substitute, though it might require students to learn a particular syntax and such software doesn't always provide the desired results (such as Siri). Also, using a tool to perform calculations does not necessarily mean that the student understands the mathematical processes.
For the visually impaired, math materials are often presented in 2D, but these students need to experience them in 3D. Food always seems to attract attention, so cutting a clementine (approximation of 3D sphere) in half could create a (relatively) flat 2D surface for students to touch. Yet, this flat 2D surface offers tactile distinctions; the central column (which can be thought of as the center of a circle) can be distinguished from the segment walls (which can be thought of as radii, if the peel is removed, or the peel measurement could be added as a constant). Unfortunately, computer tech doesn't yet have the ability to replicate these tactile experiences, but tech allows teachers to record (and re-record to correct mistakes) audio that the student can access as many times as they need to (the audio file could be made available via social media).
