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Week 7: Not for everybody?

Part 1

Find three techy pieces you like. You can reuse the pieces from previous weeks. Name what the piece is (a video, an interactive, a solver, etc.). Write a sentence on why you think the piece is good for learning math.

Part 2

For each piece, name five or more populations who are unable (or barely able) to use it. Identify the barriers preventing each population from using that piece. Think of different types of barriers: language, age, tech savvy, gender, socioeconomic issues, disabilities, social acceptance, etc.

Part 3

Find an article, a podcast or a video addressing one of the barriers you identified, and ways of accommodating across that barrier. Write a brief summary here.

Part 4

How would you re-design your piece to make it accessible to more people? Should you, and why?

Task Discussion

  • Green Machine   April 29, 2013, 3:06 a.m.


    Part 1

    Khan Academy is one of my favorite math websites because it provides a plethora of challenging math activities and videos that may be used for tutoring, extensions, or re-teaching purposes.

    TI NSpire scientific calculator. Seriously, who does not want one of these. This by far has to be the best calculator experience I have every had. Integration of spread sheets, word documents, graphing, and more. A complete and powerful tool that every institution with math or science should have.

    GeoGebra. The more I have been using GeoGebra, the more I love the applications of this program. It’s a great tool to reinforce your geometrical skills. I cannot wait to introduce it to my scholars.

    Part 2

    One barrier could be impoverished communities or individuals who have their priorities mixed up. People who are not tech savvy would be another obstacle and from my experience, possibly, older teachers who are reluctant to try new techniques.

    Part 3


    The article touches on the issue of technological resources in industrialized and developing countries and how to address the fact that some developing countries are attempting to keep up with the technology in the classroom. It also noted that a lot of money is spent on purchasing technology and training teachers, but most of those resources are barely utilized. The writer felt like technology has been oversold and underused. I can agree with that notion because I believe that you make use of whatever technological resources the local environment has available. Technology is a powerful when combined with other practices and adds a level a differentiation to all activities.

    Part 4

    I would redesign the TI NSpire by having an emulator free for computers or tablets. If that was not possible then I would make sure that funds were appropriated where these calculators are now the norm within my educational environment. I don’t believe that the actual piece of equipment needs to be modified and the price is affordable.

  • Gina Mulranen   March 3, 2013, 5:38 p.m.

    Part 1

    One online tool that I have used before for practice problems is What I really like about Hotmath is that the practice problems not only provide you with the correct answer, but also a step-by-step guide on how to get an answer. What I also just discovered today is that has solutions for the Algebra 1 textbook that I use! However, not all the solutions are free to view without a subscription. However, I have used the site to search for specific concepts and all of them have been free. Here is an example of a practice problem and the step-by-step solution for solving a quadratic equation: (Note: You have to click the down arrows to see each step.)

    Another tool that I have also used from the internet before is online manipulatives from the National Library of Virtual Manipulatives. Here is a link to the website: I have used the Algebra balance scales for my Pre-Algebra students when they were first learning about solving equations.  It was a great way for the students to see why to do each inverse operation to both sides of the equation (in order to keep the scale balance) and to see the steps written out when solving the equation. There are a lot of great resources on this website that can be used for a variety of grade levels. The website provides the objective and directions for each activity.

    A third online tool that I have used is for quick data graphing is from Here is the link: Students have the option of graphing line graphs, pie charts, or bar graphs. The data is easy to input and you can change the intervals and the title. It is also printer friendly. I feel like this is a better website for graphing then what I have used before from This website seemed too elementary for middle school.

    Part 2 would not be appropriate for elementary students since the content in the website starts at the middle school level. The website also has components that require a subscription, which the lower income families or school districts might not be able to afford. I also did not see an option on the website to translate the English into another language, which would impair students who cannot read English. The way that the steps are written would benefit visual learners, which would prevent people who are visually impaired or who are auditory learners. Since you have to click to see each step of the problem, this might also be difficult for students who have trouble with their fine motor skills.

    The NLVM website is also an online based program, which could not be accessed by people who do not have access to the internet. It also requires that students know how to maneuver around the different activities with the use of the instructions, which may prevent some students who are not tech savvy from using the program correctly. The manipulatives available on this website is geared towards a high school level math curriculum and therefore younger students would not have the prerequisite skills necessary to understand the content or fully benefit from the activity. Since these activities are also visual, those who are blind who not be able to use this resource. It also can impair students who are auditory learners, since the directions are written and not explained verbally. There are also no tutorials to explain to students how to use the different programs, which could inhibit a visual learner from understanding the directions. Some of the activities require a lot of clicking and moving objects on the screen, which can be very difficult for someone who has a disability that affects their fine motor skills.

    The graphing tool is another online, visual program that students who have no internet or who are visually impaired would not be able to use. I think that students do have to be tech savvy also in order to figure out how to change the labels on the graphs and graph the data. The site does not provide very good instructions on how to do so. This tool would also not benefit those students who have not used or seen graphs before, since there are no instructions or tutorials on graphing.

    Part 3

    I found a website about managing students with computers. This website addresses a lot of the different barriers that students and teachers face when using technology. I focused on how to accommodate for students with different skill levels with using technology. The article talked about assessing the students’ computer skills by giving a pre-assessment before giving them computer access. Then when doing the activity on the computer, the teacher should leave time and activities for tech savvy students to work independently and coach students who are struggling. Another option that I liked was assigning tech savvy students with those students who are not tech savvy to offer peer support when working on the activities.

    Part 4

    The article that I read in Part 3 really got me thinking about how to structure lessons and activities that have computer-based or computer-delivered activities. I have run into trouble when using resources online because my students have such a wide range of computer abilities and some students spend so much time struggling to understand the technology. I think that using an informal survey in class before using computer-based activities would help me assess my students’ computer abilities with the skills they will need in order to be successful with the activity. I also really like the idea of using the computer lab in school and having students work in pairs or groups of 3 that has at least one tech savvy student that can help the other students in their group with the activity. I always try to encourage students to teach each other since they achieve a higher level of understanding when teaching the concept in their own words and the other student benefits from hearing a different way to solve a problem. By doing the computer work at school, I am also accommodating for the students who do not access to the internet or a computer at home.

  • Maria Droujkova   March 6, 2013, 1:21 p.m.
    In Reply To:   Gina Mulranen   March 3, 2013, 5:38 p.m.

    Gina, your focus on computer literacy (and its varying levels) - and your solution of labs and groups - made me think of an interesting trend. There are types of meetings where everybody uses tech, but people are still together. Many conferences now encourage Twitter or other microblogging tools so attendees all communicate online at once. There are of course LAN parties, and have been for years. Then there are events for working groups called hack-a-thons. And more long-term hubs for coworking, where techies who work online can be in the same space physically (and bounce ideas off one another as needed). And there is the grown-up version of students working in pairs, the pair programming used in agile software development methologies.

    So what you are teaching kids in math classes (and programming enrichment!) are lifelong skills needed to address the same issue, in professional settings!

  • Gina Mulranen   March 6, 2013, 5:21 p.m.
    In Reply To:   Maria Droujkova   March 6, 2013, 1:21 p.m.

    I agree! I think that students will be working together in any job they take. They will have to problem solve and work with their coworkers to come up with and carry out ideas. We should definitely be incorporating more group work, especially over technology where so many kids have varying skill levels. I have used online forums in my online course to have my students post questions they have from a chapter study guide that other students can answer as a way to help both students study for the test. There are so many different avenues for people to colloborate and communicate using technology.

  • Katherine Hanisco   March 3, 2013, 2:38 p.m.


    Part 1

    The three pieces I chose are graphing calculators, Scratch, and Wolfram Alpha. Graphing calculators may not be the most sophisticated and cutting edge technology, but I think they are very powerful tools that students can use to learn a lot about the relationships between functions and their graphs, and since they are portable, they aren’t as limited as to where that learning can happen. Scratch offers an accessible platform for people to learn the basics of programming without having to learn any specific programming language, as well as access to a wide community of users for collaboration and support. Wolfram Alpha is a very comprehensive tool that covers an extensive range of math topics. 

    Part 2

    Graphing calculators: Students with low socioeconomic status face barriers to using graphing calculators since they aren’t cheap. The older population may also have difficulties since the screen is very small and can be difficult to read. This also applies to students with visual disabilities as well as students with disabilities that affect fine motor skills because the keys would be difficult/impossible for them to use.

    Scratch: One thing that I think makes Scratch such a powerful educational tool is the community, but this could represent a barrier to people who aren’t accustomed to participating in online communities and may not understand how online cultures works. Socioeconomic status is also an issue with Scratch since the real learning happens when students get to use the program itself, which means there needs to be access to computers. If schools don’t have a computer lab where many students can use them at once, it would be very difficult to give all students the chance to use Scratch. Students with visual disabilities would also have a very difficult time with Scratch.

    Wolfram Alpha: Since there is a specific syntax that must be used, Wolfram Alpha can present barriers. For example, students who don’t have experience using the web to hunt around for directions, help, or explanations would get stuck. There are also barriers for students with weak math backgrounds since you need to know a little bit about math to understand how get started. It doesn’t feel to me like a great tool for beginners. It would also present a challenge for English language learners since even though there is a visual component, there are still a lot of words in the directions, explanations, examples, etc. Again, this would be a difficult tool for students with visual disabilities.

    Part 3

    This blog post talks about a survey that indicates teachers say the biggest barrier to technology in their classrooms is a limited budget. Naturally, this is going to affect the low-income schools more than affluent schools. The post links to the PBS Learning Media which is a collection of free digital resources that PBS has created to help meet the needs of under resourced schools.

    Part 4

    PBS has a long history of providing the community with free educational resources, and their collection of digital resources for educators is one more example of this. Rather than using graphing calculators, which present a significant barrier for low-income students, teachers can incorporate the use of free online graphing models. This gives low-income students access to technology to explore the relationships between functions and graphs even if they do not have access to a graphing calculator. 

  • Maria Droujkova   March 6, 2013, 1:34 p.m.
    In Reply To:   Katherine Hanisco   March 3, 2013, 2:38 p.m.

    Katherine, you mention that Scratch does not require any programming language, and it certainly feels this way - it was designed to feel this way. Technically speaking, Scratch uses a version of Logo, an old (ancient!) programming language a lot of math educators have been refining over the years. Lego Mindstorms uses a more sophisticated (and harder to learn) version of Logo, to give another example. 

    What is interesting for programmers about Scratch is that the language is object-oriented. That is, different sprites have different variables, and other parts of code inside them, and sprites can "call to" one another for actions. It's a pretty modern approach to programming - however, you don't have to go there when you start in Scratch. 

    Emulators are tools that re-create some object on a computer. We looked a lot at virtual manipulatives, and now you use an example of calculator emulators. As long as the person has a computer, everything else can be in the computer, virtually! The big push for cheap laptops that happened in the last ten years definitely helped. But it's also up to individual companies and people programming things. PBS - yes! Kudos to them. Wolfram making its Wolfram|Alpha accessible for free is a big change, because the tool it's based upon (Mathematica) is quite expensive. And kudos for every individual who makes available even one virtual object, like GeoGebra and Scratch applets people made in this course.

  • Lisa Ritt   March 3, 2013, 2:16 p.m.


    Part 1:

    1-SCRATCH :has been by far my favorite techy education piece that I’ve come across. Getting comfortable with computer programming is not something I thought I’d ever feel very comfortable with, but was able to accomplish. I’d say that programming is a largely based in math. Here is a great example of a fun geometry scratch: CLICK HERE or I think we are all frustrated by how much testing is occurring in schools, it is forever a measuring tool. ixl has a million practice questions/problems for students to use on every math subject. I LOVE WHEN YOU GET AN ANSWER WRONG THERE IS A STEP-BY-STEP EXPLANATION OF HOW TO SOLVE THE PROBLEM J

    3-smart boards: to me, this is an invaluable tool for teachers to use in the classroom. They bring computers, the internet and an ability to create your own lesson examples all together is an understandable format.




    Part 2:

    For #1 & 2, obviously any group of people who don’t have computers, who don’t have internet access on a regular basis, students that are unable to use the internet on their own, for example anyone with mental, physical or emotional disabilities would possibly not have access to websites.


    For #3: Not every school has a smart board in their math classrooms. Many districts that fall in low-income neighborhoods have less money to spend on this kind of technology (although there has been a good amount of progress here) then, you may have teachers who have smart boards, but haven’t been properly trained to use them. When there isn’t someone who knows how to troubleshoot a smart board that will create an inability to utilize. Students that are blind may not be served well by a smart board however some of the lesson can be audio (either with the teacher or thru recorded material). & I guess lastly, I d say deaf students would not always benefit if there is a good bit of audio in the lesson. I would assume it’s possibly to find ways for translating smart board lessons into brail or possibly having a sign language translator available for deaf students. Of course, all this becomes quite expensive. The bottom line for most of these barriers is money most of the time I’d say.


    Part3: CLICK HERE

    This article talks about the benefits of using ixl for kids that have ADHD. What’s so nice is that students can work at their own pace and use this website whenever they have time at home. It also features a parent & teacher piece to track your child’s progress…where they are doing well or where they need extra practice. I think it’s an incredible tool for teachers and parents for K to 8 math education!


    Part 4:

    I’d absolutely have SMARTBOARD training & tutoring be a requirement at the beginning of the school year as part of professional development for new teachers. Here is the list of that came up when I went on YouTube and searched for “smart board tutorials for teachers”: (over 600 results of FREE GREAT EXAMPLES that are FREE TO SCHOOLS!!!! –NO NEED TO BUDGET FOR TRAINING!! HOORAY!)



    Here is a link

    About using ActivInspire software which is available to use with various types of SMARTBOARDS

    Anything that makes it EASY & less time consuming to have lessons more visually stimulating is HUGE and keeps the learning more engaging!


    Also- any teacher can have the students doing many of the SMARTBOARD motions…getting used to how to do these things on their own computers…which of course is invaluable these days!

  • Maria Droujkova   March 6, 2013, 1:42 p.m.
    In Reply To:   Lisa Ritt   March 3, 2013, 2:16 p.m.

    Social tools like YouTube can help teachers (and students!) share what they know. There are tutorials, which address the issues of access to training. I also like the little (or sometimes long) conversations that happen in comments by some of the videos. You can ask questions, and be answered. More training!

    On-demand, step-by-step feedback can be done by a computer, and done really well - as long as we stay within parameters of standard exercises. When I worked with Pearson making teacher training materials, I used the tool for programming such "smart" responses to exercises. You can tell it what responses to give students depending on the sort of answers they input. For example, if you ask what is 2*3 and the students responds with 5, you can say, "This was multiplication, not addition!"

    I am looking forward to smarter AI tools, though. So far, computers can't really be programmed to give immediate feedback for higher-order tasks (creating, evaluating, analyzing) - just for closed-ended exercises.

  • SueSullivan   March 2, 2013, 5:31 p.m.


    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 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:  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, 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

    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). 




  • Maria Droujkova   March 6, 2013, 2:23 p.m.
    In Reply To:   SueSullivan   March 2, 2013, 5:31 p.m.

    Focusing on the population that is difficult to serve (visually impaired students) is a worthy cause, for this assignment and for teaching in general. I met blind mathematicians, and read about blind students who were exceptionally successful in math. One feature that I found striking and surprising is how well they can... well, not visualize, of course, but "virtually construct" mathematics in their minds. You can think of mental math as a sort of mathematical storytelling, where math worlds are created and then analyzed in the mind. Well, it looks to me like blind people's minds develop stronger tools for that purpose. I wonder how these strengthes can be shared with sighted peers?

    And for a strange and exotic link, here is a site about a technique blind people use for echolocation:

    There are groups of the blind who do mountain biking and other sports that depend on them constructing the world in the mind. At some point, I want to interview members of these circles about their learning of math - maybe particular topics, like the circumference!

  • SueSullivan   March 8, 2013, 5:16 p.m.
    In Reply To:   Maria Droujkova   March 6, 2013, 2:23 p.m.

    Thanks so much for the link - WOW.  I too would love to learn what such people think about math, learning math, etc.

  • MgnLeas   Feb. 26, 2013, 8:59 p.m.

    Part 1 & 2 I did not know how to do these separate so I did them together!

    I really like Geometer’s Sketchpad. I used this interactive software in my college online geometry class. I got to play with the software on my own time and terms. I did have a textbook that went along with the software that helped me to learn how to use it. I think it was great in learning different rules of geometry because I could manipulate the objects without having to erase or redraw things. It was very ‘hands on’. There are a few populations I think may have trouble with this. The first would be young kids. The software is not very exciting (not animated like Scratch.) Another would be not tech savvy people; they may get frustrated easily and give up. Some populations that would have barriers would be due to socioeconomic issues. They may not have access to computers outside of a classroom or be unable to get the software. Some older parents may have issues with the software as well, and be unable to help their kids. Another barrier with respect to age, parents who have been out of school for a while may not remember what they learned in geometry.

    I am not sure if this counts but I love Project Euler. This would fall into the category of solver perhaps or game? These challenging problems are a great way to push students to think outside the box when it comes to solving them. Some of the solutions would take days, literally, to solve without the use of technology. So they must problem solve a way to solve the problem! This helps to teach problem solving and creative thinking. The first barrier I think of is people with not a lot of patience! People that want the answer quickly and easily may not like these problems. Again some of these problems will be beyond what some young kids can comprehend. I am sure there is a 3 year old somewhere that can do them all, but I do not know her! People with no knowledge of algorithms or computer programming may struggle. Some of the problems are easily solved once you come up with a plan for solving them. Some people who may be able to solve these problems may never be exposed to them because of socioeconomic status. Language could also be a barrier. I think they have the problems in other languages but I am not sure, and sometimes words lose their meaning when translated into another language which could make the question be more confusing. This is a game site for math as the title would lead you to assume! I like this site because there are a wide variety of games. This site is geared for younger kids, so older kids might get quickly bored. (However they do have a site for older kids, to help with this barrier.) Parents that are not tech savvy might not be able to help kids with issues that arise. Kids that do not have access to computers or internet, for whatever reason, would not be able to use this site. People that get easily distracted (like me) might get hung up on the fact that the cursor on the screen is the numbers 1-6 that move around the screen when you move the mouse. Not going to lie, I moved the mouse around for a few minutes giggling!  Adults would get little to no usefulness out of this site!

    Part 3

    I looked into Geometer’s Sketchpad for part 3. One thing I came across was an app for Ipads called Sketchpad Explorer. I have not downloaded it yet to see what it is all about, but I will in the next little bit. The cool thing is it is a free app. So maybe if someone cannot buy the full version they could at least download this app to be able to use the software. This still leads to the barrier of do you have an ipad? In looking for videos, I found a crazy amount of video lessons on you tube. This would help both students and parents trying to help their children to be able to use the software more efficiently. The parent could look ahead to see what their child will be doing in the next few days or weeks and look for lessons online so they could then know how to help. These lessons would also help not tech savvy people perhaps feel more at ease with the software.

    Part 4

    I feel that Geometer’s Sketchpad is great as it is. After finding all those lessons on you tube, I feel it is more accessible. I do remember the software being a little expensive, but in relation to the math textbooks I was buying it was not that bad comparatively! I would somehow make it easier for people who maybe cannot afford it to be able to get it. Perhaps if a school is using it they get a discount of some sort and could pass this on to families. Or (costly for the school) provide the software for the students to be able to download on their home computers if they have one.  This would just enable many more people to be able to use this awesome software!

  • Maria Droujkova   March 6, 2013, 2:30 p.m.
    In Reply To:   MgnLeas   Feb. 26, 2013, 8:59 p.m.

    Meagan, you wrote: 

    "The parent could look ahead to see what their child will be doing in the next few days or weeks and look for lessons online so they could then know how to help."

    I would like to support this line of thinking, and to encourage teachers to plan for such activities. Technology makes it possible, and doable. Some tools can capture what happens in the class, and to make it available for families. For example, homework, lesson plans, topics... If you pair it with online resourse, such as videos - in the way you describe - students and their families get a powerful support for learning.

    Some software learning programs have built-in tracking tools like this. Khan Academy is one example, which is completely free and comes with a gamified system (similar to Project Euler, but with less creative problems) for tracking progress:

    Another is Aleks Math, which has a free trial: