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Week 6: Computer-based math, reloaded

Last week, we discussed computer-based and computer-delivered mathematics. Course participants raised quite a few teaching and learning issues and dilemmas related to the topic:

Name three math ed issues (problems, difficulties, dilemmas) you consider to be most challenging while using computer-based mathematics for teaching and learning. Sketch some propositions for pedagogical solutions that can address the issues.

Here are a couple of vids for inspiration. (the lead developer of GeoGebra)

The second video's transcript has some issues listed:

More videos from the same source:

Task Discussion

  • Green Machine   Feb. 25, 2013, 12:52 p.m.

    1) The availability of technological resources within the community or household. I often find that many households lack the proper technological resources to meet the needs of today. Some house may have computers but they could be out dated or no internet connection or no printer. I have also noticed that many households don’t prioritize their funds towards education. They may have the latest clothing, phones, video game system, cars, and etc… but claim that they cannot afford critical pieces of technology that can advance their child’s intelligence. I am often disgusted when I see scenarios such as the second.


    Some solutions could be to direct the family to their closet free library, offer extended hours after school where scholars could use the technological resources that they lack at home, or develop a lending program. The lending program would be available to scholars who exude responsibility and are in need of a piece of technology for the school year or a period of time. A contract would be used to hold the family liable for any damages, lost, or stolen items. I have also heard of programs that offer free or reduced computers, laptops, and internet access based on a family’s income.


    2) The technological gap between adults and children. Another issue I have noticed is when scholars do have access to a lot of technology resources available, it is often the parents who do not know how to use the technology or don’t bother to learn how to use it. There are many things that scholars are able to discover on their own but some may need to assistance of an adult or peer to make sure they are doing what is asked in reference to their assignment. Some possible solutions would be to offer classes that teach adults or peers how to use the technology of today, provide a list of free apps that scholars could use to work on math concepts through the use of a smart phone or tablet, and you could guide scholars and parents to youtube videos that explain in detail the uses of a certain piece of technology and how to operate it.


    3) Technology can have a crippling effect. I have noticed that some scholars become too dependent on technology to complete their assignments or exercises. Every scholar learns differently and has their own obstacles to overcome but they should not depend on technology to solve all their educational problems. I have run into some scholars who wouldn’t complete their work until they received a calculator. This was fine but they lacked the skills to explain/show their work or complete simple calculations without technology. I believe that we as educators must teach the scholars that the technology is used to check computations, model exercises, and apply theories. Scholars should also possess the skill to solve complex math exercises without the use of technology.

  • Maria Droujkova   March 5, 2013, 1 p.m.
    In Reply To:   Green Machine   Feb. 25, 2013, 12:52 p.m.

    I was thinking of the three problems you posted in terms of designing teaching and learning tasks. 

    (1) Availability -> sharing -> group math projects. If you pose tasks that require collaboration, fewer computers/phones/cameras can work for more people. Some technologies, such as One Laptop Per Child, are specifically designed for sharing (for example, these laptops network among themselves without central routers, so you can have a little intranet for your remote village).

    (2) Generation gap -> multi-age learning groups. Kids and adults can work together, if math problems are deep enough to engage adults, but accessible enough for kids. Grown-ups often have better time and task management skills, and math knowledge. Kids have better tech skills. One example of a project that implements it (not just for math): Generation Yes!

    Graphic of 3 students

    (3) Overdependence on tech -> tasks that require uniquely human qualities. If you ask me what 2345*33274 is, I will be offended if I can't use calculator, because I consider the task not appropriate for humans. However, if you ask me to design a poster (say) showing WHY the answer is 78027530, I will do my human math and be happy.

  • Lisa Ritt   Feb. 25, 2013, 12:05 a.m.

    The first thing that comes to mind when using computer based math is the general issue of technology taking a longer time to literally. I timed how long it just took my computer to bring up this screen from the computer being totally off to it getting me to where I needed to be. It was almost 3 minutes. First the most part, the computers I've seen at schools, this is the case. In the time students are waiting for a video, or website, or waiting for other students to finish with a computer for them to use creates alot of down time. Time is such a precious thing within your math period. There is just so much to learn in such a small window of time. I almost feel like if a teacher wants to use computer based math teaching, the teacher really prior to the class arriving should have all the computers up and running on that particular website at each students desk to eliminate the time it takes for everyone to get up, get their computers, bring up the correct website, not be distracted by other websites or other things they can do on the computer while waiting for their lesson to their, etc etc. This is the biggest issue for me is prep time & down time prior to and during class.

    The second thing that comes to mind is that students can easily lie about whether they are really getting a concept thats being taught to them. I witness kids skipping over the lesson part of the computer based teaching and going right to the quiz because technically thats what they have to do. They arent really being graded on it, so they may not care about whether they do well on the quiz. They don't want to have to repeat the work, so they tell the teach they understand their mistakes. This is a a danger to me. I feel like the teacher of students with proven skills to work independently this may not be the case with, but the students that I've worked with who generally are below proficient, I don't see computer based math working without constant supervision from the teachers.

    A third issue a see is what I've seen other list also which is the technology not actuallly working. I find this is the case with a significant amount of technology in the schools I work in or observe in. Smartboards, laptops, projectors, calculators, etc..there doesn't seem to be enough budgeted to keep the technology in schools working properly all the time. There also isnt emough training for educators to use the technology to its fullest capacity. Nor is there necessarily any obligation for the teachers to us what IS available to them. 

    Another issue I find is that its really a challenge to keep students on the lesson website or software when you are trying to do computer based teaching. If students simultaneously have access to being online in other capacities while they are supposed to be working independently on a computer based lesson, this tends to be abused. I see about half of every class when they are supposed to be on website, travelling to YouTube, videogame websites, or other social media sights. Is there a way to assure students only have access to the 1 website the teacher is on? And then, if the teacher wants the students to research something, be able to switch it to having access? I'm not sure. 


  • Maria Droujkova   March 5, 2013, 1:23 p.m.
    In Reply To:   Lisa Ritt   Feb. 25, 2013, 12:05 a.m.

    Lisa, I think you are well on track with the first issue. Like you, I learned to have sites up and running, videos preloaded, and (sometimes) other links disabled when preparing short computer tasks.

    Another possibility is to have longer, immersive experiences such as two hours of programming in Scratch (with short breaks for the eye and back health, of course). Even then, you want to have everything up and ready ahead of time. I usually ask a volunteer for help with that.

    Cheating and lying is a curiously complex subject for an educator, because it's both a tech and a moral issue. I like to address that subject with task design. For example, kids can lie about whether or not they used a calculator to find 3*58. But if their task is to write two sentences about where numbers 1, 7, and 4 in the answer come from, or how (and why) 4 will change if you replace 58 with 59 - they won't be tempted to lie about THAT particular thing anymore (they may still tell you their dog ate their computer cable so they could not submit the answers, though). If there is systematic lying, I believe adults need to take big steps and change the tasks, the environment, or some other systematic things.

    In a bigger sense, lying is always a sign of fear, and fear indicates there is some sort of coercion going on, that may need to be addressed. This goes for the fourth issue you named, as well (students doing what they aren't supposed to be doing). Are these students even consenting to be taking that lesson? However, these bigger issues of fear and consent, while important for every educator, are beyond the immediate scope of math ed.

  • Katherine Hanisco   Feb. 24, 2013, 11:12 p.m.

    The first issue that comes to mind with computer based math is ensuring that we use technology to enhance learning, not as a replacement. In the video above, Conrad Wolfram talked about the myth that computers “dumb down” math. While I completely agree that there is nothing inherent in technology that dumbs math down, it needs to be carefully integrated in a way where the technology is not a replacement for the learning. For example, having students do endless long division problems by hand is a tedious way to teach division that wastes a lot of time, but giving students a calculator and showing them a sequence of buttons to push doesn’t teach them the concept of division. I think that talking about this goes a long way to addressing it since it makes us think about how we use technology. I believe that thoughtful planning can prevent technology from being used mindlessly in the classroom.

    The second issue is accessibility, which is something I talked about as a possible topic for my tech week project. Last semester, I did fieldwork in a low-income school where almost 90% of the students came from economically disadvantaged homes. Many of them did not have access to computers at home and there were limited resources in the school. I recently read an article written by someone who believes that libraries are obsolete thanks to the internet and technology, but not everyone has access to those resources and eliminating free public resources would be a devastating blow to the people who don't have other options. The same thing applies to computer-based mathematics. If the focus shifts to computer-based math curriculum without also addressing issues of accessibility, schools with limited resources are going to suffer even more and those students will be at an even bigger disadvantage compared to privileged students. It may not solve all the issues with accessibility, but I think that one way we as educators can address this is by participating in a community that supports free and open collaborative math technology resources. Creating blogs, encouraging contributors, and participating in collaborative projects are all ways to support the free and open exchange of resources and ideas, which can help issues of accessibility. Another way to address this is to use resources in the classroom that make the most of teaching multiple aspects of technology. If students have not had frequent access to computers during their lives, then they may lack general computer skills. Tech resources that teach math concepts as well as incorporating other general skills could benefit these students.

    A third issue is the constantly changing world of technology. It’s impossible to be an expert in every piece of technology that could help students in the classroom, and it’s even more difficult as newer and better options become available. This can put an additional strain on teachers to learn every piece of new technology. When we did the task where we looked for stories on ScratchEd, I found a story about a project where classes in geographically and culturally isolated areas connect with global projects using technology. One class learned how to use Scratch from Scratch experts halfway around the world through a videoconference. By taking advantage of the networking aspect of technology, students can learn a wider range of technologies from true experts which is a much more efficient way of both teaching and learning.

  • Maria Droujkova   March 5, 2013, 2:19 p.m.
    In Reply To:   Katherine Hanisco   Feb. 24, 2013, 11:12 p.m.

    What would be a good computer-enhanced division task? That is a million-dollar question. Literally. Designing computer-based learning tasks is still hard for the humanity as a whole. It's like the Dark Ages, before the widespread use of the positional number system, when (using your example) only a few individuals could divide large numbers, and even those people were neither fast nor reliable.

    The second issue is hard to address as an individual. But we can make do with some task design, for example, group work (where tech is shared). Some countries now mandate internet access as a government-subsidized right of every citizen. With the prices of technology dropping, this seems to be in sight. For example, a cheap laptop or a tablet with internet capabilities now costs about the same as one textbook!

    One thing we can do for your third issue, as math ed people, is focus on "general patterns" rather than particular interfaces. For example, focus on what cycles are in programming, rather than how to write "Repeat 10" in Scratch. Then people can move from one piece of software to the next, when they need to do so. 

  • SueSullivan   Feb. 23, 2013, 8:24 p.m.

    The first challenging issue that comes to mind regarding computer-based mathematics is that of syntax (such with WolframAlpha).  Learning how to 'talk to the software so that it understands' is yet another thing to learn - some students might not be bothered by this, but it might drive those who are already feeling challenged/overwhelmed over the edge.  One solution to this problem would be to teach students the necessary syntax in advance and make supplemental materials and other tech support readily available.

    Availability of the necessary technology is another issue.  Students may have access to computers at school, but what if they don't have one at home?  The automatic answer is often 'oh, they can go to a public library and work' or 'they can stay after school and use the school's computers', but this isn't always an option (maybe the child doesn't have anyone to accompany them to the library, incompatibility with after-school care arrangements, lack of transportation, etc.).  It's a 'Digital Divide' issue.  Ensuring tech access to each and every student is a political issue and even then, the best of intentions may fall short of the goal.  I think this is the most challenging issue surrounding computer-based mathematics instruction, but I don't have any practical answers as so many different factors create the Digital Divide (though socio-economic-political activism might be a good starting point).

    Lastly, teachers need to remember that parents might not be as tech-savvy as their children, and this lack of familiarity with computer-based math may hinder parents' ability to help their children with homework or understand educational objectives.  A remedy to this would be to offer some sort of tech support to parents.  

  • Maria Droujkova   March 5, 2013, 5:31 p.m.
    In Reply To:   SueSullivan   Feb. 23, 2013, 8:24 p.m.

    Sue, tech support is the number one solution to UI and syntax issues, of course. Something I would like to propose as a math solution: look at the underlying structures! In all computer languages, you have some ways of declaring dependent and independent variables, for example. When I learn a new language, I just look for "a way to declare a variable." Of course, we are running into a chicken-and-egg problem here. What if we want to teach kids about variables via programming? Then they won't know variables yet!

    Scratch works reasonably well for beginners in part because you can hardly mistype any syntax in it. You assemble premade pieces of the puzzle.

    You may be interested in looking for projects and programs designed to bridge digital divides, either technologically or mathematically. Ironically, Montessori started her projects with the poorest of the poor kids. Her designs were aimed at using homemade, cheap tools - and situations where one teacher deals with many students of very different ages (from toddlers to pre-teens). By now, a set of "official" Montessori materials is not something most schools (let alone parents) can typically afford. But her ideas are still free. One Laptop Per Child has both curriculum and tech solutions for the divide:

    The generation of people who are now parenting lived through a large tech transition, even a revolution. Most of us started out without computers (though computers already existed). Most of us ended up computer users, in the Western world at least. It is the largest shift in adult literacy of any sort that I know! We should be congratulating ourselves, as a generation, for getting there more-or-less in one piece. 

  • Gina Mulranen   Feb. 23, 2013, 6:35 p.m.

    One math-ed issue that I feel surfaces from using computer-based mathematics is losing the ability to differentiate for students different ability levels. Part of a teacher’s education is learning how to teach a concept in different ways to reach the needs of the different learners in their classroom. By using the computer-based math, students are interacting with the computer program as it is designed. If they are not able to understand the concept that is being taught in the way it is presented, they are now stuck. In the classroom, they can raise their hand and tell the teacher that they do not understand and the teacher can then try to explain the concept in a different way. A way to address this issue if using the computer-based math in class is making such to provide guidance and support for students as they work through the program so they can still get their questions answered. If the computer-based math is being done as part of a homework assignment or project, the teacher should provide additional resources for students who need more instruction on how to use the technology and learn from it. The teacher can also spend time in class explaining the computer-based math activity before AND after the students do it in order to explain how the program works and how well it worked.

    Another math-ed issue that I foresee happening with using this new math technology that we are learning in this class is not being able to answer students’ questions when they hit a problem using a program. For example, let’s say I assign a project involving Scratch and ask students to create a program that explains or uses a property of triangles. Then I have a student who cannot figure out how to move the Sprite a certain way or change a color of an object when an object is clicked. On one hand, I would feel very uncomfortable giving students an assignment like this without being an expert in the program myself. On the other hand, I can use this as a learning experience for me and the student. We can meet and work together to figure out how to solve the problem. I also think that another issue that can come up is when parents are not able to answer questions on an assignment if they have never worked with the technology before. If the students and parents cannot figure out the problem working together and it takes a lot of time, it becomes frustrating and the parents usually shed a negative light on the integration of these programs, saying it takes more time to work with the technology than the math concepts. That is another issue that I have already addressed and will address in my tech week on computer programming.

    Another issue that arises when students are working with computer-based math is tech issues. Teaching in a cyber environment, I have encountered plenty of students that say their laptop does not support the program or the recording was choppy because of the internet speeds at their house. I also run into issues with websites that take down videos or resources that I link to. As a teacher, I need to stay up-to-date with all the links and program updates so I can make sure everything works properly before I post the assignment.

  • Maria Droujkova   March 5, 2013, 5:40 p.m.
    In Reply To:   Gina Mulranen   Feb. 23, 2013, 6:35 p.m.

    Gina, your first issue made me wonder about two things. First, is there software that is more versatile, I asked myself? Yes, I answered myself! Bigger "maker" platforms, like Scratch, seem to touch different learners in different ways. The more particular the software, the smaller its target audience. Unless it's "Angry Birds"!

    Second, maybe we can offer collections of different tools (for each topic), rather than just one. Then students can become conoisseurs of tools, with proper guidance of course.

    Something that can address the second and (to a degree) the third issue you raised is online human support. For example, the online-based Open Study group goes well with iTunes U collection of computer-delivered math courses: There were 171 people online just now when I logged in to grab that link! People help one another in real time.


  • Gina Mulranen   March 6, 2013, 5:16 p.m.
    In Reply To:   Maria Droujkova   March 5, 2013, 5:40 p.m.

    I am loving this open study group. When I logged on there was 178 people online and they said that questions were answered in about 5 minutes! Wow! I have heard of online homework help, but not that fast! I really think that there are so many resources out there that every issue you think you could have with technology has an answer out there in the web somewhere. Thank you for providing all these great resources. These are fantastic tools for MY tool box that I can share.

  • MgnLeas   Feb. 23, 2013, 2:06 p.m.

    One issue that I hear over and over again is that the use of computers in math actually takes away from the material being taught. By this I mean, the students are simply imputing data and have no idea what happens next and then they get the answer. Well, I have to admit I used to be someone who agreed with this statement. However, after opening up my mind and thinking about it for a while, I realize this is not the case. The students need to have some knowledge of what will happen so that if the results are way off the student will be able to see that and make adjustments. As the teacher, I need to make sure my students have the basic information they need in order to be smart computer users. The computer will allow for the students to learn more material in the long run. For example, when learning function transformations, I could have them graph each change one by one. This will take a long time and they may not get through all the graphs in the time allowed. However, if I have them use graphing software, they can get through many examples and be able to see the transformations quickly. This would also allow me the freedom to come up with harder more complicated functions for them to analyze. I could give them the parent function and a transformation and have them work backwards to see what happened to the parent function.

    Another problem I can think of is parents/ administrators feeling as though I am letting the computer teach the student the material, instead of me teaching it. As the teacher, I need to know the material and be available for questions. Computers cannot explain things like a teacher can. If I see the student is really struggling I can reword my statements to help the student learn. I need to be the one in charge, so to speak, of what is happening in the classroom. Simply because the students are working with technology does not mean I can sit at my desk and relax for the day.

    Lastly, my favorite dilemma TECHNOLOGY IS NOT WORKING TODAY!!!!!!! So I have created this amazing lesson using computers and today the computer program has decided it does not want to teach or help. For this I say always have a plan B; whether it is teaching the lesson another way or teaching tomorrow’s lesson toady and coming back to this assignment when the program is working. We should always be prepared for an issue to arise and need to be extra ready for technology issues. I do not want to waste a whole lesson on why won’t this work. I will lose not only a day but the interest of the students.

  • Lisa Ritt   Feb. 24, 2013, 7:15 p.m.
    In Reply To:   MgnLeas   Feb. 23, 2013, 2:06 p.m.

    Your LASTLY, is always my biggest fear! Because I don't feel like a super tech trouble shooter, I get very nervous about this. WE have such a limited time to get our lessons taught & this is an ongoing battle in every classroom I visit!

  • Maria Droujkova   March 5, 2013, 6:38 p.m.
    In Reply To:   MgnLeas   Feb. 23, 2013, 2:06 p.m.

    Your function transformation task is an excellent illustration to that key question teachers must keep in mind:

    What are students doing?

    We can plan for technology, and we can plan for what we will show or do. But what we must plan, no matter what, is student actions!

    Reading your second issue made me emotional, because it touches on several big problems. Some people would want to sell one recorded lecture million times and call that "teaching." Some people provide recorded lectures to students who had nothing before (no teachers, no lectures) and these students are very thankful to have something. 

    Also, teachers who use technology well work very hard. Technology is new, and figuring out how to teach well with it is a creative, difficult endeavor. How can we make that work visible? I am reminded of the popular math teacher blog called dy/dan, where a lot of strong discussions about teaching with technology take place: Sometimes Dan posts how long it took him to prepare a lesson with technology. He runs into 10 or 20 hours of lesson prep.