The Reflective Educator

Education ∪ Math ∪ Technology

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Month: April 2012 (page 2 of 2)

The next big thing

Stephen Downes shared this article about the next big thing in network analysis. He writes:

Valdis Krebs argues that the next big thing in network analysis will focus on the contents of what we read (and not just the titles as entities) in order to draw connections between people. It’s a natural evolution of network analysis. "It is not just the also-bought data that matters (which books bought by same customer), it is what we specifically find interesting and useful in those books that reveals deep similarities between people — the hi-lites, bookmarks and the notes will be the connectors. Our choices reveal who we are, and who we are like!"

I’m going to argue that what would be even more valuable than a better way to determine who is most similar to us would be what important ideas do we not know, and perhaps we should. We have this crazy amount of data on what people read, what videos they watch, and who they chat with, which should in theory be able to help determine what "important" things they have not yet read, and even some of what they do not know. We should be able to use network analysis to direct learners into new learning experiences.

This is similar to the Netflix (and Amazon, etc…) recommendation engines, which suggest similar titles to what one has experienced already. Unfortunately this approach leads us isolated in a bubble. Instead, what if these recommendation engines looked at what was in our circles, and found something important to know that is perhaps an opposing point of view, or a different perspective on what we know. I’d happily sign up for a service that culled the best of the opposing ideas to my own perspectives and shared those new perspectives with me.

Instead of finding better ways of leading people to re-inforce existing knowledge, can we find better ways to direct them at new ideas?


Fixing audio from a video track

The problem:

Our students had recorded video of themselves, but the audio from the video was too quiet to hear. Unfortunately, they had recorded their video on a Flip camera from a distance of 7 or 8 metres in a large open space, and forgot (or did not know) that this would result in extremely poor audio.


A solution:

We don’t have the kind of video editing software readily available for students that would fix this kind of problem (I think our film course has access to Final Cut Pro), so I wanted to find a free solution for fixing this audio.

I found WinFF, which is an open source video conversion tool, which happily converts from a video to audio, essentially isolating the audio from a video file. I downloaded it, and installed it to my computer. After some experimentation, which I did with the students, I discovered that the following settings worked best for this process.



I then imported this audio into Audacity, and used the volume adjustment option (see below) to increase the volume of the audio track of the video.



Once the audio volume was adjusted, I then imported the video and the new audio track into Windows Live Movie Maker, where we muted the original video, and used the new enhanced audio track. Queue the excited students who no longer have to re-record their video!


The follow-up problem:

This is essentially a magic tech recipe that the students may be able to reproduce, but I doubt they will be much better at trouble-shooting their own tech problems in the future. As I outlined the solution for the small group of students I was working with, some of them were interested, others were not. They displayed many of the signs I see when I see math taught the wrong way. They have no idea what the OGG audio format is, or why it would be the best choice to work with Audacity.



  1. How can we make learning technology more seamless? I see technology as a tool for other activities, but some of our current technologies are so difficult to work with that something which should be simple (increasing volume of a video) is difficult.
  2. Is is better not to help these students in the long run when the task they want to do is beyond their current technology skills? Is there a reasonable balance we should strike between assisting students finishing the project today, and helping students become more independent tomorrow?
  3. How is this related to mathematics education today? How often do we help students solve fabulous open-ended problems with magical mathematics techniques they don’t really understand?

Mathematics education blogs

Here is a list of people who blog about mathematics or mathematics education. Please let me know if you blog about mathematics education, and you’d like your blog to appear in this list. I’d like this list to be exhaustive, rather than exclude people. You can either contact me, or add your relevant information to this form.

So far this list has 347 (!!) blogs. Now that Google Reader is going to be taken offline, I’ve moved the list to a spreadsheet instead of a Google Reader bundle. You can access it by clicking below.

Find the list of blogs here



Should students learn how to graph functions by hand?

Software to create graphs of all different kinds electronically is ubiquitous. There is no question in my mind that we do students a great disservice if we do not give them opportunities to learn how to use at least a few of these programs. That being said, does the use of these programs potentially make learning concepts related to graphing, or through graphing, more difficult than it would be if the students used traditional paper and pencil graphing techniques?

It should be clear the skill of graphing is different when using technology. Some tasks, like choosing an appropriate scale, which are typically difficult for students are much easier using technology. One can replace time spent learning how to space lines correctly on paper with time spent learning how to choose the space between the lines in the software. In either case, time should be spent on visual design principles and why we might want horizontal lines in the first place.

One problem with using technology for graphing, especially when the purpose is to use the graph to determine a relationship between variables, is that the technology can potentially make the job of graphing too easy. A mind, recognizing that a task is easy, can potentially put insufficient energy into the task, and the mind’s ability to distinguish patterns is reduced. This born out by research on the effect of font type when people learn through presentations, and by Veritasium’s research on effective science videos. A mind insufficiently challenged, either by the task of character recognition, or on it’s misconceptions, is a mind that is less likely to learn.

On the other hand, some very useful learning tasks are so difficult to do when using paper and pencil techniques as to be pointless to do. These tasks can be much more manageable using technology. For example, the standard equation of a parabola, y = ax^2 + bx + c, can be explored through a graphing program. What effect does changing the values of a, b, and c have on the equation? Try this task with paper and pencil and then with technology to see why I ask students to do this task with technology. See the applet below for an example of this (requires Java).

This is a Java Applet created using GeoGebra from – it looks like you don’t have Java installed, please go to

There are many graphing tasks which are typically learned very poorly by students. From my experience, there are many middle school students running around with muddled concepts of the equation of a line, wondering what the ‘x’ in the equation is for, and being asked to learn mechanical tasks related to this y = mx + b. I usually find that some exploration of the equation of a line in graphing software typically clears up at least some of these misconceptions.

Some tasks when done with a graphing program can disguise important concepts. There is something to be said for visually placing points on the coordinate plane for understanding coordinate systems, for example. I don’t think it matters if one uses a mouse for this activity or if one draws the point with a pencil, either way, the student has carefully chosen the location of the point. If one types the coordinates into a text box, and just sees the point magically appear, I suspect that one will find learning coordinate systems more difficult. This suggests that the choice of software matters, since some software will let you plot individual points "manually" and some software does not.

I suspect that these issues are less about which technology we use, since paper and pencil is itself a form of technology, and more about how we interact with the technology when learning graphing (or any other mathematical technique). We need to think carefully about what the technology allows us to do, and what underlying concepts we want students to learn. It may be that some concepts that used to be fundamental no longer are with the new technology, and other concepts become more important to learn. I suspect that insufficient research has been done on how pedagogy should change with the use of various technologies in mathematics, particularly ones that change so fundamentally the task of the student.

Online education is as effective as face to face instruction

 Online education is as effective as face to face
(Image credit: ASU presentation)

The research highlighted below the statement "Online is as effective as face to face" was used in a presentation at the ASU Education Innovation Summit to justify students in a k to 12 setting taking online courses.

From the first meta-analysis written by the US Department of Education,

"The meta-analysis found that, on average, students in online learning conditions performed modestly better than those receiving face-to-face instruction…"

Sounds promising, let’s read the rest of the abstract, shall we?

"…An unexpected finding was the small number of rigorous published studies contrasting online and face-to-face learning conditions for K–12 students. In light of this small corpus, caution is required in generalizing to the K–12 population because the results are derived for the most part from studies in other settings (e.g., medical training, higher education)."

That sounds a lot like the authors of the meta-study specifically recommended against using this meta-analysis as support for online learning in a k to 12 setting. I wonder why the presenter used this study?

We cannot draw conclusions on the effectiveness of online learning (as opposed to blended learning – wherein a student learns from a mixture of online and classroom activities) for k to 12 students based on the effectiveness of online learning in a post-secondary setting.

  1. The motivations of k to 12 students and post-secondary students are different.
  2. Many post-secondary classrooms do not represent the most effective pedagogy, so it may be easier for online learning to be equivalent or superior.
  3. Access to resources necessary to be successful in an online setting (like a computer) are more prevalent in a post-secondary setting.

A problem with digital books

A bookshelf full of books
(Image credit: Harold Bakker)

When I was growing up, my house had a 50 foot wall full of books which our family had inherited from my grandfather with the house. Whenever I was bored, and the weather was ugly, I would pick a book off the shelf and read it. I devoured books from the shelves, some of which were probably inappropriate for my age, and some of which are considered classics. The library available in my home helped me become a better reader because I never ran out of something to read.

This is an experience my son has now, because we have a library of books in his room (albeit a much smaller library). However, as books become digital, it will be much more difficult for our library to be visible and accessible to my son. Parents will tend to make more choices of what their children should read. Licensing on books that prevents them from being copied means that children will likely have to explicitly ask for permission for every book that they read from their parent’s collection. Books will be selected less at random, and because we will be more likely to select books entirely based on our own interests, we will be less likely to be exposed to new information. Note that it would be relatively straight forward to set up "book servers" in houses that could act as personal libraries, and serve the same function, but current digital rights management on books makes this impractical (not impossible, every DRM has its weaknesses).

We are headed toward a society where books are not visible and accessible in our houses. If the books are invisible, they might as well not be there.

Separate science history from science inquiry

Zombie Feynman on Science
(Image credit: XKCD)

It occurrs to me that we have two goals for science education. One is to teach students what existing science is known, and how it can be applied to our lives, or how it is interesting to us. I call this first purpose, "Science History." The other goal is to teach the process of doing science, of thinking scientifically. This purpose, I call "Science Inquiry."

I think we should separate these two purposes into separate courses or domains, because the purpose of the first is diluting the effect of the second. Many children finish school thinking that science is a collection of facts known about the world, and do not spend enough time learning how those "facts" were derived.

Labs are a good start to learning science inquiry, but many experiments done in labs have issues.

  • The labs are rarely designed by students. This leads to underestimate the difficulty in designing a good experiment, and to over-emphasize the paperwork portion of science.
  • The labs rarely take more than 30 or 40 minutes to complete. Students rarely have to repeat a lab because of experimental error. They learn from this experience that laboratory science can be easily parcelled into sitcom-like episodes.
  • Students do not learn enough about the reasons why we have designed lab reports, and think of the portions of a lab report as blanks to be filled in. Quite often they will fake data so as to complete the boxes faster.

A Science Inquiry course would focus on the process of doing science, and less on the students learning existing scientific knowledge. Obviously students would be likely to find connections between the Science History course and the labs that they design, and hopefully they will also see connections between their Science Inquiry and other domains of knowledge.

A Science History course would focus on what existing scientific discoveries we have made, who made these discoveries, and what are the stories around these discoveries, and how these discoveries impact our lives. It might cover some principles behind the philosophy of science, as well as the connections between science and other domains of knowledge (like math for example).

Right now, many schools see Science Inquiry as optional or even an inconvenience. This suggests to me that some people think that thinking scientifically is an inconvenience or too troublesome to teach, and this scares me. While "thinking scientifically" isn’t the only way to think, it’s an important one, and certainly, we should all learn how to do it. I also think that Science Inquiry is indistinguishable from thinking scientifically. If you remove the inquiry, then it isn’t really science.

Tinkering for students

I watched Caine’s Arcade yesterday (see below) and while it is a bit sad to me that an amazing kids’ endeavour has turned into an opportunity for a film-maker, the movie itself is very touching. I recommend watching it.


Caine is not an unusual child, but he has had a number of unusual circumstances which have allowed him to create his arcade. First, he has dedicated space that has been created for him to pursue his interest. This is unfortunately extremely uncommon for many children today. He has parents who completely support their son’s exploration, and act as mentors to assist him. He has access to the materials and tools he needs. He is not judged on his creations by a rubric, or by a test, but rather his creations are seen as part of a description of who he is. The creations Caine has made are only physically distinct from him; they can be seen as an extension of himself.

Tinkering to me means, the ability for kids to create and explore in ways not bound by the current rules and structures of schools. The original explorations of programming using Logo to me were more about tinkering than computer science. Unfortunately, over time, tinkering on a small scale looks like a useful activity for students to do, and so it gets scaled up. For example, this page about using Logo in learning now includes sample projects with "step by step" instructions. When creation becomes scripted, it ceases to be creation, and becomes assembly.

So instead of scaling up tinkering, what I’d prefer to see is individuals given freedom and resources to produce what they think tinkering space should look like. Instead of thousands of identical tinkering spaces, each space should be unique and suited to the community in which it exists. The explosion of art work created in community centres has happened not because we tried to create a formal structure for people to do art in society, but because we provided spaces and resources for these centres to develop.

I’d like everyone to have the opportunity Caine has, to explore the world and build extensions of themselves in it.

Computing in schools

A possible future for computer science in schools

Gary Stager posted "Dumbing Down" a few days ago, which is a passionate plea for computers to be used for computing in schools. He writes:

Although I’m only 48, I have been working in educational computing for thirty years. When I started, we taught children to program. We also taught tens of thousands of teachers to teach computer science to learners of all ages. In many cases, this experience represented the most complex thinking about thinking that teachers ever experienced and their students gained benefit from observing teachers learning to think symbolically, solve problems and debug. There was once a time in the not so distant path when educators were on the frontiers of scientific reasoning and technological progress. Curriculum was transformed by computing. School computers were used less often to “do school” and more often to do the impossible.

Gary’s argument is (mostly) sound, and indeed, I argued for almost exactly the same thing in the keynote I presented in Alberta in February. Of course, both of our arguments have a flaw.

Our purpose in introducing computing is to both use the full power of a computer in schools. Indeed, the way we currently use computers in schools is much like using cars for their heaters; sure the cars will keep us warm, but it completely misses their potential as transportation devices. This analogy is somewhat apt, since the computer (as Dr. Papert has pointed out) can be used to transport kids to Microworlds.

Peter Eden said:

“I am interested in your comment that the power of computers as a tool is almost superficial until you learn to program. Others peoples’ programs are like using the computer to do something that can be done by other means. Word processing is really just typing. Many maths programs are really just calculators. A database is really just a record keeping system. But once you begin to program a vast new world opens up. Everything you program becomes a new tool. Because its your tool you can modify it. You modify it in ways you never imagined when you began.” (Peter Eden, personal communication, January 29th, 2012)

So we agree that learning how to program is an excellent endeavour, and one that basically everyone should learn how to do. What I think Gary and I disagree about is whether or not this particular learning should happen within the formal structure of schools.

Gary points out in his article that they had "tens of thousands" of teachers involved in learning how to program so that they could teach their students. Tens of thousands is a lot, but there are millions of teachers world wide. Tens of thousands is a drop in the bucket compared to the number of people who are teachers.

If we were to teach them all (or a sizable subset of all of the teachers) how to program so that they could teach their students, we’d have to institutionalize learning how to program, and I think that this would be a disaster. We’d end up with benchmarks, prescribed curriculum, and standardized testing.

I did a mathematics degree, and one requirement of the degree was that I take a course in computing, which I think is a perfectly sensible requirement. The problem was, I had to do a 1st year computer science course, and this course was ungodly boring. It was so boring, that despite attempting twice to finish a 1st year computer science course, I gave up, and did a "Computing for Mathematicians" course instead. Of course, I knew how to program already, so the programming skills themselves were not very useful to me. However, what I learned from this experience is that it is tremendously easy to take something full of life and turn it into something deadly dull. If every student was forced to endure the same kind of learning I experienced during that 1st year computer science course for 12 years without the opportunity to opt out, none of them would ever touch a computer again.

It is common for instutions like schools, to take endeavours which are exciting and interesting on a small scale, and attempt to bring that exact same experience to everyone. Unfortunately, most often these endeavours pick all of the wrong parts of the activity to "scale up." In scaling up mathematics education, we took an experience where people mostly played around with ideas, and turned it into fill-in-the-blank worksheets, completely destroying the purpose of learning mathematical thinking. Computer science in schools would fall into the same trap as science education has, which is that people think the purpose of science education is to teach facts about science, instead of a way of thinking.

What I would prefer is for space to be created outside of instutions for this type of thinking to occur. Much like we have community centres for art, and for physical activity, we could have recreational centres for computing. Instead of instutionalizing (and eventually centralizing) the learning of computing, I’d like to see it de-instutionalized. I’d like to see a thousand different models for learning computering rather than the inevitable staleness that would occur if it were introduced en masse to schools.

The language of technology

Technology has a language, a history, and it shapes our culture. While the focus of this article is on the language of technology apparent in Microsoft Word, every technology we use has similar traits.


Check out the "ribbon" (or menu bar) of Microsoft Word.

Microsoft 2010 Ribbon


First, when you examine Microsoft Word, and many other programs like it, you’ll notice that there are many visual cues within the program as to how it works. What is less obvious is that each of these visual cues relies on the person viewing it to understand what the cue means. These visual cues are a form of language, and it is often this language which poses a significant barrier to using the technology. If you don’t understand the language being used, then every function of the program you want to use requires you to memorize the sequences of steps needed for that function.

Look at these examples of how language is used in Microsoft Office. It’s probably somewhat obvious what B, I, and U stand for, but what does the little triangle to the right of them mean? My mom didn’t know what the abc meant, and I know some people don’t know what the x2 and the x2 mean either.



The question mark might be obvious, and it might not. It doesn’t look like a button, so one might not know that one can click on it for additional information. Further, buttons themselves are a form of language, and so even if this were shaped as a button, someone could conceivably not know it was something to be clicked on.

Help icon


In the margin bar, there are a couple of interesting 5 sided polygons lined up on top of each other. These are intended to indicate the different types of margins and indents you can apply to the document. Why are these icons chosen?



The origin of the icons chosen for the shape of the margin/indent icons in Microsoft Word appear to be very similar to the shapes originally used to represent the same functionality on a type-writer. Why those shapes were chosen for the type-writer, I don’t know.
(Image credit: Awkward Science)

More examples: 


Triangle drop down


As a final example, look at the Save file icon. Virtually none of your students will know the origin of this icon since none of them likely grew up using a computer with a floppy disk drive. Still, they know that they click on it to save their work, but this is language they’ve learned from us. 

Save icon

Instead of thinking of teachers or children as being digital immigrants or digital natives, we should think of their exposure to the language of technology, and how knowledge of this language influences their ability to use technology.