Year: 2012 (page 10 of 14)

From the National Mathematics Advisory Council of 2008 final report:

The use of “real-world” contexts to introduce mathematical ideas has been advocated, with the term “real world” being used in varied ways. A synthesis of findings from a small number of high-quality studies indicates that if mathematical ideas are taught using “real-world” contexts, then students’ performance on assessments involving similar “real-world” problems is improved. However, performance on assessments more focused on other aspects of mathematics learning, such as computation, simple word problems, and equation solving, is not improved.

It seems to me that if a real world focus in mathematics makes students more able to use mathematics to solve problems from the real world, then this would make much of the mathematics instruction we do more useful. What exactly is the goal of those simple word problems anyway? Aren’t they an effort to add some context to the learning of computations, so that students are able to use mathematics to solve problems? And if students are going to graduate from school, aren’t the problems they are most likely to face going to come from the real world?

Well, okay, some people do burn themselves twice, but hardly anyone. The message is loud and clear, touch the stove and you get burnt, which hurts. There are lots of other things in life people learn the first time.

I was mouthing off in class one time about how much I hated the school newspaper, when Michelle turned to me and nearly with tears in her eyes said, "Do you really think that, David?" Of course, I was just making noise, and didn’t really mean it, but nothing I could do could fix that moment. I had jammed my foot far into my mouth, and I was not able to back-pedal smoothly. 20 years later, and I can still remember this exact moment. I didn’t need 15 slightly different examples with the answers in the back of the book to remember this moment, and the lesson that came with it.

How can we make more of the learning in school have the same kind of stickiness? Do I remember these lessons because they hurt, or because I had a strong emotion attached to that moment?

I love this quote shared by Gary Stager via the Daily Papert.

“They first learn engineering, then from there they progress to learning the ideas behind it, and then they learn the mathematics. This would be inventing, it’s a little probe toward inventing a different kind of content. It’s not a different way of teaching; it’s not pedagogy. It’s different knowledge. It’s a good example of turning knowledge – turning learning – upside-down. Instead of starting with this abstract stuff we had from the nineteenth century, let’s start with stuff that’s really engaging for the children, out of which the deeper ideas can develop.” Seymour Papert, 2004

Instead of students learning a bunch of theory, and then being able to apply it to practice, they would engage in building and in creating, which would provide a need and a motivation for the knowledge behind the thing that they are building. One thing that is missing in great degrees from our school is motivation. Why do I need to learn this math when I can see no use for it?

It’s not to say that there aren’t fascinating ideas which are worth learning without something practical to support them, but this is not the general tendency of school. We do not usually teach (with obvious exceptions being good teachers) that which is interesting. We teach practical knowledge. We tend to say, "Oh, we’d like kids to be able to be doctors. Well, what do they need to know? Let’s teach them that." with the result that students do not see the connection between what we teach, and what they can do with it.

So I read some interesting research on student incentive progams which has a couple of very important paragraphs. Here’s the abstract:

This paper describes a series of school-based randomized trials in over 250 urban schools designed to test the impact of financial incentives on student achievement. In stark contrast to simple economic models, our results suggest that student incentives increase achievement when the rewards are given for inputs to the educational production function, but incentives tied to output are not effective. Relative to popular education reforms of the past few decades, student incentives based on inputs produce similar gains in achievement at lower costs. Qualitative data suggest that incentives for inputs may be more effective because students do not know the educational production function, and thus have little clue how to turn their excitement about rewards into achievement. Several other models, including lack of self-control, complementary inputs in production, or the unpredictability of outputs, are also consistent with the experimental data.

Notice the sentence in bold. Incentives for outputs (like let’s say student test scores) does not improve performance. Incentive for inputs (like increased collaboration, more training, working in high needs schools) does. Of course, the benefits gained by the incentives are not terribly strong (with the exception in the study of students being paid to read more) and so any benefit from paying teachers for changing the inputs to education may be minimal.

The merit pay for teachers movement has it all wrong, and the very people in promoting merit pay for teachers have access to this research. In fact, the list of acknowledgements at the beginning of the paper is a veritable who’s who of the leading education reformers in the US.

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?

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.

Questions:

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?