Tag Archives: complexity

That moment when…

We live in a pretty safe world. Or at least, where I am it is pretty safe. Despite the excessive portrayal of violence in the news, the chances of injury from either accident or crime has been on the decline for some time. Parents may become (needlessly?) overprotective, and students can develop a sense of complacent protection. That is, if there is possible danger, that Someone is Taking Care of It.

So yesterday we were talking about the flotsam and jetsam of the solar system – comets, asteroids, meteors etc, and we were discussing the recent bolide over Siberia, the close approach of 2012DA14 on the same day, and the Tunguska event of 1908 – when one of the students asked “So what do they do when they see that one of these is going to hit Earth?”

“Who is ‘they‘?”

“You know, astronomers and NASA and stuff”

“Well, there isn’t really a ‘they’. To look for these requires funding, and with tight budgets, few government bodies want to fund projects that do not have foreseeable, immediate benefits. So there aren’t many people looking.”

“Ya, but, if they do find one, what do they do? Like, just…” I think he was waiting for me to finish his sentence. Which I didn’t. “Just… just…”

“Crash a nuke into it?” another student suggested helpfully.

At this point I had to make their world a little bit less safe, and I explained that, at present, there is nothing we can do. Only if a potential impact is discovered years in advance is there any chance of altering the course of even a small asteroid, and even that requires technology we don’t actually possess. Not that it isn’t theoretically possible, but it would require a very rapid design and construction, and it could only be launched within a narrow window of opportunity. It’s not the movies, and it’s not off-the-shelf parts. In other words, at present, there is nothing we could do.

The take away message of the discussion was there is still plenty of opportunity for Science to save the world, and a need for people to step up and make it happen. Though maybe not a worldview change for most students, it was a chip in the safe bubble they see of the world, and a real, practical. and important application of what we have been learning.

And that’s all I can ask for.

Losing the narrative

Please bear with me as I muse over these ideas on paper – well, digital paper. As i tell my students (or, as they might say, nag them), put ideas down to help you think them over, because you can only juggle so many ideas at once in your head.

And there I go again, providing back story…

Most of us in the teaching profession have commented, lamented, bragged, or at least observed that teaching and learning ain’t what it used to be, due to some combination of changes in students, their teachers, society, culture, and values. In particular, I am finding that over the last few years I am losing the narrative.

Have you noticed that when you study a complex subject in depth, that it seems to get easier the more you learn? At first glance this seems counter-intuitive – you might think that the more you learn the more you have to remember, making it harder. What is happening, however, is that we are completing a giant puzzle. At first, the pieces are separate, and make little sense. But the more pieces we have, the easier it is to see the picture, and everything starts to reinforce everything else. We begin to understand the system, rather than having to remember the pieces.

It has always been my stated goal to help students move toward understanding the system, rather than trying to remember the pieces, and so I try to provide as much context as possible, to weave a narrative around the whole on which the parts can be pinned. But I am finding it more and more difficult to transfer that narrative. Maybe it’s me, maybe the students, maybe the curriculum, but I think it is some combination of all three.

A few years ago a colleague from a different school took a sabbatical year, and as part of his research, he read the Campbell Biology textbook from cover to cover. He said the truly remarkable thing was that it read like a novel. It is a good text, but when read from start to finish the entire text is a narrative, with each new concept carefully pinned to the storyline. Meanwhile, I am finding the Science curriculum I am required to teach to be more and more characters, and not enough plot.

One contribution to the problem is the shift towards brevity. I am more of an old-school orator, and trying to weave a complex contextual framework in a soundbite world is a challenge. I struggle somewhat with trying to balance context and facts – there is really only time in a course to do one of them well. Experience tells me that context is harder for the students to learn, while facts are easy to dig up in the information age. But it is also less concrete, and harder for the students to see the relevance of. They see the facts and details as the things that should be “taught”, because that is what they are used to. And what their parents are used to, and what we are used to.

I find that while students today are capable of finding out information quickly, they develop the sense that any question has an answer than can be found quickly, and they are less likely to spend time digging and working through problems. As a result, they need more guided work time during class when I can help get them unstuck as they work through the more complex material. They are less likely to complete those tasks on their own at home. So while context an narrative is becoming more important to teach than ever, I have to chop my lessons down to “just the facts Ma’am” in order to maximize hands-on time.

Flipping the classroom (which I am experimenting with in my grade 9 astronomy unit) is one way to help deal with this issue, though so far my results have been mixed. Modelling is another approach that helps students build their own context as well as facts, but it requires considerable training to accomplish. Blended learning can provide a self-guided course with teacher supervision and support, but requires a certain maturity and self-motivation from the students to be effective.

I’m not sure what the answer is, or even if there is an answer. Certainly not a quick answer. But it is a problem worth spending time exploring. My students are worth it.

Getting to “I don’t know”

I like Isaac Asimov’s quote about Science:

The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ (I found it!) but ‘That’s funny …’

I tell them repeatedly that all the interesting stuff in science is the unexpected. When things don’t quite turn out how we thought it doesn’t mean its wrong – just that there is more going on than the oversimplification of textbooks would lead us to believe. I love it when we encounter something odd – for me, the best thing that can happen in a Science class is the students push the boundaries of what I can explain, so we have to learn together. I love getting to “I don’t know”.

Today, we were examining resonance in a tube open at both ends, when it resonates after being “bopped” on one end. Here is the spectrogram:

Frequency is on the vertical axis, time horizontal, and intensity is the brightness. Hitting this tube clearly produces frequencies of 200 & 400 Hz. The fundamental frequency of a 40 cm tube open at both ends is 400Hz. So where does the 200Hz sound come from?

Ah, well, hitting the tube on one end temporarily makes it closed at that end, so it should, at that time, resonate at 200Hz. Fine. But why does it continue to resonate at 200Hz? The 200Hz resonance clearly continues well past the peak of the 400Hz resonance, and yet the tube should not be able to sustain it with both ends open. So why does that happen? I don’t know.

Isn’t Science cool?

Moving toward authenticity

Consider the following question:

A dog running for a ball takes 4.6 seconds to reach the ball that lands 59 metres away. How fast did the dog run?

That is a fairly typical introductory physics problem, dealing with uniform motion. It is also the type of question used in grade 6 to practice the manipulation of fractions. So it’s an easy question. It is easy because all of the values are provided explicitly, and the formula to solve it is straightforward (v=d/t). When explicit values are given, a physics problem – even a more complicated one – devolves to a cookbook math problem: find the right recipe, apply the correct formulas, spit out the answer. The end result is an excessive reliance on explicit information, and a dissociation from the actual, authentic events.

It also leads to an over reliance on the math to make a question more challenging. Not that there is anything wrong with more challenging math, but that should not be the sole determination of difficulty.

So let me show you how I pose the same question:

How fast is my dog?

[stream flv=x:/www.teachscience.net/wp-content/uploads/2010/12/dog_run_1.flv embed=false share=true width=640 height=360 dock=true controlbar=over bandwidth=med autostart=false /]

(full res .mp4 here)

This is essentially the same question as above, but suddenly much more involved. And it has no “correct” answer – the best anyone can do with this is provide a reasonable value. The complexity arises from having to measure (or determine) values that are not given explicitly. Which is all of them (well, almost. There is a metre stick lying in the grass…). And as I have written before, having to make measurements requires a lot more in the way of critical thinking.

There are a number of ways a question like this can be analyzed, which I will cover in later posts.

Moving Beyond GRASP – GAP Analysis in Problem Solving.

When I was in school, we were taught a process of problem solving called GRASP, an acronym for:


At the time it drove me nuts, because it was the least helpful technique for problem solving imaginable. Analyze and Solve. Right. How? GRASP provides no insight whatsoever on how to solve problems, it is just a format for making answers look pretty, and to provide formatting a teacher can grade using a checklist. It is not a problem solving technique, it’s an answer presentation format.

To my great consternation, I find that GRASP is still used as a “problem solving technique” in today’s textbooks. My goal here is to provide an alternative that is actually useful.

Many problems in science require steps that are not immediately apparent to people learning the material for the first time. With experience to draw on, students can relate problems to ones they have seen before, but the first time a problem is encountered there should be a procedure they can use to solve it without relying on previous experience. Experienced practitioners can solve novel problems, so how do they do it? Many people would say that they develop an “intuition” for problem solving, but this simply means they are unaware of the steps they are performing. From careful analysis of my own problem solving “intuition” and that of colleagues, I have pieced together a series of steps that can be used to solve novel problems that mimics that “intuition”.

I call this approach the Bridge Method, or the GAP Analysis Process (where GAP recursively stands for GAP Analysis Process…). With this method, the concept is to lay a framework for the problem, starting from the answer and working backward towards the question. Once the framework is complete, the solution can be worked out sequentially.

The process begins, as with the GRASP method, by jotting down the given information and the type of information required for the answer. The difference is that these pieces of information are written on opposite sides of the paper (or screen or whiteboard). This forms the gap we will span:

The next step is to identify what is required to solve for the answer. If sufficient information is available in the question, then the problem can be solved immediately. Otherwise, we must identify what is required to solve for the requirements for the solution, and so on. Repeat until a requirement can be fulfilled using the givens in the question:

Framework complete!

By working backwards toward the question, we now have a trail of breadcrumbs we can use to guide us, step by step, back to the answer:

If you are an experienced problem solver, you probably perform the first steps in your head. By working backwards from the answer, you build a mental framework of how to get to the answer from the given variables. But that skill comes with practice and experience. It is human nature to want to start at the beginning – we are very linear creatures that way. Students seeing a problem for the first time, don’t have that reverse-engineered mental framework; they want to start at the beginning, so the first step is not intuitively obvious. Therefore, it is important to teach effective problem solving explicitly, and model the steps frequently to show them how to build those skills.

I am not so immodest as to think that this is the only method to solve problems – I am sure there are countless others, as well as many riffs and variations on each. But this is a method I use, one I teach to my students, and one that seems effective.  And it can work equally for almost any type of complex problem – it need not be numeric. Questions in physiology and ecology can also be solved using this process, as long as there is some causal chain between the starting point and the conclusion.

Information Ecology and 21st Century Learning

(Originally published on my Budget Astronomer website)

I like organic metaphors for information transfer and learning. I trained as a biologist, so it is not surprising, but beyond that – there is something right about a complex, non-linear  process, as opposed to an orderly one. Orderly things are only that way because constraints have been put on them.

One of the ideas I really like is that of the Information Ecology – a term I am sorry to say I did not coin. It is a concept that relates the flow of information to an ecological system. So, let’s go back to a little refresher on ecology….

Remember what you leaned in school long ago about food chains and food webs? Producers, consumers, more consumers, top predator, detritovores and decomposers? Well, here’s the tough news. You never learned it right in the first place, and here’s why. Your teacher didn’t understand it. Your teacher learned it from a textbook that was as dry as the one you learned from, and was even more outdated. More’s the pity, as the real beauty of ecology is in the complexity and interractions – things that are very difficult to convey effectively in a textbook.

In any ecology, There is a foundation, and that is the producers. Electromagnetic energy in the form of light is used to convert CO2 to chemical energy, in the form of biomass. This can then be used to sustain each successive level. At each level, however, there is less useful energy, as much of it is used up by the previous level. As a result, in most food webs producers have the largest numbers, and each successive level of consumer has fewer and fewer numbers. This does not mean, however, that the producers are the most important, per se, since each and every trophic level is entirely necessary for the web to function. Remove one, and the entire thing collapses. There really is no “Most Important”.

The Information Ecology can be outlined with many parallels to a food web. However, it needs to be drawn upside down. In the living world, producers are common and produce a large but finite amount of usable energy for the next level. Each level is smaller and smaller in number, with final consumers being the most scarce. In the Information Ecology, primary producers are scarce, and produce a limited amount of primary information. This information, however, can be consumed an infinite number of times by information consumers. These consumers, in turn, can settle for mere consumption (terminal consumers), or they can take the information and in turn produce something of their own using what they have gleaned. When information is consumed and something new is produced, there is a significant chance that the quality of that information will decline. In other words, the information gets ground up in a rumour mill. Broken telephone. Take your pick of metaphors.

So in an information ecology, we should be able to qualify information by its proximity to its origin (of course, whether the origin itself is reliable is another matter altogether!). Is this to say that all information should be tracked down to its source? For graduate studies, definitely. For the purposes of K-12 education, the source information might be too rich, and completely indigestible. A secondary source may provide similar information presented in a much clearer fashion.

One thing that is clear, however, is that in an information ecology, pure consumers do nothing of benefit. It is only producers who cause the information ecology to grow.

So what is the take-away lesson? It is that quality learning is tied to the quality information, and that information is really only processed when it is used to produce more information. Today’s learners should be encouraged as much as possible to both produce and consume as close to the primary production level as possible.