Science and math, by virtue of the paper medium through which they are most frequently disseminated, are intrinsically oversimplified. The questions used have explicit values, and a single correct answer. Questions like:
Two trains leave Montreal at the same time, one heading east at 110 km/h, and one heading west at 130 km/h. How far apart are the trains after 2.5 hours?
Many students will tell you, “who cares.” And they would not be far off. This is not an example of a physics problem in uniform motion, but a simple calculation exercise. Now, to be fair, exercises in calculation are useful to practice and build skill in calculation, but this is only worthwhile if these skills are to be used for something else. Even more “realistic” and challenging questions, such as:
“A pen rolls off a 0.89 m high desk with a horizontal speed of 0.2 m/s and falls to the floor. How far from the base of the desk does it land?”
still require only that students follow the steps to solve the problem, without any real science happening. The main reason is that they are given everything. When values are given explicitly, a question becomes one of a mathematical solution, rather than a discovery or investigation. Over use of this type of question instills the notion that science is clear-cut, and has unique “correct” answers. This is why it is important to provide students, as early and as often as possible, questions that require them measure for themselves. Measuring requires actual thought and analysis – what units should be used? What angle should it be viewed at? Which part should be measured? How do we know the measurement is accurate and reliable?
In physical science, the concept of significant figures revolves around the precision of measurement, but without experience in measuring, this concept is lost, and becomes abstract and theoretical, rather than necessary. This ties in to our disconnect from craftsmanship that I discussed previously, because those who work with wood or metal or fabric have an intrinsic sense of what measurement means, and its limits.
At the start of this year, I gave my grade 9 students an assignment: go home and measure your cat. Or dog, or hamster or goldfish. This simple activity provided all manner of challenges – how do you measure a flexible, fuzzy, mobile creature? Do you include fur and whiskers in the measurement? do you measure them standing up or lying down? Naturally elongated, or stretched? Asleep or awake?
In the end, those that succeeded at least came back with a number they could be reasonably certain of – in centimetres. None of them could be certain of a number in millimetres. And this provided the first actual example of why significant figures are important. It also provided a question that only they could answer – I have no way of knowing the size of their cat, so their answer, if reasonable, cannot be wrong. But nor can it be “proven” to be correct. So the value is data, data that they have ownership of, and data that only they can verify. And that is a powerful thing.
So the simple act of measuring for themselves can empower students, promote critical thinking, and give them a better and more intuitive grasp of scale, units, measurements and error. So if you are reading this, and you rely heavily on textbook problems, I encourage you to wean your students off the paper, and send them off to measure the values for themselves.