Looking back on my time spent in college and recalling some of the best and most interesting times I had, there are several instances that stand out. Surprisingly, to some, most of them were the labs and research I worked in. Whether it was the tedious photometry of 1,500 stars in a cluster during

my internship, or the laborious pouring over journals and trying to come up with a future research plan for

my flare star research or even the advanced physics labs in which we spent far too much time for far too little credit demonstrating principles we had long since taken for granted, that final result of getting an answer and knowing that it was

*meaningful* was a wonderful feeling of success.

So what is it we teach in high school labs?

Thinking back to the labs I did in high school, I can only remember about three labs. One was rolling blocky cars down inclined planes and trying to measure the force of gravity. One involved some pulleys and who knows what the point of that was. The last was spinning electrons in a magnetic field in some manner that caused them to scintilate and the diameter of the circle could be measured to determine the mass of the electron.

I always liked labs at that point, but in reflection, it was for a very different reason. It was a free day or two to not have to think. All we had to do was blindly measure what we were told, plug it into the equation we were given, and pop out numbers that were off from the values we should have been getting by, quite often, nearly an order of magnitude.

I can't be certain that my high school experience is completely indicative of the situation in the majority of schools (although Time magazine did choose my high school as representative of American high schools in 1999 when they did an

expose on what life in high school is really like since Columbine), but assuming such conditions are common, I see two major problems with this.

The first is that such labs don't hold the students accountable for why they do anything they do in such labs. There is little connection between what is taught in the lecture portion, and how the lab was created to illustrate or test the concept in question. Pick up any journal article and there is always a lengthy section right at the beginning setting up the theoretical framework before

*any* description of methodology in an experiment is even approached. Yet this has always been absent from my memory of high school labs as well as the introductory astronomy labs I taught during my time at KU. While I was able to insert this material in my own labs via my lectures prior to the start of lab, this, as best my memory serves, was completely absent from any labs in lower levels.

The other thing that is similarly neglected in high school labs is something that actually stands out like a sore thumb: The amount of error. Error in measurements is, of course, unavoidable. Whether its due to inherent limitations in tools, or variables that cannot be constrained at such levels (eg. how do you try to approach friction and drag in carts when the math needed to do so is at least two years of college beyond what most high school students will ever obtain), the order of magnitude errors I discussed earlier are often just swept under the rug.

So what does this tell students? The message is that science is sloppy. Measurements can be wildly different and it's ok.

What's not included, but I feel should be, is at the very least, some sort of quantitative analysis of the error involved. In my own classroom, I've seen this attempted, and the way I've always seen it done for low level classes is wholly disappointing. In most low level classrooms, the method to determine error is that you take the difference between the "True" value and your value, and divide it by the "True" value. This gives the amount that you're off.

But since when does real science have a "True" value by which to compare the derived value?

Never. And we wonder why people nod in agreement when creationists push the notion that science is dogmatic when we're the ones putting ideas of "True" values in their head?

This methodology seems entirely counterproductive. While equations to determine error are obviously beyond the capabilities of high school students, I feel there is still a solution.

Although the capability to carry out higher mathematics is certainly constrained to such students, what I do not feel is limited is the ability to show the qualitative reasoning

*behind* the math. Even the concepts of calculus aren't beyond the capabilities of students.

To give an example: In the lab I taught at KU, we had an assignment in which students were required to measure the position the sun set along the horizon throughout the semester (ie, the azimuthal angle). One of the questions we required students to address was "When was the rate of change the fastest?"

To those that have taken a calculus course, the answer is instantly obvious: the highest rate of change is the point on the graph with the steepest slope.

While, as an instructor, I can point this out to students and they'll swallow it, the point becomes even more convincing when a bit of dimensional analysis is performed and I demonstrate that the slope of the graph does indeed give the correct units for the rate of change!

Similarly, I feel that, even if an important equation is, in a quantitative sense, too difficult for a student, we should at least approach it qualitatively, and then do the quantitative bits for them. In other words, the instructor should solve the equation for the given lab so that students (once they understand what the equation is doing) may simply plug in the necessary numbers.

This alleviates the problem I have presented; Instead of telling students that there is error and doing vague hand waving claiming it's "friction" or other ways of sidestepping it, it lets students know that, in real science, not only do we consider the error in our techniques, we can even say

*how much*!

There is, of course, another, probably simpler solution: Get rid of labs with such high inherent errors. Instead, find labs that can be easily constructed with minimal tools that still result in high accuracy measurements.

My favorite lab I've seen along this line is one involving measuring the speed of light with nothing more than a bag of chocolate chips, a microwave and a ruler. I've done the experiment myself and even gone through complete error analysis. The result I got for it had less than a 1% error and fell, within significant digits and the error bars, right on top of the canonical values of the speed of light!

Now why didn't I ever do this in high school?