How Deep is Deep Enough?

“Perfection is the enemy of the good”
Voltaire

 

Education is about depth. Generally, we start with overviews and the big picture. Then we move on filling in the gaps and providing additional information. To fulfill one of my general education requirements, I took an Introduction to Western Civilizations course. We covered the rise of western civilization from prehistory all the way up to the modern age. This course included only the most essential points.  If I had gone on and studied western history, we would have expanded on the main points covered in the Introduction to Western Civilizations course.

As an example, there were courses on the Middle Ages like The Medieval World and Introduction to Medieval People, and then going into more depth Medieval Women. Each course led to a narrower but deeper dive into the topic.

Another example of this depth occurred during my science education. In my Introductory Chemistry courses, we learned about the laws of thermodynamics; there are four laws if you include the zeroth law. The laws of thermodynamics were only a single chapter in my introductory textbook, covered in just a couple of class periods.

Several years later as part of physical chemistry, I took thermodynamics, a required course for chemistry and biochemistry majors.  We spent the entire course studying the laws of thermodynamics, including mathematically deriving all the laws from first principles.

While I have used a lot of my chemistry over the years, I’ve never used that deep dive into thermodynamics. There are fields and research areas where this information is needed, however, I wonder how many chemistry students need this deep a dive into thermodynamics.

Determining what to teach students and what depth they need to learn each of these topics is a critical point of the educational design process. There has recently been a change to a topic that all (US) science students need to cover, the International System of Units abbreviated SI for Système International d’unités or classically the metric system.

The SI system is the measurement system used in scientific research. The SI system has seven base units, and 22 (named) derived units (made by combine base units).   In the US we teach students the SI system because the US is one of three countries that didn’t adopt the SI system. Science students need to use the SI system; the question is how much they need to know about the system.

The French first established the original two unit’s, length (meter) and mass (kilogram) in 1795. The system was developed to replace the hundreds of local and regional systems of measurement that were hindering trade and commerce.  The idea was to create a system based on known physical properties that were easy to understand, this way anyone could create a reference standard.  The definition of the meter was 1/10,000,000 of the distance from the North Pole to the equator on the Meridian that ran through Paris. The Kilogram was the mass of 10cm³ or 1/1000 of a cubic meter of distilled water at 4°C.

Basing the units on physical properties was supposed to give everyone the ability to create standards, in practice difficulties in producing the standards meant the individually created standards varied widely.  In 1889 the definitions of the meter and kilogram were changed to an artifact standard; an artifact standard is a standard based on a physical object, in this case, a platinum-iridium rod and cylinder located just outside of Paris France.

The original Kilogram stored in several bell jars.
National Geographic magazine, Vol. 27, No.1 (January 1915), p. 154, on Google Books. Photo credited to US National Bureau of Standards, now National Institute of Standards and Technology (NIST).

The use of the artifact standers lasted for quite a while; however, as science progressed we needed more accurate standards and the definition’s changed again, the new idea was to define all the base units on universal physical constants.  Skipping over the krypton 86 definition, in the 1960s the definition of the meter was changed to the distance light travels in a vacuum in 1/299,792,458 of a second (3.3 nanoseconds).

The speed of light was chosen to define the meter because it contains the meter, the speed of light is 299,792,458 m/s. This definition might seem a little strange, but it makes a lot of sense.  The speed of light is a universal constant, no matter where you are the speed of light in a vacuum is the same. To determine the length of the meter, you measure how far light travels in 3.3 nanoseconds. If your scientific experiment requires higher precision, you can make a standard with higher accuracy, instead of using 3.3 nanoseconds you could measure how far light travel in 3.33564 nanoseconds.

On November 17, 2018, the definition of the kilogram changed at the 26th meeting of the General Conference on Weights and Measures. The new definition of the kilogram uses the Planck’s constant which is 6.62607015×10-34 Kg m2/s.  Like the meter, the definition of the kilogram applies a constant that contains the standard.  Just like the meter the determining the precision of the kilogram is dependent on the accuracy of the measurements.

Up to this point, we’ve taught the kilogram as an object; the definition of the kilogram was a cylinder just outside of Paris no matter what happened that cylinder was the kilogram. However, with these new definitions, it becomes possible for students to derive the standards themselves. Scientists at the National Institute of Standard and Technology (NIST) created a Kibble or watt balance, the device used to measure the Planck constant, built out of simple electronics and Legos.

It is surprisingly accurate (±1%) you can read about it here. Using the Kibble or watt balance, it would be possible to develop lab activities were students create a kilogram standard and then compare it to a high-quality purchased standard.

With the change to the kilogram standard, is now possible to use the metric system to teach universal constants and have the students derive all the SI standards based on observations and first principles. The real question is, should we? For the bulk of the science students and scientist for that matter, how deep does their knowledge of the SI system need to be? Most are not going to become metrologist’s the scientist that study measurements and measurement sciences. With the ever-growing amount of scientific information, we need to think about not only what we teach but how deep we teach. What do you think, students can now derive the standards of the SI system from first principles, should they? We can’t teach everything how do we determine what to teach and how much to teach?

 

Thanks for Listening to My Musings

The Teaching Cyborg

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