From: Ronald Wong (ronwong@inreach.com)
Date: Sat Jul 12 2003 - 17:56:25 PDT
Message-Id: <l03102800bb2a28801e75@[209.209.19.126]> Date: Sat, 12 Jul 2003 17:56:25 -0700 From: Ronald Wong <ronwong@inreach.com> Subject: Re: significant figures
Recently, Paul asked:
>One of the summer teachers asked if there are any real world examples
>that can be used to motivate students about the use of significant figures?
>
>Got any ideas?
>
>Paul
>D
If, by "real world examples", the teacher meant situations in our daily
lives in which significant figures arise, then any measurement would serve
as an example of significant figures.
We are all familiar with our height and weight for instance. Ask someone in
the USA for these measurements and you'll get something like: "Five feet 9
inches and 147 lbs". To the nearest inch means that the height, 5' 9", has
4 significant figures and, to the nearest pound, the weight of 147 lbs has
3.
The fact that most of us don't think in terms of significant figures when
we give our weight and height is simply because the level of precision in
these measurements is usually not an important issue. Giving one's height
to the nearest inch and the weight to the nearest pound is all that others
require and, as a result, it's the level of precision that most of us
resort to when we give them our height and weight.
Of course, if you are a carpenter installing a prefabricated sliding door
in a home or a merchant dealing in precious metals, you would want greater
precision than the nearest inch or pound (measuring the length to the
nearest 16th of an inch or the weight to the nearest ounce, for example).
This leads to a greater number of significant figures for a given
measurement and consequently more precision in the actual value of the
length/weight/mass.
On another level, a high level of precision would be important if you were
a contractor installing sliding doors in the homes of a large housing
development where saving money in terms of time and material is important;
or a dealer in precious metals where, in large quantities, small
differences in mass/weight add up to a lot of money.
So much for "real world examples" in terms of common, everyday activities.
_______________________________________
If the teacher is interested in motivating "students about the USE of
significant figures" in his/her science class, then the best "real world
examples" are those that can be found throughout the field of science.
Making measurements is a given in the work of a scientist. It's an
important element of every experiment performed during a scientific
investigation. From these measurements will come the evidence that will
either support or challenge a hypothesis and, should that be the case, the
theory that prompted it.
Precision plays a central role in this process. The greater the level of
precision, the stronger the claim. This is where the role of significant
figures comes into play.
Keeping all of this in mind, it should be clear that every science course
should cover the importance of measurement, the need for precision, and the
role of significant figures - especially at the high school level - if our
students are going to get any idea what science is all about.
The laboratory activity of a science course is the perfect means for
achieving these objectives.
If their laboratory grade is dependent on how well, in light of the
objectives that were set forth for a particular investigation, they
INTERPRETE their data, students will put a lot of time and effort into
making sure that they draw the right conclusions based on the analysis of
their data - even when the conclusions contradict that of other students,
the teacher and/or the text book. They will even come back on their own
time to run a lab again in order to either confirm their original analysis
or investigate new possibilities suggested by their analysis of the
original data.
Nothing creates a buzz like the discovery that one team of investigators
had discovered something that no one else had. Depending on the lab, this
sometimes led to a frenzy of renewed, after-hours lab activity by other
teams to see to what degree the new developments were valid (this
occasionally leads to new discoveries. Discoveries that sometimes were at
odds with their textbook) - a classic model of "real" science in action.
Talk about motivating students about significant figures (and the fact that
science can be "interesting").
In order to create this kind of atmosphere the students must focus on the
objectives of a lab and the degree to which his/her interpretation of the
lab's data is in line with the objectives. This requires that the teacher
take the time to show them how one goes about doing this (I did this over a
series of lab activities).
Since all of the investigations begin with measurements, the first step in
this process involves introducing the students to the concepts of accuracy,
precision, and significant figures. Fortunately, this takes very little
time (one week max) and can be done by the students on their own time - if
you have the resources (when I was teaching, I had a few computers in my
office that the students were free to come and use on their own time. There
was - and I suspect still is - very good interactive software for dealing
with just these topics. Very little time was taken in the classroom to
cover these topics. The motivating factor was a test on the subject matter
after their first lab - a "fun" lab that addressed the issues of
measurement, precision, accuracy and significant figures).
_______________________________________
Much more can be said but hopefully enough has been covered to give your
teacher some ideas regarding significant figures and motivation.
ron
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