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2012 October 13

When is a line graph not a line graph?

Filed under: Uncategorized — gasstationwithoutpumps @ 21:39
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I recently discovered that elementary school teachers have taken to calling histograms “line plots”, and that this definition has gotten quite widespread:

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer then 25 numbers. It is a quick, simple way to organize data. [http://ellerbruch.nmu.edu/classes/cs255w03/cs255students/nsovey/p5/p5.html]

A line plot shows data on a number line with x or other marks to show frequency. [http://www.icoachmath.com/math_dictionary/Line_Plot.html]

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data. [http://www.mathplanet.com/education/algebra-2/equations-and-inequalities/line-plots-and-stem-and-leaf-plots]

This page contains worksheets with line plots, a type of graph that shows frequency of data along a number line. [http://www.superteacherworksheets.com/line-plots.html]

Of course, no one outside the elementary school teachers uses that term, which is confusingly similar to the standard term “line graphs”.  Even the superteacherworksheets site acknowledges the terrible confusion that the “line plot” term generates:

Line Graph Worksheets Line graphs (not to be confused with line plots) have plotted points connected by straight lines.

“Line graph” is a common term, even among educators:

Line graph is a graph that uses line segments to connect data points and shows changes in data over time. [http://www.icoachmath.com/math_dictionary/line_graph.html]

Line graph: A graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens). [http://www.mathsisfun.com/definitions/line-graph.html]

line graph definition: a diagram of lines made by connected data points which represent successive changes in the value of a variable quantity or quantities. [http://dictionary.reference.com/browse/line+graph]

Was it just because they couldn’t spell “histogram” that elementary school teachers had to invent a new term confusingly close to an existing standard term?  I feel sorry for the kids subjected to this poor choice of nomenclature, as they will have to do more unlearning before taking high school or college tests, where they will be expected to know what a histogram and a line graph are, but not anything about “line plots”.

2012 May 29

LinReg for physics class data graphing

Filed under: home school,Software — gasstationwithoutpumps @ 09:58
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A blog I only recently subscribed to (Physics! Blog! by Kelly O’Shea) had a very nice plug (LinReg for physics class data graphing) for a graphing program I’d not heard of before: LinReg which is available free from Pomona.

My son and I use gnuplot, which is a moderately powerful script-based graphing program that produces good graphs and has a good parameter fitting command, but I’ve given up recommending it to people, because of the extreme difficulty in installing it.  It is also overkill for a lot of high school classes, where fitting a straight line is considered complicated enough.

LinReg looks like it is nearly ideal for high-school and middle school science classes.  It forces students to label their axes, use units, and express the precision of their measurements. It computes error values for the intercept and slope values, using a reasonable simulation approach (sampling Gaussian distributed points about each measurement and refitting).  Kelly claims that her Honors Physics students pick the program up quickly and choose to use it without prompting after the first few uses (unlike Excel, which they always see as a barrier rather than as a tool—an attitude towards spreadsheets that I share).

Data entry in LinReg seems to be mainly manual, which would be a big limitation for me even for the home-school physics class (the speed of sound lab generated several hundred data points just for the ladder measurements).  Because my son and I have successfully installed and mastered gnuplot, I see no reason to change to a more limited program, but I can see the attraction of using LinReg with a class, so that less time can be spent teaching the tool and more time using it.  The limited feature set looks like a very good match to most high-school science classes.

2012 March 30

Google plots

Filed under: Uncategorized — gasstationwithoutpumps @ 17:51
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My son has been using Google search as a calculator for a while (it is handy, because it can keep track of units in physics calculations, though it sometimes has weird ideas about operator precedence).  [Correction: he told me that he has been using Wolfram Alpha as a calculator, but not the Google search box.  I’ve used the Google search calculator a little, but I find it easier to grab my HP 32S II calculator and use it, since it has RPN entry and doesn’t require so much parenthesis matching.]

Google in now pushing their search box as a 3D graphing tool:

Graphing on Google.com – Now in 3D – Inside Search.

2012 February 15

More science fair advice

Filed under: Science fair — gasstationwithoutpumps @ 14:25
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Today I gave my 35-minute spiel to the teachers at the K–8 school that I judged at last week.  I did not cover everything in my notes (yesterday’s blog post: Science Fair advice), but got through the first 10 points.  The last two (on graphing and poster design) would probably have taken more time than I had even if I had just covered those two topics.  My discussions on poster design with college seniors and grad students usually take about an hour, and science fair posters aren’t any easier to design—in fact the wider range of audiences, from grade school kids to experts in the subject, probably make them even harder to design well.

A few things came up that I did not have in yesterday’s notes:

  1. Good science fair projects take time.  There is a long process in going from a topic to general questions to preliminary experiments to specific questions.  The process needs to be started in October or November and done a little at a time, as a series of littler assignments, rather than a huge push at the end that overwhelms the kids and invites parents to rescue them.  Getting buy-in from the kids and the parents is essential for any sort of homework, but a longer, less intense project is likely to lead to easier relations between parents and teachers.  Kids will almost all need help with time management, but spreading the work out will reduce the conflicts with other demands on their time.
  2. Different grade levels should have different expectations of what students need to do, from very scripted group activities at the kindergarten level, to almost independent projects at the 8th grade level.  The transition from teacher-directed to student-directed projects is a gradual one, and each teacher will have to find the level of autonomy that works best with the kids they have to work with.  For example, at third grade, the teacher may decide to limit kids to the physical sciences, because of the greater ease of repeatable measurement and, hence, smaller acceptable sample sizes.
  3. Are mentors a good idea? One teacher pointed out that some parents saw having mentors as “cheating”, since the students with mentors were more likely to produce well-crafted, carefully thought-out projects. But mentors can provide much more detailed, specific feedback to students than one teacher can, and are often essential for kids to really learn the topic they are researching. So I’m strongly in favor of encouraging the pairing of kids with mentors.
    In an ideal world, all the students would have mentors, but the supply of mentor time is somewhat limited. For the mentors, the reward is working with kids who are excited by science and interested in topics that the mentor is interested in.  Working with a kid who was just going through the motions and didn’t care about the subject would burn out a mentor and not do the kid much good either.
    Mentors do not need to be scientists or engineers, if the subjects that the students are researching overlap the interests of others.  For example, a kid very interested in music could talk to music teachers about interesting questions that come up in music that can be answered by experiment (for example, what makes an interval consonant or dissonant?).  A kid interested in dance could talk to dance instructors about measuring balance, speed, muscle strength, or ability to follow a rhythm.
  4. We talked a lot about the use of preliminary experiments.  For example, if a student builds a trebuchet to play with, the preliminary experiments are usually all over the place: looking at different projectiles, different counterweights, different launch angles, different sling designs, and so forth.  Most students stop at that point and try to write up a poster.  But that is really the starting point for designing an experiment.  What properties were easy to measure? (Distance traveled is easy, time of flight is harder, maximum height of projectile harder still.) What manipulations seemed to have a big effect?  The careful experiment can then be designed to test one particular variable that appeared to be important in the preliminary investigation (for example, just the launch angle) and many repetitions done.
    These preliminary experiments should be done in November or December, so that there is time to design and carry out the “real” experiment, or to change projects, if the measurements needed turn out to be too difficult to do with available equipment.

2012 February 14

Science Fair advice

Filed under: Science fair — gasstationwithoutpumps @ 18:49
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I’ve judged at three school fairs this year, and will be judging at the county science fair as well (I haven’t decided about state yet—it depends on whether I have to go to Los Angeles then or not).

At one of the science fairs, one of the teachers was reminiscing about the teacher workshops that the county used to run, two or three coordinators ago.  I remember giving a talk, “”Notes for Science Teachers from a Science Fair Judge” for one of the seminars in Feb 2000 at the Long Marine Lab. I think it would be an excellent thing to start up that series again, as there has been a lot of turnover in the teachers over the past decade, and many of the newer teachers are a bit clueless about science fair.

At another of the fairs, a teacher who was doing the judging (along with me and a parent) suggested that I give a talk to the school about ideas for improving the science-fair experience at the school.  Everyone does science fair every year at this K–8 school (though the kindergarten project is a single project for the whole class, and the 1st grade projects are animal-habitat dioramas and library research, not experiments), so all the teachers are involved.  The principal invited me to give a talk tomorrow in the 45-minute weekly teacher meeting.

So now I have to organize my thoughts about teaching science fair. My experience is mainly as a parent and a long-time judge of science fairs—I’ve not been a classroom teaching supervising a dozen or so projects. So some of my advice may turn out to be infeasible at classroom scale.

A lot of parents hate science fairs, and they are a lot more work to organize than just doing the usual classroom demos, labs, reading, worksheets, and lectures. So why do them? We need to have a big enough pedagogical payback to justify the investment of time and resources.  There are several reasons:

  • The science fair project is one of the few academic things in elementary or middle-school that takes sustained attention.  The good science fair projects take weeks or months of regular work, unlike the 1–2-week “unit” that dominates middle-school curricula. There are non-academic things that kids are expected to do for months (sports, music, dance, and theater, for example), but most academic subjects are set up as short cycles of cram-and-forget.  Doing a sustained project is an excellent educational experience (as long as the student does it, and not the parent).
  • The science fair project pulls together several of the academic disciplines: science (obviously), math (generally in the form of simple statistics and graphing), writing, library research, and even art (or at least graphic design) for the poster.  For science fairs in which kids are interviewed, there is also the practice at speaking about one’s work to a stranger. (I prefer the fairs with interviews, but it takes a lot of judges, so the logistics is often difficult.)
  • The science fair itself, when parents and friends come to view the posters, celebrates both education and science.  There is far too little celebration of education in US society, and almost none of science.
  • Science fairs allow students to do science, instead of just learning about science.

To get the full benefit of the science fair, kids have to spend time on the projects.  Since most kids through 8th grade don’t have the executive skills needed to plan and manage their time for a project as long a science-fair project, teachers and parents have to help them manage their time.  This includes things like requiring a project proposal well before the project needs to start, setting intermediate goals, and making sure that steady progress is made, trying to prevent a last-minute rush that invites rescue by panicked parents.

Advice 1: do an original project.

I’ll be happy if I never see another lemon battery (a classic demo that has spawned many terrible projects from students who have no idea what causes the battery to work, what affects the voltage and current, or any of the many interesting questions in elecrochemistry and engineering that could make decent project about batteries).  I think that the Stroop effect plays the same role of too-often-repeated cookie-cutter project in the behavioral sciences, but I try to stay away from judging behavioral projects.

Science fair judges like to see students raising questions that come from themselves, rather than copies of standard projects from the web. So the first step in getting students involved in science fair projects is to have them brainstorm investigative questions. It may take a few weeks to do library and web research on a number of questions to figure out which ones have reasonable theories to suggest probable answers, and of those, which ones generate hypotheses that are experimentally testable with experiments that the students can do.

Advice 2: don’t do an original project.

The first advice should not be interpreted as meaning that students should come up with all their own all-original experimental design—a lot of questions have been asked before, and students should research what experiments other people have done to try to answer similar questions. For many of the questions students ask, there are good experiments that they can do, using standard protocols that are widely accepted by other researchers.  Use standard protocols when they are feasible, so that students can concentrate on the ideas and on executing the protocols, rather than on designing and debugging the protocols (unless, of course, the design of the lab protocol is the point of their project).

Advice 3: keep a lab notebook.

Both county and state fairs require an original lab notebook—the place where the questions are written down, the experiments are described, and the measurements are recorded as they are made.  It does not have to be terribly neat, just readable, but it does need to be the original record, not a later cleaned-up copy.

Advice 4: involve the school librarian.

Students must research their investigative questions before they design their projects.  The school librarian is often an expert at finding information that is both relevant and accessible to the students, but obviously can’t help every student in the school individually for very long.  For the older students (7th and 8th grade, and maybe 6th), have the librarian teach the students search skills and how to evaluate the stuff they find.  For the younger ones, it may be better to have the librarian work with just 2 or 3 kids at a time, finding them books and other resources at an appropriate reading level—general web searching will come up with too little that is kid-friendly, and the students will get overwhelmed.

There are some good resource sites for science fair projects, but far too many kids will use these to get cookbook projects, rather than ideas for techniques to answer their own similar questions.  Thus the use of science-fair resource sites is risky.

Advice 5: a hypothesis is not a guess.

A lot of elementary school teachers, convinced that “hypothesis” is too complicated a concept for kids, simplify it to “guess”.  That does a major disservice to science education. More correctly, a hypothesis is a prediction made by a theory.  For a hypothesis to be meaningful, there must be a competing theory that provides a different prediction.  For example, one could have a theory that heavier objects fall faster than lighter ones, and a competing theory that says that how fast objects fall is not dependent on their mass.  Just having one wild guess does not make a hypothesis.

Students should carefully research their investigative question, learning about the theories that might be relevant, before they make a hypothesis.

Many times students will start with a topic (horses or catapults, for example), rather than a question.  It makes sense to research the topic before trying to formulate investigative questions, then do more research on the question before forming hypotheses.

Advice 6: do a preliminary experiment.

If the question is novel enough that no accessible theory can be found, then students may have to do two experiments.  The first, preliminary experiment is done to generate plausible theories.  Then a second experiment is designed that will produce different results for each theory, to try to eliminate those that don’t work.  Note that this takes a lot of time—most students end up barely getting a preliminary experiment done, and never check whether their analysis of the data holds up in further experimentation.

In fact, almost all science fair projects benefit from doing a preliminary experiment to figure out what can be easily measured and how accurately it can be measured.  Often the result of preliminary experiment is to redesign the experiment to remove some unexpected variables that confuse the measurement—replacing a handheld thing with a mechanically supported one, for example, or making a launcher to provide uniform throws of a paper airplane.

Sometimes the preliminary experiment indicates that the available measuring techniques are not sensitive enough to test the hypothesis, and the whole project needs to be rethought.  Therefore preliminary experiments should be done very early in the process, so that there is time to rethink the experiment or even start over on a different project.

Advice 7: measure the right outputs.

It is important to measure something that answers the investigative question.

For example, students often want to do science projects about generating power with windmills, solar cells, batteries, hand-cranked generators, fuel cells, tides, or other means.  In doing such projects, it is important the students measure the power and not just the voltage.  For generators, the open-circuit voltage has little relationship to power—technically, there is no power delivered in an open circuit.  The fix is simple here: teach the students Ohm’s law and have them used a fixed load (like a resistor), so that measuring the voltage across the load will allow them to compute the power delivered.  A tiny change to the experiment makes a huge difference in the quality of the project.  (More advanced students can look at the effect of different load sizes on how much power is delivered—it turns out to be best to match the load to the source, so that different sources will result in different loads for best performance—most of the theory is accessible to anyone who has a little algebra.)

Another common experiment involves growing bacteria and seeing how many there are. The correct technique for measuring bacteria depends on what the investigative question is.

  • If you want to know how many bacteria there are in the initial sample, then you dilute the sample appropriately, put a measured amount onto the petri dish, and count how many colonies grow.  Each colony corresponds to one culturable bacterium in the measured amount, which can then be scaled appropriately to get the number of bacteria in the initial sample.  It may be necessary to do several different dilutions from the same sample, in order to get a plate with an easily counted number of colonies.
  • But if your investigative question involves how fast the organism grows under different conditions, then counting colonies is probably the wrong way to go.  Instead, you might want to start with a stock solution of bacteria or yeast, split it equally into the different conditions, then measure the growth by the opacity of the liquid culture.
  • Another common test is to measure the effectiveness of antibiotics by putting a disk of the substance on a petri dish and measuring the radius of the zone of inhibition around the disk.  One problem with this approach is that it is hard to compare different substances fairly, since the zone of inhibition depends both on the strength of the antibiotic and how fast it diffuses through the agar.  That is, the output is easy to measure but the input (how much antibiotic there is at each distance) is hard to measure.
Advice 8: measure inputs as well as outputs.

Science is often about the relationships between the inputs and the outputs of some process.

A lot of student projects suffer from a common problem: measuring the results of some experimental change, without having a really clear idea what the change was.  For example, students may count the colonies growing on an agar plate, but have no idea how big a sample they smeared on.  Or students may measure the resistance between two electrodes, but not know how far apart the electrodes are or how long they are.

Advice 9: collect lots of data.

Many student projects suffer from having too many experimental conditions and too little data in each condition.  When dealing with living subjects (human, animal, or plant), there is a lot a variability.  It is best to minimize problems by testing large numbers, and (when possible) testing the same subject under the multiple conditions.

If you measure 16 different things once each, it is very hard to know how much of the difference you see is due to random variation in the measurement and how much is due to the difference in the conditions.  If you have time for 16 measurements, it is much better to do 2 conditions 8 times each, or 3 conditions 5 times each.  (Doing one thing 16 times doesn’t tell you much, as you don’t have anything to contrast it with.)

Advice 10: draw good graphs.

All the judges I know are very, very tired of the terribly done fake-3D bar charts with unlabeled axes that seem to be the default output from Excel. Graphs are about using people’s excellent visual processing to get them to understand the relationships between things. It is not about distracting colors and visual gimmicks that hide the data.

For many science fair projects, the correct type of graph is a scatter diagram, with the x-axis having the experimentally manipulated variable and the y-axis having the measured variable, with one point for each measurement made.  If the theories being tested predict particular relationships (a straight line, an inverse-square, an exponential decay, …) then it may be worthwhile to show the theoretical curves superimposed on the scatter diagram.

When large numbers of data points are collected, it may be more useful to plot averages (and inter-quartile ranges) rather than all the raw data points.

For teachers, I recommend reading Edward Tufte’s The Visual Display of Quantitative Information, to get an idea what graphing is about and how to do it simply.  Most of what students are doing with Excel is “chartjunk”, not proper graphing.

Advice 11: use big fonts.

Posters need to be read from 3 or 4 feet away, twice or more people’s usual reading distance.  That means that fonts need to be twice as big as usual. Small print may be 18 points, and most of the body text 20–24 point.  Note: there is no reason to use small fonts to cram more stuff in.  If you have a lot to say, use a bigger board.  The county and state guidelines allow poster displays 4 feet wide, 2.5 feet deep, and 6 feet high (6.5 feet for state).  Many of the winning projects have so much stuff that they need the larger boards.

 

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