When the mode is not the mode

When a number appears more than once in a list and there is a multi-way tie at that frequency, the mode function in spreadsheets malfunctions and produces an answer when the answer should be "no mode." There is no single mode.

For as long as I have used spreadsheets, spreadsheet software will always pick a number from the multi-way tie and report that number as the mode. This would not necessarily be problematic, however different spreadsheets produce different results.

In a Lubuntu 11.04 Natty Narwhal equipped computer laboratory, the students have access to and are free to choose from LibreOffice.org Calc, Gnumeric, or Google Docs.

Given the data 2000, 640, 256, 128, 128, 1000, 512, 512, 384, 256; LibreOffice.org chooses 128 regardless of the sort order. Google Docs chooses 512 regardless of the sort order. And Gnumeric chooses a member of the tie that changes with the sort order.

Note that technically all of the spreadsheets cited are incorrect. The correct answer for this data set is that there is no mode. There is some wiggle room for suggesting that the data is trimodal, but the data has no unimodal value.

The data was loosely based on reality and used for a midterm examination in statistics.

Run to The Village

I was asked what a District Three fun run might look like if the run started at The Village and ended at Nett Elementary school. Would that be five kilometers? The discussion also looked at transportation issues, which raised the possibility of a Nett Elementary five kilometer out-and-back.

Having been unable to get a run in during last week, I took the opportunity to get in a run and gather some data at the same time.

Nett Elementary is three kilometers from Dolihner via Pohnpei campus:

A five kilometer out-and-back would turn around at the house seen below. One could theoretically try to place the turn-around exactly at 2.5 kilometers, but that location is simply a banana tree next to the road.

For road race distances the route should not be short, an extra 140 meters ensures that the route is indeed at least five kilometers given the GPS unit position error of up to 10 meters.

A more logical District 3 turn-around would be this bridge on the Nett-U border. That would generate a 5.8 kilometer out-and-back course.

If one wanted a one-way five kilometer run that ended at Nett Elementary, then the start would be at this rock in U.

A more logical one-way route start would be up at The Village. A start at The Village junction would be a six kilometer run, and a scenic one at that. The run down from The Village includes views of the Pacific and the misty mountains of Pohnpei.

Should one opt to start at The Village restaurant, the run would be almost 6.5 kilometers back to Nett Elementary. End at the nahs at Nett Elementary and you would have a 6.5 kilometer fun run, equivalent to four miles.

Although I should have turned around and headed home for an 18 kilometer evening run, the sun was sinking into Nett Point. The outbound run had been slow, taking me an hour and six minutes to reach The Village. I called in my evacuation team for a nice evening ride home.

Lubuntu LXDE

I spend a good deal of time reminding my students in the computer laboratory to use alt-tab to try to recover lost windows. The new Unity desk top in Ubuntu Natty Narwhal 11.04 is simply confusing for the students. The launcher is an unusual metaphor in this virtually Mac-less nation.

The computer lab computers being older 512 Mb RAM machines, there are also problems with the resource intensive Unity desk top. After a hour of running, the launcher will often fail to auto-hide for LibreOffice.org Calc.

For other reasons, I stumbled upon Lubuntu LXDE. Test runs on two computers in my office show LXDE to be faster and more responsive than Unity. The real plus, however, is that students were able to instantly understand and use the desk top without any assistance. With the rest of the campus running Windows Vista and Windows 7, the similarity of LXDE is a real plus.

I am more than pleased that Lubuntu will become a full sibling to the other Ubuntu distributions with 11.10. With all the chatter I see on line about how to dump Unity and run Gnome 3, Xubuntu, Lubuntu, and other spins, I have to wonder whether the core Ubuntu group has been wise in committing all of their futures to Unity. Somehow Unity appears like a case of Mac dock envy.

My thanks to the Lubuntu team for their excellent work!

RipStik Pairs Racing 2024 Brisbane Olympics

In preparation for the introduction of caster boarding to the 2012 Olympics in Brisbane, the kids are practicing their racing skills, both pairs and solo work.

 In the female pairs competition, these two are well ahead of the rest of the planet. Solo riders are globally distributed, but pairs riders are far less common. Teamwork and rhythm and a keen sense of pairs balance are critical assets in this event.

The pairs riders are off on a racing loop of the RipStik track, also known as Pohnpei International Airport parking lot near sundown. With only one plane per day near midday, the lot is all but deserted as the sun sets.

The male pair riders have established a strong lead on the turn into the back stretch.

Foot placement and positioning is another critical element in this sport. Years of practice are required just to get to this level of togetherness.

Note the parallel front foot stance for the female pairs. This is essential to remaining upright and moving forward.

The old man demonstrates proper... uh... scratch that. The old man demonstrates nothing of benefit to the future Olympians.

In pairs group RipStik dancing, the two pairs exit a criss-cross passing maneuver. Timing is absolutely split-second in this maneuver. When castering in formation, the pair will maintain a tight one meter board-wing to board-wing separation.

The two older riders engage in a solo racing lap of the parking lot, driving hard for the finish line.

Remember, do not try these things at home. Seriously. The above riders really do have years of experience, even the smaller riders have over a year of experience with the boards.

Exploring momentum

Laboratory 042 was followed the constructivist variation piloted spring 2011. I ran the set-up in the same manner in which I set-up last spring and last summer. I first asked the students to predict the result prior to any marble collisions. Then I released one marble on a shallow ramp. The marble rolled down and collided with a line of five marbles of roughly equivalent mass.

 Ariel presents results as MacArthur and Alden watch

I repeat this with two, three, four, five, and even six inbound marbles. For the latter cases I shift the focus to the "break-away group" retaining the inbound number as the released marbles also tend to continue on post-impact and evetnually off the ramp.

Once the students grasped "marbles in" equals "marbles out" then I focused on the penultimate marble.

How does the penultimate marble "know" whether it should stay or go? How does the penultimate marble in the line "keep count" of the number of inbound marbles?

Connie Eperiam shares her group's findings. Elbert, Ariel, Jonnie, and MacArthur listening.

I then demonstrated that "speed in" is equal to "speed out." When I asked the students to formulate explanations one student suggested that the "force" was the reason. I then usually return that back to them, "What is force? What is pressure?" "Why does that cause only an equal number to be ejected from the line?"

This term as in prior terms I had the opportunity to discuss the misuse of "magic" words that the speaker does not actually understand. For many of the students, tossing around "force" is the equivalent of saying "magic." Neither word explains how the marbles "know" what to do.

Rico's group took the approach of measuring outbound speeds only over a distance equal to the inbound distance. This ought to have reduced the errors introduced by friction for the lower velocity impacts. They came up with this approach on their own.

I almost always tie this back into the Dyson quote from laboratory one. The marbles know what to do and are doing it. That nature is mathematical is true, as to why nature is mathematical is a central mystery.

Katsandra shows their marble placements on the ramp

Once the students have their minds wrapped around the mystery of the marbles, I ask them to form small groups and to try to attach numbers to the system. To make qualitative measurements of mass and velocity for the marbles. I provide no further guidance nor correction. I do circulate and try to be helpful to groups that seek assistance.

Donnalynn explains the what her group measured and how they took those measurements

Although I had suggested a three ruler set-up after the summer run, I went ahead with the two ruler set-up I had used in the past. Unlike summer term, all of the groups found approaches to measurement, building tables and graphs. I now do not know they the students this past summer seemed to be unable to move forward. My only hunch is that the summer term is too fast, too furious.

With the groups apparently moving forward, I intentionally stepped out of the laboratory for over twenty minutes. I wanted the groups to wrestle with the equipment and the set-up on their own. Whenever I am present, the students look to me for answers and, most often, confirmation that they are doing the laboratory correctly. "Is this right?" they ask.

Jessica Nanpei explains, her partner Charleen on the right, Deffeny at the back

I always face questions when I return, but by then most of the groups have started making measurement of one sort or another. I remain fascinated by the fact that a number of students still do not fundamentally grasp what speed means from the point of view of trying to measure a speed. That speed is distance divided by time is well covered by the time of laboratory four, yet there remain some students who cannot translate that abstract understanding to measurements in the laboratory. My sense is that there are many students who pass laboratory science classes with good grades but little more than a very superficial understanding of the material that they have encountered.

This term I had prepped the students to not form groups of four shy students, that each group would need a presenter. This seemed to help.

Elbert explaining the set-up used by his group

I still feel, as I did last summer, that a modification of the set-up might be useful. All the groups that tackled inbound speed tried to measure the time versus distance on the sloped ramp. The groups were all using a two ruler set-up. The result is a underestimated inbound speed. A three ruler set-up, one ramp and two on the flat, five marbles at the junction of the two on the flat, might provide a more visually obvious way to measure the speed of the inbound marbles.

This term I tackled the issue of an underestimated inbound speed by reaching back to a finding of laboratory three: speed increases when an object accelerates. I put on the board the following:

0  2  4  6  8  10 

I explained that if the above numbers represented the speed of a marble as it accelerated down a ramp, then the speed one obtains by dividing the distance by the time is the average speed. The sum is 30, divided by six numbers, is five centimeters per second. I argued that the average is typically half of the actual terminal velocity at the bottom of the ramp. I intentionally avoided going symbolic in this explanation as that would surely lose the class.

The above came up because a couple groups had good enough numeric data to "confirm" that the outboard marbles were moving faster than the inbound marbles.

Jonnie explains as MacArthur looks on

Three rulers might help, but there is good bit of speed loss on the ramps and the junction between two ramps is usually problematic. Ultimately the marbles will never be as good as air carts, but air carts are definitely magic and marbles are everyday.

Flowers

Arc of a ball and acceleration of gravity

Exercise 031, the mapping of the parabolic arc of a ball, was modified again this term. I wanted more data points than the exercise traditionally generates. Last fall I hit upon the idea of keeping the arc wholly on the white board and using an army of students with markers to capture the ball arc data points.

I repeated this again during the spring term, although the marks were not as accurate as I might have hoped. I also did not leave enough time to explain the theoretic function, how to enter it into a third column in a spread sheet, and then graph the actual data and the theoretic curve on the same chart in a spreadsheet. Spring term I had 34 students, checking their RipStik accelertion homework took longer than usual. Although the homework check uses time, it also provides a valuable opportunity to see what each and every student is able to do and not do.

Fall 2011 the homework check took time and I again did not have the time I would have liked to introduce the theoretic function and how to enter the function correctly into a spreadsheet. I did, however, develop a new way to get the arc up on the board. This time I used four balls and I sectored the board into four sections.

I had groups of two students per quadrant map out the arc of a ball using magnetic doughnuts. I used the space balls which are large and easy to toss.

After the students had marked the path with the magnets, the students connected the dots using white board markers. This produced four fairly parabolic paths on the board. I made measurements of one and then introduced the function.

The homework was only to graph the theoretic function, no measurements were made other than r and k as seen above.

Laboratory 032 involves timing the fall of a ball to determine the acceleration of gravity g. The students drop a small superball from heights of 100 to 300 centimeters inside the classroom.

I began by making measurements in a demonstration at the front of the class, averaging a series of drops from various heights and then sketching the result.

This proved beneficial as it led to most of the groups using the average drop time for repeated measurements, which reduced the error for many groups.

 Merna prepares to drop a superball.

 Trasleen steadies the meter stick just after Katsandra has released the small green superball. Agnes records data.

Connie calculates the average for multiple drops from a specific height.

MacArthur looks over some of his data.

Gorang makes calculations while MacArthur observes: laboratories get students doing and discussing science. Even simple laboratories.

The second half of the laboratory is held up in the computer laboratory where I assist students in making the two graphs. Charleen is working on her second graph in the image above. My own data at 8:00 was within 1% of the actual value of g, the smallest error I can recall.

Lycophyte and monilophyte presentations

Students in SC/SS 115 Ethnobotany gave presentations on the botany and local names of cyanobacteria, lycophytes, and monilophytes.

 Pauleen covering the life cycle of Lycopodiella cernua

Jeanette lectures on the life cycle of a fern.

Trisha was part of a team that covered fern morphology.

The following Thursday was our visit to the Pohnpei Traditional plants garden. There the students were given an introduction to healing plants and a tour of the garden.

Barnson, Maylanda, and Pauleen liten to the presentation.

Con-ray on the tour observing a climbing Pandanus.

 Maylanda, Pauleen, and Noeleen in the front. Verginia, Trisha, Christlynn, RinaRuth, Lisa in the second row. Claralyn, Neelma, Jeanette on the third tier.