I took surveying classes and worked as a surveyor/mapping assistant in the SF Bay Area decades ago. I thought those skills might help me in pursuing a part-time career in archeology and indeed, I helped map as a volunteer in Israel and Guatemala. I didn't ultimately pursue either surveying or a career in archeology (too much time spent away from family). Instead, my interests led me to teaching science and geometry through my own educational company. I design lesson plans, all of which I try to tie to real-world situations. So, some of my classes involve plane tables, mapping, navigational instruments. I came upon this forum because a friend sent me information about an important base line in Yolo County, CA. I will make use of this in one of my lessons for students from that area. Although I am interested in modern surveying, I have to admit I'm more attracted to historical means. Something about older instruments brings the geometry more real to me. Any suggestions for which forums might be good for me? I'm currently living in New Mexico, but still have many ties to friends and students in the SF Bay Area and Yolo County.?ÿ I'm also visiting lots of archeology sites in NM; one of the reasons I moved here.
Welcome. I hope you find some interesting discussions.
I have volunteered on three small archaeology projects here in Iowa and attended numerous lectures. I have been particularly impressed by how much more information can be squeezed out of a site when precision 3-D mapping is done with a surveying total station instrument as opposed to the old grid square method.
Having the electronic data not only carries more detail; it makes it practical to quickly generate plots such as density of each artifact type across an area at different depths/ages.
In one case a site first opened in the 1960's was re-investigated using this technique. From the depth of each end of a bone or lithic point they were able to distinguish artifacts missed in the 1960's and thus tilted in the backfill, from undisturbed items below a certain depth from an earlier occupation. I thought that was ingenious.
The plots showing type of artifact and location clearly indicated where the fire was, where butchering, hide scraping, cooking, and refuse disposal were. The information helped estimate the size and seasons of occupation over time.
I'm getting long-winded, so I'll finish by saying that while I agree the older survey instruments and methods better illustrate geometry, there is a lot of education potential in newer technology, too.
@bill93?ÿ
yes, you're right about modern surveying in archaeology. What type of sites were you working on in Iowa?
The first was in an area near a river along which many prehistoric occupations have been found.?ÿ We were doing test digs to see if an area that looked right for a village and had a few surface finds was actually a village. I dug and screened for three days with them. The conclusion they reached was that it was unlikely as a village, and the artifacts had been dragged downhill by farming (before the land was turned into a park) from a known winter camp.
The second project was to confirm the location of a trading post that had been there to deal with the Meskwaki before they were moved further west.?ÿ We found abundant confirmation of the site, and could locate the building within perhaps 10 meters.
I was sorely disappointed that there was no way to use the GLO survey notes that gave bearings to the trading post building (what feature?) that was still there when they came through.?ÿ There doesn't seem to be a section or quarter section corner record, and unlikely any preserved corners, for considerable distance because so much land was in common ownership from shortly after the settlement period (see Amana Colonies).
That investigation used 10 meter squares and estimated positions within them.?ÿ We started with surface collection (cornfield before planting was ideal), flagging locations, and bagging per square. The density of flags indicated a need to add squares on one side of the layout, although after 150 years of farming you could find scattered artifacts anywhere in the large field.?ÿ Then we ran metal detectors and flagged hits.?ÿ Since this was historical occupation, we found a fair amount of metal.
The project manager was puzzled by one square having many times the metal detector hits of the adjacent ones.?ÿ She asked me to confirm them.?ÿ I only found about as many as adjacent squares, so went over and tried the other volunteer's boots.?ÿ Yup. Steel toes.
Then they did auger tests in several locations where the flags had been dense, and found things like chinking hardened by the fireplace, bullets, and a few shards of broken chinaware that pretty much confirmed it was EuroAmerican occupation, as well as the trade goods like broken clay pipes and a few beads,.
After I was off the project, a 1x1 meter square near a rich auger test found a trash pit.?ÿ Somewhere on the site someone found a couple coins from the right period.
The third project a year later was to learn more about the Meskwaki occupation that the trading post had been set up near.?ÿ We walked an area maybe 1/8 mile downriver from the trading post for surface collection and did some test holes.?ÿ There was evidence of both their occupation with Euro goods (pipes, bottle glass, a piece of a steel trap, factory-made beads), and an earlier one making lithic tools.?ÿ They hoped to find post molds from lodges, but didn't during my time on site. The location seemed to fit well with local tradition, there being an older resident or two close by whose great grandparents in their younger days had seen the Meskwaki village.
It was interesting.?ÿ I wouldn't have wanted to make it a career, but I would do it again if convenient.
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archeology
Cool.
Some of my favorites:
400 meter tracks; circles, tangents, perimeter and area of odd shapes, etc.
https://www.dimensions.com/element/track-and-field-400m-running-track
Airports; Compass deviation, lines on graphs, angles, slopes, create a coordinate system with (0, 0) at the end of a runway and calculate other ends by slope and length, etc.
https://www.fly.faa.gov/Information/west/zab/abq/00012AD.PDF
Baseball diamonds; angles and distances, Pythagorean theorem, diagonals of kites, quadrilaterals, is it really 90 feet from 1st base to 2nd base?
http://www.markersinc.com/athletic/baseball-field-dimensions.pdf
Food for thought; you probably have a thousand more.
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You may like the problems presented in the old Professional Surveyor magazine.
Go to their archives and look for the Problem Corner.?ÿ I just checked and there are 256 problems and their solutions presented by myself and Dr. Bloch.
I am now presenting problems to the American Surveyor magazine under the Test Yourself articles.
Dave's problems were often good brain teasers, requiring an inventive approach, rather than basic tutorial problems. I enjoyed those that came to my attention.
Watch out for required but unstated assumptions on a few, though. Use the minimum assumptions that give the problem a unique solution. Was that intended to be a right angle or not? Is that a tangent curve? Are those lines parallel? We had a long thread once arguing over which assumption was more reasonable on one.
I usually used those practical things as labs or enrichment lessons or connections to the real world, whatever suits your fancy. They were excellent for days when outsiders were observing me. Lots of interaction, questioning, and thinking. My normal days were pretty much the same, but the teaching goals were harder for outsiders to follow and comprehend. They didn't always know if I had done my job or not.
I did one on staircases for an advanced functions class. Tread and riser, slope angles, heights, and Pythagoras, building codes, why ratios were important -- all stuff that lots of kids took for granted until they studied it for 90 minutes. They had to gather data, make calculations and match what they saw to the building code, using the steps in our rotunda.
The lesson plan was hand-written on 2/3 of a sheet of paper. I did type the data and calculation sheets. R&D?ÿ time, though, was about 10 days off again and on again.
And, you know, I learned as much putting it together from scratch as my kids learned doing the exercise.
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I owe a good part of my career in surveying to my high school geometry teacher. I almost flunked everything else but aced geometry. It was the teacher as much as it was me. Then I started surveying on weekends and was hooked.?ÿ
I have thought that roller coasters would be a great way to get students interested in geometry. The old ones must have the same grades, vertical curves, horizontal curves, tangents, spiral curves and superelevations as highways and railroads but much more fun. And the new ones must have some fancy calculus involved. Of course I have never, will never ride one of them.?ÿ
This has been interrupted by Covid, but it looks like it might go in 2022. We entered three projects back in 20?? (out of Prevagen) and took two busloads of students to Charlotte for the judging, winning one token prize.?ÿ The real winners were impressive.
https://www.carowinds.com/groups/student-and-youth/engineering-day
I, too, was inspired by a hs math teacher. Don't know if I inspired anyone or not; hopefully I didn't create any criminals.
@bill93?ÿ
That's a great story about the steel-toed boots. On a somewhat similar topic, I'm writing a lesson plan about Peary and his theft of the great Greenland meteorite. After it was on his boat, they discovered they could no longer use their magnetic compass for navigation.
thanks for your ideas! Are you still a math teacher?
Ha! You don't like thrill rides? I found that as I got older I grew less frightened.
@dave-lindell , @bill 93
I will be interested to look up those problems in the American Surveyor magazine. I'm a pretty simple sort of mathematician, but I do have lots of curiosity and interest. Luckily, that goes far with my students. I recently took a trip to Chaco Canyon with a group led by a professional archeologist. One of the curiosities of Chaco Canyon is their architecture, including squared window corners. Well, I haven't actually seen that particular feature mentioned in the literature, but I was wondering how they got the windows so square. "What tools did they use?" I asked Paul. I guess it came down to a plumb bob.?ÿ
@camilla?ÿ
No, why would I subject myself to fear. I also do not like tall cliffs or buildings. But I'm fine with airplanes or sailboat mastheads. Go figure!
@camilla?ÿ
I've been retired for six years and don't participate actively in teaching, but I'm forever thinking about how I would present this or that or looking at problems in textbooks or sample SAT or AP Calculus problems.?ÿ
I admire people who can produce sound lesson plans that cover a unit or several days. Mine always blew up?ÿ because of a fire drill or an unplanned assembly or some piece of the topic that proved more difficult than I had anticipated. The lab stuff percolated for days before it ever came together.
Whatever you do, include a technology piece. The easiest thing to do is to include the use a graphing calculator. But teachers are clamoring for lessons that use laptops. Some free software that you can utilize are the FooPlot grapher, Geogebra, and Google Sheets. FooPlot is bare bones basic, but it's accurate and allows for plotting both points and functions. Geogebra is a full-function small computer algebra system. Google Sheets is Excel lite.
Here's a screen shot of a Sheet that solves simple linear equations. The idea is to get students past the pencil and paper stage and to the think and program stage. I selected cell with the answer for the "One Step Solution" to show the cell's formula. That's what I mean by the think and program stage.
So, develop a lesson on say, the tangent function and right triangles. Go through the background stuff, solve some problems, and end with a spreadsheet assignment that enters the knowns and calculates the unknowns.
See, students learn spreadsheets as a byproduct of solving math problems and, if you can program it, you truly know it.
Good luck and speak of me kindly when you're rich and famous!
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