So many things are different right now: recording myself talking to my computer rather than talking to students, drawing on an iPad rather than a whiteboard, testing out what feels like a million apps to do the things that are so easy in a real classroom. So many things are different that it is easy to forget that some things are exactly the same: concepts that students struggle with in a physical classroom are still challenging for them in a virtual classroom.
This year, as every year, I asked students to do a short reading about geological structures, and then answer some questions:
Name two planar features that you can think of that are geologically important, and describe how their orientation would reflect a deformational process.
Name two linear features that you can think of that are geologically important, and describe how their orientation would reflect a deformational process.
Every year, I compile their responses and share them in class. And this year, like every year, the list revealed a lot of confusion about lines and planes and moving between two- and three-dimensional representations of lines and planes.
Different this time: no opportunity to go over the list and misconceptions in person, so I made a screencast instead. Feel free to watch if you want to see the compiled responses and how I tried to sort through them.
This is a screencast showing the answers my students submitted and how I went over them "in class." Anne Egger, Central Washington University Download Lines and planes screencast(MP4 Video 57.6MB)Details
The same: confusion about the actual feature (e.g., bedding) and a measure of the orientation of that feature (e.g., dip). Confusion about things that show up on maps as lines but are planes in the real world (e.g., faults).
Different this time: Insight! Of course they think of contacts and faults as linear features—the last time they had me as a teacher, in their introductory field methods course, I was encouraging them to "draw lines on your map!" We would walk along a contact and they would draw it on their map: a line. Good thing I've had, oh, eight years or so to figure that out. **palm-to-forehead** In the video, as a result of this insight. you'll hear me talk about things that show up as lines on maps (and in cross-sections, of course), but are planes in three-dimensions.
And the same: a general lack of comfort and/or familiarity with what I think of as basic spatial and geometric concepts. One student came to my Zoom office after doing the reading, answering the questions, and watching my follow-up screencast, and said, "Lines and planes... so, I still don't understand the difference." I held up a piece of paper—a plane—and my pen—a line. We talked about how many points are needed to define a line and a plane. We talked about what kinds of geological features would be like the piece of paper and like the pen.
This is hard for me. I come from a family of architects, engineers, artists—we all convert the three-dimensional world to paper plans and maps and visualize from plans and maps back to the real world all the time. Teaching others something that you don't even know how you know is really challenging, whether it is in person or online. In person, I use my hands a lot and draw stuff on the whiteboard. Online, I can try to do something similar, but it can be a little more difficult to uncover exactly where a student's ideas are coming from, to get at the root of their confusion. My little insight this year doesn't quite get me there.
So I welcome your suggestions and insights about these things that stay the same: how you've overcome your own challenges, or strategies that have worked particularly well for you in teaching lines and planes and describing their orientation in space.
Follow up (added 4/16): Confusion continues. Here are three comments I got from students in a follow-up assignment:
I am having trouble with linear vs planar features.
I am still a little shaky what plunge and trend is and why they're used. There's a lot of terminology that sounds really similar and I'm having a hard time understanding why just strike and dip don't suffice.
The most challenging aspect of this for me is keeping very similar terms separate conceptually, ie- dip from dip direction, plunge vs. dip.
So I made another little video, using a piece of paper and a pen to illustrate a plane and a line, and my fingers to show the number of points in space needed to define them.
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Me illustrating that a plane is defined by three points in space.
Provenance: Anne Egger, Central Washington University Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
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Me illustrating that a line (my pen) is defined by two points in space.
Provenance: Anne Egger, Central Washington University Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
I used these to then illustrate why you need trend and plunge for a line and strike and dip for a plane to define their orientation. I hope it helps. Any additional feedback is welcome.
We’ve been working on this since January. I finally got to ductile rocks this week... and, in virtual world desperation, I gave them a picture of my tiger-striped cat, just showing one side. I asked them what they would see under her throat if she was lineated, and what I would see on the top of her head if she were foliated. They did a good job with that, better than I expected from past exams. (In desperation, I started asking whether various structure were lined or planes on exams. They did not do well, despite having been in the field and measuring stuff.)
And, it's more than just distinguishing lines from planes. It took me completely by surprise many years ago when I learned that, when I use terms such as horizontal, vertical, above, below, up, down, before, and after, many of my students aren’t visualizing what I expect, because they have different (and deeply ingrained) personal definitions for these words that are at odds with what I intend for them to visualize. For example:
•When I ask my structure students on one of the first homework assignments to define horizontal and vertical, at least 1/4 of them define horizontal as something that is east-west, and vertical as something that is north-south. This clearly stands in the way of my students visualizing an accurate and meaningful picture of what I mean when I talk about the orientations of structures. This is also a very difficult visual misconception to dislodge even when my students have learned to write accurate definitions of the terms. They can define it correctly, but when they are talking in class, they drop right back to their own ideas of what horizontal and vertical are.
•Many of my students also use horizontal and vertical as relative terms and describe something as horizontal to something else (confusing it with parallel to) or vertical to something (confusing it with perpendicular to).
•Many of my students use above to mean to the north of and below to mean to the south of.
•Many of my students think of inclined as being upward (going up an incline) rather than downward and would describe units that dip to the SE as being inclined to the NW.
•When asked about stratigraphic order, some of my students will say that “the Cambrian units are after the Ordovician units”. Whereas we use after in a temporal sense, some students use after in a “list” sense - they read a strat column from top down and get to the Cambrian units after the Ordovician ones.
For online classes: If you have synchronous sessions, you might try the exercise more or less as written, but showing the class one block at a time. You could even send them into zoom rooms of 2-3 students to discuss and gesture at each other. If you are meeting only asynchronously, you might give a homework assignment with several blocks, have students sketch their answers instead of (or after) gesturing their thoughts, and then reveal the answers after they upload their sketches. Or you might just make a video where you pause to give students time to gesture their answers. I'd be interested to know if anyone tries something like this in an online course.
We’ve been working on this since January. I finally got to ductile rocks this week... and, in virtual world desperation, I gave them a picture of my tiger-striped cat, just showing one side. I asked them what they would see under her throat if she was lineated, and what I would see on the top of her head if she were foliated. They did a good job with that, better than I expected from past exams. (In desperation, I started asking whether various structure were lined or planes on exams. They did not do well, despite having been in the field and measuring stuff.)
And, it's more than just distinguishing lines from planes. It took me completely by surprise many years ago when I learned that, when I use terms such as horizontal, vertical, above, below, up, down, before, and after, many of my students aren’t visualizing what I expect, because they have different (and deeply ingrained) personal definitions for these words that are at odds with what I intend for them to visualize. For example:
•When I ask my structure students on one of the first homework assignments to define horizontal and vertical, at least 1/4 of them define horizontal as something that is east-west, and vertical as something that is north-south. This clearly stands in the way of my students visualizing an accurate and meaningful picture of what I mean when I talk about the orientations of structures. This is also a very difficult visual misconception to dislodge even when my students have learned to write accurate definitions of the terms. They can define it correctly, but when they are talking in class, they drop right back to their own ideas of what horizontal and vertical are.
•Many of my students also use horizontal and vertical as relative terms and describe something as horizontal to something else (confusing it with parallel to) or vertical to something (confusing it with perpendicular to).
•Many of my students use above to mean to the north of and below to mean to the south of.
•Many of my students think of inclined as being upward (going up an incline) rather than downward and would describe units that dip to the SE as being inclined to the NW.
•When asked about stratigraphic order, some of my students will say that “the Cambrian units are after the Ordovician units”. Whereas we use after in a temporal sense, some students use after in a “list” sense - they read a strat column from top down and get to the Cambrian units after the Ordovician ones.
Barb: DITTO. I see exactly the same thing. It's far worse with the students in my intro course, but I'm always shocked to see it in the structure students, many of whom are in their last quarter of the major. And again, I find myself flummoxed about the best way to teach this given that it is just so obvious to me.
This is from Dave Pollard:
I think your examples are spot on for thinking about lines and planes. Using a pen and a piece of paper provides the conceptual associations, and discussing the number of points to define a line (2) and a plane (3) starts to deepen and quantify that understanding. The photos of you touching the pen with 2 fingers and the paper with 3 fingers reinforce the fundamental concepts.
From there I would like to suggest two additional steps that serve to reinforce the basic concepts. These steps help students connect the concepts to what they have learned in their math courses, to the procedures they will use to gather structural data in the field, and to the methods they will use to analyze that data in the lab.
The first step uses two points on a line to define the unit vector directed from one point toward the other point. This is the classic “two point problem”. It provides the orientation of the line, which can readily be converted to trend and plunge to relate to field measurements. It also provides the direction cosines for analysis in the lab.
For the plane, this first step uses the three points to define two unit vectors directed between a given point and the other two points. This is the classic “three point problem”. The normalized cross product of the two vectors provides the unit normal vector, which defines the orientation of the plane. This is readily converted to strike and dip or used to plot on a stereonet.
The second step uses one of the points on the line and the unit direction vector to define the vector-valued function for the line. For the plane one takes one point on the plane and the two unit direction vectors to define the vector-valued function for the plane. These vector-valued functions provide the tools for quantifying curved lines and curved surfaces.
Because geologic structures are only approximated locally as linear or planar, getting to curved lines and planes is pretty important. For example, if you want to talk about the geometry of folds, the second step is necessary. Still, some instructors may believe that this second step is “beyond the scope” of their undergraduate course.
My experience at Stanford was that undergraduate students could handle this, especially with some dynamic graphics support using Matlab to enhance thinking in 3D.
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