CS382:Staticmodel-outline

Static Modeling

Overview

• Static models are typically the simplest form available for describing some aspects of the real world, although one should not let their simplicity fool you. Even in a static model there are plenty of opportunities for errors to develop.

Background reading

• For whom is the reading? Teachers / students / extra reference -adressed

For Students

Shiflet, Introduction to Computational Science

• A high level overview of what static models are.

Collection of Tufte visuallization literature

• The notion of visualization is an important concept here, because it deals with the issue of determining the best way to coherently represent a static model.

Computational Science Lab 1, A Simple Static Model, Charlie Peck

• Provides an outline for the lab procedure.

For teachers and TAs

• As far as this goes they should just read all the stuff for the students and beyond that there really isn't much else that they would need to read. The reading in general for this unit is something of a work in progress as it is difficult to find truly relevant, good, easily accessible reading beyond what is already listed.

Lecture notes

Lecture 1:

• Basics, See Shiflet: What is a static model?
• Explain the difference between validation/verification accuracy/precision
• Introduce Tufte, explain the difficulties of visualizing tabular data.

• Explain the first phase of the lab using the Measuring Wheel
  • Logistics, etc
  • Why it can be considered a static model

Lecture 2:

• Clarify confusion concerning the lab.
• Google Maps is a good example of an effective static model
  • Why can it be considered a static model?
  • How does it present information without overwhelming the user?
  • Why doesn't it show every pizza place in the USA when you search for pizza?

• Explain the next phase of the lab, including Google Earth and GPS.
  • How does this portion relate back to the Measuring Wheel portion?
  • How do you use the GPS (There should be a resource reiterating this on the wiki)
  • How do you use Google Earth (see above)

• Why do we need all three?
  • Q: Wasn't the measuring wheel enough?

Lecture 3:

• Clarify confusion surrounding the lab procedure.
• Talk about how static models can usually be really great beginnings to probabilistic and deterministic dynamic models. Specifically, how making a static model of the area of the heart could lead one to being able to make a dynamic model of something like how the chairs on the heart move. This, or a model in the same vain of using the static model as a component, could be made by the time the class is offered and used in this lecture to show how what they're doing scales to more interesting problems.

Lecture 4:

• Show a more complicated series of static models generated using similar procedures. Within this show and explain things that might not seem like static models at first just to make sure they see as many different types of static models as possible.
• Show how an appropriate static model is crucial to getting useful results from any computational model
• Now bring the discussion back to the static model of the heart that the students are currently working on. The contextual components in the previous section will probably make them curious about how their lab assignment fits into all of this.
• Add a dynamic aspect to the static model by asking the students how they would model chair movement on the heart. There are a fixed number of chairs randomly oriented on the heart. As people move these chairs around, to sit with friends or for other reasons. How would we go about modeling this behavior? Is this a hard problem? What's the first step in using our static model to observe how conditions (in this case the orientation of chairs) change over time 'iterations' based on probabilistic and deterministic rules.
• Further complicate the model, adding additional variables, such as friend groups and weather conditions. Where are individuals and groups most likely to claim a spot on the heart? if it's bad weather there might not be much competition for chairs, or if it's sunny students might be more inclined to move their chairs under a tree for shade. How can we go about simulating these probabilistic aspects using our static model of the heart as a basis?
• Since the labs should have been completed by this time, go over any general difficulties people faced to have notes for future iterations of the class.

Classroom response questions

• How does one refer to something that is simply very consistent?
  • A. accurate
  • B. definite
  • C. precise
  • D. correct

• Which of the following is not a static model?
  • A. map
  • B. a sketch of a person
  • C. a flight simulator
  • D. a graph

• Which tool will give the absolute area of the heart?
  • A. measuring wheel
  • B. GPS
  • C. Google Earth
  • D. none of the above

Lab activity

The lab procedure will involve modeling the area of the heart using GPS, Google Earth, and an old-school meter wheel. Students will then decide the best way to use all three to determine the best way to get the highest accuracy.

First Lab Section

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Measuring Wheel

• The first lab component will involve using a measuring wheel to determine the area inside the "heart." This first stage will be especially effective in reassuring students that this whole notion of computational models is not outrageously complex. We're purposely starting off simple to allievate stress and worry. Sweet

Second Lab Section

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The second lab component will consist of the two procedures outlined below. The purpose here is to demonstrate how different data collection methods have a different level of accuracy, and challenge the students to derive their best possible estimation of the true answer given a large set of data.

GPS

• The Computer Science owns some GPS devices that can save a path, and then (assuming the path is a loop) can calculate the area enclosed within that loop. Each lab group will check out a GPS from the department and use it to determine the area of the heart according to the GPS. This won't require any math, however it might be difficult to instruct a large class on how to use the devices. The TA's will circulate to help groups with technical issues.

Google Earth

• Google Earth renders maps and topography from an immense database of geographic information. The students will use google earth's ruler tool to once again estimate the area of the heart. The students will navigate Google Earth to the Earlham campus, and use the ruler tool to determine the length of the path. The procedure will then require they determine the area using the appropriate equation.

Bill of materials

• GPS devices, assuming this class is as big as possible then we'd need somewhere around 20 of these, unfortunately I am unaware of their cost but I know Charlie knows because we already have a few.
• Meter Wheel, I'm assuming we have these

Bring it all together

• The students will now have three different data sets, and they must determine which, if any is valid. What criteria dictates which of the data sets is most accurate? Clearly the google earth calculations must be a little off, because the images are coming from space, etc. But then again gps satillities are in space, and they suffer from signal latency due to topography and large buildings. This final component of the lab will ask the students to relate the lecture content to the three different activities, and use their knowledge and intuition to come up with a reasonable answer.
• Students will be required to visualize this data in some way. In the case of once they have determined their best data points, they can determine the best way (given tuft) to visualize this data.

Static modeling metadata

The Scaffold Approach

• This unit will teach the students to create a model of their own. They will use three different techniques to measure the same area, and compare the results. Lectures will focus on reinforcing the concepts introduced in the first few weeks. This unit will be a good early unit because it won't bombard them with too confusing concepts. Everyone has probably seen the area function, and this unit will introduce them to the more subtle aspects of modeling the real world. The next two lab steps introduce some technology that might complicate issues, but will utilize the same underlying equations and math. Finally the students will put it all together into a report that explains the results and accounts for differences between data collection methods.

Scheduling

To clarify what had been said earlier, this unit works fine with being either second or third in the class and the distinction really sits with Charlie.

General Education Requirements

Abstract Reasoning

They focus substantially on properties of classes of abstract models and operations that apply to them.

• The concepts covered in the static model are intentionally abstract, and rely on the lab activity to ground those abstract concepts in a practical application.

They provide experience in generalizing from specific instances to appropriate classes of abstract models.

• Yes, because the static model is an abstract framework that we're contextualizing using an activity that grounds the abstraction in something as concrete as 'the heart'.

They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level.

• Eh, again, this unit isn't geared towards this as far as I can see.

Quantitative Reasoning

Using and interpreting formulas, graphs and tables.

• The students will work with tabular data to get a feel for the balance between accuracy and precision

Representing mathematical ideas symbolically, graphically, numerically and verbally.

• Yes. Well... maybe not verbally. The groups will be using the abstract notion of a static model to solve a real world problem.

Using mathematical and statistical ideas to solve problems in a variety of contexts.

• Yes. described above.

Using simple models such as linear dependence, exponential growth or decay, or normal distribution.

• Maybe...Not too sure about this one.

Understanding basic statistical ideas such as averages, variability and probability.

• Yes. To fill in some of the gaps in their data, students will need to be prepared to formulate estimatations.

Making estimates and checking the reasonableness of answers.

• Totally

Recognizing the limitations of mathematical and statistical methods.

• Oh yeah...

Inquiry Based Learning

Develops students' understanding of the natural world.

• The students are making static models of the natural world.

Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.

• Students will define a new framework for describing their environment in a static model.

Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.

• Again, the students are collecting data and developing an effective way to represent that data to describe a physical space.

Comments

Looks interesting, engaging, and useful. I wonder, since Tufte is being introduced at least twice by this point (depending on if he shows up in Unit Foundations and Dynamic Models), the last part of the lab should emphasize the neat and effective presentation of the data/conclusions the students have come up with, in addition to all that other stuff.