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. A static model is a visual representation of something in the real world that doesn't change over time and isn't interactive.

Background Reading 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.

Understood. Feel free to include less accessible resources for TAs/teachers, though.

Reading Assignments For Students

Shiflet, Introduction to Computational Science

A high level overview of what static models are, chapter 1 of this book addresses this.

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.
Readings located throughout various sections of the book.

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

Provides an outline for the lab procedure.

Reference Material

Lecture notes

Lecture 1:

Basics, See Shiflet: What is a static model?
Explain the difference between validation/verification accuracy/precision
- Accuracy - getting the right answer
- Precision - getting a consistent answer that isn't necessarily the correct one
- Validation - solving the correct question
- Verification - making sure the question is being solved correctly
Introduce Tufte, explain the difficulties of visualizing tabular data.
- Tabular data is messy and hard to quickly get specific information from.
- Largest problem stems from difficulty in figuring out an interesting, simple, and clean way to display the data.

Explain the first phase of the lab using the Measuring Wheel
- Measuring wheel use is quite simple and innovative, all one has to do is push and it will display the distance covered.
- 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?

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.
Explain different ways to visualize static models. The students will be familiar with Tufte, and this can be a good jumping-off point to begin a discussion on how best to visualize the data points gathered from the lab activity.
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.

Lab

The lab procedure will require students to build static models of the heart. Students must (in groups) figure out the best way to calculate area using tools that measure length. This lab intends to teach students the importance of accuracy and precision in developing good models.

Process

Use the measuring wheel to determine the area of the heart.

Next use the GPS device to make the same calculation. Reset the distance field on the device and walk around the heart at the inner edge of the sidewalk. Repeat this step three (3) times. Record Results. The TA's will circulate to help groups with technical issues.

Google Earth renders maps and topography from an immense database of geographic information. Use the ruler tool to make your measurements.
- Start up Google Earth. These directions require Google Earth 5.0
- Enter Earlham College in the search box.
- Zoom into show the heart on the front campus.
- Use the ruler tool to draw a path. Length data is visible in a popup window.

Write-up

Include a table of your calculations, including three trials of the three different methods. Include standard deviation and mean for each method.
Calculate the area for each of your nine (9) cases.
Explain and justify your results. What do they say about the accuracy of each method? Can you draw any conclusions about which is most reliable? Least reliable?
Draw a diagram (for each method) illustrating the measurement path.
Model the entire campus using the techniques above. (sans measuring wheel) Since using a measuring wheel or GPS is infeasable at this scale, can you think of other means to gather this data. (ie maps)

Software

Google Earth. Free. All platforms.

Bill of Materials

GPS devices, assuming this class is as big as possible then we'd need somewhere around 10 - 15 of these.
Meter Wheel

Write-up by Mikio Takizawa (April 24, 2009)

I did not have a measuring wheel or GPS unit. Instead, I walked along the diameter of Heart and counted the number of steps.
Heart is under construction now. Thus I could not walk measuring the whole Heart.
Heart is more like elliptic than circle. But I modeled it as a circle for simplicity.

By Walking

Mikio's one step = 0.823 m

Experimental Data (step): 76, 74, 74, 75, 76, 72, 78, 78, 79, 76

Average: 75.9 steps

Standard Deviation: 2.1499 steps

Experimental result: The diameter of Heart is 62.47 m ± 1.77

Area of Heart: (62.47 / 2)^2 * pi = 3065.02 m^2

By Google Earth

Image of Experiment from Google Earth

Circumference of Heart: 227.62 m

Diameter of Heart: 227.62 / pi = 72.45 m

Area of Heart: (72.45 / 2)^2 * pi = 4122.56 m^2

Evaluation

CRS 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

Quiz Question

What are the types of problems that static modeling is used to help solve?
- A. Weather prediction
- B. Calculating the area of a given space
- C. Infectious disease
- D. Gravity

Why is it that tabular data is an unacceptable method for displaying results?
- Tabular data makes it too difficult to quickly scan for information and it just looks atrocious.

What purposes do the verification and validation serve?
- To ensure that the right question is being asked

Static modeling metadata

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.

Concepts, Techniques, and Tools

Using models, modifying models, developing models
Abstraction
Accuracy vs precision
Validation and verification
Interpreting a graph
Creating a graph
Data collection
Measuring Wheel
GPS
google maps

General Education Alignment

Analytical Reasoning Requirement

Abstract Reasoning

From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:

They focus substantially on properties of classes of abstract models and operations that apply to them.
- Complete. 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.
- Complete. 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. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
- None.

Quantitative Reasoning

From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:

Using and interpreting formulas, graphs and tables.
- Complete. 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.
- Partial. 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.
- Complete. The groups will be using the abstract notion of a static model to solve a real world problem.
Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
- None.
Understanding basic statistical ideas such as averages, variability and probability.
- Complete. To fill in some of the gaps in their data, students will need to be prepared to formulate estimations.
Making estimates and checking the reasonableness of answers.
- Complete. Yes, students are asked to make estimates to effectively interpret the data they collect.
Recognizing the limitations of mathematical and statistical methods.
- Partial. A portion of the lectures will be devoted to explaining the limitations of static models and modeling the real world in general.

Scientific Inquiry Requirement

From the [Catalog Description] Scientific inquiry:

Develops students' understanding of the natural world.
- Complete. 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.
- Complete. 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.
- Complete. The students are collecting data and developing an effective way to represent that data to describe a physical space.

Scaffolded Learning

Nice work!

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.

Students are building computational models of the real world using data they collected, and bringing together past knowledge to determine the best way to calculate area, a process that even the most math-impaired student can understand.

Inquiry Based Learning

In this unit a majority of the last lecture centers around what the students can think of for all of the variables of the model. The better part of this last class will be spent strengthening their understanding through almost nothing but questions.

Static Modeling Mechanics

General Feedback

A list of items maintained by the authors, Charlie, and the Reviewers.

Lab Feedback

Feedback specific to the lab component. Either in-line notes or a link to a separate page.
Some thoughts about what to look for:
- How long did it take?
- How appropriate is it to the material in the unit?
- Are the instructions complete or did you have to fill-in gaps.
- Is it too easy? Too hard?
- Is what to look for, collect, and analyze clearly delineated?
- Can you easily see what the purpose of the lab is and what you learned from it?

Archived Feedback

This is good but we need more detail. For instance, someone coming into this needs to know what you consider the basics of static modeling, even if you just list them as bullet points. Another for instance, what are the difficulties of visualizing tabular data? This will help the instructor and also help the reviewers and class now see where you're going with some of this and if it all ties in well.

Make sure you add your quiz questions.

Need more content and breakdown here.

Need more information here, not sure where you're going with this.

Make sure you answer your own rhetorical questions! Same as above so we know where you're going with this.

Also if we could get a copy of this online on the wiki to refer to, or a link to it somewhere in Charlie's stuff online, that would be helpful.

You mean a subsection of this book, right?! Please specify which parts.

Some definition here of what a static model is would be helpful.

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. - addressed

Yeah, I totally thought we were talking about a human heart until I read your unit description. :P You can delete this comment, hopefully you got a laugh out of the non-Earlhamite because of it. -addressed

Need some more content here, about how they're going to do it, what instructions they'll be given, etc. etc. -addressed?

Ok, once you find it out from him, make sure you document it here.

It might help to print out a map of the heart and specify which areas you want them to do. Maybe stay within an area contained by sidewalks or something.

Make sure to indicate which answers are correct by making them bold.

This has a lot of room for speculation and discussion about the model, but I'm not sure there's much content in this lecture other than talking about the lab. We need some content to draw the discussion from the lab back into what this unit is all about.

Authorship

Philip Jurov and Bryan Purcell

CS382:Staticmodel-outline

Contents