CS382:Unit-foundation-templated

Foundations of Modelling

Overview

This unit covers all of the basic skills needed to create and vet models.

Specifically we provide the answers to three question:

1. What data do you need for a model?
2. Where do you get that data?
3. What do you do with that data?

Background Reading for Teachers and TAs

• A worked through fermi-problem
  • Shows the teachers and ta's the basics of fermi-questions and how to solve them.

Reading Assignments for Students

For lecture 1

• Shiflet et al. Chapter 1 "Overview"
  • A good introduction to what models are and how to build them.
• Wikipedia on modelling
  • Pretty pictures and a description on what models do.

For lecture 2

• Wikipedia on scientific visualization
  • An introduction and overview of what visualization does. I don't think this is detailed enough to step on anyone's toes

Reference Material

• a collection of fermi-problems
  • a list of fermi-questions that we can use homework and class questions.
• Fermi's yield calculation a good example of how simple a model can be
  • Historical info on the first "fermi-question" by Fermi himself. Also a good example of how simple a model of a complex system can be
• The Unreasonable Effectiveness of Mathematics in the Natural Sciences
  • Background on how modeling applies in the natural sciences.
• Hartmann Models
  • Analysis of what models are and a number of questions surrounding them
• [1]
  • more analysis of what models are and how they apply to life

Lecture Notes

Lecture 1

• Introduction to modeling
  • What is a model?
    • a model is a simplified version of an aspect of the real world, or of a theoretical situation.
    • A predictive tool.
  • Why do we use models
    • we use models to simulate events in the real world
      • especially things that are hard to measure and large systems.
    • Models are useful in all natural sciences and more.
  • Models are not perfect representations of the world
    • That would be pointless as they would be too complex
    • Modelers try to simplify the world in a model.
      • this necessarily means they are simplified
    • It is necessary to understand that models have limitations.
      • Nondeterministic systems are much more difficult to model
      • Simplification means that they are different from the real world
      • For smaller/ better understood systems models correspond better with the real world
        • Ex: modeling the fall of a ball
      • For large and poorly understood systems models are much more likely to diverge from the real world
        • Ex: Hurricane tracking (need to add link to various tracks.
  • Show the poster from springwood lake water data.

Nice work!

• What data do you get?
  • Modellers need to have an intuitive understanding of what is significant
    • Bring in a jar of Jelly beans. Ask students to guess how many there are. Ask for which measurements are necessary to get a good guess. Have them split into groups of 4ish to discuss what is important.
    • Ask a big (rhetorical, at least for this unit) question... IE what is the area of the Heart. Ask for people to state factors and theorize as to which are significant to a good measurement. (This provides a theoretical background to the measuring lab.)
  • Establish a feeling for what is too detailed
    • Explain what the difference is between a back of the napkin calculation and an exhaustive one
    • Provide an example of a model and how to make it tractable.
      • Dropping a ball 10 meters (useful data: Gravity. not really useful: Drag, Gravity at our altitude, ball surface etc.)
  • Introduce the idea of orders of magnitude
    • Show powers of 10 to the class
    • Talk about fermi-problems

Lecture 2

• Where do you get data?
  • Making all your own data is hard.
    • Unlike in high-school copying is good, just remember to cite
    • We don't want to reinvent the wheel each time we build something.
    • Ask how many piano tuners there are in Chicago
      • Work through the fermiproblem
      • discuss where assumptions were made and why they were likely good ones
  • But do we trust other people's data?
    • Discuss the notion of vetting sources
    • explain scientific rigor
• What do you do with your data?
  • We need to extrapolate sometimes
    • Explain how to properly extrapolate from known data to what you need.
    • Explain how to defend your extrapolations (Show calculations, explicitly list assumptions, etc)
  • Show how to bring data together
    • Revisit the worked fermi-problem
  • Explain that data can be evaluated based on accuracy and precision. Explain the difference between them
  • Explain how to present data as information
    • In the case of monitoring springwood lake
      • take data with sensor devise and GPS
      • synchronize sensor time with GPS time, mush up those, and create table(time, data, location)
      • visualize data as you want, for instance plotting, google earthing, or both
  • Return to the basics of what models are, and hint at where the class is going.

Lab

Nice work!

In this lab we will get some experience in estimating a variety of scales of objects. The goal is to help you acquire a sense of how to make intelligent estimates by scaling up from easily countable numbers. By being able to take measurements from a small scale and extrapolate them you will be equipped to create simple static models using either your own measurements or someone else's.

Process

• What to do, step-by-step
• Divide up into lab groups
• The instructor has placed the jar of jellybeans from class in the front of the room. The first part of the lab is to look at your estimates from class.
• The instructor will show how he/she has made a guess (counting the number in a square centimeter and extrapolating or the like)
• Take 10 minutes to try to find a more accurate way of doing a measurement. (we have provided scales, empty jars, extra jellybeans, and a tape measure)
• Record the measurements that you took and what they yielded.
• There is a jar of sand. Adapt the measuring techniques that you used for the jellybeans to count the number of grains of sand. Take 20 minutes measuring and recording (possibly have the internet available to look up mass of a grain of sand)
• Go to the hallway on the second floor of Dennis, estimate the number of floor tiles.
• Record your results and your reasoning
• In 10 minutes estimate the number of tiles in the whole of Dennis
• Record the calculations you used and your estimate.
• Now head to the computer lab. CSX has been running radio ads saying that a freight train can move a single ton of freight 423 miles on a gallon of fuel.
• Prove that this is correct using primary literature. (hint the DOT may help)
• Record all calculations that you have done and be sure to cite sources.

Write-up

• Recordings of all of the measurement that you have made
• Recordings of all of the calculations that you have made
• Discussion on the reasoning behind the assumptions that you have made.
• Discuss how you could measure the number of grains of sand on a beach using the techniques that you have developed
• Extra credit: Find measurements of a beach and calculate the number of grains of sand on it.

Software

Firefox

Bill of Materials

A jar of jelly beans: $5.00

Extra jars of the same size: $2.00

Jar of sand: Free

Scales: Free

Measuring tape: free

Evaluation

CRS Questions

Which of the following represents low accuracy but high precision:

A) 5 measurements of a meter stick which measure the length as 100cm, 101cm, 99cm, 98cm, 100cm.

B) 5 measurements of a meter stick which measure the length as 80cm, 79cm, 81cm, 82cm, 78cm.

C) 5 measurements of a meter stick which measure the length as 90cm, 110cm, 109cm, 91cm, 100cm

D) 5 measurements of a meter stick which measure the length as 80cm, 95cm, 50cm, 130cm, 200cm.

Which of the following is likely to have the least impact on a model of a ball dropping:

A) Rate of acceleration due to gravity

B) Size of the ball

C) Height of the ball

D) Whether or not the ball is attached to a parachute

About how many squirrels are on Earlham's "front" campus:

A) 1 to 10

B) 10 to 1000

C) 1000 to 100000

D) 100000+

Quiz Questions

• What qualifications make a source authoritative?
  • Answer should include discussion on peer review, citation, and the notoriety of author as well as source.
• What are computational models good for?
  • answer should discuss the applicability of computational models to the natural sciences. In addition the answer should include examples of large scale and small scale models.
• What makes a parameter useful to include in a model?
  • Answer should discuss the impact that a useful parameter has on a model as opposed to the little change that a non-useful parameter has on the outcome. Ideally the answer should include examples.
• What limits do computational models have?
  • answer should discuss the inherent error of excluding parameters, the difficulties of modeling poorly understood systems and the problems that nondeterministic human behavior introduces. A good answer will include examples of simple models that we have high confidence in versus large models that can produce many different results dependent on assumptions, ex: climate change.

Foundational unit Metadata

To teach how to make and get data.

To teach how to present data

To teach how to make good estimates of hard to count problems

Scheduling

First, its the introductory unit after all.

Concepts and Techniques

• Using available sources to find information
• Quickly vetting sources
• Acquiring a feel for how to determine what factors are significant
• Learning how to make estimates where figures are not available
• Learning how to show and defend the reasoning behind extrapolations
• Being able to make quick back of the napkin calculations
• Understanding of what significant figures are and how to calculate them
• Understanding the difference between accuracy and precision
• Learning to present data so that it is useful

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 entire unit centers around learning how to create and use abstract models. We work on first what they are and then how to use them.
    • They provide experience in generalizing from specific instances to appropriate classes of abstract models.
      • Complete. The lab provides hands on experience in generalizing and extrapolating from a specific small scale problem to a larger instance of that problem. The lab further focuses on getting students to put together a toolkit of techniques to create simple abstract models.
    • 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.
      • Complete. See above about the lab. Also we apply word problems in the form of fermi-problems encouraging students to make and defend measurements and create numeric results.
  • 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 discussion of vetting materials requires and creates an understanding of how to interpret quantitative information. In addition the lab teaches students how to generate quantitative information. This unit briefly touches on visualization of data
    • Representing mathematical ideas symbolically, graphically, numerically and verbally.
      • Partial. The exercises in lab as well as the fermi problems beget skill in representing data numerically and verbally. We discuss representing data graphically and symbolically but do not go into detail in this unit.
    • Using mathematical and statistical ideas to solve problems in a variety of contexts.
      • Complete. the lab design is geared toward teaching how to solve counting and statistical problems in multiple contexts.
    • Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
      • Partial. we discuss the creation of these models however the ones that students use in this unit are likely to not fulfill these.
    • Understanding basic statistical ideas such as averages, variability and probability.
      • Complete. we introduce statistics in the context of models and discuss their usefulness
    • Making estimates and checking the reasonableness of answers.
      • Complete. in both the lab work and the other problems for the students to solve this unit requires strong support for all assertions that students make
    • Recognizing the limitations of mathematical and statistical methods.
      • None. Yet I need to add this in the introductory portion
• Scientific Inquiry Requirement - From the [Catalog Description] Scientific inquiry:
  • Develops students' understanding of the natural world.
    • • Complete. this unit lays the framework for students to explore the natural world through counting and modeling.
  • Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
    • • Complete. one of the major take-away points of this unit is how to develop a scientific knowledge of a system. In order to test hypotheses students need to build models and apply them to the real world
  • Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
    • • Complete. the lecture emphasizes analysis of data and the basics of how to collect it. The lab focuses on the collection of empirical data.
    • Collecting data is divided into first-hand experience and using other people's data (theoretical analysis)
      • Complete. the lecture emphasizes analysis of data and the basics of how to collect it. The lab focuses on the collection of empirical data.

Scaffolded Learning

The lab presents a chance for scaffolded learning. Students are given a series of estimates that they have to make, each one building on the techniques developed for the previous one. Students get to use their calculations to build a large model and to verify previously made measurements.

Inquiry Based Learning

Estimation of Jelly-beans and area of the heart involves students and promotes collaboration. This lets students make decisions on how to count and find the best way to do so. The extra credit of the lab extends the learning to have the students search for data.

link to old version

To Do

• Consider adding a sibling of Denning's article on computation across the disciplines to the reading and lecture component. It's a theme of the class in some sense.
• We had thought editing Wikipedia article could help them with verifying facts and vetting information, and also learn to use wiki. Obviously at end of the semester they wouldn't need to learn to use the wiki, but could they tie together the bits by finding an article that covers something in Wikipedia that we covered in class and improve it. Consider this idea.
  • Possibly could look at proposed articles and make sure they're not contentious.

Unit Foundation Mechanics

To Do

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

Comments

• I'm a little confused about this - does this also cover the heart estimation (see above)? But in addition to that, how do we know the ballpark for the bricks on one side of Dennis?
• Are they supposed to go out and do estimation at all for the estimates for the whole building and the dorms? We should probably make sure we know which ones have which sizes then. This could also be potentially frustrating. Having data about which buildings exist on campus as well as how many floors are on each could help.
• This is a lot of discussion, which is good on one hand but the TAs leading the lab may not be up to this kind of interaction. Talk with Charlie and see what he thinks about this.
• Lab has been changed to be more clear on requirements. The discussion will now be more within groups.

This has gotten some great revisioning since the last draft! Way to go, keep it up! thanks.

I'm not sure this unit really addresses this point. It does a great job of estimation as is now but it needs more tie in to these central points. One of your sources could help with that... see below. I have talked with Kay about this and I am going to add a new lecture section which contains "what is a model?"

Need synopses for these! I think this provides the basics, if not tell me.

This is very interesting, and I think Charlie recommended it IIRC, but I'm not sure how it's fitting into this unit (where down below this point in the wiki page is this applicable?). Valid Comment, removed.

Need synopses for all of these! I think these provide synopses of what the usefulness of each reading is, if you want more tell me.

Synopses...

I think incorporating more information from this essay, about what models are the classes of models, from a high level could be very beneficial. Working on incorporating this into the lecture.

Ditto for this one, though less so.

You do an excellent job talking about everything behind modeling, but it's missing something (or somethings) in the lecture to draw it all together about what models are fundamentally. I have added an Introduction to modeling to the lecture which addresses these concerns.

I'm a little confused about which estimations are going where. Jelly bean is in class, but the heart is during lab? There's no info about it in the lab section., Addressed in lab section.

Amongst other places, this could be a good place to tie back in the concept of what models are. Fixed above.

This is very well done. Good job breaking down the steps. The only question I would have, and this may be more for discussion in class than for you, is whether this will take enough time to do. I think so. It tracks well with the length of labs that I have been in.

It would be cool if we knew the exact number and could do comparisons of people's answers. Maybe you could even throw something in about their multiple ways of measuring and precision and accuracy. Counting is a good idea, probably something for the TA's. As for discussion of precision vs accuracy it will be discussed in class, I will consider adding a note for the person running the lab.

I like the extra optional item, but it might help to be a little more specific. Ie, how big is a beach? What counts as a beach? I am not sure if we have any beaches on campus, I think the questions of how big a beach is and what counts as a beach should be answered by the students

Does physics have scales (you would know better than me ;) yes

Also does physics have this? yes

Don't forget, you're supposed to indicate which answers are correct by bolding them!

I like the difference between questions A and B. I'm not sure the others are as clear. Need more info to make change

How do you define "front" campus? I think it might be helpful to give them the area of campus so they're not estimating two things at once. Front campus is the area with buildings on it.

Don't forget to put answers to these! done.

Unfortunately, just saying we support it isn't going to be enough for the review committee, and also saying it in one (or even two) lectures isn't enough to argue strong support. We need to tell which parts specifically of the unit are addressing these. This is part of what's being turned into a document for Charlie to bring before the review committee, so we need specific prose about the unit, etc. I have overhauled all of my descriptions to be much more detailed.

Will there be any gradation in "how much" each of those estimates is required? If we're expecting the lab groups to gather each time after an estimate, the entire class will lag if one group lags. On the other hand, if you let them go at their own pace, some groups may be able to get further than others (which may be a good thing). These concerns have been addressed in the redoing of the lab

How is this inquiry specifically, though? Addressed above

If there's anything you want included in this new version from the old one, make sure you copy it over! done

• Add to the lab component (or lecture?) figuring-out if the ton of freight so many miles on a gallon of fuel bit is accurate. Done