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
• Edward Tufte, Sparklines Theory and Practice

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

For lecture 2

• Wikipedia on scientific visualization
• Edward Tufte, Sparklines Theory and Practice

Reference Material

• a collection of fermi-problems
• Fermi's yield calculation a good example of how simple a model can be
• The Unreasonable Effectiveness of Mathematics in the Natural Sciences
• [1]
• [2]

Lecture Notes

Lecture 1

• 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 question... IE what is the area of the Heart. Ask for people to state factors. (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
• 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

Lecture 2

• • 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, goolge earthing, or both

Lab

Divide students up into groups. Have students estimate the number of bricks in one side of Dennis. Provide tape-measure and chalk. Time bounded, 10 minutes max. When they have made an estimate check to see if its within the ballpark. If so have them estimate for the whole building. Ask them what factors they took into account. Then ask them to estimate the number of bricks in all the dorms. Repeat questions. Ask about all campus buildings.

Software

N/A

Bill of Materials

• A jar of jellybeans (to be counted by TA's) $5.00
• Chalk
• A tape measure per lab group

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 100

C) 100 to 1000

D) 1000+

Quiz Questions

• What qualifications make a source authoritative?
• What are computational models good for?
• What makes a parameter useful to include in a model?

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.
      • Solid support
    • They provide experience in generalizing from specific instances to appropriate classes of abstract models.
      • Solid Support, we dedicate an entire lecture to this
    • 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.
      • Kinda what the whole unit is about
  • 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.
      • The discussion of vetting materials strongly supports this objective
    • Representing mathematical ideas symbolically, graphically, numerically and verbally.
      • Tufte. Strong coverage of this
    • Using mathematical and statistical ideas to solve problems in a variety of contexts.
      • Our discussion of how to use data covers this
    • Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
      • Strong support
    • Understanding basic statistical ideas such as averages, variability and probability.
      • Strong support
    • Making estimates and checking the reasonableness of answers.
      • Vetting data covers this
    • Recognizing the limitations of mathematical and statistical methods.
      • Analysis of this unit's support or not for this item.
• Scientific Inquiry Requirement - From the [Catalog Description] Scientific inquiry:
  • Develops students' understanding of the natural world.
    • We lay the framework for understanding the world through models.
  • Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
    • One of the major take-away points of this unit is how to develop a scientific knowledge of a situation.
    • In order to test hypotheses students need to build models and apply them to the real world
    • Well established in this unit
  • Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
    • The second major point in the above lecture notes is how do we collect data
      • Collecting data is divided into first-hand experience and using other people's data (theoretical analysis)
    • Well established in this unit.

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 previous one. Students get to use their calculations to build a large model.

Inquiry Based Learning

Estimation of Jelly-beans and area of the heart involves students and promotes collaboration.

link to old version