CS382:Unit-foundation

Unit-foundation-templated

Fermiproblems - Use fermiproblems to encourage students to be comfortable making estimates and discovering ways to estimate with only limited data available. Worked examples are available here

• A list of Problems is available here

Scheduling

Needs to be first

Preferably followed by static modeling

Also will probably need to be 1 week

Skill-set

• 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

Materials needed

• Problems which are relevant to the models which the students will later be constructing in the class
  • Decide on a list of some problems to choose from in a later draft, when the other units are solidified and we know exactly what we're doing.
• Worked through examples showing a complete model and demonstrating which information is necessary for a ballpark estimation and which is not.

Will this be the piano tuners? ...adapted versions of the above list of problems from University of Maryland for Earlham?

• Problem sets for the students to work through
• A quick example of scale such as powers of 10

Lecture Outline

Lectures are ideally divided into 3, What data to get, Where to get the data, and What to do with the data. However since the 3rd part is shorter than the other two it is feasible to divide into two lectures after discussing that making all your own data is hard. If this is going to be a one week unit with 1:20 classes, then the 2-lecture structure will be necessary. Depends on how the final structure ends up, of course, so just hang onto this for now

• Needs some kind of intro hook! Lest the course start out too "dull" for wavery freshmen

How to build a model

• (this was supposed to be the overall theme, right?)
• What data do you get?
  • Establishing a feeling for 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.
    • There will need to be a good way to do this (maybe using the clickers or division into groups), or this will descend into noisy chaos, especially as the course scales upward in size
    • Ask a big question... IE what is the area of the Heart. Brainstorm. (This provides a theoretical background to the measuring lab. Same as above
  • 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
    • 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
      • For a later draft, more detail
  • 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

Lab Work

• Take a lab period to rework a wikipedia article.
  • this couples learning wiki syntax and vetting information
  • Split up into groups of 2-3.
  • Give each group a page which we have identified as needing work and being at least incidentally relevant to the course.
  • Might prove annoying or excessively time-consuming to come up with 20-30 separate pages that need editing and are relevant, as the course scales in size
  • Provide a tutorial of how to edit wiki's
  • Make sure that members of the group switch out who does the editing and who does the research.

• I'm a little concerned that this, as an initial lab, is a little too unstructured, a little vague (also hard to come up with a good evaluation method for this assignment, since each is going to be different); it's very easy within this kind of assignment for the students to just screw around (of course we can just give them a bad grade, but that isn't teaching). I'm not exactly sure what would be a good modification, but it is something to keep in mind.

Background Reading

• Needs a brief synopsis of what these readings are and how they tie into the lecture/unit
• For whom are these readings? Teacher? Student? Extra reference?

Edward Tufte, Sparklines Theory and Practice

• For instance, will this be referenced in the lecture? This seems to be more about effective ways of presenting data once you have it and have made something with it.

Shiflet Chapter 1

how to edit mediawiki.

Classroom Response

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.

• Cool. This is perfect.

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

• Also good.

Which of the following websites best represents a reliable source for scientific research?

A) facebook.com

B) Wikipedia.com

C) acm.org

D) ebay.com

• This one almost seems a bit too easy / facetious... it doesn't really help solidify knowledge of vetting sources. What about significant figures or orders of magnitude?

Comments

• Seems solid.

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.

Other comments

Pros

• What makes a good model vs. what makes just a model

Cons

Comments

• Is this included in all of the other units, or also use this and then use these skills in lots of other places?
  • We need to make sure that this - if it's a unit on its own - that it isn't a very boring first unit
• Include talking about orders of magnitude, scale, significant figures, accuracy vs. precision, pattern recognition

To Do

• Sam has a high school teacher who has a list of many examples, he is going to get in contact with them.
• Think about and perhaps talk to Fitz/Brad about how much from Fire could be used to address this foundation unit
• Think about fractals, shoreline measurements, telecommunications patterns
• Train industry estimates that it moves 1 ton for 423 miles with 1 gallon of fuel - see if this is tractable for the estimating stuff part
• Incorporate Nate's introductory materials