wendystjohn

The exam will consist of multiple choice and matching questions, along with some fill-in-the-blank and short answer questions. You will also be asked to upload calculations for some of the problems, so be prepared to show all your work and make sure they are legible and clear, as we discussed in class on the 14th. This guide should help you focus the time you spend studying, but it is not meant to be exhaustive . . . there may be additional concepts from lecture or the readings that will be on the exam. However, if you familiarize yourself with the material in this guide, you will be well prepared. In addition to the topics below, review the main points of all reading assignments.

Estimates and Models

  • Understand the difference between qualitative and quantitative data. Which type can be used in the course of scientific investigations?
  • How does this relate to continuous vs categorical data.
  • Understand the four types of quantitative methods, and the types of data and mathematical approaches they may use.
  • What was the outcome of the experiment that investigated student interest in games vs lectures?
  • What is a model? Know the examples discussed in lecture.
  • What are the steps in making a model?
  • How can models help us make decisions?
  • When might we want to use quantitative methods for decision making?
  • Understand the typical mathematical modeling process.
  • What is risk? Why do we need to consider it?
  • What does a heat map represent?
  • What is an estimate? Why and when should we use estimates?
  • How can we decide how accurate our estimates need to be?
  • Be able to read through a scenario, and recognize the important quantities that would be needed to calculate a reasonable estimate.
  • Be prepared to make an estimate without looking up any values (in other words, just using your “gut” instinct).
  • What would be required for humans to achieve equitable diets globally?
  • Understand the structure of a tree diagram, how it can assist you in making an estimate, and how to create one.
  • What are endpoints, and how do they relate to determining ranges of values?
  • What is the difference between the arithmetic and geometric means? When would you use each?

Divide and Conquer

  • How can mathematics be used as a tool for critical thinking? Why might we need to use this tool?
  • What is the principle of charity, particularly in the context of this course. 
  • What are the limitations of quantitive argument? 
  • Why is it important to be able to make reasonable estimates? 
  • Understand tree diagrams, and be able to draw and/or interpret one. Make sure to understand how endpoints are used. 
  • Understand the difference between the arithmetic and geometric means.

Cognitive Biases

  • Understand the common cognitive biases
  • What are the problems that biases can help us address? How can biases be helpful?
  • When are biases harmful, individually or societally?
  • Think of some times when you have exhibited a confirmation bias.
  • What are some ways of building awareness of confirmation bias, in order to avoid it?
  • What makes a strong argument? How can quantitative data be used to support an argument?
  • What is the principle of charity?
  • What types of questions can not be informed by quantitative data?

Quantities

  • Be able to define and discuss quantities, dimensions, and units.
  • Why can quantities have different magnitudes even though they represent the same physical object or property?
  • What are the primary systems of units used today? 
  • What is a conversion factor, and when are they used? 
  • Know what happened to the Mars Climate Orbiter, and the cargo flight in 1999.
  • What is dimensional analysis? 
  • Be able to perform unit conversions using factor-label conversion. (I will provide you with any unusual conversion factors, although I expect you to know the common ones, for example inches to feet to yards; cm to m to km, minutes to seconds, etc). 

Data-driven Decision Making

  • What is DDDM? 
  • What steps can you take to ensure your decisions are as unbiased as possible? 
  • How can using data as a starting point be of benefit to decision making? 
  • Understand the essential questions to ask
  • How can data help inform solutions? 
  • What is racial profiling? 
  • Understand the difference between implicit and explicit bias. 
  • What is the purpose of a “reconcile” column? 
  • What does it mean to “clean” your data? 
  • Understand the function of the COUNTIF formula.

Significant Figures

  • What does it mean to say that there is uncertainty in all measurements? 
  • Understand the difference between accuracy and precision.
  • What is the difference between random and systematic error? 
  • Know and b able to apply the rules for significant figures. 
  • Why are excess significant figures unnecessary?

Place Value

  • Understand the numbering system used by the ancient Egyptians, and the Babylonians. Why was it important to these early civilizations to develop systems of written number? 
  • What is a place value system? How does it work? What are the benefits over a tally system? 
  • Why do most human cultures use a base 10 system? 
  • Be able to convert the following bases into decimal: binary, octal, hexadecimal, vigesimal, and sexagesimal.