Quantitative Reasoning

How can we convince ourselves, or other people, that an assertion is true? Students in Quantitative Reasoning will think deeply about how to address real-world problems through quantitative analysis and will consider what one may reasonably expect from such analysis. Seeking insight into different ways of representing the world in numbers and marshalling quantitative evidence to demonstrate the truth or plausibility of a proposition, students will engage a variety of modes of assertion and demonstration, ranging from rigorous mathematical proofs to standards of evidence appropriate for empirical and social science. This course will be project-based, with frequent exercises involving writing and speaking about quantitative material, culminating in a research project in which small teams of students gather and interpret numerical data on a topic of current interest.

The module aims to develop students’ confidence and facility in reasoning quantitatively, coupled with a sense of what kinds of argument are appropriate to different situations. Students will come to understand the modes of reasoned persuasion, often called “proofs”, which apply in various contexts, ranging from the well-defined but abstract concepts of mathematics to the less clear-cut real-world situations where statistical methods are employed. This should provide good grounding for later studies applying statistics in natural and social sciences. Students will gain skills in presenting such arguments themselves, both verbally and visually, and in critiquing the arguments of others. They will also learn to appreciate that decisions are not always made formally, and learn to recognise and analyse less formal methods of decision-making.

Since this module is part of the Common Curriculum, it is intended to be suitable for all students. Students will benefit from working in diverse student teams that encourage peer-to-peer learning, and aid those with less preparation in certain aspects.

Examples of course content

This module explores a range of quantitative methods in a manner accessible to all students regardless of level of preparation. Examples are generally chosen from the social sciences, but the methods themselves are applicable to a wide range of topics. Special attention is paid to helping students develop their skills in presenting and analysing quantitative information. Students in Quantitative Reasoning will:

  • Learn how to criticize and question claims in an informed way.
  • Learn to think clearly, to understand logical and intuitive reasoning, and to consider appropriate standards of proof in different contexts.
  • Develop a facility and comfort with a variety of representations of quantitative data, and practical experience in gathering data.
  • Understand the sources of bias and error in seemingly objective numerical data.
  • Become familiar with the basic concepts of probability and statistics, with particular emphasis on recognising when these techniques provide reliable results and when they threaten to mislead us.