The attached document explores various ways of inuitively understanding negative numbers, especialy the product of two negative numbers. When working with positive numbers, repeated addition and scaling are ways to understand multiplication. However, the same techniques do not work in explaining the product of negative numbers.
This document contains tasks to introduce mathematical thinking to students, including defining objects, coming up with conjectures, stating axioms precisely, and proving conjectures from axioms and definitions.
Conceptual Inquiry involves the investigation of abstract concepts such as parallel lines, species, free will and democracy. It cuts across disciplines and is important in order to understand where disagreements really exist and where words just have different meanings for different people. The attached document and the embedded playlist explore Conceptual Inquiry through case studies including parallel lines and democracy.
The attached document is a guide to preparing classroom material and scenarios for a course on Moral/Ethical Inquiry, involving the construction of moral theories. It contains a lot of examples of scenarios which can be introduced to students in order to get them to think about how they should live their lives.
The attached documents are an example of a mathematical inquiry class. This is an example of a class which can be taken with students who are not yet ready for the rigor of proofs. It requires students to come up with conjectures after being exposed to curated examples of shapes made of straw.
Mathematics is the study of possible worlds. The attached document explores, through examples and exposition, the nature of mathematical inquiry as well as the concepts involved in the study of mathematics, namely axioms, definitions, conjectures, proofs and theorems.