Reasoning, logic, and critical-thinking skills are the building blocks of intellectual inquiry. This course focuses on developing these skills through problem solving and exposure to a wide range of topics in mathematics. Students learn to distinguish between inductive and deductive reasoning and examine the roles played by each in mathematics.
The students’ introduction to inductive reasoning begins with a search for patterns and creating recursive and explicit formulas to describe those patterns. Students master material by considering algebraic and geometric concepts, patterns, and real-world questions that can be answered using inductive reasoning.
As they move on to the concept of deductive reasoning, students learn to use a system of logic to draw conclusions from statements that are accepted as true. Students learn about this style of reasoning with a variety of topics such as symbolic logic, truth tables, and syllogisms. Emphasis is placed on the importance of proving conclusions using valid arguments.
Like the other CTY courses I’ve instructed and TAed, this was an intensive, 3-week summer course. This one was from a younger age group, with students aged 10-12. It was a lot of fun to help kids that young develop their mathematical reasoning skills!