A Review of "When Einstein Walked with Gödel"

It's incredibly frustrating to see beauty where others do not. This isolation is one of the main problems about studying mathematics. Whenever I answer the question “What do you do?”, I expect my answer to immediately kill this line of discussion. Not only do people have little idea about what I do, they hate what I do. This is the isolation: what I love, others loathe. Where I see deep, rich beauty, others cannot avert their eyes fast enough. This is why attempts to popularize mathematics interest me. They offer me an opportunity to connect with others, and those I love, over my life’s passion.

Read More

Functional Roles of Math Symbols

in

A discussion of the functional roles that common mathematical symbols play. This post is a response to misscalcul8's post Math Symbols Test. Her post featured a table of definitions for mathematical symbols, which I suggested be subdivided by the area of math and the role each symbol played. This post explains these roles and their differences.

Read More

Advanced Slope Studio

in

A Geogebra file and accompanying lesson ideas for a subtle but important aspect of the slope of a line. Students often think of slope as "rising 2 units and run 1 unit". But they will struggle to see that "rising 1 unit and run 1/2 a unit" is the same slope, not just producing the same slope. This is tied to seeing that one ratio can have (infinitely) many forms, e.g. 2:1 = 4:2 = 1:0.5 = 2 x : x (for any nonzero value of x). The lesson shown here, with the accompanying Geogebra file, tries to address this lack of understanding, as well as introducing students to other ideas.

Read More