Colorized Logs
How I use color to distinguish terms in the definition of logarithms.
Read MoreHow I use color to distinguish terms in the definition of logarithms.
Read MorePrinting the graph along with questions on extrema and/or inflection points has changed some of my calculus 1 lessons.
Read MoreExploring common wrong answers to an exam question about writing out a polynomial with specified real and complex roots.
Read MoreFour roles that variables can play in math.
Read MoreAlternate ways of writing, or notating, arithmetic can provide new insights for students. In this post, a tree notation for arithmetic is briefly explored. (And by tree, I mean the computer science variety of trees.)
Read MoreA description of an online textbook which is much more sophisticated than a simple PDF. An online textbook can have merit badges!
Read MoreA report on my experience using OneNote to keep handwritten lecture notes, which I plan to distribute to students.
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`f(x) = 0`. This could be a definition of a function, `f(x)`, to the constant value of `0`, or it could be an equation between a function `f(x)` and the value `0`. The symbol '=' is ambiguous! I cover four different semantics of '='. Can you find more, or do you think there are fewer?
Read MoreA 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 MoreA 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.
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