In our Mathematical Reasoning class tonight, we discussed this problem: Can your age in years be written in terms of the difference of two square numbers? If so, what two numbers? There are at least three mathematical problems contained here: Given a specific whole number (0 or a positive integer), attempt to find two square…
Month: August 2012
Logarithmic notation: Mathematics vs. computer programming
One of my concerns as an educator is the way in which peccadilloes of mathematical notation can get in the way of understanding. In the case of logarithms, this has become more troublesome as general education about numeric bases at the secondary level has apparently evolved primarily into an interest of computer programmers. The notation…
Minimal Eulero
Eulero is a grid-based logic puzzle. Like Sudoku, it involves Latin squares; however, while Sudoku relies on a single Latin square, Eulero consists of two overlaid squares, one of numerals and one of letters. An additional constraint is that each letter-number combination has to appear exactly once. This got me thinking: What are the fewest…
Trigonometry as the Study of Circles
I recently read John Derbyshire’s book, Unknown Quantity: A Real and Imaginary History of Algebra (Plume 2007 edition). I recommend it overall, although the second half becomes increasingly inaccessible to the layperson. One bit that particular stuck in my head, because of the way it caused me to rethink a mathematical concept, was this passage…
The Prefix Dia-
A good teacher is always aware that there are things they can learn. One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used elsewhere. For instance, “median” in mathematics refers to a number in the middle of a…
PEMDAS and negative numbers
By standard mathematical convention, \(-1^2=-1\). At the same time, students are taught to refer to \(-1\) as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed below. Furthermore, while the first convention is generally taught in high school, the mathematical argument…
Well… is algebra necessary?
Except for the final grades, I’ve just wrapped up teaching six weeks of credit recovery for Freshman Algebra. It’s tough enough packing nine months’ of material into six weeks, but consider these are the students who didn’t do well enough the first time to get a passing grade (in this case, a C or higher),…