On Monday, January 18, my son turned 1 week old. We have a cute little sign to mark his age, but the sign is in months, not weeks. So, the question was, “What is 1 week in months?” It is a fraction, but it is not one quarter. If every month was 4 weeks, then … Continue reading 3/13 Months Old
There is so much to say about nothing. Choosing nothing breaks false dilemmas. This or that? None for me, thanks. Some of my favorite books about math, such as Seife’s Zero: The Biography of a Dangerous Idea, were written with zero as the main topic. Earlier this year, Amir Aczel published an account of his search for the earliest … Continue reading The Power of Zero
We like reversible processes. If I earn 5 dollars, I want to be able to spend 5 dollars. Subtraction undoes addition. It is the inverse process. All is well, until you subtract 5 dollars from your account that only has 3 dollars in it. You might have some negative feelings about that. Multiplication has an inverse process … Continue reading What to the what?
A student asked me recently what it means when we multiply a negative by a negative. Specifically, she was asking: “Why is a negative times a negative a positive?” Negatives are strange, sometimes counterintuitive. If all you remember about negative numbers is a disconnected set of rules, those rules may have ended up in a bit of a knot. Students … Continue reading Negative Numbers
I have been working with some middle and high school students this fall. It has only been a few short years since they were learning the basics. They retain some of those basics as disembodied rules, rules with no meaning or purpose. The situation seems to hinder them from experiencing the beauty and wonder that is high … Continue reading Repeated Operations
My mind tends to consider extremes. From thinking I have no options to feeling overwhelmed by options, making choices can be challenging. Counting, when possible, calms my mind and simplifies reality. As summer was beginning, I posted about Pascal’s Triangle, a tool for counting combinations. Considering combinations turns our thinking from a set into a variety of possible subsets; a … Continue reading Combinations
We have opportunities to count everyday. Some of the counting is done for us, such as the number of likes on your favorite social media post. We even celebrate victories when the count, the score, is a desired result. Too often though, numerics bring a gravity—an unfortunate heaviness—to life, especially when we are asked to do … Continue reading Permutations