The benefits First, let’s consider the pros. There are benefits for the athletes (scholarships, character building, career opportunities, etc.), benefits for the fans (entertainment), benefits for the university (income, prestige, etc.), and benefits for the community (economic stimulation, bringing the community together, etc.). These things are not to be disregarded. As we proceed to consider…
Category: Education
A different view of the multiplication and division algorithms
The “traditional” methods for multiplying or dividing numbers have generally been taught by rote memorization or with minimal explanation. By reframing these processes, I hope to make it more clear what is happening. Column method of multiplication This is similar to the column methods of addition and subtraction, although multiplication is slightly more complicated. Here’s…
One thing at a time: how make effective assessments
This is specifically from the perspective of math education, but may apply to other areas just as well. Why do we give assessments? Surely the answer is to find out what students know and what students can do. Not in general; we want to know specifically whether students know certain things. We have learning targets…
The state of math in the world today
I went to the grocery store today and at the self checkout, one of my items was not recognized by the barcode scanner. It scanned successfully, but it wasn’t in the system and couldn’t give a price. An employee came over to help. He was young, no older than his 20s, though he looked like…
Equality, equity, equivalence, identity, indistinguishability, isomorphism, resemblance, congruence, and similarity
While the title of this post might as well be a thesaurus entry, my purpose here is to investigate the differences between these concepts and how they operate in different contexts. Mathematical equality The reader is almost certainly very familiar with the equals sign or = used in math. Many of us first encounter it…
I like nonsense the best
I have often said that my favorite way to sort objects is alphabetically by color name. For example, if your objects are colored red, yellow, green, blue, and purple, then you would put the blue one first, followed by green, then purple, red, and finally yellow. But why? Partly for humor. I think it’s funny…
A plea to teach sig figs in math class
Measurement is an essential part of math. Quantities encountered in the real world are usually one of two things: a count or a measurement. Counting is what we learn first about math, before doing anything else with numbers. Counting is a way of measuring a quantity of discrete objects, but it is different from other…
The paradox of incentive
If something is incentivized too strongly, it becomes disincentivized. Extrinsic motivation has important social utility. It can both drive prosocial behavior and inhibit antisocial behavior. In many cases, extrinsic rewards are natural. Praise is a natural response to someone doing something we want them to do, for example, as is expressing anger towards someone for…
On learning by mimicry
Consider sports, music, and foreign language. Most people grow up being exposed to what these things are, and in particular often observe experts in action: professional athletes and musicians and native speakers of foreign languages. People also often have opportunities to engage in learning these things from a young age, and their education or training…
Educator disability, my experience
Around two and a half years ago, I became a schoolteacher. In less than two weeks from now, my resignation will go into effect. When I have read stories of other teachers resigning, I have seen people often point to difficulties with students as the main reason for leaving. Not for me- my students have…
thoughts on mind 