A computer animation showing scutiods, complex 3D geometrical shapes (like an irregular prism with a hexagon on one end and a pentagon on the other, with the sides broken up in such a way as to create several irregular polygons, some planar and some non-planar, that let two identical scutoids fit together in multiple different ways.

Fun with Geometry — Biological and Theoretical

For some reason today I was thinking of the 3D shape scientists recently discovered in our cells — I had to look it up just now to refresh my memory. Not being an expert in geometry, I would describe the “scutoid” as an irregular prism-like shape with a hexagon on one end and a pentagon on the other, with the sides broken up in a specific way that allows the shapes to be packed together.  I confess I’m not entirely clear on whether these biological building blocks grow that way, or they take on that shape based on the way…

Ungrading after 11 weeks

Mathematics professor Robert Talbot reports on his ongoing experiment with ungrading — giving feedback and emphasizing the students’ metacognition, rather than encouraging them to fixate on “marks.” (Students who are less equipped to self-evaluate might actually benefit from the clear signposting provided by grades, so in his experience, removing grading from education does not magically remove inequities in the classroom.) I think it’s possible to have a hybrid setup in a lower-level course (like I’m teaching this summer) where the work that addresses the lower reaches of Bloom’s Taxonomy is graded using specifications with marks, while the upper levels of…

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“We hate math,” says 4 in 10 – a majority of Americans

If 30% love math, and 30% are neutral about math, then the 40% that hate it could be the largest group, hence the majority. If so, then the headline might actually be brilliant. EDIT: Or not. A “majority” means “more than half.” The word I was thinking of is “plurality.” For the record, editors often write their own headlines to fit the available space, or to generate more traffic. Here’s how CNN reported this story (under the  headline “The most unpopular school subject“): “Twice as many people said they hated math as said that about any other subject.”  

Big Calculator: How Texas Instruments Monopolized Math Class

My math education predated the widespread use of graphing calculators. I remember writing my own BASIC programs to graph simple functions, but that was in a summer school programming class during middle school, not part of my high school curriculum. I’m amazed these old calculators cost this much. Bulky and black, with large, colorful push buttons and a low-resolution screen, TI graphing calculators resemble top-of-the-line design from the 1990s and are functionally the same as when Texas Instruments first launched the TI-84 Plus in 2004. Even the price has remained almost the same. When my mom bought my TI-83 Plus…

The history of Tetris randomizers

A pleasantly detailed analysis of how the various editions of Tetris chose what piece was next. In 1985, Alexey Pajitnov and Vadim Gerasimov released Tetris to the public. This fun and highly addictive game challenged players to fit pieces together that were dealt in a random order. Since then, over 150 licensed versions of Tetris games have been released. Varying in game modes, rules, and implementations, they all play slightly—or very—differently. In Tetris, a randomizer is a function which returns a randomly chosen piece. Over the years, the rules of how pieces are chosen has evolved, affecting gameplay and actual randomness. Several…

One Teacher’s Brilliant Strategy to Stop Future School Shootings

Every Friday since Columbine, one schoolteacher has asked her students to to submit a list. Who would they like to sit next to next week? Who has been an exceptional classroom citizen this week? Chase’s teacher is not looking for a new seating chart or “exceptional citizens.” Chase’s teacher is looking for lonely children. She’s looking for children who are struggling to connect with other children. She’s identifying the little ones who are falling through the cracks of the class’s social life. She is discovering whose gifts are going unnoticed 
by their peers. And she’s pinning down—right away—who’s being bullied…

Columbia Journalism Review

Sorry, Wrong Number

Numerical errors usually occur for one of these five reasons: A journalist mishears a correct number given to them by a source and fails to double-check it. A source unwittingly provides a mistaken piece of information and the journalist fails to verify it. A source deliberately fudges the numbers and the journalist fails to verify them. A journalist or editor miscalculates a figure. A journalist re-reports a mistake made by another media outlet. Columbia Journalism Review

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Journalism by the Numbers (a pedagogical play in one scene) #math

(Lights up on a college journalism classroom. The professor enters, surveys the room.) Professor: Math! Students: (Shocked reaction.) Professor: Math!! Students: (Scattered cries of “No!”) Professor: MATH!!! Students: NO!!!   (Blackout.)   (40 minutes later.)   Professor: So, at the very least when you encounter numbers in your reporting, contact sources who can help you interpret those numbers critically. Seek out a variety of credible views on the provenance and significance of the numbers your sources provide; don’t automatically publish figures you find on .org websites or on signs that protestors carry. Many of us chose the humanities because of…

What Khan Academy’s Fun, Free Learning Empire Has to Do with Dystopian Social Control

Over the Christmas break, I’ve been churning through Khan Academy math drills, so that I can be a more effective homeschool parent. It’s actually kind of fun watching my score go up, and earning badges. In the way that birds who are trained to peck buttons for food think it’s fun to peck their little beaks bloody. As a grad student ploughing through Kant and Derrida, I found it an intellectual relief to run a computer program through a compiler and see a list of exactly what character on what line of my program triggered an error (divide by zero? missing semicolon? stack heap error? undeclared variable? illegal…

How to Lie with Data Visualization

Data visualization is one of the most important tools we have to analyze data. But it’s just as easy to mislead as it is to educate using charts and graphs. In this article we’ll take a look at 3 of the most common ways in which visualizations can be misleading. —Heap Data Blog.

The Value of Failure

Upon reading that recent message from my inbox, I wanted to shout out “let your child fail.” The shouting was not due to frustration, rather to be sure that my voice was heard by many. And when I say fail, I mean fall. Let them fall. How can we learn to get back up if we never fall? Or if someone else always picks us up. Too often today, students are given every possible opportunity NOT to fail. But why? Why are we afraid of failure? Putting students in frustrating and uncomfortable situations is a tricky part of my job.…

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Students say “math class is stupid and boring,” and they are right. –Mathematician Paul Lockhart

I am working on some conference papers that touch on coding as a liberal art. While reviewing classics, like Stephenson’s In the Beginning Was the Command Line and Knuth’s approach to “Literate Programming,” From the insightful and quirky “A Mathematician’s Lament,” by Paul Lockhart. A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed,…

Surprise! ‘Star Trek’ gold shirts more deadly than red shirts

Fascinating. Barsalou then goes all math geek and applies to the data the Bayes’ Theorem formula for calculating conditional probabilities. After a little mathematical shake and bake, he determines there is a 61.9 percent chance that any given casualty is wearing a red shirt. That still sounds high, but it’s not really once you consider the sheer number of redshirts running around the Starship. “Although Enterprise crew members in redshirts suffer many more casualties than crew members in other uniforms, they suffer fewer casualties than crew members in gold uniforms when the entire population size is considered,” Barsalou writes. “Only…

Journalist math fail: “New pay-per-mile scheme would boost taxes 250 percent”

Hold on… An on-again, off-again move by the Obama administration to scrap the federal gas tax in favor of a pay-per-mile fee would boost the tab to Americans as high as 250 percent, raising their current tax of 18.4 cents a gallon to as high as 46 cents, according to a new government study. —New pay-per-mile scheme would boost taxes 250 percent | WashingtonExaminer.com The math example doesn’t illustrate the point the writer is trying to make. If you start with 18.4 cents a gallon, and “boost” the tax 0%, you still have 18.4 cents/gallon. If you start with 18.4…

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Mathematics and What It Means to Be Human

A humanities faculty member and a math faculty member collaborate on a course about the meaning of math. “Don’t worry;” I told them. “You can’t find this more frightening than I do.” And it was true. Ever since the word problems my father forced on us at dinner, I’ve always been terrified of math. I probably skipped dessert for all of fourth grade in order to escape some design to have me calculate how to share five ice-cream cones among eight friends who had a variety of flavor preferences. (As if I’d ever share ice cream, no matter how good…

Khan Academy: The hype and the reality

Sal Khan has done something remarkable in creating such a vast and varied library, and he deserves to be recognized. His commitment to making the site free is a rare and selfless act, and he deserves to be praised. Sal Khan is a good guy with a good mission. What he’s not, though, is a good teacher. Unfortunately, the media hype surrounding Khan Academy has created a level of expectation far beyond what it – indeed, what any person or website – could ever reasonably deliver. Reporters have confused journalism with sycophantism, and the entire narrative has become a head-scratching…