How to Avoid Thinking in Math Class (Part 1)

Math With Bad Drawings had a terrific series on how students try to avoid thinking in math class. A quote:

In teaching math, I’ve come across a whole taxonomy of insidious strategies for avoiding thinking. Albeit for understandable reasons, kids employ an arsenal of time-tested ways to short-circuit the learning process, to jump to right answers and good test scores without putting in the cognitive heavy lifting. I hope to classify and illustrate these academic maladies: their symptoms, their root causes, and (with any luck) their cures.

Here is Part 1, introducing the series: http://mathwithbaddrawings.com/2015/01/07/how-to-avoid-thinking-in-math-class/

Preparation for Industrial Careers in the Mathematical Sciences: Creating More Realistic Animation for Movies

The Mathematical Association of America recently published a number of promotional videos showing various mathematics can be used in “the real world.” Here’s the first pair of videos describing how mathematics is used for computer animation. From the YouTube descriptions:

Dr. Alex McAdams, Senior Software Engineer at Walt Disney Animation Studios, talks about how mathematics is used to make realistic, yet art directable, animations.

Prof. Joseph Teran of the Department of Mathematics at UCLA gives an overview of the numerical linear algebra and iterative method techniques that are used to simulate physical phenomena such as water, fire, smoke, and elastic deformations in the movie and gaming industries.

Nutritional Science Isn’t Very Scientific: the research behind dietary recommendations is a lot less certain than you think.

Here’s a nice article about the inherent difficulties faced by nutritional scientists and the perils of observational studies (as opposed to controlled experiments): http://www.slate.com/articles/life/food/2015/04/nutritional_clinical_trials_vs_observational_studies_for_dietary_recommendations.single.html

Money quotes:

Most of our devout beliefs about nutrition have not been subjected to a robust, experimental, controlled clinical trial, the type of study that shows cause and effect, which may be why Americans are pummeled with contradictory and confounding nutritional advice.

To wit:

Many nutritional studies are observational studies, including massive ones like the Nurses’ Health Study. Researchers like Willett try to suss out how changes in diet affect health by looking at associations between what people report they eat and how long they live. When many observational studies reach the same conclusions, Willett says, there is enough evidence to support dietary recommendations. Even though they only show correlation, not cause and effect, observational studies direct what we eat.

Apart from their inability to determine cause and effect, there’s another problem with observational studies: The data they’re based on—surveys where people report what they ate the day (or week) before—are notoriously unreliable. Researchers have long known that people (even nurses) misreport, intentionally and unintentionally, what they eat. Scientists politely call this “recall bias.”

The coupling of observational studies and self-reported data leads some observers to the conclusion that we know neither how Americans do eat nor how they should eat. A recent PLOS One article even suggests that several national studies use data that is so wildly off base that the self-reported caloric intake is “incompatible with survival.” If people had eaten as little as they reported, in other words, they would be starving.

Peter Attia, a medical researcher and doctor, started questioning the basis of dietary guidelines when he saw that following them didn’t work for his patients. They didn’t lose weight, even when they virtuously stuck with their diets. When he took a look at the research supporting the advice he was giving to his patients, he saw shoddy science. Attia estimates that 16,000 nutritional studies are published each year, but the majority of them are deeply flawed: either poorly controlled clinical trials, observational studies, or animal studies. “Those studies wouldn’t pass muster in another field,” he told me.

Lessons from teaching gifted elementary school students: Index

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on various lessons I’ve learned while trying to answer the questions posed by gifted elementary school students.

Part 1: A surprising pattern in some consecutive perfect squares.

Part 2: Calculating 2 to a very large exponent.

Part 3a: Calculating 2 to an even larger exponent.

Part 3b: An analysis of just how large this number actually is.

Part 4a: The chance of winning at BINGO in only four turns.

Part 4b: Pedagogical thoughts on one step of the calculation.

Part 4c: A complicated follow-up question.

The number of digits of n!: Index

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on computing the number of digits in n!.

Part 1: Introduction – my own childhood explorations.

Part 2: Why a power-law fit is inappropriate.

Part 3: The correct answer, using Stirling’s formula.

Part 4: An elementary derivation of the first three significant terms of Stirling’s formula.

Free resource: History of mathematics

I recently received an e-mail promoting the following free website: http://www.wwu.edu/teachingmathhistory/index.shtml

From the e-mail:

[This] is a collection of materials directed at either teaching a math history class or including math history ideas in other math courses. Things that are available:

  1. An extensive set of problem-solving lessons that include student materials, teacher commentary, problem sets, problem commentary, associated writing topics, and references…originally this was prepared with the intent it would become a “300-page” book, but now is being made available for FREE.
  1. A broad collection of materials that supports a Math History course … writing assignments, paper topics, writing prompts, rubrics, etc.
  1. A multi-level reference list of historical resources that focus on the history of mathematics, ranging from texts to articles. It can be used to build identify resources in the writing of papers and guide the broad understanding of the history of mathematics. If students need reference info on topic or mathematicians, please share this with them….might lessen the over-emphasis on Internet resources.

Free resource: Historical mathematics problems

I recently received an e-mail concerning the following free resource: http://mathhistoryproblems.wwu.edu/problem_select.asp. From the e-mail:

[This] is a data base of more than 1600 historical problems connected with mathematical topics, skills, and concepts taught in secondary schools and colleges. The problems are categorized within broad areas of number, algebra, geometry, measurement, trigonometry, number theory, probability, statistics, pre-calculus, calculus, logic, discrete mathematics, and recreational mathematics. Revealing international contributions and changing cultures, the problems span the full history of mathematics (2000 B.C. – 1940). Each problem statement includes its source and solution commentary.