During the recent EARCOME 7 conference, one of the exhibitors was a group of Japanese who showed participants how to create a lot of concrete learning materials (manipulatives) such as origami sculptures. I assume that they are members of The Association of Mathematical Instruction (AMI) because they gave me a complimentary copy of AMI’s *Principles of Mathematics Education*. Read the rest of this entry »

I recently presented a poster and a paper at the 7th ICMI-East Asia Regional Conference on Mathematics Education (EARCOME 7) last May 11-15, 2015 at the Waterfront Cebu City Hotel.

Shown above is a picture of me with Frederick K. S. Leung (who was the honorary plenary lecturer) and Catherine P. Vistro-Yu (who was the international program committee chair).

The poster and the paper were based on parts of my dissertation with Dr. Vistro-Yu as my advisor. The poster had the title “Assessing Proportional Reasoning Skills and Understanding Using the Water Rectangle Task” and was co-authored with Dr. Vistro-Yu. (A copy of the poster is here. The poster is the one on top in the photograph above.)

The paper had the title “Teaching Proportional Reasoning Concepts and Procedures Using Repetition with Variation” and was co-authored with Dr. Vistro-Yu. (A copy of the slides is here. Also shown in the photograph above is the session chair Enriqueta Reston.)

It is generally accepted by mathematics educators and by scientific calculator companies that in the “correct” order of arithmetic operations, multiplication and division are done from left to right. Thus, 48÷4×12 is evaluated as 144. The Casio fx-82MS and the Casio fx-350ES shown above give this answer. There is, however, some disagreement whenever parentheses are used to indicate multiplication.

My daughter’s high school teacher asked her to evaluate 48÷4(12). My daughter’s answer was 144; her teacher’s answer was 1. What answer is given by the calculators?

Read the rest of this entry »

A few months ago, I bought a copy of *Math Doesn’t Suck* by Danica McKellar at a BOOKSALE outlet. (Click on the images to see higher-resolution versions.) I know she has experience being a mathematician, but I didn’t know how much experience she has being a mathematics educator. I had done some study on conceptual and procedural knowledge in mathematics so I was very curious to know which she would introduce first—concepts or procedures—and which she would emphasize more. Read the rest of this entry »

In a tribute to the mathematician Israel Moiseevich Gelfand (*Notices of the AMS*, vol. 60, no. 2, p. 162), Dusa McDuff recalls meeting Gelfand in Moscow.

Then [Gelfand] gave me his recent paper on Gelfand-Fuchs cohomology to read. It was titled “The cohomology of the Lie algebra of vector fields on a manifold”, but I had been so narrowly educated that I didn’t know what cohomology was, what a Lie algebra was, what a vector field was, or what a manifold was.

I know one definition of a vector field, but it’s probably not the same as the one in the paper mentioned. Right now I also don’t know the definitions of the other three terms.

I recently bought a copy of Martin Gardner’s *The Universe in a Handkerchief* (New York: Copernicus, 1996). (In a future blog post, I’ll describe in more detail how I bought it.) The book’s subtitle is “Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays.” I present here some items in the book that I found very interesting. Read the rest of this entry »

In an earlier blog post, I showed the solution to a first-order linear system of two (ordinary) differential equations with constant coefficients for the case where the characteristic equation of the (constant coefficient) square matrix has repeated roots. In particular, I considered the system , where are real constants and are real variables, for the case where and . Now I look at the case where . Read the rest of this entry »

Here’s a funny comment on this answer at Mathematics Stack Exchange.

On being presented an equation where the left-hand side’s terms have a factor of 1/2 and the right-hand side is constant, a user asks “why not multiply through by 2?” Another user replies “Because this is physics.”

I was looking through the Rare Books section of the AbeBooks website a few days ago and searched for some books with the keyword *math*. The first entry is shown above, a book by Copernicus published in 1542. (It seems that the books with the highest prices are listed first.) A quick internet search reveals that the $350,000 price for this book is reasonable. (But I doubt that anyone interested in buying the book would have it shipped for $6.50.)

The second book on the list is shown above, a book published in 1990. There are three copies of this book for sale. Which one would you choose, the one priced at $149.90 or the one priced at $118,935.97?