31 January, 2014
Volume 19 No. 5
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In This Issue

Solutions: 2014 Mathematics Game

Function Carnival

An Investigation of Subtraction Algorithms


Online PD

Orientation Sessions

Problem Based Learning Courses

Graduate Credit:
Mathematics Teaching and Learning Certificate

Master's Degree


Solutions: 2014 Mathematics Game


Tomorrow, we'll post solutions to the 2014 Mathematics Game. Students have already sent us their arithmetic from every region of the US, plus England, Australia, Singapore, India, and Israel.

... but we still need answers! Sixty-seven and 87 have so far defied expressions made from

  • the digits in 2014
  • standard operations
  • grouping symbols

Several other odd numbers near them, in the bottom half of the pull-down menu of solutions, have garnered only one answer apiece. So whether you've blazed a new arithmetic path, or just taken a commutative detour, come share your basic ops wizardry here:


PoW taking place: math problem-solving moment of the week

"This is one of those problems where submitters used methods I didn't think of, and almost nobody used the method that I imagined everyone would use! Raphaella R. from Mesa Union Junior High School mentions, in her first solution, the key to the second method that both she and Britney used to solve the problem."
- Annie, commenting on the Geometry PoW's Latest Solution

Function Carnival


Step right up, step right up — and plot some fun with Desmos' new Function Carnival!

First, watch the animations of

  • the flight of the human cannonball, dressed in green
  • the route of the green bumper car
  • the trajectory of the ferris wheel's green cart

Then, represent those heights or distances over time by pointing, clicking, or dragging in the nearby graph. Press the blue "play" button to set in motion a blue cannon man, blue bumper car, or blue ferris wheel cart that acts out what you sketched, all while the original light green figure re-plays in the background for comparison.


A dashboard lets teachers track students' drawings and further explore the meaning of holes, multiple values, discrete points, and other features of their graphs. For an activity guide, visit


Clarifying common misconceptions about graphs with instant feedback, Desmos' Function Carnival came out of a collaboration with Christopher Danielson and Dan Meyer, who blogged about the pedagogical value of their "online math happytime" here:


Now taking place: math education conversation of the day

"If that happens in your school as well, you would have students who never take geometry. Finally, it may be my own personal prejudice, but the logic and proof elements of geometry are an important part of teaching students to think, and I believe that they are ultimately more important than the properties of quadrilaterals when it comes to turning out 'educated' citizens."
- Evelyne, posted to the secondary (grades 9-12) discussion group of the Association of Math Teachers of New York State

An Investigation of Subtraction Algorithms


How do you subtract?

Does your method follow the same steps that your ancestors took?

A PhD candidate in mathematics education has identified four distinct subtraction algorithms from 18th and 19th century America; and in the current issue of the Mathematical Association of America (MAA) journal Convergence, she discusses what this means for teachers today.

Illustrated with images from printing press textbooks and handwritten "cyphering" books that date back to 1785, Nicole M. Wessman-Enzinger's article also offers video demonstrations modeling the four procedures that turned up in her research:

  • equal additions
  • decomposition
  • complement
  • Austrian

Out of hundreds of scanned source materials, Wessman-Enzinger found scores of references to the first and third techniques — but none whatsoever to decomposition, which predominates now. Observing that "decomposition was perhaps not an implemented subtraction algorithm in North America" as recently as the Civil War era, she then goes on to address the questions and implications that arise from this revelation.

Before pursuing her doctorate, Wessman-Enzinger taught high school math for five years, then — as an assistant mathematics professor at her college alma mater — calculus, statistics, and several courses for elementary teachers.


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