Tuesday, November 27, 2018

What to do with a Broken Calculator that's Broken...

Duncan Keith's app
What to do with a broken calculator that is really broken? Back in 1989, Judah Schwarz developed a software package named "What to do with a Broken Calculator?" It was a simple, but brilliant idea. Take a simulation of a calculator that allows the teacher to break (disable) some of the keys and challenge the student to produce an answer, of say, 50 with most of the number keys disabled. This can be a challenge and an important learning experience for young students.

Unfortunately, because of the vagaries of Java-based applications all of the really good versions including Cut-the-Knot, Seeing Math and Mathcats don’t work any more because of “unsupported plug-ins.”  Alexander Bogomolny who developed cut-the-knot.org writes: “While a good deal of the site has lost its interactivity (Java failure), most pages remain interesting and informative, whereas many others that do not use Java, are still interactive. The situation is unfortunate for which I am deeply sorry." Alex had a working version of Broken Calculator which we may never see again. But then who knows. Stay tuned. If there’s a way and time to do it, Alex will figure it out. (Unfortunately, Alex passed away on July 7th, 2018.)

In the excellent, but ill-fated On-Math NCTM publication, Broken Calculator was one the issue’s themes. Here’s a quote from the article:
Broken Calculator is, in effect, an inexpensive, versatile number laboratory. Using Broken Calculator to solve problems forces students to explore operations on numbers and representations much more deeply than does rote application of algorithms. Most important, working with Broken Calculator shifts the responsibility of finding and expressing the answer to the student. Solving problems means inventing a wide variety of strategies to work around the limits set by the disabled keys or functions. Students deepen their number sense, problem-solving capacity, and understanding of the number system— and have fun at the same time! 
So is the idea of Broken Calculator lost forever? Or is it alive somewhere? Alas, there is a working remnant(?) of Broken Calculator alive and well on Duncan Keith's site. I say remnant because it's not the open ended one that was developed by the staff at Concord Consortium and others, but rather by an independent software developer Duncan Keith who somehow manages to keep this site going despite the unpredictability of Java updates. If you go here you will meet Eric (below).

The program has a built-in library of challenges (levels). The one drawback is that it has a timer that may be intimidating for some students. Also it's designed to be used by students independently so it would be difficult to use with a whole group of students to analyze strategies. (Read this.) Also, the calculator does not do order of operations.

So until we hear from one of our Broken Calculator champions of the past (or future) Eric smashing his calculator is our best hope for now.

Unless, you prefer...

There is a low tech version provided by Dan Finkel developer of  https://mathforlove.com. Here's a New York Times article about his Broken Calculator approach.


  1. Hi Ihor,

    Math Playground has a broken calculator activity that works on all devices. This may help fill the void. https://www.mathplayground.com/monster_mischief.html


    1. Colleen - How nice to hear from you! Your app is great. A nice addition to my blogpost.