"Spy Hacking" Game Brings Algebra to Life
Imagine algebra being taught inside a game where spies try to decode enemy secrets and hack into enemy computer systems. Many students have fun imagining engaging in such tasks and students who struggle with learning disabilities are no different. There are many fictional spy movies and historically based movies such as The Imitation Game where math is used to save lives and win wars. This motif can turn learning dry algebra skills into engaging in “life-and-death situations.”
Within this intriguing scenario, each student is given the responsibility to protect the secrets of their own country. Each student then devises codes to protect their country’s top-secret information and uses math to break the codes of other countries.
Learning tedious algebra skills such as solving for x comes alive as these skills become crucial to success in the "Spy Hacking" game. As one student described it, the worksheets on algebra skills now have a purpose: to protect your secrets and expose the secrets of your classmates’ countries.
The first type code we used consisted of an integer sequence that starts with 1 and an algebra formula that generates the sequence.
For example, when shown the sequence
1, 3, 7, 15, 31, 63, 127, ...
students try to break the code by creating a formula that generates that sequence.
2x + 1
Substitute any number in the sequence for x in the formula 2x + 1 and it produces the next number in the sequence.
To ease my students who struggle with math into the game, I start them with simple sequences, until their code-cracking skills are polished. The main reason is that I want the students to succeed initially and not get frustrated by overly complicated formulas. In the jargon of game design, the students “level up” to the next more sophisticated challenge. When students are challenged to build their own sequences, I have found that they try to construct very complicated formulas that they think their classmates will not be able to crack. Many times they succeed and it will take several class periods before a complicated code is cracked. At other times, however, they learn that just because a formula looks complicated does not mean it actually is. Formulas can often be simplified to a much shorter one that is equivalent, as shown in the following example.
2x + 4 + 5 – 6 – 2 = 2x + 1
As students learn more operations, I transition them to using formulas. Initially, I allow only multiplication, addition, and subtraction to be used in a formula. Later, I introduce the use of exponents. Lastly, I advance them to using decimals instead of integers by allowing division and roots.
What does a successful code-breaker win? Usually, just the satisfaction of breaking a classmate’s code is sufficient—maybe with a little gloating added in. However, I also keep track of the number of codes they each break and also have their country pay them handsomely for their service—say, “a million dollars” for each code they break.
Since code-breaking using paper and pencil can be slow work, the students are eventually taught how to use a spreadsheet so they can try out many formulas very quickly and thus crack the more difficult codes faster.
Overall, adding the imaginative theme of the high-tech spy world can transform some of the toil of learning algebra into an adventure with a grand purpose: to use your math skills for the service of your “country” and have bragging rights over a classmate when you break their “unbreakable” code.
The mathematician Neil Sloane has created an encyclopedia of integer sequences with information about who created each sequence and what phenomena each sequence helps explain: https://oeis.org/wiki/Welcome