Zipheron works to utilize the unique communication potential of computer animation to generate compelling educational media.  The majority of our work focuses on math content because we believe that the current state of math education is particularly worrying.

The conventional wisdom of our educational institutions and the resulting perceptions held by students express a profound misunderstanding of the nature of math.  Zipheron is working to challenge these common misconceptions.


“If I have a calculator, I don’t need math.”

It’s important to make a distinction between math and arithmetic.  Arithmetic is the rote number crunching that a calculator can perform, but math is the vision and understanding of the quantities and patterns around us and the creative problem solving that a calculator can never perform.    Solving a piece of arithmetic is the last and usually most uninteresting step in a much broader, engaging mathematical process.  However, math education too often focuses only on this last step.  Granted, a math student should understand arithmetic, but that number crunching isn’t the goal, but simply a means to a much more interesting end.

When learning the game of chess, one must remember the way in which the pieces move:  bishop moves diagonally, rook moves orthogonally, and so on.  But playing chess is not simply learning the semantics of how chess pieces move, but being able to apply the bigger strategies of the game.  Similarly, using mathematics isn’t about being able to regurgitate the semantics of arithmetic.  It is about applying these concepts and using them to understand your world.

“In order to learn math, you have to do a lot of drill and practice.”

Long lists of arithmetic problems are something that only exist in the contrived world of math text books.  In no other place will you ever encounter mathematical ideas in pre-packaged chunks of arithmetic.  When we truly apply mathematical thinking, it is a matter of seeing the world around you through a lens of logic and reason, finding a pattern or structure to how quantities come together, encoding that relationship into the language of math, and then performing the arithmetic to find the answer.  This process can’t be conditioned into our brains like rote muscle memory.  It requires flexibility in thinking to adapt to new circumstances and see a potentially confusing situation from a simpler, novel perspective.  However, if these ideas are repeatedly presented to students as long “drill and practice” activities, it can condition them to believe that concepts in math will always come to them pre-packaged as homogenized, disembodied, abstract chunks of arithmetic. 

“In order to learn math, you have to do a lot of memorization.”

There are many things that, in order for a student to remember, they must memorize. The act of memorization brings the presumption that there is no logical structure behind the content.  In order to remember information that has no logical structure, such as the order of the days of the week or the order of the planets in our solar system, memorization with clever mnemonics can offer the best approach.  But when learning math, the embodiment of logical structure, this approach is disillusioning.

For example, when a child learns the alphabet, they have little choice but to memorize it.  Starting with the letter A, there is no way to use logic to figure out what letter would come next.  To make the task easier, we often use a mnemonic – students sing the alphabet to “Twinkle twinkle little star” to make the randomly agreed upon order of letters simply sound right.

At the same time, children are taught to count.  Once the child knows the digits zero through nine, and has a grasp of place value, there is no reason to memorize the order of numbers.  No student would say “I can’t count past 1000 since I haven’t memorized the numbers past that point”

No one would attempt to teach students to count with rote memorization.  Such an approach would not only be strange, but crippling.  Students couldn’t progress beyond their capacity to remember digits.  Yet we build most of our students’ understanding of math on memorization.  They memorize the multiplication tables like a list of phone numbers, and in the process, they become blind to the beautiful patterns and structures it contains.  They can multiply equations with the mnemonic “FOIL”, and although they can blindly follow this recipe, they can remain ignorant to what they are doing and never see the significance of the equation in the first place.

The fundamental spirit of math is to understand and actively manipulate logical structures.  Approaching mathematics with memorization runs completely counter to this empowering goal. 

“Here is your formula.  It works because I said so.”

Too often, we must take on new ideas on the mere faith that the concepts are valid.  We expect students to build their knowledge of math based on memorization and acceptance that what they are being shown is true.  Ultimately, the learner holds no understanding of what the concepts actually mean.  As the student progresses through their curriculum, they are expected to build upon their presumed knowledge and construct a taller and taller edifice of alien concepts.   Eventually, what the student learns isn’t math concepts, but an ability to accept one’s growing ignorance.

Although teaching an idea on faith and not understanding is errant for any discipline, it is particularly insulting to teach math in this way.  Through math, we encounter the framework for logical proof.  This concept of proof is quite powerful; it challenges us and gives us the tools to critically examine what we know and how we know it.  Yet we expect students to learn concepts in math devoid of any proof whatsoever.  The functions and usefulness of math must be accepted on faith alone, completely contrary to the nature of mathematical proof.

Memorizing the rote fact that a=1/2bh will help a student find the area of a triangle.  However, knowing how the formula works and seeing how to derive it provides a skill that transcends triangles.  We become better able to reason our way through new situations and unexpected circumstances.

“It’s fine to dress up math with fun games and tricks as long as it keeps the student working.”

More and more, math education is relying on clever games and eye candy in order to hold students’ interest.  One might think that these gimmicks are fine, and that as long as the student is doing their work, they are ultimately beneficial.  However, this approach brings with it some dangerous consequences.

First of all, much of the games and eye candy contrived to package the curriculum hold little or no relevance to the content.  Students may play games such as “shoot the aliens that have prime numbers on them”.  Even if a student is able to master the game, there is the resulting impression that the irrelevance of the game shows how there is no real use for prime numbers.  If there were any practical use for the content, then the information could be conveyed within some relevant framework.  Instead, the content is merely a trick to learn an inane game.

Secondly, when information is dressed up to such an extreme in order for it to appear “fun”, it gives the message that the underlying ideas are fundamentally distasteful.  Only something extraordinarily awful and boring would require such gimmicks and distractions to make it tolerable by the average student.

Candy-coating math with tricks and irrelevant games shows a lack of faith in math and a lack of vision for what it can mean to a student to truly own these ideas.  At its core, learning math is rewarding since empowering oneself with logic and a perspective for understanding the world around oneself is exciting.

“Math is technical and boring.  There isn’t anything creative about it.”

The limitations that math seems to present from its stringent, logical structure and right and wrong answers may seem contrary to creative thinking.  We therefore may need to rethink what it means to be creative.  Creativity isn’t simply open self-expression without any limitations.  Often, creativity must work within limits.  In fact, it is often extreme limitations that push human creativity.  A prisoner who can break out of jail with explosives and power tools isn’t being nearly as creative as the prisoner who can escape using a ballpoint pen and toilet paper.

So how is math creative?  Granted, the arithmetic of long division may not be a very creative endeavor, but what one can do with that arithmetic can be creative.  History can provide us with countless examples of people creatively harnessing math to amazing ends. 

It is difficult to see a Renaissance painting apart from the math that helped construct it.  The projective geometry that helped define the perspective,… the ratios of color,… and the angles of surface vectors of objects reacting to rays of light, all give the painter tools for realizing their vision.

Even outside the world of art, we can’t help but see the creativity and ingenuity of mathematicians.  When we see how Thales in the sixth century BC was able to measure the height of the great pyramids of Egypt… and the distance of ships out at sea with some simple observations,… or how Eratosthenes in the third century BC was able to measure the size of the Earth with some elementary geometry and the length of two shadows, we can see how profoundly creative mathematical thinking can be. 

“Math is difficult, and ultimately irrelevant.”

With the conventional wisdom and common perceptions in math education, it is no surprise that so many students feel detached from their math curriculum.  Reason for Math acknowledges these potential negative attitudes in students and uses them as a starting point for inquiry into the true nature of math.