One important aspect of reexamine teaching and learning through the lens of sense-blending and digital technology is understanding distinctions between the core logic of content information with form, function and pattern, via vie experience. Synesthesia or sense-blending is a complex process in which the brain makes associations with different sense information by assigning it a neighboring sense analogy, i.e., high-pitched notes are bright and low-pitched notes are dark. Similarly, ideathesia or sense-metaphor is the process of assigning sense-based characteristics to more abstract information, i.e., a calendar presents days as squares, weeks as a line of squares and months as a page filled with boxes.
When examining how the human mind constructs links between information and sense metaphor, there is often an internal logic, but such of the assigned associate is seemingly random, experience-based and subjective. In translating this process of the digital medium, while systematizing and scaling the process, all such connections most possess consistency and clear logic. There must be a reason why certain bits of information are presented to the left, right, up or down from other information. They must be assigned their respective colors due to their characteristics and association with other information.
Therefore, in commencing such practices with arithmetic, rather than say language, due to the fact that math entails concrete quantities, one must examine and confront a basic and consistent fact of information presentation, there is never in any academic discipline pure logic. I say pure logic from a strictly objective vantage point, that is, information that makes no distinction between the experience of the learner or teacher.
When considering the core logic of mathematics, let us consider the relation of the basic functions: addition, subtraction, multiplication, and division. We know addition and subtraction are opposites, likewise multiplication and division, multiplication is the compound of addition and so on. All such foundational understandings in mind, a two-dimensional grid modeled after the Cartesian Plane can be utilized to clarify such applications. That stated, we must consider that Base 10 lies at the heart of our math fundamentals. But when you think about core logic, this is not the way a computer calculates arithmetic, they use binary metrics. This is because most humans possess 10 fingers and toes (sense the term “digits” which merely means fingers).
This is why one key element of deconstructing our subjective based 10 math structures and then reconstructing the logic, applications, and patterns of such system is key to transferring the knowledge to computer-based sense-blended programming designed to assist instruction.
Here are some examples of how we can understand the patterns of Base 10 Math. Multiples from 2 to 9 are color-coded to decipher the structure. The numbers are counted from left to right and down to up.