"Oh my God, I can see it." The young English professor realized, knew in her heart, that she was seeing numbers in a way she never knew existed, an instinctual way. Using her innate skill, shared with other mammals and birds, she was subitizing ordered three-dimensional shapes that represented large numbers. She was not seeing quantity for she now understood that quantity only applies to numbers represented in base ten, the standard, the decimal number system. No, she was seeing numbers , really seeing their shapes, organized simplistically in various base systems to help trigger her latent visual talent. She was subQuanning.To subQuan is to suddenly identify the numbers of each place shape in descending size. If the container size was 'based' on ten then she could say that she can recognize very large quantities within seconds. She was having a Rain Man experience when she saw 7,832 colored plastic boxes and stated such in less than five seconds. Later, she saw 23546 in container shapes based on seven, or simply, base seven (SEE PICTURE). SubQuans are verbalized in the same fashion as one would say a phone number - one digit at a time. The subQuan, 23546b7, is spoken as two-three-five-four-six base seven. It is NOT spoken as twenty-three thousand, five hundred and forty six because it is a subQuan, not a quantity. Twenty, thousand, hundreds, and forty are unique words only valid in base ten. In fact, the decimal equivalent, the quantity, of the subQuan 23546 base 7 is six thousand one hundred ten. The Theory of subQuanWhile this foundation has taken many, including Dehaene, down a path of research into the idea of approximate number sense (ANS), Cooper Patterson has instead focused on that small The distinct organization of objects and the repetitive use of subitizing each place can create confusion with the true meaning of subitize so a new word was coined: In 2009, Cooper turned to virtual reality to continue examining the phenomena of subQuan, and discovered other extremely relevant, yet equally as easy to see, patterns. Creating ever expanding groups, larger than Cubes, reveals a repeating pattern of Seg-Square-Cube shapes, albeit based on larger and larger Cubes. This second easily recognized pattern leads to the concept of Place Shapes, instead of the more abstract and artificial concept of Place Value. This sequence of pictures for the numbers above depicts an unbelievable connection to modern Algebra and higher level mathematics when viewed symbolically along with the shapes expressed exponentially. A snapshot of the equation board, shown below, for these pictures shows the relevance of subQuanning: polynomial equations can be seen! x. Hopefully, the understanding that any quantity NOT in the sequence can be calculated is equally clear. The importance of laying a foundation of numbers based on our instinctual ability to see subQuans will hopefully provide the motivation necessary for learning higher level mathematics rather than the blind faith memorization inherent in our current decimal- and symbol-centric mathematical instruction! |