From Dejection to Bijection

If there’s one aspect of Vision Therapy that I’ve really learned to appreciate over the years, it’s the understanding that vision and thinking are usually joined at the hip.  With other sensory inputs contributing to the overall input structure, we may be hard pressed to refer to the relationship between vision and thinking as a model for symbiosis, but there certainly is an interweaving that helps the two benefit from and thrive off each other.  As an example, how many children have come to us struggling in school and wallowing in an abysmally low level of self confidence only to discover one completing Vision Therapy that they can solve the problems before them. Sure, working eye movements and focusing skills may have contributed to their overall improvement, but of equal or even greater importance is the detection, understanding, processing and reaction to their visual world.  This is where some of the real changes occur.


My latest reminder of this notion was in a young man we’ll call “Mark”, who has been visiting my Vision Therapy room once a week for the last eight months. When we first met, Mark had just begun first grade and lacked what his mom referred to as “thinking skills”; in fact, upon recent review of mom’s initial goals for Mark from when he began his program several months ago, she wrote the words “help him think and understand”.  After teasing out a lot of other ideas, we learned that Mark’s mom was referencing his abilities to draw conclusions, specifically in math. In fact, the mere mention of math to Mark produced anger, frustration and dejection.  Math was tough and in many ways, he just didn’t understand the basic concepts. Clearly, there was a lot to work on.

Bijection, more commonly referred to as one-to-one correspondence, is function between the elements of two sets, where every element of one set is paired with exactly one element of the other set, and every element of the other set is paired with exactly one element of the first set. There are no unpaired elements. This compliments of the wisdom of Wiki.


In the therapy room, we often introduce this concept with blocks – preferably, inch cubes – as a concrete method for teaching value, conservation, quantity, and grouping, just to name a few. We count blocks, we work how the number changes when one is added or subtracted, and we work to understand that as the above definition suggests that there is a relationship between each block and and the numbers on the number line. Every block is assigned a singular value. We also work to build the understanding that assigning a number to each item is systematic and sequential, not arbitrary.

As Mark progressed through these concepts, they naturally were made more challenging.  Changes in spatial arrangement, changes in the number of blocks, and changes in how the questions were asked; all the while specifically probing whether or not he understood and “owned” the concept that one item is to be paired with the next number in sequence, and which direction the sequence would move depending on if a block was added or subtracted.


One particular area of struggle for Mark was in the understanding that spatial orientation did not change the value of each block within the set. For example, four cubes stacked neatly were the same as four cubes slightly spread apart, which were the same as four cubes scattered around the table.  The number didn’t change just because the block’s orientation to each other did. We worked on this forward and backward, inside and out, from the left and from the right, and even switching roles occasionally. It was slow and tough, but we kept moving forward with gentle reinforcement of previous concepts learned.


Down the road, Mark also worked to understand that quantity does not always equate with value. For instance, a child with ten pennies may think they have more money than the child with one quarter; not understanding yet, of course, that each item has an assigned value, and that quantity becomes less significant in that equation.

As school ended a few weeks back, Mark brought in his final math test of the year to share with me. It was the adding and subtracting of double digit numbers on which he scored 100%. Not bad for a kid who six months ago could barely remember what number came after 4.

As Mark bragged about his test, I subtly opened his home VT book and watched his face light up as I pointed to his first goal, where on day one of his VT program he had written the words “help with math”.

Mission accomplished.


Posted on June 18, 2014, in From My Perspective.... Bookmark the permalink. Leave a comment.

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