Let’s Look at Math!

Based on a talk Dr. Harry Wachs gave
at the 1999 Third International Congress on Behavioral Optometry

Children who have internalized visual cognitive skills through early childhood experiences in sandboxes, in bathtubs, and with toys, usually demonstrate high math achievement. Others learn required arithmetic computations by rote performance or memory. Although teachers often ascribe mathematical competence to children who can count up to ten or twenty, many of these children lack the inner conceptual foundation needed for higher level math.

This foundation cannot be taught or learned by rote. It requires active participation by the child through sensory experience with concrete objects. Through active engagement with sensory stimuli the child creates in his mind concepts such as same/different, greater/smaller, first/last. Only then can he manipulate incoming information in a meaningful way.

My clinical research shows three basic foundational needs essential for successful math understanding.

1. Visual Thinking. This is the ability to make sense out of one‘s sense of sight. Important visual thinking concepts are parts-whole, figure-ground, perspective, and time perception. A child who is deficient in visual thinking will be disorganized and easily confuse graphic representations. Activities using parquetry blocks and pegboards can enhance visual thinking.

2. Numerical Literacy. This is the ability to read numerals, position commas, and understand place value. Intellectually healthy, well developed children should be able to read 1073 by mid second grade. Upper second graders should easily recognize 91101011 as a quantity greater than 39899898. By upper third grade they should accurately put in commas, label the groups, and read 1073517, as well as identify the value of each 7.

3. Visual Logic. this adds the component of logical reasoning to visual thinking. A child needs a rudimentary grasp of one-to-one correspondence, order, conservation of mass, weight, volume, number and linear length, as well as classification, seriation, and probability to learn traditional academic arithmetic or geometry. Children with poorly developed visual logic might master basic computations but will be unable to solve word problems.

Piaget’s conservation tasks can help to develop visual logic. The conservation of clay mass task, for example, encourages the realization that changing the shape of a clay ball from a sphere to a sausage does not alter its mass. A child deficient in visual logic will center on the thickness of the sphere or the length of the sausage and perceive that one as being "more clay." A sausage cut into pieces might look like "more clay" than a whole one. Presented with two strings of equal length, this child might perceive the straight one as longer than the curled up one. Play with materials like clay, play dough, sand, water, sticks, strings, and blocks can help children to internalize the principle of conservation.

To develop visual perspective, a prerequisite for understanding another person’s "point of view," play Object Perspective. Four children, A, B, C and D, sit around an open doll house, each with a tray and duplicate pieces of furniture. A arranges the furniture the way he thinks B sees it, B the way C sees it, and so on.

For more on the relationship between vision and thinking and hundreds of games related to every aspect of visual cognitive skill, read Thinking Goes To School by Hans G. Furth and Harry Wachs.

[Initially published in New Developments: Volume 7, Number 3 - Spring, 2002]

All material in this web site is given for information purposes only and is not to be substituted for advice from your health care provider.

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