Mathematical Imagination and the Preparation of the Child for Science: Sparks from Mary Everest Boole

Mary Everest Boole's psychological, logical and ethical analysis of the early introduction of mathematics and the natural sciences hinges on her description of the scientific attitude. The scientist goes through phases reverence and amazement in front of nature and of insight; of analysis and then of synthesis of phenomena; the path to knowledge passes through errors and wrong impressions, which must be embraced with perseverance in search of the Not Yet Known truth. The scientific educator needs an understanding of the child’s way of thinking, acting and imagining in contact with the goads from the world, connecting with his/her poetical appreciation. When introducing the puzzling ideas of mathematical imagination to the young child, one should stop and realize “the grandeur of the idea involved”: for example, the trajectories of celestial bodies and the underlying forces, and the “mathematical lines” such as tangents and axes that help us to understand or explain them. Mathematical imagination is developed by means of storytelling, helping children to place themselves in the context that explain the birth of great ideas such as number, the decimal system, fraction, unity and negation. Her most celebrated contribution, curve stitching in “Boole cards”, is better appreciated in this general framework: curves appear under the child’s fingers, as envelope of the family of lines created by the thread, and thus the idea of tangent line opens its way in the unconscious mind. Unconscious conceptions (what she calls “natural”) fostered by mimesis of animal characters (the rabbit and the dog) prepare the ground for formal, “artificial” ideas in secondary or higher education. Thus, observation, talk, and hands-on experience disclose the power of the child's mind, the power of his/her mimesis and fantasy, which is enhanced by narration but also by geometrical suggestions