Mary Everest Boole (1832–1916) set herself the task of disseminating and popularizing the ideas of her husband, George Boole (1815–1864), developed in his major work The Laws of Thought (1853), on which she had collaborated. Yet Mary's extensive body of work—books, articles and journals—reveals both her forceful personality and her highly unconventional ideas about mathematics and how it should be taught. She emphasizes the psychological dimension of mathematical understanding and invention. Children should encounter mathematical situations from a very early age. Various methods can help them—girls and boys alike (she stresses the education of girls)—form mental images that will lead them to think independently and, where appropriate, gain access to the most abstract mathematics: stories, objects, drawings…
The following diagrams appear in Lectures on the Logic of Arithmetic (Clarendon Press, 1908).
No explanation is needed. This diagram "illustrates" the following standard arithmetic identity: (n+1)2 = *n 2 + 2n + 1.
It also illustrates that the sum of the first n odd integers is equal to *n 2, that is, 1 + 3 + 5 + … + (2n – 1) = *n 2.
Mary Everest Boole remarks that a good mathematician will need no further explanation. For students, however, this diagram will leave an image in their memory that they can summon when the need arises.
These diagrams were quite innovative at the time.
