The glass wall Why mathematics can seem difficult

This perceptive text suggests that the physical world and the mathematical world are separated by a "glass wall," confronted by people in their frustrating attempts to use the natural language of the physical world (as applications of mathematics) to understand mathematics (as a special world itself). To overcome this barrier, Smith suggests that people must focus their attention on "understanding mathematics," which necessitates "an appreciation of the relevant network of mathematical relationships, the numerical patterns that determine and justify applications." It is interesting to note that the author has a long career as a cognitive scientist with a focus on language, reading, writing, thinking, and learning, but has reflected for the past ten years on the world of mathematics, confronting the "glass wall" himself. The mathematics addressed in the text is limited to the concepts, terminology, and skills usually taught at K-8 grade levels, but the author's insights and suggestions easily extend to more advanced mathematics. A useful reference list is provided but includes notable gaps such as important contributions by David Pimm and Liping Ma. Highly recommended to a wide audience--teachers, students, parents, and the general public. J. Johnson Western Washington University