Seeing the Macintosh, back in its infancy, we were simply quite impressed by the ways its designers had used spatial information to solve problems whose solutions eluded the developers of the PC and the DOS operating system. We naturally asked ourselves whether there were problems in our teaching that might be solvable by using the Mac's graphic capabilities. Turing's World proved highly successful and so we got hooked on the power of visualization in reasoning. Visualization is an aid in reasoning in part because it helps keep the student focused on what they are reasoning about, something in the world, not the syntax of the goal sentence. In formal proof systems, it is all too easy for students to forget the real goal and focus instead on the shape of the goal sentence, rather than the information it contains.
Visual information helps keep students focused.
That was our initial idea with Tarski's World . But using Tarski's World led us to realize that visual information does a lot more than focus the mind. The interaction of visual information and sentential information gives rise to ways of reasoning that simply don't fit the traditional account. This method of instruction has gone out of fashion in learning other languages. It should also be tossed out as a way of learning the first-order language.