Proportions must be exact and fit the design model else the object will not work properly. The world is built on structure and balance. Structure is one of the first things taught in mathematics although it is not labeled as such. It is simply incorporated into the curriculum and it is learned without it having been thought about much.
Structures are space oriented an not contained within walls or graphs but are related to a child’s ability to build mathematical formations that will build a solid foundation for future math. A little later on in their elementary education they will use these structures to learn how to quickly multiply and to add.
To a child particularly adept at imagining castles in the air, it will be thrilling when he sees positive proofs that they indeed do exist. In his mind numbers and symbols co-exist. It is delightful when he recognizes concrete evidence that his spatial knowledge is useful and contributes to finite constructions.
The reasoning behind the practical application of this first beginning foundational structure for a lifetime of viewing math structures as something real is a deliberate educational tool. Rather than using math to build imaginary spatial structures that will disperse as the class is dismissed, using modeling that is familiar binds the idea to the useful and commonplace. It then is retained, because it is something readily seen. It ceases to be only a theory one learns in school.
In no time as second or third grade elementary student is introduced to what is right about the math structures, he will discern what is wrong about them. Some structures simply will not fit into a particular grouping.
For a particularly gifted student, seeing something as useful but not as interesting as say literature, he will view the latter as simply a part of his mathematical world and will combine them. Literature and reading in general, will be an enhancement to his structural mathematical world. For his purpose, they will become one indivisible whole.
At least that’s the idea of what structured math is all about. If it must be first met in its cold and calculated high tower, it is understandable to seasoned thinkers how this can be intimidating to beginners and will possibly sour them on mathematics and its principles forever.
Once they learn the beauty of precision and structure and order and begin to apply it to their everyday life, and problem solving in general, mathematics is an adventure with which to build structures that stand the test of time. The A received becomes a triangle with dimensions that house untold treasures of structural possibilities.
Solving mathematical problems becomes as simple and as meaningful as finding another key to a hidden vault in life of structured living. Everything meaningful takes on its own essence, shape and occupies its own space and time frame.
Structured mathematics teaches problem solving by showing the truth or the falseness of every statement about how solutions can be found to mathematical problems. Understanding and mastering this approach is part of the building of a firm foundation for a lifetime of reasonable living and a balanced, structured life.
Life takes on shapes that are, at first rudimentary, flat and non-spatial, but gradually with learning and practice become two-dimensional and third dimensional and beyond.
Creativity, long thought not to have much to do with mathematics, is a big part of its dynamic concept. Each object interacting together must relate to a particular group, either by shape, purpose, or content, or some other pre-stated necessity, or it will be false. It will lend itself to work, play and to life in general. (Have you ever noticed how many children and adult games begin by counting?
With expertise, children learn how to change the structure of math by adding to, taking away, dividing and by multiplying. They then enter into a world via other pathways and go deeper into mathematical principles by learning how to measure, and how to add this to time itself.
How long will it take me to walk to the store? They figure this out as seeing time and distance as a certain length. I will get to this place in this much time if I walk at a certain pre-determined pace. In this way mathematics is used to structure time and distance as well as to measure the structures that are visible.
Mathematics then, for the mathematician is nothing more than a long structured walk from birth to death following pre-arranged blueprints drawn up by a masterful Creator.