Mathematicians view math as a search for meaningful patterns and structure. Students often view math as a tedious and often arbitrary set of computational problems to solve.
There is a STRUCTURE versus SOLUTION rift in the way mathematics is practiced at a high level and the way it is perceived by novices. In this line of work we ask these questions:
1.How do we train students to appreciate structure?
2.If students are proficient at solving, will they be equally proficient in structure identification?
One might think that the simplest way to teach structure is to explicitly point out structure. But there are many documented examples of failure to learn structure when it is explicitly taught, because the ways of representing structure are often abstract and opaque to learners.
So in this line of work, we take an indirect approach to learning structure. The hypothesis in this line of work comes from how we learn about the structure of three-dimensional shapes in perception: By experiencing many variations of some shape and then extracting the invariant structure (see the teapot example below). Perhaps in the same way, children, after experiencing many variations of a mathematical structure, can extract the invariant information (see word problem example below).
Structure in Elementary Mathematics