There is a well-documented link between math skills and what is called spatial sense, described by the National Council of Teachers of Mathematics (NCTM) as “an intuitive feel for one’s surroundings and objects in them.” According to the NCTM’s Principles and Standards for School Mathematics, "Geometry and spatial sense are fundamental components of mathematics education. They offer ways to interpret and reflect on our physical environment through abstraction. They support creative thought in all mathematics."One of the best ways to develop spatial sense is to make things. Unfortunately, they have eliminated play with blocks from most schools, parents are giving their toddlers laptops, and we are not exactly moving in the right direction except for some notable exceptions, like the boat building projects in this month's Wooden Boat magazine. Thanks, John for the link.
According to the Standards, “spatial visualization includes building and manipulating mental representations of shapes, relationships, and transformations.”
You will note that important word in the Standard's remarks "reflect on our physical environment through abstraction." One of the primary problems with modern education is that we expect children to deal with abstraction without starting with the concrete, as suggested by so many early educators.
As stated by Otto Salomon, developer and promoter of Educational Sloyd, "education should move gradually from the concrete to the abstract."
Manipulation of real objects, tools and materials needs to be the starting point of all education, and we learn best when we are provided the opportunity to revisit those objects, tools and materials throughout our process of growth and maturity.