Gov. Jerry Brown wants California’s public institutions to take a hard look at MOOCs. Along with the Bill & Melinda Gates Foundation, he is encouraging experimentation with MOOC platforms for introductory and remedial courses.
California is the Fertile Crescent for massive open online course providers, at least the for-profit ones. The state is also shaping up as a testing ground for phase two of the MOOC experiment, which includes fees and a path to college credit, and where public colleges try to use material from MOOCs to help meet student demand in gateway courses.
One way children transfer the number concepts learned at each level is through visualization. Once children have internalized an abundance of concrete number experiences, the teacher may tell number stories that encourage children to vi sualize the process.
“The child is the principal agent in his or her own education and mental development. Development and growth occurs through an enormously complicated and continuous process of interaction with the environment. Through activity, the per son discovers understanding by re-inventing what he or she wants to understand. This process takes time.”
Chil dren usually have not encountered mathematical symbols in the con text of their natural environment. Often, their first experiences oc cur in schoolrelated activities. Numerical and mathematical symbols are introduced at the con necting level. Mathematical symbols (e.g., +, –, =) are even more abstract than the mathematical language they represent. Both vertical and hori zontal equations should be experienced.