Can we improve the methods we use to teach math in schools — so that everyone develops proficiency? A grade-school math program is changing how children learn based on the assumption that all children can achieve a high level of understanding.

Due to recent brain development research, educators are working to add more math education into pre-school and kindergarten classes. Studies show that children of this age are actually extremely receptive to numbers and learning geometry.

Critics in today's world often say that computers and technology are impeding the social skills of the very young. But Zoo U, a computer game for children, helps kids develop the skills they need such as empathy, impulse control, and communication.

Clean water and healthy ecosystems are becoming increasingly difficult to come by. With floating islands and other inventions, eco-entrepreneur Bruce Kania thinks that biomimicry - such as reconstructing wetlands and growing biofilms - can tackle the toughest of water problems.

Concerned with colony collapse syndrome in honey bees worldwide, scientists, farmers and tech companies teamed up in Australia to create a micro-sensor that collects data on the bee's environment.

Preschoolers in the U.S. who misbehave are increasingly being expelled. In Connecticut, trained counselors educated teachers about how to deal with emotionally traumatized kids which reduced expulsions.

Preparing the young for elementary education is a priority to nurture reading and social skills. For 16 years, Tulsa Oklahoma has instituted a state funded preschool, staffed with teachers trained in early education. Tulsa’s Pre-K initiative has shown that their children are more prepared for literacy skills and math; however, maintaining the positive results is a long-term challenge.

What about the world’s poorest, for whom new, expensive gadgets are out of reach - what types of innovation would be most beneficial for them? Through “frugal innovation”, people are designing products specifically to meet the needs of the world’s poorest citizens.

Around the world, a new way of teaching and learning is gaining traction – and seeing results. Rooted in educational theory from the likes of Socrates, Piaget, and Montessori, this method is led by students’ curiosity and ability to learn and grow independently; essentially, the students control their own learning. Such methods make success more attainable in places like Matamoros, Mexico, who has seen exceptional improvement from students who experience learning this way.

Universal preschool is a policy that is often hard to pass on voter referendums. But, as evidenced by examples in Detroit and New York, such an investment means that more children would do well in kindergarten, fewer would need special education or other extra help and down the line, fewer would drop out of high school, end up unemployed — or in jail.