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.

In the Renton School District, teachers found that only a very few fifth-graders could solve problems with the skill that, in other schools, was common in third or even second grade. So they turned math lessons into carefully guided conversations in which students explain their approaches, defend their reasoning and critique each other’s ideas.

New water management technology implemented along the Columbia has significantly helped the fish population - specifically salmon - return to healthy numbers and has restored much of the community and industry that revolves around the river, including for native peoples.

In the Mumbai slum of Dharavi, an NGO called Society for Nutrition, Education & Health Action (SNEHA) is working to make life safer by teaching men the importance of not being violent towards women. Through an app called Eyewatch, community members are able to document acts of domestic violence, which helps SNEHA team members locate victims and their abusers.

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.