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.

Wolves in western America were once hunted to near-extinction but have now been reintroduced into certain territories with notable success. More wolves often means more attacks on ranchers' livestock, however, so cowboys are working to track wolf packs by computer to reduce conflicts.

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.

Many different people are inventing health devices for resource-poor settings, but some organizations - like M.I.T.’s Little Devices group - are empowering developing communities and increasing access to healthcare by building medical devices that nurses and doctors in very poor settings can adapt themselves — or kits for making their own, often harvesting parts from toys to cleverly rig up medical equipment. It’s part of a major idea shift, one that’s transforming the design of foreign aid.

Often it is faster and easier to harvest molecules for medical purposes from nature than to make them in a laboratory. A scientist is looking for cancer-fighting molecules in coral and sponges in the tropical Pacific.

Middle School 88 in Brooklyn is part of a broad evolution in teaching math, employing technology through a non-profit called School for One (Teach for One) to provide each student with a personalized lesson generated and monitored by computers to match their learning level.

Despite significant increases in funding and advances in biomedical research, the rates of new treatments and drugs for illnesses that reach the market every year have plummeted. A group called the Myelin Repair Foundation, along with several other foundations, uses an intensely goal-directed and collaborative method to tackle the bottleneck.