In mathematics, application is the practice of using abstract mathematical theory to solve real-world problems. Enrichment aims to provide students with an understanding of the real-world uses of knowledge, so application projects are naturally conducive to achieving enrichment objectives. An effective application project presents students with a problem in a practical field -- such as business, technology or programming -- and asks students to find a solution using mathematical theory. Examples include C++ program design, business plan writing and electrical circuit building.
Interdisciplinary study is a way for students to learn the relevance and importance of mathematics. Mathematics is used extensively in physics, chemistry, economics, astronomy, computer science and engineering. Mathematics also plays a heavy role in history, as mathematicians have paved the way for the technological and scientific innovations that made enlightenment and modernity possible. An effective interdisciplinary math project would require a student to give a presentation on the importance of math in another field. Topics could include math in business, math in history and math in science.
Independent research is often a favorite activity of gifted and talented students. Many gifted students have a high level of intellectual curiosity, and learn best by being able to pursue independent interests outside the prescribed curriculum. Independent research would give students the opportunity to pitch a project, presentation or paper idea, and develop the idea in their own time. The only criteria would be that the project arrive at demonstrable results and relate to mathematics.
Group problem solving is a way to make learning fun for gifted and talented students. Many gifted students are highly competitive and thrive on being able to test their skills in an interactive setting. Group problem solving arranges students into groups and presents the groups a problem, allowing a certain amount of time for students to arrive at a solution. The first group to get the answer gets a point for that round.
Interactive games are a way to teach math to students who are bored by conventional instruction. Many gifted students find lectures tedious and intellectually stifling. These students may perform reasonably well on achievement tests, but not as well as their aptitude scores suggest. Getting these students engaged requires an unconventional approach, and the use of computer games can be one such approach. Academic Skill Builders has a database of online video games that integrate mathematics into the game strategy.