New technique teaches 5-year-olds calculus

Dr. Maria Droujkova plans to revolutionize the way we teach mathematics to our children, allowing them to learn calculus and algebraic concepts from an early age using methods that complement the natural way we learn. The traditional curriculum-based progression learning, where students start with arithmetic, then work their way up to geometry, trigonometry, and finally calculus, “has nothing to do with how children grow and learn or how mathematics is built,” claims the PhD candidate.

The current implementation of mathematical learning is organized in a sequential manner and does little for instilling a purpose when the focus is arithmetic drills. For example, students begin learning the fundamentals of algebra, moving on to more advanced levels, before completing the course and advancing to the fundamentals of geometry. This rise and fall approach does not teach children about patterns and structures; the heart of what mathematics is about, and instead strips children of curiosity to actually explore the medium and its intersection with every other disciple ― music, art, computer programming, and science.

Via XKCD

Droujkova likens this to a film director learning about lighting, costumes, and other technical aspects rather than how to tell a story. Instead, her approach is aimed at teaching the easy as well as complex aspects of all branches across multiple boundaries, “my quest, with several colleagues around the world, is to take the treasure of mathematics and find the accessible ways into all of it.”

Her approach focuses on creating a fundamental basis for understanding advanced concepts by beginning with a hands-on, metaphoric play. This is called the free play level, where students learn to connect abstract mathematical concepts to things they can touch and feel, such as making “mirror books,” mirrors attached to one another like book covers that can be angled around objects to introduce the concepts of infinity and transformation. By starting with an informal level, students could begin noticing patterns and discussing ideas while retaining the playful aspect of mathematics metaphorically similar to those embodied by actual mathematicians who play with abstract ideas.

The goal is to create interest by showing a real world application or example of the subject from an early age, rather than diving headlong in tedium. By broadening the approach to include multiple branches of mathematics, students will find their own niche based on what interests them naturally, “Children need to be exposed to a variety of math styles to find the one that suits them best. But they also need to see meaningful (to them) people doing meaningful things with math and enjoying the experience” adds Droujkova. By providing them with logic puzzles or open projects, we’re promoting a view that math is the realm of explorers and designers.

The biggest quarrel with traditional curriculum-based learning is the emphasis this movement places on letting children decide which math activities to participat. for how long, and at what level of mastery. Discipline must be enforced by the role adults play in finding a connection between math and whatever the kid’s doing. They must have a variety of interesting materials available; too many folks tempted to replay their math education with their kids, states Droujkova.

Via TheAtlantic