Calculus for 10-year-olds

Here are some resources to get you started on your research into Calculus for 10-year-olds. Keep in mind that you will be asked to choose one big idea to use as the basis for your presentation.

"Easy complexity is how a five-year-old learns calculus. Tell stories, make art, and find analogies that make your math friendly. Gently grow your happy familiarity with complex ideas. [M]ake math easy enough for open play and complex enough for advanced mastery."

–one of the seven principles of Natural Math

5-Year-Olds Can Learn CalculusWhy playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to math

For more resources from Maria Droujkova, check out Natural Math.

This is an interesting presentation that speaks against the traditional hierarchy of mathematics education: Math is Not Linear

Calculus Better Explained takes you through a calculus course, presenting the ideas in a different manner than what we've done in class.

The Essence of Calculus is a series of videos created by 3Blue1Brown with the goals:

to get at the heart of the subject
so you feel like you could have invented calculus yourself
to cover all the core ideas in a visual way that makes it clear where the ideas come from and what they actually mean

I'm not the only one thinking about calculus for 10-year-olds. Have a read through Chase Orton's blogpost "Calculus for All." Towards the bottom of the post there is an invitation with links to two Desmos classroom activities that may give you some ideas for your presentation.

"At the very least: Once someone knows area, they can think about integrals; and once someone knows slope, they can think about derivatives."

The goal of the final project is to focus on the big ideas of calculus, while demonstrating habits of mind of a mathematician. What do mathematicians do? Mathematicians:

take risks
make mistakes
are precise
rise to a challenge
ask questions
connect ideas
use intutition
reason
prove
work together and alone

(from Being the Math Teacher You Wish You'd Had by Tracy Johnston Zager)

Curricular competencies from the calculus course that will be addressed through this project:

estimate reasonably
model situations with mathematics
develop, demonstrate and apply a conceptual understanding of mathematics
visualize to explore and illustrate mathematical concepts and relationships
communicate mathematical thinking in many ways
use mathematical vocabulary and language
represent mathematical ideas in a variety of ways
explain and justify mathematical ideas
connect mathematical concepts to each other and to other areas

Some things to consider:

You need to use mathematical language, but you can't assume that the students you are presenting to will be familiar with the words. Don't make any assumptions! It is important to include mathematical vocabulary, but you may need to find a way to make it understandable to your audience. You will need to be specific and precise with your language.

You will need to be able to convince your audience about your thinking.

You are going to need to practice your delivery. There will be no powerpoints.

What do you want your audience to discover?

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