Innovation integrates existing resources first. Most likely, you already have all you need to bring powerful pedagogy to your school community. 

How would a school innovate their curriculum?

It all starts with joy.

Ask any child what their favorite period of the day is. Go ahead. On second thought you don't need to. You already know.
For most of them, it's Recess. Especially if they have choice in what they can do.

Recess is more than a time to blow off steam. It's an opportunity to build up steam. Games are full of math, and rules, and debate, and history, and ethics. What child doesn't get incensed about cheating? You want your students to write? They'll write a letter to the President of the United States if they thought it would level the playing field in capture the flag. 

Tap into the things that light kids up, and you've already illuminated your curriculum.

What's their second favorite class?
Odds are, it's PE. Which in some schools is essentially organized recess: heavy on the P, light on the E.

Physical Education is full of education. It's literally in the name.
Lean in, and watch the kids learn about their bodies, and their health.
If you have a finger you can measure your pulse, which is literally a rate (CCSS.MATH.CONTENT.6.RP.A.2, 6.RP.A.3, 6.RP.A.3A, 6.RP.A.3B, 6.RP.A.3C, 6.RP.A.3D...)  Throughout a gym curriculum you'll find fractions (CCSS.MATH.CONTENT.4.NF.B.4, 4.NF.B.4A, B &C), statistics and probability (CCSS.MATH.CONTENT.6.SP.A.1, 6.SP.A.2, 6.SP.A.3, CCSS.MATH.CONTENT.6.SP.B.4), endless operations and algebraic thinking (CCSS.MATH.CONTENT.4.OA.A.1, 5.OA.A.1, ... do we need to keep listing these standards?...) 

If you're not collecting data in your PE classes, you're just running in circles.

For some reason math classrooms still use textbooks, with questions about trains leaving Chicago, or boxes in factories, or some abstract person purchasing boring items from a non-existent store. What the heck? Our kids are already shopping, in real time, at real places. We don't have to invent anything, and certainly not read examples from a textbook. Go shopping with them. Plan a party. If you can, connect with the school cafeteria and look at bulk prices. Let kids see what's under the hood in their immediate environment, and listen as the follow up questions start revving up...

And we haven't even begun to talk about the mathematics that underwrite history.
The injustices of the world are laid bare by the statistics of the world. 

Nor have we talked here about STEAM, a class jockeying closely for 2nd-fave with PE, if I do say so myself.
Or the Future, a realm so fascinating the possibilities are literally endless, and unknown.
Or the Arts, where ratios, volumes, and histories are as varied as the mediums you engage.
Or Genius Hour, where anything is possible, and everything is awesome.

Even the traditional disciplines of traditional school are transported into deep dives when the content is interwoven and interrelated.
For example, What if the study of the Industrial Revolution in a traditional History class supported the mathematics study, the sciences study, and the literature study, and energized conversations around the ethics and the engineering of the time. How deeply would students understand the period being discussed when every discipline danced together in its exploration?

It sounds complicated, and yet simple, almost obvious. How is that?

It sounds simple because it is simple. It may not always be easy, but it's simple.
Learning to listen to the language of learning takes energy.
Giving students real responsibility takes effort.
Giving them real opportunities to fail takes courage.

It's simple because it's intuitive. It's how we learn, now that we've grown up. It's how we explore. It's how we connect. With each other. With ourselves.

How would a school include the community?

Invitations are but the beginning. Inclusion is essential. No breakthrough in education ever came from the top down. Change happens when people are invested in the outcome and in their input. True leadership taps into the roots of the culture, the shoots of the community, and the blossoms of creativity heard and seen throughout the halls. Change is exciting when it's energized by everyone involved.

Innovation starts with what's already alive and well in your communities of practice.

Where would I even start?

You start where you are. Now.

The Present is more than just a stepping stone to tomorrow. It's everything. Right here. Right now.
Observe things as they are, Research how they came to be, Reflect on their current efficacy and value, together. 

The Future is more than just a fact of life, it's a field of study, one in which everyone has skin in the game.
Wonder what's possible; Discover what's probable; Determine what's preferable, together. 

Explore the planet, together.
Bring life sciences into the lives of our young scientists when the world is at its most mysterious, magical, and adorable. Nature is powerful, elegant, and cute-beyond-words, especially to an adolescent. 

Throw an image of a baby-(insert ANY animal here) on the board - now you've got their attention.
Explore the animal and its amazing natural talents and abilities - now you're strengthening their affection.
Prototype a machine that integrates those talents into a solution to a problem - now you're cultivating their genius.

Present your discoveries to lower grades in your school - now you've developed their leadership, educated your community, and lit sparks in your youngest scientists, artists, designers, and engineers. 

All with a baby-(insert ANY animal here, again)

Can this get any cuter?