Kamaliʻi Mathematics: Kilo X + Y

Through a partnership with Nā Pua Noʻeau Kauaʻi, I had the opportunity to teach a second cohort of Kamaliʻi (grades K-5) across the pae ʻaina! From Kauaʻi to Hawai’i Island, we met virtually over zoom and gathered together to Kilo + Scratch. Our Fall Institute focused on letter writing (with our Weather Letters), digital storytelling and Kilo X + Y!

You may be asking yourself, what is Kilo X + Y? Allow me to share a little more about how I arrived at this idea!

As some of you know, Scratch is a free programming language, which is both visual and block based, through which children can create their own interactive stories, games, and animations. This is an AMAZING web-based application that allows young children to express themselves digitally while also encouraging creativity, imagination, logic, and reasoning.  

The Scratch interface, particularly the stage (see below) is a great way to introduce young children to the concept of X and Y. The stage is set up as a Cartesian coordinate system! Do you remember learning about the x and y plane and managing to find the slope of a line between two coordinates using the equation y = mx + b? Can you tell that I’m a little excited about math? 

Ok, let's get back to the connection to Scratch. Since the stage is set up as a coordinate system, we can teach young students, even as young as kindergarten to understand the concept of (x,y). How can this be done? You can have students place different sprites (or characters) at a specific coordinate on a stage. In my example below, you’ll notice that the ‘I’iwi (custom designed sprite) is at (80,93)

With that said, this is not the initial way I introduced students to this mathematical concept. We learned it during our kilo practice by superimposing the x and y coordinate system over our viewing plane. I had students trace a coordinate system on the clear cover of their curriculum folders (see example below).

On our first day, we learned about origin (0,0) and then moved into the concept of negative and positive values for x and y. We coupled kilo with kinesthetics by having our students stretch their limbs horizontally and vertically to help them visualize and understand the x and y axes. It was fun and amazing to see our youngest students grow into their own understanding of the coordinate system! By the last day of our session, our kamali’i were observing and documenting their observations at specific coordinates on their Kilo X + Y views. Below, Hi’ilei, a fourth grader from Kaua’i, explores Kilo X + Y in her ahupua’a. 

As we transitioned from Kilo X + Y to Scratch X + Y, it appeared fairly smooth for our kamali’i to place their different sprites at specific coordinates in their stages. As we advanced through their digital storytelling, it was time to code or program Pueo flying across the Scratch X + Y stage. We talked through the movement of the Pueo across the third and first quadrants and the changes in x and y that would permit his exit through the top right hand corner of the stage. Take a moment to watch Hiʻilei's completed Scratch animation in which she applied what she learned from Kilo X + Y to code the flight paths for Pueo and ʻŌpeʻapeʻa across the first scene.


Here are my BIG takeaways from teaching our kamaliʻi this session:

  • The ideas around introducing and teaching our keiki mathematical concepts through incorporating kilo seems within reach for educators and our keiki! I believe that we should explore and share teaching methodologies that encourage more abstract thinking, imagination and evaluation.
  • Coupling kilo and kinesthetic movements can help our kamaliʻi imagine and understand abstract concepts like the coordinate system. Let's find ways to share the magic of math with our kamaliʻi.
  • Scratch can be used to reinforce and ground students in the application of these mathematical concepts that oftentimes can feel foreign and too abstract. 

Kilo X + Y is an interesting teaching experiment that aims to dismiss the belief that certain mathematical concepts need to wait until our kids are older. As a coding teacher and fan of mathematics, I have come to recognize the impact of mathematics in my own trajectory. Why do we have to learn mathematics? Because, mathematics can impact and change the world! And that's is something we can all rally around!

A special mahalo to Malia Chun, program coordinator for Kauaʻi Nā Pua Noʻeau and co-teacher for this Fall’s Institute & to our ‘ohana and kamaliʻi who came with open minds and hearts to learn & to Devi Berg for capturing Hiʻilei's learning journey and sharing it with us!