Body Measurement - Situating yourself in the Mathematical Context
Today's lesson in the garden began with some frontloading of the various kinds of measurements humans have used, and how we ended up with a common agreement of standard units. We began to see that the task at hand has not changed throughout time, and instead what has shifted is our way of accessing the practice of measuring something. Our most common frame of reference when calling measurement to mind is a yellow and black ruler, and the long wooden beige meter stick; using these tools to access the practice of measuring. This method serves the purpose of efficacy and accuracy, but a distance is created between perception of measurement in relation to one's physical body. Susan began to paint a vignette of the moment Newton was bumped by a falling apple, prompting him to question why the apple always falls down, what is making the apple behave in that way? We now know this is gravitational force. Newton’s story calls for us to recall relationality on all levels, not only does the apple pull earth - the earth also has pull to the apple. Susan then lead us through some former practices of measurement using one’s body (see picture below!), and having us measure our own bodies in relation to the ancient units. We compared our measurements and did not find too wild of differences between the group! Using our own unit of measure, for example, one’s own step length, we then measured how many of my steps the garden was both long and wide or the dimensions of the garden bench - which allowed us to see our own selves within the practice of measurement. The concept of relationality and mathematics is one that can narrow in on entry points to understanding math on a way in which we can feel and observe, which was so lovely. To do this practice in the garden made things all the more meaningful, we were reminded that not everything is perfectly linear, or organized, that measurement serves a purpose of knowing, familiarity rather than precision and efficacy. This practice lead by Susan was a wonderful way to set our minds up for inquiry on connecting our surroundings to mathematical thinking and how we could use nature to allow comfortability through familiarity and knowing to invite mathematics to go beyond a white sheet of paper and a pencil, but into our everyday surroundings, serving a multitude of different purposes
Coding unplugged in the garden
Next, we had a special guest in the garden, Erica Huang, who is an experienced high school mathematics and computer science teacher and a curriculum developer. She is currently a PhD student at UBC. Erica came to teach us about some ways we could teach our students about coding without using any technology and in a garden setting!
Before we started any activities, Erica went over with us five main principles of Computational Thinking:
Algorithmic thinking
Decomposition
Evaluation
Pattern recognition/generalization
Abstraction
These principles are what we would be teaching to our students through these activities, so Erica highlighted that it is important for us to keep these principles in mind while we go through the workshop.
The first activity that Erica led is called “human robot.” We got into groups of three and one person was the robot and the other two people were the programers. The two programers brainstormed on a piece of paper the necessary commands to progam the human robot to walk, reach, and pick up a water bottle. The programers could only use the commands that they wrote on the paper. If the programers wanted to add new commands after they started guiding the human robot towards the water bottle, they had to send the human robot back to the start to “fix the bugs in the programming.” I think this activity is really great as it relates to algorithmic thinking since the programers are problem-solving by breaking down the task of guiding the robot to the water bottle into a series of clear, logical, and step-by-step commands. This activity also covers evaluation since the programers are assessing, testing, and debugging the performance of the commands they came up with for the human robot. This activity is an effective, hands on way to introduce students to programing, algorithmic thinking, and evaluation.
In the second activity, Erica taught us how to represent the numbers 1-7 in binary code using sticks and rocks found in the garden. Binary code is the fundamental language of computers, representing data and instructions using only two symbols: 0 and 1. These digits correspond to “off” and “on” states in electronic circuits. Groups of these digits, known as bits and bytes, allow machines to process, store, and display complex information. In our example, the rocks represent 0 and the sticks represent 1. I think introducing binary code in this way to students would provide an easy access point and would allows students to begin to grasp this concept without feeling overwhelmed. Binary code could be an abstract and daunting concept to students learning about this for the first time, so presenting it in nature and in a garden setting could help to calm nervous students.
Another interesting note, Erica told us about Mike Naylor, a mathematical artist, teacher, and researcher, who wrote a poem titled Run, Hero, Run! which was inspired by the binary numbers 0-7. Mike Naylor recognized that when saying aloud the binary numbers 0-7 that it has a nice rhythm to it and that it could be turned into a poem. Mike Naylor wrote his poem by switching the word zero for hero and one for run.
Mike Naylor’s poem Run, Hero, Run!
Hero, hero, hero
Hero, hero run!
Hero, run hero.
Hero run run!
Run, hero hero
Run, hero, run!
Run run hero.
Run run run!
This poem is a great example that math has so many ways of being an interdisciplinary and creative subject. I think that learning and applying math through poetry or song is a fantastic way to help students to have a deeper understanding of the math concept being studied as well as to find joy and fun in math.
- Katie, Kirstin, Sara
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