It all started with the tweet from Sarah Caban a few days ago.
I decided to have a chat about it with the Kindergarten class, ask my grade 3 students, and one of our grade 5 teachers kindly agreed to ask the same question to her grade 5s. Here are the answers and some context from three different grades. At first, I planned to throw it all into a google doc and share with Sarah. Kindergarten kids’ ideas got me excited. When I started reading the other grades’ responses, I realized it’s worth sharing with anyone who might be interested.
Students in kindergarten have already learned some shapes vocabulary and identified different shapes in their environment. I started with pointing at their shapes wall, “I see you have been learning about shapes, we are learning about shapes in grade 3 too. Can you tell me what does it mean – “a shape?” A forest of hands.
“It’s a heart!”
“It’s a diamond!”
“It can be a circle.”
“A small triangle can be a shape.”
Students were pointing at shapes around them.
After recording all their “shapes” ideas, I asked, “What do all these things have in common? Why do we call them all shapes?” I was surprised how quickly kids considered the question and were all ready to discuss their ideas.
“Shapes are everywhere”.
“Everything is a shape but I don’t know what shape is.”
“We are made out of shapes”
Then someone mentioned that some letters are shapes. But not all. Students did not seem to have a consensus on that point, and the discussion continued around particular letters.
“C is not a shape, but you can make it a shape.”
Our kindergarten teacher who kindly invited me to talk math with her kids today, ask the student to explain what he means.
“You need to draw a straight line to make it a shape.” He drew a line connecting two “ends” of the letter C together. “Now it is a shape.”
Grade 3 students have just started talking about polygons and sorted their polygons and non-polygons into two groups. Their thoughts about shapes were likely affected by this recent activity. Students answered the question on the post-it notes and we did not have time to discuss it yet.
“A shape is something that has vertices and edges.”
“A shape is random line but with curves and edges.”
“A shape is a structure that most things are made out of. It is something that makes up everything.”
“A shape is something that you can outline.”
“Shape is something that you can use for a pattern.”
“A shape is something that connects. A shape means a thing that has no opening.”
“Shape is an object.”
“A shape is something to represent slots, key slots and other items.”
“Shape is 2D which means it’s flat.”
“A shape is something that is 2D or 3D and it needs a face.”
“A shape is something with vertices and everything is a shape.”
“A shape is something that has to have vertices/faces/edges and more than 2 edges or vertices.”
And the one that really made me pause and contemplate.
“A shape is a 2D or 3D object that is drawn or held by humans.” – I thought bringing in the point that shape is something manipulated by people was really interesting.
I am also curious about this.
“Shapes are everything you see in life. You can find anything and it falls under 1D, 2D, 3D and 4D shapes.”
Grade 5 students worked on describing 3D and 2D objects and sorting quadrilaterals in the beginning of the year. They explored points, lines and did a lot of “hands on” geometry work.
“A shape is a thing that makes everything.”
“A shape can be a polygon and it can be irregular.”
“A shape is some sort of structure.”
“A shape is a structure of an object with all connected lines. Sometimes shapes have lines with holes.”
“A shape is a form of geometry that represents objects in their form. They are the appearance of an irregular or regular object.”
“A shape is something that can have sides, vertices, straight edges or none, so they can be anything like a soccer ball.”
“A shape is something like a symbol of math.”
“A shape is geometric combination of lines and curves making a closed region.”
“A shape is a closed 2D object with nothing inside it.”
I found it interesting to observe how the intuitions unfold with age, to see how students would use new and more sophisticated vocabulary to grasp the same concept. How they start looking at new mathematical concepts and to compare them with their idea of “shapes”. How they try and test new learned attributes to define a shape. When I started organizing these notes, I realized how much this simple question can actually tell me about my students’ mathematical thinking.
When other teachers look at all this students’ thinking, what do they notice? Just like these kids use different structures to define “a shape”, how are our “teaching structures” that we use to interpret students’ thinking are the same or different. Not sure it makes sense. “Everything is a shape but I don’t know what shape is.”