"Many people think of geometry mostly in terms of vocabulary-do students recognize triangles, do they know what a square is, do they know what shapes are round, and so on. But, in fact, geometry is the study of special attributes of shapes, how shapes fit together, and how shapes are located in space. Attributes of shapes include things like number of sides, how pointed the corners are, whether they are round, whether they are flat (2D), whether their parts are all the same size, and so on. It is the recognition of attributes of shapes and the implications of those attributes that helps students more effectively use shapes in their lives. Knowing that round shapes are not stable for building on is as practical to a young Kindergarten student building a structure as it is to an adult designing a real building. Representing shapes, taking them apart, and putting them together are ways to encourage students to explore more carefully the attributes of those shapes."
Big Ideas from Dr. Small, pg. 63
Being mindful of the quote above and reflecting on the information found in the resource book "Big Ideas from Dr. Small", we set out to offer the children an abundance of experiences that would elicit curiosity, wonder, investigation, and exploration, involving hands on activities and materials to manipulate.
We began with this open ended provocation set out to familiarize the children with both 2D and 3D shapes.
According to Dr. Small, "we often confuse students when we use a concrete, or 3D representation for a 2D shape in order to allow students to manipulate the shape, for example, a yellow pattern block for a hexagon. The pattern block represents a 2D shape, but it is actually a 3D shape because it has three dimensions."
Big Ideas from Dr. Small
Based on some of our discussions, interesting questions and thoughts were generated...
What do you notice about these shapes?
"You can't pick up the shapes on the paper but you can pick up the ones that are wooden!" K. C.
"They're different on the paper and they're different wooden shapes." S. F.
"Some are the same from the paper and wooden ones." A. R.
"What do you mean?" Mrs. Ralph
"The circle is the same as this ball, and these two squares (cubes) match this square on the paper." A. R.
"This triangle is the same as this wooden shape because they both have three sides and three points." S. T.
"But the wooden one (triangle based pyramid) has four sides and the one on the paper (triangle) has three sides." B. P.
"All triangles have three sides and the wooden one (square based pyramid) has more." J. B.
"I can hold the cone but I can't hold the triangle." Z. G.
As a way to explore and investigate 2D and 3D shapes further, we decided to invite to children to build a structure and use the overhead projector to sketch the shadow of their structure.
While building and sketching we captured the children's thinking...
"It wouldn't be 3D it would only be 2D when you sketch it, the shapes are flat on the wall." C. C.
"I just made a house. This is different, these have lines (hexagonal prism) and this doesn't (shadow). This is a triangle and this is a cone. A cylinder on the side turned into a circle." A. J.
"A cylinder turned into a rectangle on the wall!" A. F.
A. J. painting his 2D shadow sketch.
"This is a cylinder but the shadow looks like a rectangle. I think the cone will make a triangle shape." Z. G.
"This is a cube and this is a square! I think it's the fake of the solid. The shadow shapes are 2 dimensional because I can't pick them up!" M. O.
J. K. sketching the shadow of is structure.
"I built with a round cone but on the wall it looks like a triangle. You can pick up the shadows, I can' hold the cones I builded with and drew them on paper. The cylinders are looking like rectangles on paper. The shadow is bigger on the paper than my church I built." B. P.
"The structure is made with wooden blocks and the one on the paper is made flat with pencils, the colour on the wall is brighter than looking through the blocks." L. B.
"It's tall, it's 13." E. C.
"They are black and flat and some have colours in the blocks. I used all the blocks to make a city." M. K.
"The blocks are higher than my picture. You can hold the blocks but not the shadow. The shapes are different like the cone is like a square in the shadow." K. C.
Other thoughts...
"It's a cube it has points, four points!" R. S.
"They are kinda like the same but the picture is brighter and flat. The blocks look different, a cone looks like a cone but black and black on paper." S. T.
"It's black, it different shape." F. W.
"You can build with the blocks, pick them up and pick up the shadow but you can't build with a shadow." A. R.
"The block tower is wigglier and the paper one is not. The cone is a triangle! The cylinder is a tall line almost a huge triangle!" C. D.
"The blocks were big to build with and I don't see lines on the paper." N. M.
"They are different because I traced the one I sketched but I built the one I built with my hands. I also used my hands to trace but the block is wood and the pencil is a pencil. The big blocks show colours and the small blocks are dark." P. C.
"My castle was made with not the see through blocks so it's a black shadow on the paper. When I look at the shadow I don't see the lines from the blocks it just disappears." L. C.
"It is easier to build then to trace them. They are flat on the wall to touch, you can't hold them." E. B.
"The shadows you can't grab, the wood blocks we can grab and build." M. N.
"Once you put it on it makes a shadow, a cone is on top, it looks like a tower." C. T.
"The light goes on the wall in the colours like blue and red, sometimes when it's taller it faces the ceiling or wall." J. B.
"The shadow was bigger than the blocks The shapes are flat on the paper and the blocks are not flat, like you can hold them and stuff and build with them." D. F.
"Young students should become familiar with both 3D shapes and 2D shapes. Generally, 3D shapes are explored first because they are a concrete part of a child's everyday life when they see balls (spheres), boxes (prisms), cans (cylinders), and so on. And, because 2D shapes are found on 3D shapes, for example, squares as faces of boxes they see, it makes sense to begin with 3D shapes."
Big Ideas from Dr. Small, pg.65
Exploring Shapes
Our bulletin board display!
I always enjoy seeing how everything evolved throughout the process, and the examples of student work along with the thinking helps so much. Your last paragraph still has me thinking, as in the past, I always taught 2-D before 3-D, and know a large majority of teachers that do the same. Things switched for me this year because of our Twitter discussion. I wonder what others choose to teach first -- 2-D or 3-D -- and why. I know that I'll be starting with 3-D from now on. Thanks for building my math knowledge too. :)
ReplyDeleteAviva
I agree! Fabulous post Anamaria! I too enjoyed seeing the process for students' as they built understanding coupled with the research from Dr. Small that you shared from a professional lens. You have me thinking a great deal...since I always teach 2D shapes before 3D. Like Aviva, I will also be rethinking this for next year and digging deeper into the "why" in the coming months. Thanks for sharing!
DeleteJocelyn
Thanks for the comment Jocelyn! I find this resource book (Dr. Small) to be incredibly hands on complete with critical thinking questions and activities to extend learning. With the exploring of 3D shapes first, children are able to manipulate and interact with them as well as being able to note their attributes which can lead to the discussion of 2D shapes e.g., a square based pyramid has a square base and triangle faces. Made a lot of sense to me!
DeleteI'm planning a math lesson on 3D shapes for a grade 3 class, and was going to review 2D shapes first. My thinking has changed after reading about your experience, and I agree that students have more concrete experiences with 3D shapes to "hang" their learning about 2D shapes onto. So glad you shared this!
ReplyDeleteI agree with Dr. Small's quote re: "Generally 3D are explored first" but my wondering is do we need to teach 3D and 2D shapes in isolation or, as it appears you have done with this investigation, is it more empowering and can children develop a deeper understanding by playing with both? What do they come to us already knowing and how can we build on that knowledge while going deeper with new learning?
ReplyDeleteI completely agree with you Heather! In my initial provocation I set up both 2D and 3D exploration alongside each other on the same table. I feel they are so linked together that it actually makes more sense to teach them simultaneously. Most 3D shapes include 2D attributes which can be discussed with children in their natural play. Thanks for taking the time to read this:)
Delete