More Math at Sycamore
Thinking about math is one of our favorite preoccupations here at the Sycamore School.
By Hanna Walker
We started out this theme cycle with a research project on animals. All of the 1st and 2nd graders picked a reptile to research. We were focused on measurement at first. We started collecting the data by having them ask questions about their reptiles. How long are their tongues? Where do they live? How long do they live? How fast can they go? Where are they fastest? (in the water, on land). After researching, we found that it was difficult to answer some of their questions. From questions we could answer, they chose to show how many species of their reptile there are.
So we made a plan (the purple writing on the white board)
They used this infographic from Animals by the Numbers a Book of Animal Infographics by Steve Jenkins as inspiration. Next, we made the graph from linker cubes to see how it laid out and what format they wanted.
Building our graph from cubes with them was actually a really valuable experience because they were able to figure out how to use each cube as 5 instead of 1 to be able to include B’s 1,500 gecko species. We were able to pick a scale, build it, and see how the data changed. I really enjoyed this process.
This graph was our first iteration. You can see that the kids added a key at the top so we would remember how much each cube represents.
Next we created an iteration with paint dots on paper. They had to think about the title and what labels were needed for someone to make sense of the graph We finished this one and we had a discussion about accuracy and how our data was not “true,” because we couldn’t include all of B’s data, and it is very “disorganized,” so it’s hard to read.
For our last version, we decided to use stickers so that each data point would be more uniform. We ended up with kind of a disorganized pie graph.
We know that talking about our work is the best way to ensure long-term retention and transfer of knowledge to other situations, so we always debrief at the end of working on something at Sycamore. Here are some reflections from the kids...
Why did we make a second graph?
“I think we went away from this (first graph) because we didn’t feel like it looked right or we couldn’t fit B’s data. I feel like it didn’t look the way we thought it was going to look like” H- “What did that do to our data?” “That turned it really different, some go really small, some go really big and they are not in a certain order and it just did a lot to our graph.”
Explaining how the disorganization might cause someone to misinterpret the data... “I think someone might think that if two dot are connected they might think that it is one dot or if one dot only half of it got put down they might think oh that equals two and a half.”
Observations about their last iteration:
”I like how we put all of the animals on the stickers and I also like how we put all of the animals on the side and wrote it on the note” H-Why do you like that we did stickers? “Because it kind of actually shows how many reptiles there are and it actually shows the reptile” C-Do you think if someone looked at this graph they would be able to see easily that one reptile has more species over another? “Yeah, because when we did the other graph you couldn’t really see all of them and you didn't really get to do the real number.”
“I think it’s much more accurate (final iteration), because you actually see the reptiles and it is really easy to tell. On that one (first) it is really hard to tell, because some of them are the exact same color. It is easier to tell on the second one, because you can actually see what they are.”
One student recognized we left an important detail out... “It’s missing the key, because they might think the gecko are only 300 but they are actually not. I would put on that each sticker equals 5.”
Reflection can often prompt another iteration- “It’s (Last iteration) way more accurate because Billie fit 300 on there. This one they more know what the animal looks like. One thing I like about that is the dots are colored so like the blue dots are turtles, the red are tortoises, the green are lizards. I kind of like a mix of both of these, I like this one (second) because it is more accurate. I like that one (first) because of the triangles. So maybe we could have drawn the animals in the color for turtles, tortoises, lizards…”
This project includes lots of number thinking (connected to tactile manipulation) & thinking about how we represent data (creating meaning).
This was the first project that I have led where I felt like it served many purposes and had a lot of depth. Even simple things like practicing skip counting (with the blocks and different scales) and figuring out how many data points they have to add for their specific reptile. Students were able to observe, collaborate, and live imaginatively. They worked through challenges, stretching their adaptability, critical thinking, mathematical, and problem solving skills. What I love about this project is how it shows that the PRODUCT that students create doesn’t always show all of the learning; we have to pay attention to the PROCESS of learning as well!