Third and last post in this group of postings that are meant to help me clarify and remember where I am at in my thinking about the work that I do with students in schools.
After years doing bookmaking projects to make with children, I realized that many of the art and design skills I use every day align with some of the skills that mathematicians aim to develop. Part of the reason this alignment caught my attention is that I have a great affection for the mathematical thinking that I want to encourage.
In the relatively short time I am in schools with students, I hope to have a positive influence. My experiences and interests have led me to an unusual place where I can use colorful, artful materials to help kids create projects that enrich mathematical thinking. My place isn’t to teach art or teach math, but rather to plant seeds of engagement and excitement.
It seems to me that children intuitively understand concepts that are recognizably both artful and mathful. More and more, my thinking is centered around how to engage and encourage that which is already inside of students.
For instance, kids absolutely understand the idea of scale. They realize that their hands are the same, but smaller versions, of dad’s hand. Same with their shoes, their shirts, everything in their world.
There is no room in the school day for formal study of scale until the intuitive connection to it seems to have long disappeared. Turns out that scale doesn’t only have to do with making large models smaller, but it also is intrinsically connected to relationship thinking, predictive thinking and to the recognition of trends.
Discovering that children are naturally inclined to embrace symmetry has been another exciting area for me to explore with kids. When making books or other structures with students, there is nearly always symmetrical folding going on. I have choices when I teach folding: I can introduce what I do as step-by-step directions, or I can nudge the students to see the symmetry of what’s going on so that they can predict for themselves what the next fold will be. The latter way gets them to see the project in a more global way, draws them in because they have understanding which includes them, rather than being like a little robot that is being programmed to do this then do that.
Symmetry is deeply embedded in math thinking, so I have been talking to children about connecting symmetry to what they are learning right now in math. Specifically, I talk to them about how when they are looking at an equality, such as 5+3 = 8, that this expression is balanced on both sides. It can also be understood as 5+3= 4+4. If I add 6 to one side of the equation, then I have to add 6 to the other side so that the symmetry of the equation remains true. Talking to students about equations as balanced forms just might help them, later on, when they will have to maintain balance in an equation to solve for x.
As far as I can tell, the only time symmetry is formally taught in elementary school it’s part of the examination of lines of symmetry in regular geometric objects. I like to be able to at least offer hints that symmetry has richer applications.
Children seem to have an innate sense of parts that make up the whole, which seems antithetical to the reality that teaching fractions is unfathomably difficult. Is it possible, though, to focus on having students work fractionally from a very early age, way before we introduce the numbers that describe the fractions?
Playing with blocks was one of my favorite activities as a kid. I certainly noticed halves, fourths, and wholes, but I didn’t make this connection between the blocks and fractions until I was much older. This makes me value not only exposing kids to artful mathematical thinking, but also, sooner rather than later, to help students connect their hands-on activities to the numbers.
There’s more I have to say about all this. but I reminding myself that I have to get to work getting ready for classes.
Am going to end with my list of ideas that I want to keep in mind, not all of which are explained here. Maybe I will get to writing about all these here and there through my teaching season. If not, at least I will have them here to keep me on track.
Art/Math concepts to explore with kids:
- Pattern recognition
- Pattern Building
- Continuous magnitudes
- Relationship thinking
- Problem solving
- Parts of a whole