Posts tagged symmetry
I remember that when I was little, I derived a sort of enjoyment, a feeling of accomplishment, from doing math worksheets. For better or worse, my son is the exact opposite. Worksheets do nothing, but turn him off math. And so do most of the puzzles. But he loves stories. So a lot of what I do is tell stories.
The first time I told a cut-and-fold story was a long time ago. We were exploring symmetry, playing mirror games and building with blocks before. That first time I folded pieces of paper only 1 or 2 times before cutting while telling a story. My son really loved it, but then we moved on to other things…
But a few weeks ago I read a wonderful post on the Map is Not the Territory blog. In her Scissor Stories post, Malke not just posted the pretty photographs of symmetry art (like the one above), but wrote a detailed script, a story she told to a group of children. While my stories were monologues, she conversed with children, asked them questions, and helped them notice the math in the story. I encourage you to read Malke’s post. It was so inspirational to me, that the very next day I tried our cut-and-fold stories again, this time in a way Malke’s done it.
The story I told my son was about three friends. He immediately made it about him and his two best buddies and how they were ninjas. Each friend was represented by a square of origami paper. We then folded each square, trying to predict what would happen to them after each fold. Then each square ninja had some adventures along the way and made some tough choices. In the end, we tried to predict what each square would look like. Typically, my son does not like guessing, but he was so into the story, that he kept offering his predictions throughout the game. And, unlike his usual answers of “I don’t know” and “A million” and “17 million and twenty five” the guesses he offered were well thought-out and he could usually explain how he arrived at them.
Unlike Malke, I totally forgot to take pictures throughout the game or record the narrative. But honestly, if you read Malke’s post, you will know exactly what to do and will see all the opportunities for improvisation.
I promise that next time I tell math stories to my son, I’ll keep a better record of them. Would you be interested in these stories? Do you tell math stories to your children? Would you like to share them on this blog? If yes, e-mail me at yelena(at)moebiusnoodles.com If you already have your stories posted on your own blog, please share a link in the comments!
Today’s post comes from the wonderful Malke Rosenfeld of Map is Not the Territory blog. Malke combined her background as a percussive dancer with her love of math in a unique Math in Your Feet program. It is a fusion of math, dance, rhythm and the creative process that helps children build deeper understanding of mathematics.
Malke: On my blog I often write about the times when mathematical inspiration hits but, most of the time, our daily lives are made up of smaller, less dramatic math moments. It’s during these lovely transient events where I really get a good glimpse at how my daughter is thinking, mathematically speaking, and how she is applying her understanding in a number of different contexts.
How we play:
My approach to math exploration at home has been hands-off, necessitated by a child who likes to captain her own ship. Math generally happens in bite-sized pieces around here. While I do influence the process, I hardly ever make formal plans. Instead, I am always looking for new games, thinking about what she might need or want to learn next and also how to introduce new things in a way that has the appearance of being at least 50% her idea. I also leave stuff lying around to be ‘discovered’ or engage in my own pursuits, which inevitably leads to some curious inquiries from the wee bystander.
Here are some examples of the small moments of math that have been happening around our house lately, all symmetry related.
This originally started as a whole lunch, but when the kid saw the design with a whole tomato in the center she insisted in cutting it in half before eating:
I am a big fan of the Reggio Emilia approach, particularly, of a belief that the child’s environment can and does influence children’s learning in very powerful ways. This includes meal time! I like to arrange meals in a pleasing manner and this plate lent itself wonderfully to creating a rotation design of four pieces of a whole, round chicken patty alternating with the tomatoes.
You can also use any items that interest your child to make spontaneous symmetry designs, anywhere you are. One morning I noticed my daughter creating a reflection design after breakfast, utilizing her rock and mineral collection.
This kind of activity can be initiated by anyone, though, as long as it’s done with a playful spirit. The main point is that balance and symmetry are pleasing to look at but also a joy to create. As a parent, you are in the best position to model the spirit of discovery through these playful moments. Often, all I have to do is start an inquiry with blocks, tangrams or other shapes and the kid takes over within minutes. Little jewels of math are all around us just waiting to be discovered at unexpected moments!
Key words that you can introduce during such activities are
Additionally, you can offer these activities, suggestions or make observations during and after play time:
- “Look! I can turn your lunch on this plate and it looks the same no matter how far it turns around!”
- “We’ve got five on one side and only four on the other – let’s balance out our design by making them the same on both sides. How can we do that?”
Symmetry is something that even the very young children can joyfully explore as long as you modify the activities to match your child’s age and developmental stage.
Baby: Cut out large symmetrical shapes to hang above the baby’s changing table or crib. Add a mirror (safe non-breakable) to your baby’s selection of toys and place objects in front of the mirror forming simple designs.
Toddler: Use larger items, model making simpler designs while offering child a chance to help you.
Young Child: Observe child as they play and find those ‘small moments’ as they happen. Initiate reflection and rotation designs at a playful moment – sidewalk chalk at the park (make a chalk outline of your child, have them draw a line down the center of their body) or be on the lookout for examples of symmetry as you go about your day. Take a look at the ‘symmetry finder’ game on Yelena’s blog which is easy to do anywhere and anytime you notice reflection symmetry happening.
Some more ideas for exploring symmetry through playful activities and art include
Butterfly designs using cut paper (Adult narrates while folding and cutting):
“Let’s make a butterfly! What color paper should we use?”
“I’m going to fold this paper in half. I’m cutting out the butterfly shape.”
“Here is what it looks like when the wings are folded. Let’s open it up and see the whole butterfly!”
“Let’s decorate our butterfly! I’ll color a spot on one wing and you draw the same spot in the same place on the opposite wing.” [Or, you could pre-cut some paper shapes – circles, stripes – and glue them on with gluestick.]
Line Designs (Adult says, drawing a line down the center of a piece of paper):
“Let’s make a design on either side of this line using our Cuisenaire rods (or pattern blocks, or legos…)”
“When I put down a blue rod next to the line on my side, you put your blue rod next to the line on your side.”
Adult leads for a while then asks child to lead. You can alternate turns. Try to keep all block placements in relation to the line or other blocks already placed. For older kids, you could use graph paper to position your blocks. (“How many squares is this block from the line?”)
Be My Mirror
Even toddlers would love a chance to be your mirror! Notice your reflections in the mirror with your child. Give your reflection a (gentle) ‘high five’. Notice how your reflection’s thumb and fingers match your own. Use this idea at other times to initiate a Mirror Game with your child. Start by saying, “Can I be your reflection? Let’s face each other and you make a slow movement and I’ll try to copy it.” If your child is ready, see if they can mirror/reflect your movements as well. Use all parts of your body, including your tongue (!), eyes, eyebrows, elbows, knees, etc.
If you haven’t had a chance to check out Malke’s blog, you are going to love it. Not only does it have lots of ideas for exploring math all around us, but also wonderful stories that, like “Small Moments of Math” and “Small Moments of Geometry” help us, parents, notice the rich mathematical opportunities in our children’s lives.