Talking Math with Your Kids has been on something of a summer hiatus as I’ve geared up for Math On-A-Stick at the Minnesota State Fair. It has been a wild ride.
I have spent the last four days playing and talking math with kids of all ages for eleven hours a day.
My number one message coming out of this work is Let the children play.
Have a peek at our flickr photo albums to see what’s been going on. Here’s a sample (Thanks to Kaytee Reid for sharing these beautiful images).
I have been paying close attention to how children behave in this space we’ve built. I’ll just write about the plastic eggs today, but they stand in as an example for all of our activities.
When children come to the egg table at Math On-A-Stick, they know right away what to do. There are plastic eggs, and there are large empty egg cartons. The eggs go in the cartons. No one needs to give them instructions. (This is by design, by the way.)
A typical three- or four-year old will fill the cartons haphazardly. She won’t be concerned with the order she fills it, nor with the colors she uses, nor anything else. She’ll just put eggs into the carton one at a time in a seemingly random order.
But when that kid plays a second or third time, emptying and filling her egg carton—without being told to do so—she usually begins to see new possibilities. After five or ten minutes of playing eggs, this child is filling the carton in rows or columns. Or she’s making patterns such as pink-yellow, pink-yellow… Or she’s counting the eggs as she puts them in the carton. Or she’s orienting all of the eggs so they are pointy-side up.
The longer the child plays, the richer the mathematical activity she engages in. This is because the materials themselves have math built into them. The rows and columns of the egg crate; the colors and shape of the eggs; the fact that the eggs can separate into halves—all of these are mathematical features that kids notice and begin to play with as they spend time at the table.
We have seen four-year-olds spend an hour playing with the eggs.
I have observed that the children who receive the least instruction from parents, volunteers, or me are the most likely to persist. These are the children who will spend 20 minutes or more exploring the possibilities in the eggs.
The children who receive instructions from adults are least likely to persist. When a parent or volunteer says, “Make a pattern,” kids are likely to do one of two things:
- Make a pattern, quit, and move to something else
- Stop playing without making a pattern
We adults have a responsibility to let the children play. We can be there to listen to their ideas as they do. We can play in parallel by getting our own egg cartons out and filling these cartons with our own ideas.
But when we tell kids to “make a pattern” or “use the colors”, we are asking the children to fill that carton with our ideas, rather than allowing them to explore their own.
Here are some ideas children have explored in the last few days. I look forward to the next week’s worth of wonder. (Photos all shared by visitor and volunteers through Twitter and Intagram—handles are in the image titles. Many thanks to all for your generous sharing.)
Hey Chistopher – Beautiful, just beautiful!! Thanks my friend. Hope to get to state fair to see you☺
Russ
Thanks so much for sharing your experience Christopher. Hearing that the kids who received the least instruction were more likely to persist in the activity than those who received instructions was especially powerful. I totally agree—let the children play!
Christopher meet Montessori, Montessori meet Christopher. You have much in common.
(Somewhere there at the fair are representatives of Maria Montessori.) Best.
“The children who receive instructions from adults are least likely to persist. When a parent or volunteer says, “Make a pattern,” kids are likely to do one of two things:
1) Make a pattern, quit, and move to something else
2) Stop playing without making a pattern”
That is consistent, I think, with Alfie Kohn’s writing and cited research on problems with rewards. When an adult sets an arbitrary, extrinsic goal, it may suck the life out of the task for the child (response #2). Or it may give the child the sense that the entire point is to hit the goal, at which juncture there’s nothing more to be seen, done, thought about, etc. (response #1).
The assumption that kids, particularly young kids, need an adult to figure out what’s worth doing in a given situation seems highly problematic to me. It appears predicated on notions that, left to their own devices: 1) children won’t do anything much worth doing; 2) children won’t do anything that “I” (the wiser adult) will value; 3) children won’t do anything that “I” (that wiser adult again) will be able to praise honestly – after all, we don’t want to be giving out trophies for “participation,” for heaven’s sake! I suspect there are other such assumptions operating for many adults, most of which are likely to be soul- and curiosity-killing for kids.
Check your assumptions. You’re assuming a world that has no children with developmental challenges.
Be careful with your judgments.
Since you seem to acknowledge that this article and my comments on it don’t apply to you or your children, I think it’s rather snide of you to weigh in with “check your assumptions” (echoing, perhaps unintentionally, one of the latest politically correct mantras – “Check your privilege” – which, while no one has aimed that one at me as of yet, I take to be intentionally shaming anyone who is targeted as insensitive to a spectrum of p.c. sensibilities.
The conversation here clearly focuses on typical teachers (and some parents) in typical classrooms with students who do not have ASD and who are nonetheless subject to far too much direction without giving them any space to explore, think, play on their own. If none of that applies to you or your children, what do you expect to gain here with your comments?
I don’t see Christopher, myself, or anyone else here judging you or your children. You have jumped into a conversation that wasn’t about you, your children, or those like you and claimed that somehow “free range” parents are “a little too quick to judge.” That might be so, but there’s a rather enormous spectrum of “free range” parenting, and I don’t think that was what anyone here was advocating. Rather, the point was that, very specifically, many educators (and in this regard I’m including parents) seem to operate with beliefs that kids absolutely must have guidance, direction, and motivation from adults. And Christopher was suggesting that there’s a lot to be gained by backing off and seeing what happens without doing that. Nowhere does he state or imply, however, that directed play or learning has no useful role. So there is room for more “direct instruction.” However, mathematics educators like Christopher have become painfully aware that the tendency in this country has been to err on the side of little or no free exploration. There are people (such as the Direct Instruction group at University of Oregon) who explicitly sell (and I use that word advisedly) curricular materials that utterly eschew anything that isn’t teacher-centered and teacher-directed. And Christopher is trying to counter that and similar notions here, though in a context most people would see as light and harmless.
Doesn’t apply to you and your children? Super. No one was pointing a finger at you here. If others have done that, I’m sorry for your pain, but it wasn’t coming from this blog or its readers. Someone reading about non-ASD children and their parents and complaining that we insensitive boors just aren’t considering your feelings reminds me of a line from an Elvis Costello song: “He stands to be insulted and pays for the privilege”
“Let the children play” applies to children of all ages. Thanks for that reminder!
It makes sense that kids will stop playing when directed to “do” something (which they already were). We need more math play in the schools.
AWESOME!!! That’s why Cognitively Guided Instruction, CGI, works! Kids understand math 🙂
Deb, could you elaborate on your comment? How is what Christopher described an example of CGI, or if it isn’t, what about CGI connects with what he describes? Thanks in advance for your help.
I really like this! Making learning fun for kids is important!
I absolutely agree! It’s amazing how wonderful of a job kids do at learning when left to explore on their own (with some supervision of course).
I love this,my son has been struggling with math,but when i read this he is much better now,because i tried to mix learning with fun.
It would help tremendously if you could add something about children with developmental challenges. For example, many children with ASD cannot play independently and need lots of direction. Even kids that appear “normal” to the average person on the street can have hidden challenges.
I understand your main point and agree wholeheartedly with it, but the way the article is currently written makes for some disheartening reading by parents of children with such challenges. Free play is great but it does not work for all children. We need to stop stigmatizing kids with ASD and similar diagnoses and stop shaming parents who are doing what they need to do for their children. Some “free range” parents are just a little too quick to judge.
I understand that your article isn’t meant to do that but as someone who has multiple family members with ASD, articles that tout the benefits of free play without acknowledging the realities that it doesn’t work for all kids struck a nerve. Seen it too many times. It’s frustrating. We need to spread understanding about ASD.
Thanks for adding to the conversation, David. There is certainly a lot of nuance and exception that my title for this piece leaves out. I will absolutely own my ignorance of the challenges of living with ASD, and of the challenges of living with children with it. Please know that my words were not intended to be exclusive of your or others’ experiences. I apologize if they came across that way.
I didn’t write about it in this piece, but we went to some effort to make Math On-A-Stick a welcoming space for all sorts of children. A young blind girl had a ball on the Pattern Machines, for instance; and there was at least one Deaf child counting on the Stepping Stones in ASL (and others in Spanish, and Hindi, and…)
One quick story about a boy with ASD who visited Math On-A-Stick. He is about 7 or 8 years old. His mother told me that he loves numbers. The Minnesota State Fair can be a bit of an overwhelming, overstimulating place for people of all types; I can only imagine what it’s like for someone who is prone to sensory overload and who struggles to separate the meaningful stimulus from the meaningless. This boy spent about 20 minutes on his knees outlining the numbers painted on the stepping stones with the palms of his hands. For him, this was definitely a soothing and comfortable place in the midst of tremendous busy-ness.
Thank you! I’m so glad I found your site. This is a perspective that I need to remember.
Learning through exploration is extremely valuable and grossly overlooked in the modern education system. Teachers are overwhelmed with trying to keep up with the demands of the curriculum and often take the shortest route towards the goal (i.e greater explanations and fewer expectations).
The onus falls increasingly on parents to create opportunities for exploration and independent learning. Thank you for encouraging teachers and parents to step back and allow children to develop thinking skills.
A friend of mine just shared a wonderful idea with me how to use Lego to show kids fractional arithmetic. I’d like to share the image with you but I don’t know where to send it. Let me know and I’ll send it over. Thank you for your wonderful blog (I have no kids yet but it’s an interesting topic)
Hi laura sophie! I’m guessing you have in mind this image right here. You can imagine such things make their way to my Facebook page on a regular basis! That’s because they are always welcome. Probably the easiest way to share images and links is through the Talking Math with Your Kids Facebook page.
Thanks for stopping by (no children required!) and for sharing the interesting and fun mathy things you find in the world.
We have so many plastic eggs from Egg surprise. 🙂 I just let my kids play and fill them with stuff or make patterns. The tray is a great idea. I’LL BE USING THAT. 🙂 LOVE your site. 🙂