# I’m not impressed.

(An earlier version of this post contained a picture of a child’s work, the child of a friend. I have checked with my friend, and she has asked me to remove the picture, which I am happy to do. I should have asked her permission from the start. I am sorry I didn’t. I have also removed my discussion of the picture, and written a different beginning to this post. I’ve kept the original comments, though.)

I wear two hats. I’m a teacher, and I’m a parent. I see the world of children and learning from under both brims. One pattern I notice is that everybody gets excited by student learning, but we often get excited by different aspects, and use different language to describe what we see.

Among my teacher friends, we talk about moments where we see a child trying to make sense, so we can analyze it. What made it possible? What’s the child thinking? How can we understand what he or she did or said? Where’d that thinking come from? What would be a good question to ask next? For example, this year on twitter, I shared this picture and my daughter’s thinking about it:

When I asked her how many meatballs there were, she counted the top row, 4, and the bottom row, 4, and said 4 + 4 = 8. Then she counted the left column, 3, and the right column, 3, and said 3 + 3 = 6. She skipped over the middle 2 meatballs, added 8 + 6, and told me there were 14 meatballs in all. When I asked her about her count, she said,

“I counted it that way because, when you count arrays, you count the corners twice.”

She had me count the array so she could explain. When I counted 4 meatballs in the top row and 3 rows down the left side, she said, “See, you counted that corner one twice!” I had an aha! moment because I realized she picked up that misconception when watching me count arrays. Her mistake helped me understand her thinking, but also my teaching. I shared it on twitter, and we had a lovely chat about it.

Among fellow parents–on facebook, at the playground, and at birthday parties–I hear very different talk about children’s learning. I’m generalizing here, of course, but I hear a lot more talk about accomplishments than I do about thinking; a lot more talk about achievements than I do about mistakes. I hear a lot of fixed-mindset language, much of it designed to impress other parents:

“He’s very intelligent. I mean, he’s doing double-digit multiplication already! I don’t remember doing that until 3rd or 4th grade!”

“She’s such an avid reader. She read Harry Potter when she was six!”

The desired response, and the one I tend to see and hear, is some variation of, “Wow! That’s so impressive!” Used this way, “impressive” doesn’t mean, “that’s really thought provoking and memorable, and has made an impression on me.” It’s more like, “Wow, your child is advanced/smart/ahead!”

So what does that usage say about learning, and our goals, and what we value?

If the goal of students’ learning is to memorize and recall facts, trivia, procedures, data, vocabulary, then we have plenty of markers and milestones, a whole ruler full of age-based hashmarks. Parents can be impressed when their children say or write or do (I can’t bring myself to use the word “learn” here) something that seems “advanced” for their age. “Jenny knows all her capitals already? Impressive.”

If the goal of students’ learning is for them to understand ideas and concepts deeply, and to build connections among those ideas, then we care less about those tangible achievements that impress friends on facebook. From the parents’ point of view, we have learning where the adult gets to listen, join in, interact, enjoy, or participate, rather than evaluate and compare to an age-based yardstick.

For example. One day on the way to kindergarten, my then 5-year old daughter Maya said, “4 and 2 make 6, and 3 and 3 make 6, and 5 and 1 make 6. How will I know if I’ve found them all?”

This is an amazing question. Was I impressed? Hmm. That’s honestly not the word I’d use. I was excited! I knew her question was the beginning of something good, not the end. I am usually more excited by questions than answers, and, “How will I know if I’ve found them all?” is such a mathematical question to ask! We spent much of the rest of the car ride exploring different wrinkles of it. For example, once she had found them all, she decided to figure out how many combinations there were:

“Mommy, is 4 and 2 the same or different as 2 and 4?”

“What do you mean?”

“Well, I am counting how many ways to make 6, and I want to know if they’re the same thing, or if I should count them separately.”

“What do you think?”

“Well, sometimes yes and sometimes no.”

“What do you mean?”

“Well, I’ve noticed that, when I add, it doesn’t matter which number I start with. 4 and 2 is 6, and 2 and 4 is 6. I usually start with the bigger number because then I have less to add on so it’s easier, but it doesn’t matter because I end up with 6 either way. It doesn’t matter what order they’re in.”

“Then why’d you say sometimes yes and sometimes no?”

“Because if I have 4 stickers and Daphne has 2 stickers, it’s different than if I have 2 stickers and Daphne has 4 stickers! We still have 6 stickers altogether, but it’s different because one of us gets more and one of us gets less, depending on which one has 4.”

There are so many rich and wonderful mathematical ideas in this conversation: the commutative property of addition, contextualizing and decontextualizing problems, counting strategies, permutations and combinations, and so on. Yet, the numbers weren’t “impressive” or “advanced,” were they? We were talking about sums to 6, numbers I think Maya chose because she could compute them comfortably in her head.

I tell all the parents I know about the Talking Math With Kids blog because Christopher does a lovely job showing adults how to engage in a conversation like this with children. Tell less. Ask more. Listen. Value the child’s thinking.

I think the first step for parents might be to evaluate less and join more.

If the outcome of a conversation about your child’s thinking is either to feel impressed or disappointed, then you are evaluating.

If the outcome of a conversation about your child’s thinking is that you and your child now know each other a little better, you understand how your child is making sense of the world, and/or either or both of you sees an idea in a new way, then it sounds like you joined.

If the conversation was short, and involved the child showing or telling you something and you remarking on their learning, you evaluated.

If the conversation was longer, rambled some, could have drifted off or kept going or even resumed after a break, then you probably joined.

If you left the conversation eager to tell someone else what your child did or said because you think that person will be impressed, you evaluated.

If you left the conversation thinking and wondering, then you joined.

If we were evaluated by our parents as kids, we tend to evaluate. Joining takes practice. It might not feel natural at first. But I am not exaggerating when I say these incidental conversations about learning–the ones that happen while my kids and I are walking down the street or driving in the car or setting the table–are some of my most treasured memories as a parent. The best way I know to invite these conversations is to stop evaluating how our kids compare or measure up, and just listen to them.

Updated:

I loved this quote, in a comment from Ed:

From the memoir of Nobel Prize winning physicist, Surely You’re Joking, Mr. Feynman:

He … taught me: “See that bird? Its a Spencer’s warbler.” (I knew he didn’t know the real name.) “Well, in Italian it’s Chutto Lapittitda. In Portuguese, it is Bom Da Peida. … You can know the name of the bird in all the languages of the world, but when you’re finished, you’ll know nothing whatsoever about the world. You’ll know about the humans in different places, and what they call the bird. So let’s look at the bird and see what it is doing — that’s what counts.” I learned very early from my father the difference between knowing the name of something and knowing something.

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## 0 thoughts on “I’m not impressed.”

1. I wonder why you drew only 4 circles for the gas but way more for the solid. Are you thinking that solids contain more “stuff”?

1. That’s a great question, Matt. The more I look at this picture, the more I see the misconceptions it creates, rather than understanding.

2. Such a simple distinction, between joining and evaluating, but a really useful signpost.

(I guess the facebook comments were in at least in part because we feel it’s right to give each other positive strokes?)

1. Thanks, Simon! And have I told you lately how impressed I am with your blog? 😉

3. “A change in perspective is worth 80 IQ points” – Alan Kay. Your point about conversations is spot on – kids need to communicate with the wisdom of the past generations to understand what they are seeing, even if it’s a simple lever, not atoms.

“Unless this classroom has access to some pretty amazing technology for a public school, they’re not observing the atomic structure of the states of matter.” But kids can easily interact with atoms via a computer models. They can observe, make virtual experiments, conjecture, and make conclusions. This is also a method of communicating about science.

Oh, and there are four states of matter, not three.

1. Maria, thanks for reading, and commenting! I’m going to push back on your argument about computer models, though. What evidence does the child have that the model represents reality? If you ask her, “How do you know this model is a good one? How do you know it shows what’s inside this table (or glass of water, or comet trail, or air we breathe)?” what will she answer?

Because my teacher told me so?
Because my computer told me so?

It’s more important to me to teach kids scientific thinking than any particular scientific content, at any age. I want them skeptical, and looking for evidence that they can observe and gather directly. That’s why I’d much rather kids experiment with water in and out of the freezer, in a plastic bag in the sun, etc. than toy with a computer model.

Dan Meyer likes to share George E.P. Box’s quote: “All models are wrong but some are useful.” It’s a great quote. At some point, computer models of molecular structure are useful. I’m not convinced that point is when a child is 7, has little context for understanding molecules, states of matter, energy, or models.

My brother-in-law is a fighter pilot who uses a simulator for training. He has the experience and knowledge to know the benefits of the simulator, and its limitations. He has a framework for understanding it. Why rush kids into the model without that framework?

1. Love the discussion, Tracy! I gather several points from your comment. First, that kids need to learn overarching scientific methods (such as skepticism or hypothesis testing) more than they need to learn any particular content area. Second, that kids need to learn to test models for validity, reliability, and other aspects that measure how wrong the models are (and they are all wrong to a degree).

It is interesting to note that both points apply to both physical and virtual worlds. Children can learn to test hypotheses of how Angry Birds fly off their catapults using the same overarching scientific principles they would use to analyze their hypotheses about a physical catapult.

But here is the third point – cross-world or cross-context applicability. That’s where we have to be careful with models, in particular virtual ones, but also our models directly derived from the physical world. Newtonian physics was good enough for the world of planet-side physics and even the Solar System neighborhood (explaining how the Moon goes around the Earth). For that matter, Ptolemy’s model with the Earth in the center was good enough for a time. But for the world of the interstellar physics, the validity of those models is too limited. This applies to our mental models of both virtual and physical events – like young kids thinking that the wind blows because the trees move, or adults thinking that astronauts don’t fly off the Moon because they wear heavy boots (hilarious story to Google). But the virtual worlds can have realities that are “more different” so to speak, and it’s a big distinction.

Why offer kids virtual models early on, despite that caveat about very different realities? Because…
– Many kids do very much want to experience what it’s like to be a fighter pilot or to dive within molecular structures (“Magic School Bus” comes to mind)
– Virtual modeling is integral to many modern professions and everyday life, so kids need to be savvy about that – to hone their skills in evaluating, judging, and criticizing virtual worlds
– Computer modeling tools give kids power to imagine, build, and design their own worlds in ways significantly different, and complementing, physical and social modeling (e.g. big data or linked multiple representations)

As a math educator, the third reason is especially close to my heart. In mathematics, we build our own worlds – like the world of complex numbers or Lobachevsky geometry. I want young kids to have that power, of building their own world using tools that can also apply to scientific explorations.

1. That’s such an interesting take. Thank you so much for your comment. It really makes me think!

I’m all for children building their own worlds, using any tools they like. Sometimes the right tool is their imagination. Sometimes it’s a physical tool, (straws, blocks, cardboard boxes). Sometimes it’s a technological tool. Great!

I am often in the position of playing the skeptic about any “thing” used in teaching, whether it’s a manipulative, a pre-packaged curriculum, or an app. It’s never personal. It’s a default position of mine. I need to hear, exactly, what the added value is before I put a child in front of a screen, every time. Sometimes, it’s there, and it’s worth it! Sometimes, it’s tech for the sake of tech. For me, the learning and teaching always come first, before thinking about tools.

So, if we want a child to have a chance to build a virtual world of his own and time or space travel (like on the Magic School Bus), then I’m OK with them noodling around on a computer model. Why not? But that doesn’t mean I think that a school district should adopt that tool for teaching content.

And, at the end of the day, I’m much happier with kids having face-to-face interactions, working with other children and adults and on their own, using trade books and wooden tools and their bodies and minds, spending lots of time outdoors, and having long stretches of time in which to think. Tech is part of our world, and should be part of theirs too, but it is certainly not the cure to our educational woes.

All that said, how nice to have this virtual conversation!

4. Reblogged this on Strike Days Adventures in Home Learning and commented:
Explore all the wrinkles: Value the child’s thinking!
I’ve been too busy to blog, busy working with e kids at Little House on the Co-op. So, sorry if you’ve been waiting for another post ;(. There are a few brewing, but for now here’s a reboot. I’m thrilled to have discovered this one that for me highlights so well the importance of honouring children’ innate wondering.
the answer to the question is another question.
Trust.

5. Ed says:

From the memoir of Nobel Prize winning physicist, Surely You’re Joking, Mr. Feynman:

He … taught me: “See that bird? Its a Spencer’s warbler.” (I knew he didn’t know the real name.) “Well, in Italian it’s Chutto Lapittitda. In Portuguese, it is Bom Da Peida. … You can know the name of the bird in all the languages of the world, but when you’re finished, you’ll know nothing whatsoever about the world. You’ll know about the humans in different places, and what they call the bird. So let’s look at the bird and see what it is doing — that’s what counts.” I learned very early from my father the difference between knowing the name of something and knowing something.

1. Ed, that is a perfect quote. Thank you so much for sharing it! I’d forgotten that passage.

6. It’s interesting that part of what seems to bother us is the abstraction — the facts the kid is stating, or the task they are performing, aren’t enough in themselves to tell us much about how he or she is really thinking about and experiencing it. We might care about what a child says about Harry Potter even if we don’t care what age they are when they can read it.

I love Jo Boaler’s online classes (one for teachers & parents, one for students) on how to learn math, but this tweet, https://twitter.com/pamjwilson/status/510172661310586880 , bothered me the same way. The writing establishes this child had good basic comprehension of what the course is trying to tell her/him and can summarize it back to us, but does this child really see herself/himself differently as a math student? We can’t tell yet.

1. Julie, I agree…products alone are *never* enough to go on. We can’t tell what a child has learned without conversations and observations too!

7. A story that I think dovetails nicely here. When my 11 yr old boy was 3 we spent a great deal of time at Barnes & Noble at the train tables in the book section. One morning two moms and their children (the kids looked to be a little older than my boy) were there. Mom A was telling mom B about how important it was to get a certain set of flash cards to start quizzing her child. Mom B seemed a bit anxious about this conversation. Mom A asked her child – ‘Honey, how many sides does a nonagon have?’ and the child dutifully answered ‘ Nine ! ‘ This made mom B look even more anxious. I could not stand it anymore so I interjected and told both moms that I was a high school teacher and we hardly ever mention nonagons.

It amounted to no more than a parlor trick – a way to feel good about her child and make others feel anxious about their children. I have no idea if either mom remembers this conversation, but I sure do.

1. Thank you for that story, Jim. I think, especially in certain populations, that kind of talk between parents is really common. I was in a bookstore yesterday and there was a whole wall of flash cards, make your baby a genius workbooks, and other stuff preying on parents’ anxiety and competitiveness. I wanted to take a picture of it and post it online with the caption, “I’m a math teacher, and I’d never use any of this stuff with my kids. Keep your money, and count the stairs on the way out!”

2. As someone who has a lot of “Mom B” friends (and maybe some “Mom A”s as well), could I make a little request? Instead of criticizing something that the parents are doing, give them an alternative that points them in a better direction.

You’ve got a lot more experience than I do, so I’m sure will have better suggestions, but maybe here you could have suggested they make and explore hexaflexagons? It will sound related to nonagons, but set them off on an investigation where there won’t be right answers, the parents won’t be experts, the whole thing is really fun, and there is a natural link between math and art.

8. Here is another perspective that could be helpful: what are you trying to do as a parent? For me, having these kinds of conversations (how many ways can I make 6) is the objective, not a means to another end. Do I really care if they can add 2+4 = 6 or 257+139 = 396 at any particular age? No. Do I really care about having them ask questions, explore, be interested and curious, be excited, be joyful? Yes to all of those. So, when they are doing those things, obviously I would get excited and involved. And the cool thing about kids is that all of that comes naturally (until we screw it up?)