Allowing Time for the Gears to Turn

This post is about patience, trust, and discomfort. It’s about having patience with your child’s learning process and trusting their innate curiosity and unique ways of thinking. And it’s about dealing with your (our) own discomfort as parents with not having all the answers and not getting them quickly.

The other day I pushed this puzzle across the table to the 8-year-old (yes…he’s 8 now!):


It’s from the puzzle book Without Words by James Tanton. The magic of this book is that there are no words to explain the puzzles. (An aptly named book, eh?) You’ve got to figure out what you’re being asked to do by looking at a few examples. Except for some open-ended hints at the back of the book, there is nothing else to guide you. The fact that there isn’t even an answer key so that you can check your work really irked my impatient “am-I-right?” self.  I took a deep breath and tried anyway, because that’s the example I’m trying to set…

So, back to the puzzle that I pushed over to the 8-year-old. He looked at the examples. He said “Oh. That’s easy,” and he sailed through the first couple puzzles. Then he hit these:

He tried to draw a path cutting through a corner. But we agreed that based on the examples, that didn’t really seem to be allowed. Then he tried to go outside the box. But again, that didn’t seem to be allowed. So then he gave up. And, frankly, I was a little bit bummed that he did. Wasn’t my goal to teach persistence? Stick-to-it-tiveness? My kid was not sticking to anything! Truth be told, though, I also wanted to give up. I wanted to look in the back of the book for the answers so I could coach him in the right direction. But the answers weren’t there. So, we closed the book and moved on to other things in our day.

Here’s the thing, though…the thing I didn’t expect. Two days later, while eating breakfast, the 8-year-old pulled the puzzle book back out and opened to the page we had been working on. He said, “Look, Mom. This is how you do it.” And he proceeded to trace a route through the grid that worked.

My jaw dropped. Seriously. It really did. How did he figure that out? After we had given up? So I asked.

“How did you figure that out?”

“I’ve just been thinking about it for a while, Mom.”

Oh. He hadn’t given up.

I had.

He just took a break from focusing on the problem, and his mind, given the time to noodle around at its own pace, had found a way. I know that this is how the mind works. I know this is how MY mind works. I just needed to be reminded.

Remind yourself often of this. It is hard for parents to step back enough to give the kids time to let the gears turn. Time to noodle around. Time to marinate in a problem. (Pick your metaphor…take all the time you need!) For some reason, this is particularly true with math. Have you ever asked your child how much 2 + 2 is? 32 + 2? 198 + 13? How much time did you allow before giving her the answer yourself? Or starting to explain how to arrive at the answer? Perhaps you can remember one of your own teachers asking such a question in class – if you weren’t the one who processed it and raised your hand first, then you may have been one of the many who (wisely, though unfortunately) didn’t even bother to try because you knew the answer would be given before you could even consider the problem. My son was fortunate that I didn’t have the answers to the puzzle we were playing with, because without intentionally planning to, I allowed him the time he needed to let his gears turn.

(Mathematically…puzzles like those in Without Words are great problems to play with. Removing the words doesn’t just make it more accessible for some, it also requires developing good observation skills, mental manipulation skills, and non-verbal analogy skills. The problems in this particular book are all connected to deeper mathematical topics…parity and probability, for example. For younger children, the puzzles can begin setting a foundation for deeper understanding of these topics later. For older kids and adults, the puzzles can bring another dimension of meaning to topics that have already been “learned” in school. Whether this interests you or not, though, is irrelevant. The puzzles are engaging regardless of our being aware of their mathematical connections.)

46 thoughts on “Allowing Time for the Gears to Turn

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  1. Good thing I’m never impatient. Or over eager to get the right answer. Or excited for my kid to get stuff right away. HA! I wish. Great reminders. Thank you!

    Liked by 6 people

  2. So when I bought my sons a Lego Movie Lego set, I was tempted to crazy glue the darn thing together. So it is only natural that I am slightly annoyed you did not include your son’s solution right?!?! 🙂

    Liked by 1 person

    1. Ha! Thank you for making me smile. One of the problems pictured has no solution. I was actually a little disappointed when I learned that…but then it gets interesting again as you try to figure out how to describe what makes one of these puzzles solvable or not.

      Liked by 1 person

  3. Great thoughtful post, thanks. I must admit when I write a blog post or short story, I often leave it for a day or two, to let it ‘marinate’ before I edit; sometimes I come back & change it immensely! What a lovely example of being taught by our children, thank you from Australia 🙂

    Liked by 4 people

  4. That sounds like a neat book–I’d have to look that up and give it a shot sometime (wish I had money now, dang it). But wow–I’d love to try it myself. Knowing me, I’d sit there and stew and lose interest instead of being smart and just coming back to it later. Maybe that’s what I need to get better writing habits–learn how to deal with being confounded by something a while and then it’ll get you.

    Liked by 2 people

    1. I think it’s about finding a balance between challenge and interest, too. If one is interested enough, higher levels of challenge are welcome, even invigorating.

      Liked by 1 person

  5. Thanks for this post. I was struggling with my daughter regarding math . I too wasn’t a keen learner of math so always assumed that she will give up too. This article helped and I will try and change my teaching method before it’s too late.

    Liked by 4 people

  6. I thoroughly enjoyed reading this article and found it engaging. Being patient takes patience itself and even more so with your children which made me think how I come across as a father to my own and if can improve on my own patience in regards to their needs, whether with school work or life in general. Thank-you for penning this and love articles that make you think and how can improve yourself and towards others.

    Liked by 2 people

  7. Right there it sounds like you are setting good examples for your kids. If they see you actively trying to improve what you think needs improvement in yourself, they will learn it is possible in themselves (and that we are all, of course, imperfect)!

    Liked by 1 person

  8. An interesting post! Mathematics have never been my forte, and these puzzle books sound fascinating! Definitely going to have to try one out and try to give myself some time to analyze the problem. I, too, tend to give up.

    Liked by 2 people

  9. Love the first pic; it’s not only reflect to child learning, but also our life learning; need a lot of patient when life just go a bit downward and you know you can go through it just need time

    Liked by 1 person

    1. For the first one…there is no solution. Which is part of the puzzle solving process, because the next question to ask is WHY? What is it about some of these problems that allows them to be solvable, while others are not?


  10. Also, i loved your post and how their mind works is amazing. Sometimes when I am with my niece, she makes me realise that at times we miss the most obvious things. Kids these days are so sharp.

    Liked by 1 person

  11. Beautiful post! Thank you for sharing this. This is an important lesson for teachers as well as parents. If we can design classrooms that do not require all students to move along at the same pace, we can create learning environments that tap into the ability of brains to noodle over something more effectively.

    Liked by 3 people

    1. Yes. Yes. Yes. It is so very hard even as thoughtful adults (and especially as adults in a data driven age) to remember this and to believe that children will naturally explore and absorb and learn because that is what they are designed to do. It is far too easy and common to believe that we must construct the same rigid learning environment for everyone in order to be fair and successful. The evidence shows otherwise.


  12. Though I am not a parent, this post makes so much sense! Sometimes I stress over making a post come together, or writing…and forget to give my mind time to breathe and let the gears turn at their pace. Thanks for the reminder! Great post!

    Liked by 2 people

  13. I love this post. I’m a tutor & I would love to use this concept with some of my students. One thing though; how do you know if what you’ve done in the book is right if there are no answers? But yeah, I shall check out your link about this workbook. It sounds like a great concept.


  14. That used to bother me, too…how do I going to know if I got the answer RIGHT? Specifically, this book gives hints to help out in that department. Generally, I learned to trust myself and my own capabilities and process, and I learned to let go of needing to know the answer NOW. It’s a different process with a different purpose and one that I don’t think we or our children get enough practice with. In fact, I have started using these types of puzzles purposefully in my own tutoring sessions, and we often leave the problems unsolved to come back to the next time. My student is often frustrated with that – he wants the answer NOW, too. So, that becomes part of the lesson. Later, when he has his “ah-ha” moment (which sometimes comes when he’s home, noodling over the nagging problem in the back of his mind) we discuss the problem solving journey.

    Liked by 1 person

  15. I work as a preschool teacher at a Reggio Emilia-inspired school, and I think you really hit the nail on the head. In my experience thus far, giving them the time to think can sometimes make the difference between rote learning and real, lasting, deeper-level learning. Every child’s pace is different, and respecting that pace is an essential aspect of giving them what they need to feel comfortable in a learning environment.

    Sometimes I have to remind myself to stop talking and let them be with their silence when I ask a question. It is easy to forget that, especially at a young age, their minds are always at work even if their mouths and their bodies aren’t.

    I need to get my hands on that book, it looks fantastic.

    Refreshing message in a well-written post, I look forward to reading more.


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