This tweet from Kate Nowak has been on my mind all day:

This part of the conversation on Twitter really got me thinking – in response to the question from Nowak “what is a hook to you?”:

That bit of the conversation caught my attention because I really liked Meyer’s definition, but at the same time I share Nowak’s concern about what happens if kids don’t have the tools to resolve the questions in their mind. However, despite sharing that concern, I occasionally show my kids ideas that are probably way over their head that I think they will find interesting.

My all time favorite example is the Numberphile -1/12 video.

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I’ll never forget my younger son (who was in 2nd grade at the time) screaming at the computer screen “no no no no no.” I loved that something about the video bothered him – deeply and almost physically – even though it was hard for him to identify what had gone wrong.

You can see how much it bothers him in this video (at 6:50) from the project below:

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After I read Jordan Ellenberg’s idea of “algebraic intimidation” in *How not to be Wrong* we talked about the series in this project:

Jordan Ellemberg’s “Algebraic Intimidation”

Ellenberg’s idea was a great way to explain to my younger son that it was ok not to believe the calculations he saw in the video.

Another fun project where the explanation was over the head of both kids was our look at the Chaos Game.

Computer Math and the Chaos Game

Around 2:17 in the video below we start down the path to an amazing result. That result – around 3:05 – was something that I hoped would plant the idea that computer math can be really fun even if the math was a little over their head.

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More recently a Dan Anderson blog post got me thinking about how to use a little computer math and 3d printing to illustrate some math ideas usually reserved for advanced courses:

Those shapes allowed us to have a neat discussion about when some ideas in math work (finding the area of a triangle by approximating it with rectangles), when they don’t (finding the length of the hypotenuse using the same approximations), and how our old friend the -1/12 series actually played a role in the first part of the project 🙂

As with the first two projects, I’m happy to show them a strange result just to show that something interesting is happening. Even if they don’t yet have the tools to really understand what’s going on, I think it gets them thinking. As my older son says around 2:04 in the video below – “things get weird when you go to infinity.”

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Here’s that project:

3d printing and Calculus concepts for kids

To circle back to Kate Nowak’s idea, I’m also a little dubious of trying to lead with ideas when kids don’t have the tools to fully understand them. Probably 95% of the math talks that I’ve had with my kids are not at all like the 3 projects I shared above. Every now and then, though, there’s been a more advanced idea that seemed like something they might find interesting. Sort of a hook to show that math has some amazing ideas that can be both fun and surprising.

You’ve seen it before, but this reminded me of the post Unsolved Problems with the Common Core.

As parents, I don’t think there is any danger of showing kids hooks or openings for which they don’t have the tools to get complete answers. Isn’t most of life like that anyway?