3D thinking - early and often!

I'm guessing that if you grew up around the same time I did, you experienced a similar progression. Master the 2 dimensional shapes and their measurements (perimeter and area) and then move on to the 3 dimensional shapes and their measurements. Throughout this process, at least in my elementary years, I'm fairly certain not a single elementary teacher I had in front of me had a degree (major or minor) in mathematics. So they did what they'd always done, show some pictures in books and talk about formulas and calculations. Once we made the leap to 3D though, my brain really struggled to "see" what was on the paper as taking up space - even with the paper nets we cut and taped into 3D objects.

Do you suffer from the same affliction I do?
I can't say that my parents didn't ask me to do this often enough or not, but I certainly needed some more practice!

Don't shy away from letting your child do this kind of spatial thinking. Have them order containers smallest to largest, and then test it out with water! Are you SURE everything in that "smaller" container will fit in the next one up? Talk about volume in cups or cubes or milliliters or spoonfuls...whatever you're familiar with - and then mix it up!

Comments

The sum is the same, no matter how you got there; so how'd you get there?

Yet another example of adults saying "But there's a better way..." No one would argue that you, adult, can add probably faster than an elementary school student. We are in the process of building UP TO that speed and accuracy. By encouraging your child to imagine the groupings, you are building their imagination (draw whatever you'd like!), their math skills (count up, make 10s), and their mental flexibility ALL IN 1 PROBLEM! Check out my NEW addition video for a little more about how this problem is VERY similar to what many adults already do! Making sense of a problem IRL isn't about having an algorithm to write out your work. Instead it's about applying what you know to a REAL situation. This is what most adults think of when they see an addition problem: But this is what many ...

It's about the learning not the grade.

I hope you (and the children/students in your life) had the chance to watch the Perseverance land on Mars recently. Or see the Dragon launch last year. Every single one of the astronauts, engineers, and technicians had years of schooling to prepare for THAT MOMENT. Every doctor or nurse has been trained through lectures, tests, and field experiences. Something that strikes me every year around this time, as our seniors are making college decisions and our juniors are taking the ACT and beginning the application process, is that not one person in any interview I've ever had has asked me about my grades or GPA. We have tied up so much time and energy into thinking that only the best survive, but we KNOW that can't be true. All that does is overstress our teens and lead them to believe that successful people never struggle. That is a damaging belief - especially when internalized by students who are struggling. Here's my take on grades:

Tools for Now, Learning for Later

That quote, is SPOT ON! I don't disagree in the least. (Bet you didn't expect that, did you??) However, I don't know any elementary school students who are sent to the grocery store to do the weekly shopping on a budget alone. Number lines, hundreds boards, ten frames, algebra tiles, and all the other physical representations of math and numbers give students something concrete to set the stage for learning. We move away from each of them fairly quickly as students become more fluent in their math facts, but they provide a perfect physical and visual reminder for students to mentally refer back to as they learn and grow. We all encourage our kids to try new things - consider adding new math strategies to that list! (And cheer them on, just like you would if they were trying a new sport or instrument.)

Demystifying Elementary Math (from a Secondary Perspective)

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