Santa brought my daughters Rubik’s Cubes this year. It brought back memories of my own experiences with one in the 80’s. I could get one side done or two, but I’m pretty sure I cheated, removing stickers and basically rendering the cube unsolvable.
Curious, I grabbed the one of the kids’ cubes last week and realized that my abilities have not improved much since then. And that the cube is no longer made with stickers…
I decided I needed help and logged in to YouTube to find a video. Here is the helpful one that I found:
In a very short while (and with an intense focus and a few bizarre looks from my husband), with the help of the video, I succeeded in solving the two first layers. It involves following some rules and progressive steps. It involves looking for patterns, strategically placing blocks before making certain moves. I had success too which was motivating.
The main reason I have now mastered these two layers is because the third layer is tricky. It involves looking at the bottom and following a set of algorithms and steps based on what blocks appear. The moves for the third layer seem so random to me right now. Plus, the steps are fast in the video, and I have trouble keeping up. Essentially, I’ve had lots of restarts. I am quite fluent now in the first two layers because of so many attempts at the third layer. My husbands’ looks have softened as I have become more adept. I am quite good at layers one and two and I could teach you to do it too!
I’ve also found this video by the same person where the focus is on the third layer, at a much slower pace:
In the video, I love that he encourages the viewer to stop and practice. I know that I need to. While I can follow the steps, I don’t have the same level of understanding that I have of the first two layers. What I have learned is that there are multiple solutions depending on a variety of factors and combinations. But jumping between videos, pausing, and re-watching has been helpful.
But I have now solved it once. My kids were pretty impressed!
I don’t think I can do layer three on my own without a video (yet). Perhaps I need a new video or way of thinking about it. Maybe something non-video that I can study.
I can’t help but to think about how this all relates to math learning and how our current students will learn things in the future. This is a combination of knowing an algorithm (a set of rules) and inquiry involving problem solving concepts.
It makes me think of this article that I read earlier this week. It’s called “No More Math Wars: An evidence-based, developmental perspective on math education” by Dr. Daniel Ansari. He states that:
While the math wars have been raging here in Canada and abroad, scientists from developmental and educational psychology as well as cognitive neuroscience have been busy accumulating evidence regarding the ways in which children learn math and what factors influence their learning trajectories and achievement success. This evidence suggests that the dichotomy between discovery-based or conceptual learning, on the one hand, and procedural or rote learning, on the other, is false and inconsistent with the way in which children build an understanding of mathematics. Indeed, there is a long line of research showing that children learn best when procedural and conceptual approaches are combined.
He goes on to conclude that: “all of the literature clearly suggests that both instructional approaches are tightly related to one another and are mutual determinants of successful math learning over time”.
I think solving this cube has been a combination of both concepts and procedures for me. I had to practice, learn some rules, explore, inquire, fail and try again. Is watching a video cheating? I don’t think so. I needed some instruction or a teacher if you will. But I needed to explore it on my own to really make the learning permanent. I would not have figured all of this out on my own.
I’ve never been one to go 100% with a pendulum swing in instruction in anything really. I agree with the author of this article – both concept and procedure are important and strengthen each other. Teaching mathematics is complex and just like this cube for me, I don’t have it all figured out!
And so I’m wondering…
How could having students teach themselves how to do something (anything!) affect other areas of learning?
What have you taught yourself to do via YouTube or other videos or tutorials? What have you learned about yourself or your student learners through this type of learning? Is it deep learning? How can you make it deeper?
How do you use video tutorials in class? When? Why?
What other factors in math learning instruction come into play and are as important as concept and procedure? For example engagement, real world problems etc.
Please push my thinking, what have I missed?