If by “practical application” you mean “motivation for learning the skill”, which is I think the way you’re using it, then yes. But that’s not the usual definition in math education, and not what most people mean by it.
Like, for example, to introduce quadratics, a good progression might be to challenge students to build a table of values and graphs for x², then x² + 3, then graph x² – 5 without a table of values, then 2x² vs. 5x² vs. ½x², –x², etc.
And if you have a Thinking Classroom, every student in the class is working on figuring out that progression collaboratively in small groups. The teacher guides students to discover the math themselves through a series of examples, and mostly interacts with the students by asking questions, never giving them the answers.
That’s not “a practical application of quadratics”—at least not in the usual definition—that’s a learning activity sequence (paired with a set of interrelated pedagogical practices).
A good, practical application of quadratics is more like a Dan Meyer “3 Act Math” lesson on predicting the trajectory of a basketball shot. Also cool, good teaching. But not a great way to introduce quadratics.
(P.S. Yes, I use and like em dashes. I’m not a robot.)
I mean motivation for why somebody cares about the idea at all, but I think that is less strict so yes. A hole in theory or something emerging from an activity are perfectly fine. But there has to be something there.
So… From the publications, looks like he uses problem solving, not “having students actually think about math”.
You want students think about what exactly if you don’t give them an application?
Anyway, thanks, I’m listing his work as evidence supporting my claim.
If by “practical application” you mean “motivation for learning the skill”, which is I think the way you’re using it, then yes. But that’s not the usual definition in math education, and not what most people mean by it.
Like, for example, to introduce quadratics, a good progression might be to challenge students to build a table of values and graphs for x², then x² + 3, then graph x² – 5 without a table of values, then 2x² vs. 5x² vs. ½x², –x², etc.
And if you have a Thinking Classroom, every student in the class is working on figuring out that progression collaboratively in small groups. The teacher guides students to discover the math themselves through a series of examples, and mostly interacts with the students by asking questions, never giving them the answers.
That’s not “a practical application of quadratics”—at least not in the usual definition—that’s a learning activity sequence (paired with a set of interrelated pedagogical practices).
A good, practical application of quadratics is more like a Dan Meyer “3 Act Math” lesson on predicting the trajectory of a basketball shot. Also cool, good teaching. But not a great way to introduce quadratics.
(P.S. Yes, I use and like em dashes. I’m not a robot.)
I mean motivation for why somebody cares about the idea at all, but I think that is less strict so yes. A hole in theory or something emerging from an activity are perfectly fine. But there has to be something there.
Remembering this for next time I clearly don’t understand something. lol