Comment on What would you do?
definitemaybe@lemmy.ca 1 day agoCitation needed.
Seriously, though, that’s not what the research is showing. Peter Liljedahl’s research, for example, supports that a very effective way to teach mathematics is by having students actually think about math, instead of just passively receiving info dumps (as is common in most traditional math classes). See Building Thinking Classrooms for details but, in short, it’s a method of getting students playing with math concepts for almost the entire class time every day.
No “practical applications” needed. Counterintuitive, but it’s a highly effective practice.
What’s core to practical applications working is student motivation, and practical applications are one easy to induce motivation. But it’s often not the best option, especially for inherently abstract skills.
marcos@lemmy.world 1 day ago
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?
definitemaybe@lemmy.ca 1 day ago
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 getting them the answers.
That’s not “a practical application of quadratics”, 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.
gandalf_der_12te@discuss.tchncs.de 1 day ago
To be honest, i’m not sure what you want.
Like, if i was the student, i think i would be extremely confused from this lesson. I would not know what you want from me. I have had my fair share of teachers trying to get me to “just think about something and figure stuff out myself” which mostly amounted to me sitting there in classroom, staring into the air, confused about what the task is, and mostly waiting till the hour is over.
My brain works differently. When i learn something, before i even start caring about what the topic is, i ask why I’m learning this; and i need to have a proper reason to learn something. The reason needs to be strong enough, and is only strong enough if it is derived from some other, stronger reason. For example, i learned maths because i understood how important it is to grasp the universal, those things that cannot be taken away from us. I grew up in a kinda abusive household, and my mother had a habit of taking away the things that were most precious to me, so i clinged on to maths because i knew that maths was eternal and not dependent on the whims of my mother. That is a clear, practical reason. Maths gives me mental stability, like a skeleton gives stability to the body. It does not shake nor break; for it’s eternal.
Now, if you want me to play around with polynomials, idk what i would do.
Typically, when i learn something, i want to know why but also how to learn something. Especially, to express it in an analogy, my brain is like the C programming language. I need to reserve memory manually, it does not happen automatically, and i need to know how much space will be needed beforehand, in other words i need to have a clear understanding of how big a topic will be before i actually start learning it. When i have no idea what i’m getting myself into, then i don’t get into it, because my brain is very very very (i hope i have made this clear enough) bad at learning many small incremental pieces of knowledge. In fact, it’s similar to if you had to put on your jacket, leave the building, go through the cold icy air into the neighboring building each time you want to get yourself a glass of water. Needless to say, you will not drink a lot of water. You will dehydrate. Obviously you would put yourself a large bottle of water into your room, for which you only have to leave the building once. The same applies to me and learning. I have to take very few, appropriately sized portions of knowledge into me at once. Not many many small ones.
definitemaybe@lemmy.ca 1 day ago
I don’t have time to get into the full 13 (? iirc) steps of Liljedahl’s Thinking Classrooms approach, but it’s exactly designed to meet the needs of students like you. Since highlights:
It’s an incredibly effective teaching method for secondary math. And there’s clear motivation every step of the way for what you’re doing and why it matters.
And the teacher only explains about 5-10% of the material; everything else is explained by the students as the carefully curated progression of activities guides them through discovering the math themselves.
marcos@lemmy.world 1 day ago
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.
Psychodelic@lemmy.world 1 day ago
Remembering this for next time I clearly don’t understand something. lol