Does anyone else hate “discovery methods?”

[kiwik]

On 11/23/2020 at 4:35 AM, Not_a_Number said:

Yeah, it really depends how you're trying to use the discovery method. I wonder if just not teaching math and doing board games is worse than doing bad direct instruction or not? To be clear, neither of those are what I would use to teach, I just have no idea which of those is worse... practically all the kids I taught calculus didn't think math made any sense, so I wonder if NO teaching and just natural interaction with numbers/shapes/logic is worse than that. 

But if you're trying to get kids to discover standard algorithms and not immersing them in numerical reasoning, then that's probably even worse than mediocre direct instruction. 

What did your much younger siblings' math education look like? How were they "taught"?  

I was only round intermittently.  less rote memorization of times tables.  calculators - we were allowed to use them from about 14 but they were really expensive so lots of people didn't. More group work - it was considered cheating in my day.  It was more the teaching model went from "sit at your own desk and pay attention to the teacher" to "the teacher is a guide and group work is king".  It makes it easy for a kid to hide their lack of understanding of they always have a strong student in their group to do most of the work. Also a change from big high stakes exams to constant internal assessment often with the ability to resit. Was our way great? Not really but everyone had some ability to do maths without a calculator.

[kiwik]

8 hours ago, Not_a_Number said:

I've seen the model where the kids are supposed to read before. I didn't really do that, although I knew people that did... I just taught for half the class and that was the lecture. I don't tend to think lecture teaches nearly as much as the practice, anyway, so doing a shorter lecture wasn't a big problem. 

I would assume you could set up an incentive system for reading and preparing at home? Short quizzes or something? Pop quizzes at the beginning of class? You'd have to tinker to make it work... but anyway, I've never tried. I only ever tried it the way I described. 

I can't tell you whether it was useful or not, though, because these classes required me to teach calculus to kids who had largely never really understood what a function was in the first place, so it was a totally impossible task. 

I would be OK with flipped classrooms if the school day were reduced to 2 or 3 hours.  I am not keen on my kids doing hours of work at home followed by a full school day.  I know one day Ds13 will have more than 20 minutes homework but not yet I hope.  I also think the kids who struggle will probably not understand the video/reading and have no one to ask.  My son's first principal said they didn't send home worksheets 'because if the kids could do them they didn't need them and if they couldn't then they should have the teacher to help".

[Not_a_Number]

2 hours ago, kiwik said:

I was only round intermittently.  less rote memorization of times tables.  calculators - we were allowed to use them from about 14 but they were really expensive so lots of people didn't. More group work - it was considered cheating in my day.  It was more the teaching model went from "sit at your own desk and pay attention to the teacher" to "the teacher is a guide and group work is king".  It makes it easy for a kid to hide their lack of understanding of they always have a strong student in their group to do most of the work. Also a change from big high stakes exams to constant internal assessment often with the ability to resit. Was our way great? Not really but everyone had some ability to do maths without a calculator.

I pretty much hate group work, lol. I don’t think it’s appropriate for most topics.

[Clemsondana]

My preferred method is short lecture followed by in-class work (individually or in small student-chosen groups - I find that groups can work fine if they are comparably good students who reinforce each other, but don't work well if some get it and others don't because they just copy the work).  This is how elementary school worked back when I was a student. 

I read about true flipped models in colleges and they found that it was something of a 'rich get richer' model - the good students did great because they could get help with the problems, but the poor students (whether academically poor or literally poor and lacking good internet to watch videos) came to class unprepared, couldn't do the work, and fell more and more behind.  Based on what I see in my classes, where the best students often take notes from my live lecture, watch the recorded lecture, and probably check out Crash Course and Khan too and then come in with questions about minor differences in how things were presented, while meanwhile the poor students don't take notes and don't watch any videos, I can see it being amplified if they don't even hear the lecture.  

Edited November 24, 2020 by Clemsondana

[Mrs. Tharp]

Yes, it is important to have methods of teaching in public settings that give everyone a reasonable shot at succeeding. The traditional format of lecture, questions & answer, practice, test & review can, if done reasonably well, challenge the advanced students while providing enough support to the disadvantaged--the poor, the English language learners, and those with learning differences. And, in my experience, all students appreciate classes with straightforward formatting. They like knowing exactly what they need to do to do well.

[Not_a_Number]

1 hour ago, Mrs. Tharp said:

They like knowing exactly what they need to do to do well.

Don’t we all? But sometimes that’s not conducive to the best learning.

That brings me back to @Xahm’s example with cooking. I’m someone who has really only cooked from recipes until very recently. I liked knowing exactly what to do to make a dish and I did it relatively well. But I didn’t understand what I was doing... if I wanted to be a really good cook, I’d definitely need to do more experimenting, discovery, and thinking about WHY I was doing things, instead of just WHAT to do.

The same thing does apply to other subjects. If you understand the WHY, you can figure out what to do if you’ve forgotten a formula or an algorithm or in cooking, if you’re missing an ingredient. If you don’t understand it, you’re stuck.

Edited November 24, 2020 by Not_a_Number

[Mrs. Tharp]

Right, but in many settings, such as public ones, adequate learning, not the best learning, is the goal. The best learning is what we shoot for in a one to one tutoring session, or when we really, really care about a subject.

5 minutes ago, Not_a_Number said:

The same thing does apply to other subjects. If you understand the WHY, you can figure out what to do if you’ve forgotten a formula or an algorithm or in cooking, if you’re missing an ingredient. If you don’t understand it, you’re stuck.

This is a lovely sentiment, but only really necessary in a few particular fields of expertise for most people. It's possible, and just fine, to spend a lifetime cooking, or driving, or a myriad of other things without understanding exactly why they work the way that they do. Experience can, and frequently does, also compensate for a lack of conceptual understanding.

[Not_a_Number]

22 minutes ago, Mrs. Tharp said:

This is a lovely sentiment, but only really necessary in a few particular fields of expertise for most people. It's possible, and just fine, to spend a lifetime cooking, or driving, or a myriad of other things without understanding exactly why they work the way that they do. Experience can, and frequently does, also compensate for a lack of conceptual understanding.

Well, I certainly drive without really knowing what's going on under the hood, and it's just fine.

But when it comes to math or science, only learning via algorithms can seriously undermine a kid's later learning. Math, specifically, is very sequential. If you understand an early concept, you can build on it. If you don't understand that concept, you're likely to be disadvantaged in later classes. And algorithmic learning really doesn't prioritize conceptual understanding. 

I spent quite a lot of time teaching calculus to kids who had never understood what a graph is. It was impossible. There was no way to communicate, because they didn't have a prerequisite concept. It didn't matter how well they could graph a line.

 

30 minutes ago, Mrs. Tharp said:

Right, but in many settings, such as public ones, adequate learning, not the best learning, is the goal. The best learning is what we shoot for in a one to one tutoring session, or when we really, really care about a subject.

Having experimented with some larger settings, I do think it matters how we approach teaching even in larger groups, although of course one gets the best result one on one. 

[Mrs. Tharp]

I've always thought that good math programs emphasized both concepts and algorithms, and that it was tacitly understood that people needed to learn both to do well. What I have seen are programs that emphasize one over the other, sometimes significantly, but never one, no matter how traditional or conceptual, that simply eliminated teaching concepts or refrained from offering any practice. It's a false debate. I think it only ever becomes an issue in a learning situation where the teacher is responsible for imparting a lesson they themselves don't understand or when the student is not getting either enough time to absorb the concept or enough practice with the work.

That said, most people only ever take calculus as a prerequisite to pursue a field of interest, not through any inherent interest in the subject. It's unfortunate that's it's a gatekeeping class to so many different fields of study, where it will rarely if ever be used, but there it is.

I agree that in higher math if students don't understand the concepts early on, they may be at a disadvantage later, but I've also heard of people doing really well in calculus without really understanding what they were doing.

[Not_a_Number]

1 minute ago, Mrs. Tharp said:

I've always thought that good math programs emphasized both concepts and algorithms, and that it was tacitly understood that people needed to learn both to do well.

I'd agree with that. But I think we expect concepts to be absorbed much faster than they are actually absorbed. Most programs move on from concepts before they are fully absorbed, and that's what leads to the trouble. 

 

2 minutes ago, Mrs. Tharp said:

I think it only ever becomes an issue in a learning situation where the teacher is responsible for imparting a lesson they themselves don't understand or when the student is not getting either enough time to absorb the concept or enough practice with the work.

I've honestly been shocked how long things take to absorb, even for bright students. So that's where a lot of my opinions come from. 

 

3 minutes ago, Mrs. Tharp said:

That said, most people only ever take calculus as a prerequisite to pursue a field of interest, not through any inherent interest in the subject. It's unfortunate that's it's a gatekeeping class to so many different fields of study, where it will rarely if ever be used, but there it is.

Yeah, calculus isn't necessarily the best example, but it's the subject I've taught in person (as opposed to in an AoPS classroom) most often. I don't think calculus is an extremely challenging subject if you have all the prerequisite concepts, though. It's just that it requires so much prior understanding that it's very easy to be missing a piece of the puzzle that sets you back.

I liked teaching linear algebra better for this reason 🙂 . You didn't need as much prior understanding to succeed! There were a LOT of kids who were really set back by a lack of understanding of fractions and division in calculus, for example... 

[ieta_cassiopeia]

I disliked discovery methods in all subjects that are going to be assessed by outside parties, simply because no matter how it was framed, what I learned was invariably not what I was supposed to learn - and invariably the teachers would have no idea how I'd managed to get from what was in the discovery text to whatever idea I'd ended up with. (I did learn some useful maths that way, just never whatever it was the discovery exercise was supposed to teach me).

In maths, I encountered it in one year of maths - possibly not a coincidence that this was the first year of algebra, though my difficulties with algebra continued in direct instruction - and also the statistics course. Managed an A in the latter purely because I found a direct-teaching statistics book. However, I've found discovery methods to be far more common in "life skills", English and history classes than maths - possibly because there's a set canon in maths that everyone has to learn regardless of preferred teaching style (which means books are more likely to be direct-teaching, with perhaps some discovery-based material from the teacher preceding it).

Even in cooking, discovery methods led to no confidence and a lot of wasted food (never anything edible). I had to have very explicit instuction, and then I taught myself to experiment without ever needing or benefitting from discovery teaching in that field.
 

Some students learn well from discovery. Some find it inimical to learning. Know your student and teach accordingly.