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Why You Shouldn't Say It's Easy When Teaching

karissamck.com

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Re: Why You Shouldn't Say It's Easy When Teaching

#41

Post by kibibu »

baddox wrote: post #29
EliRivers wrote: post #5

Earlier quoted context omitted.

And it's just as specifically subjective.

Of course it's subjective. Why is that relevant? Math teachers are teaching a course with certain prerequisites, so in that context "trivial" means something like "it should be easy/obvious for people with the appropriate mathematical background for this class."

Many of the students in the class got through those prerequisites with, say, 70% on the final exam. That means they have a very tenuous grasp on much of the content, and so teaching with at least some overlap with the prerequisite is useful.

The prerequisites may have been taken 6-12 months earlier. Without constant use, a lot of the concepts that were learned in the prerequisites will be lost over that time period. Many classes will indeed start with the first lesson or two as a revision of the prerequisites for this reason. It possibly annoys those who have a firm grasp, but not everybody learns mathematics (or language, or anything else) the same way.

Re: Why You Shouldn't Say It's Easy When Teaching

#42

Post by nirkalimi »

tikhonj wrote: post #13

It's funny, because I have completely the opposite view: stop telling people stuff is difficult! If people think what they're about to learn is supposed to be "hard", they're going to give up faster and be intellectually lazy. "Oh, I just can't figure it out because it's hard ." I've found this to be particularly important with things that are fundamentally simple but very abstract. You can teach people quite a bit o…

I think context matters here. Let's take two different use cases as examples:

Case A: The student has a genuine interest in the material. The student wants to be successful, and has worked tirelessly to configure and/or understand a given problem or task. The last thing the student in Case A needs to hear is "It's easy". Obviously the problem, to said student, is not easy. This can hurt overall student moral.

Case B: The student has not a complete devotee to the material. The student is "trying it out". The student thinks the material could be achieved without professional education or training. The student in Case B may need a bit of convincing. Telling that student that something like this is "easy" could be beneficial in this case. The student will believe that understanding of the material is at least achievable.

Re: Why You Shouldn't Say It's Easy When Teaching

#43

Post by quadrangle »

tikhonj wrote: post #13

It's funny, because I have completely the opposite view: stop telling people stuff is difficult! If people think what they're about to learn is supposed to be "hard", they're going to give up faster and be intellectually lazy. "Oh, I just can't figure it out because it's hard ." I've found this to be particularly important with things that are fundamentally simple but very abstract. You can teach people quite a bit o…

That's not "opposite" that's the other side of the same coin. Don't say things are hard or easy, just teach them.

Saying things are difficult sets up negative expectations, saying things are easy means disappointment when we have unrealistic expectations.

I still think it's fine to say that most people seem to find X harder than Y…

Re: Why You Shouldn't Say It's Easy When Teaching

#44

Post by XorNot »

mden wrote: post #37
robinh wrote: post #3

Good god, if only mathematics professors would learn this. If I hear the word 'trivial' one more time I swear I'm going to scream.

I know where you are coming from... but I have started interpreting the word "trivial" (and I don't mean the math meaning of it, e.g. "empty set is a trivial solution") to be a canary of sorts. Once you encounter it and the statement that is supposed to be "trivial" isn't, that means you should backtrack and figure out what insight you are missing to make that statement trivial. Of course, this kind of depends on the…

If there's any subject which would benefit from interactive textbooks, it's mathematics.

I'd like a textbook in HTML, where when it says "trivial" I can click and expand it to the proof, with relevant references that I can keep going through until I understand how we got there.

Re: Why You Shouldn't Say It's Easy When Teaching

#45

Post by 001sky »

tikhonj wrote: post #13

It's funny, because I have completely the opposite view: stop telling people stuff is difficult! If people think what they're about to learn is supposed to be "hard", they're going to give up faster and be intellectually lazy. "Oh, I just can't figure it out because it's hard ." I've found this to be particularly important with things that are fundamentally simple but very abstract. You can teach people quite a bit o…

everything is easy in context. what you are supposed to be teaching is not "what is easy", but how to put something in context to make it so. this typically means eliminating degrees of freedom--most of what you learn in school makes you smarted by limiting your cognitive overhead. the actual calculations are 1/10th of the cognitive load; that is why experience and not aptitude are valued later on. "hard" for someone with no experience is almost always not "intellectually difficult", its simply befuddlement.

Re: Why You Shouldn't Say It's Easy When Teaching

#46

Post by danielweber »

tikhonj wrote: post #13

It's funny, because I have completely the opposite view: stop telling people stuff is difficult! If people think what they're about to learn is supposed to be "hard", they're going to give up faster and be intellectually lazy. "Oh, I just can't figure it out because it's hard ." I've found this to be particularly important with things that are fundamentally simple but very abstract. You can teach people quite a bit o…

What I've learned with my kids: it depends on the person.

Last I heard, the best approach is supposed to be telling kids they got the right answer because they are working hard. Well, I've had that one backfire. "This is too hard!!!!"

Re: Why You Shouldn't Say It's Easy When Teaching

#47

Post by chmullig »

mden wrote: post #37
robinh wrote: post #3

Good god, if only mathematics professors would learn this. If I hear the word 'trivial' one more time I swear I'm going to scream.

I know where you are coming from... but I have started interpreting the word "trivial" (and I don't mean the math meaning of it, e.g. "empty set is a trivial solution") to be a canary of sorts. Once you encounter it and the statement that is supposed to be "trivial" isn't, that means you should backtrack and figure out what insight you are missing to make that statement trivial. Of course, this kind of depends on the…

As soon as I realized this, it actually became quite helpful.

Saying something is "easy" or "obvious" is useful! It may demotivate if done poorly. However with a proper teaching approach it also signals what SHOULD be obvious. If it's not obvious to you yet, it's important to learn and understand why not, and eventually it should become obvious.

Re: Why You Shouldn't Say It's Easy When Teaching

#48

Post by baddox »

kibibu wrote: post #41
baddox wrote: post #29

Earlier quoted context omitted.

Of course it's subjective. Why is that relevant? Math teachers are teaching a course with certain prerequisites, so in that context "trivial" means something like "it should be easy/obvious for people with the appropriate mathematical background for this class."

Many of the students in the class got through those prerequisites with, say, 70% on the final exam. That means they have a very tenuous grasp on much of the content, and so teaching with at least some overlap with the prerequisite is useful. The prerequisites may have been taken 6-12 months earlier. Without constant use, a lot of the concepts that were learned in the prerequisites will be lost over that time period.…

I've never taken a math course that didn't contain some overlap. But you simply can't realistically teach everything from every prerequisite in every class. There may always be some students who snuck through a prerequisite without learning or retaining the info. That's what office hours are for.

Re: Why You Shouldn't Say It's Easy When Teaching

#49

Post by charlieflowers »

tokenadult wrote: post #14

I like teaching subjects that are intentionally advanced for the age of the learners presented with problems that require a lot of mental stretching and effort for the learners. I have a FAQ document about how people feel when they take on tough learning challenges that explains what to do when the lesson is anything but easy.[1] AFTER EDIT: I simultaneously posted with two other participants here who both made good…

I'd love to pick your brain on something. My 5th grade daughter has math anxiety, picked up believe it or not in 2nd grade. As far as I can tell, her actual ability is average or slightly above. But her self-esteem is on the line for every problem, so she won't relax long enough to actually think ... she grasps for the fastest "formula" from rote memory, and if that isn't right, she is distressed.

I need some insightful advice on how to help her out of this mindset. I've googled and looked at books, but there's a lot of regurgitated crap out there blocking me from finding the good insights.

Re: Why You Shouldn't Say It's Easy When Teaching

#50

Post by tokenadult »

charlieflowers wrote: post #49
tokenadult wrote: post #14

I like teaching subjects that are intentionally advanced for the age of the learners presented with problems that require a lot of mental stretching and effort for the learners. I have a FAQ document about how people feel when they take on tough learning challenges that explains what to do when the lesson is anything but easy.[1] AFTER EDIT: I simultaneously posted with two other participants here who both made good…

I'd love to pick your brain on something. My 5th grade daughter has math anxiety, picked up believe it or not in 2nd grade. As far as I can tell, her actual ability is average or slightly above. But her self-esteem is on the line for every problem, so she won't relax long enough to actually think ... she grasps for the fastest "formula" from rote memory, and if that isn't right, she is distressed. I need some insight…

That's a good question. Did you see the other links from the bottom of the link I posted above? I usually suggest to parents that they read those in numerical order,

1) http://www.epsiloncamp.org/ProblemsversusExercises.php

2) http://www.epsiloncamp.org/RepetitionPractice.php

and

3) http://www.epsiloncamp.org/LearningMathematics.php

to lay a foundation for their own thinking in communicating with their children. Please allow me to ponder this question overnight in my time zone and maybe I'll come up with more specifics that can arise in a future HN thread or by personal email. (I'm really tired this evening, after cloudy and stormy weather all day, so I'm not sure I can do your question justice at the moment.) Thanks for asking.

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