What's the difference between "hard" and "challenging"?

[Halcyon]

On another recent thread, a poster (forgive me, I can't remember who) said that math should be "challenging" but not "hard". I have been thinking about this ever since I read it, and I wonder what it means exactly. My son is working through SM 3A IP and yes, some of the questions are "hard" for him (some of them are hard for me!). He does sometimes get frustrated. If he encounters a problem he cannot solve, we work through it together, and then the next day, he tries the question again on his own and usually understands it and gets it right. But I definitely think some of the questions go beyond "challenging" to "hard".

 

So where is the balance? Do you skip the questions you deem to be too hard? Or do you work through them together? Where's the fine line between "challenging" and "hard" for you, and when do you decide something is "too hard" and should be skipped or revisited? (Obviously, tears are a good indicator!! But besides that?_)

[regentrude]

I think, the line is between "challenging" and "too hard". Hard alone is not bad.

Also, tears are not an indicator of difficulty - only of the level of frustration. A student may cry even if the problem is neither hard nor challenging, but just not easy enough to solve without effort. (Ask me how I know)

 

With the right resource, I accept no "too hard". If we have decided that the kids study algebra 1 with AoPS and this is basically the appropriate level for them, they will do all problems, even the challenging ones. They will get help from a parent - but a problem will never be skipped "because it is too hard". I think that would send a wrong message. If a concept is difficult, it may require revisiting and additional practice - that is a case-by-case decision. I will then call this "a difficult concept thath needs extra work" - but not "too hard".

 

If, OTOH, the whole curriculum choice was bad and inappropriate for the student's level, I would choose a different curriculum or go back a whole level - but not skip individual problems.

[Crimson Wife]

A few of the IP problems (usually towards the end of the "Take the Challenge" section) I don't even have my DD attempt but rather just follow along with me as I explain how to solve them. The idea is to familiarize her with how to solve those kinds of problems so that in the future if she's presented with a similar one, hopefully she'll be able to tackle it.

 

A couple that come to mind from 3A IP are #2 on pg. 69 and #3 on pg. 70. Those are the kinds of questions I remember being on the math section of the SAT (obviously not the hardest one on that exam but somewhere in the middle level of difficulty).

 

It's a tricky balance with a bright kid how to challenge without going over the line into frustratingly hard. If there's a better method than trial & error, then I'm all :bigear:

[Halcyon]

A few of the IP problems (usually towards the end of the "Take the Challenge" section) I don't even have my DD attempt but rather just follow along with me as I explain how to solve them. The idea is to familiarize her with how to solve those kinds of problems so that in the future if she's presented with a similar one, hopefully she'll be able to tackle it.

 

A couple that come to mind from 3A IP are #2 on pg. 69 and #3 on pg. 70. Those are the kinds of questions I remember being on the math section of the SAT (obviously not the hardest one on that exam but somewhere in the middle level of difficulty).

 

It's a tricky balance with a bright kid how to challenge without going over the line into frustratingly hard. If there's a better method than trial & error, then I'm all :bigear:

 

 

Thanks for sharing your approach. Yes, a few of the Challenge problems in 3A have been HARD for my son, such as p. 43 #2 and p. 57 #2. I think we'll continue to work these togethe,r and then my son will do them alone on a separate sheet of paper the next day.

[Crimson Wife]

p. 57 #2

 

This one my DD did using numeral tiles from our Equate game. She also used those on #2 on pg. 85 and #4 on pg. 86. Having the physical numbers to manipulate made it easier for her to solve those problems.

[Halcyon]

This one my DD did using numeral tiles from our Equate game. She also used those on #2 on pg. 85 and #4 on pg. 86. Having the physical numbers to manipulate made it easier for her to solve those problems.

 

 

Thanks! did she just do trial and error, or was there a more specific approach she used?

[angela in ohio]

I don't know that the words make a difference, but I see what you are saying. I think a big difference between "challenging" (where the student must struggle, but is able to finish) and "hard" (where the level of challenge is too great, and the student cannot continue) is in the amount of preparation and support. If a child sees something that is so far above their ability that they can't imagine the steps necessary to get there, they shut down. If, however, the parent teaches them the previous steps/knowledge ahead of time (preparation) or walks through the process at that moment with them (support,) the same material becomes merely a good challenge, but not panic inducing.

 

I tryo to do a quick "task analysis" on new material. Do they have the previous preparation to complete each of the required pieces of the task alone? If not, I either provide it first or complete it (or a similar sample) with them first.

[Ester Maria]

Do you skip the questions you deem to be too hard?

No way. I'm also of an opinion that there is no such thing as "too hard" in the regular program (obviously, if you're using something age-inappropriate, or very advanced, the child might really not be cognitively ready for some parts of it yet, but average children with programs aimed at average children, no way, even the challenging stuff there are perfectly doable with a bit of thinking).

 

I skip the easy one (to spare them time and myself the whining about how bored they are), which solve the problem by-the-scheme rather than thinking. The ones that involve actual thinking are the ones we do.

 

I let them try their best, if they can't do it, no problem, we leave it aside for a few days or even weeks for things to maybe "click" (my daughters are on a high school math already, but I've always had this habit, it's something they instilled in me back in school). Sometimes all they need is a night for things to click, or a few days and more advanced / different types of problems to enable them to go back at the old ones with a new perspective.

 

Lastly, if it doesn't work, we just go over it together, step by step, me guiding them how to solve it. Usually it starts clicking in the middle of the process anyway.

Where's the fine line between "challenging" and "hard" for you, and when do you decide something is "too hard" and should be skipped or revisited?

Too hard is what they're cognitively unable to grasp at their age and/or emotional/intellectual maturity level, or what they can grasp but at a price that's just too high (needing 8 hours to make click something which should click in a single hour, for example).

Challenging/hard is what they're capable of doing with some effort. That's what schooling should be about. Not about things they do effortlessly. :)

(Obviously, tears are a good indicator!! But besides that?_)

Tears are actually a very bad indicator of anything, if we're talking about age- and level-appropriate content. Many, many children are very capable "emotional manipulators" so they use their own frustrations to guilt you into thinking you're really assigning too difficult things to them. Most of the time, you're not, they're just a little impatient and frustrated and lazy, which maybe warrants a hug or a few minutes' break, but not giving up on it.