With our DD it is normally one or two that she might need to work to find the answer on. We try somewhere between 2 and 3 - we never do them for her but we will 'hold her hand/act as a sounding board' at times to work through the thought process. Other times she breezes right through the challenge problems and it might be an Alcumus problem that stumps her. The difference at young ages between performance when fresh versus tired (at the end of the day) is vast from what we have observed in our DD.
Some of the the challenge problems are difficult period - I am not a Maths major admittedly but I am a problem solver and some make me (and DW who is off the charts when it comes to smarts) pause to think. She may work on thorny ones for a few days on and off. The important thing is not to throw in the towel right away or to bang one's head against a wall getting nowhere - take a break and try it again next day. This does mean try to do the online challenge problems early and not the night before they are due obviously which can be easier said than done LOL but having the luxury of a few days grace to tackle the thorniest ones is a life saver.
I don't care about the grade, just that she aquires a sold conceptual understanding of the topic at hand and she can successfully map that knowledge onto solutions for real applications of them. If we have to help her to think things out or discuss occasionally how one of us might try it I consider that mentoring and not cheating.
Something to beari in mind too is that if you start to see a lot of complication in your solution then you have probably made a mistake somewhere along the line. Often exponents or numerators/denomInators tend to cancel out leaving fairly simple expressions. If it starts looks like exponent or vulgar fraction with odd combinations of numerators and denominators soup then stop and backtrack to the last time it was simple and work forward again. I hope that wasn't too incoherent.
These problems are supposed to be hard - this is why we have our DD take AoPSclasses after all :-)
YMMV
Last edited by madeinuk; 09/20/15 03:20 PM.
