More on math... ensuring a challenge?

[patchfire]

Since math is a popular topic at the moment... ;)

 

What should I be looking for to ensure dd is challenged appropriately in math? I read something a few months ago on the boards to the effect of if you give a student the appropriate challenge in math, they may only get about half of the problems correct. Not sure if I go that far, but at the same time, getting near all of the problems correct certainly isn't much of a challenge either.

 

Specific details. Dd is 10. If she were in our local institutional schools, she would be a very young (August birthday, September 1st cutoff) fifth grader. (She's probably also 2E; she doesn't have reading issues but shows pretty much every other sign of dyslexia out there, and dh & MIL both have reading issues of one kind or another.) She did Life of Fred Beginning Algebra last year, at age 9; she's five weeks from the end of LoF Advanced Algebra. She's been working on AoPS Number Theory on her own in the evenings for fun. I'm not sure what she'll do for math in January/Februay, but in March, she's going to do one of the AoPS classes (probably Counting & Probability). My next curriculum purchase is going to include AoPS Intro Algebra as I'd like her to at least do the end of chapter problems.

 

She aces LoF. I've been letting her free with Number Theory but decided to check the parts she doesn't, today (she doesn't check the end of chapter review or challenge problems). She's getting around 70% of the challenge problems at the end of the chapters correct. Erp.

 

She enjoys math, so this isn't a case of me trying to push her. I'd love suggestions for specific resources or other things to do with/for her.

[MaMa2005]

:bigear:

[regentrude]

What should I be looking for to ensure dd is challenged appropriately in math? I read something a few months ago on the boards to the effect of if you give a student the appropriate challenge in math, they may only get about half of the problems correct. Not sure if I go that far, but at the same time, getting near all of the problems correct certainly isn't much of a challenge either.

 

If my kids get every single problem correct on the first try without spending significant time puzzling and thinking, I know the material is too easy.

I still expect them to, in the end, correctly work every problem in the section. However, on the way there they should make mistakes, start it wrong, take a detour, try a few different things, even sometimes spend half an hour or an hour on one problem (DD once took two hours to solve a linear optimization problem in AoPS Intro to algebra). If all these things happen, but the eventually GET it, I know they are properly challenged.

If, however, they did all this, did not make any progress and had to give up in frustration because they could not arrive at a solution, the problem would be too hard. This would be acceptable for a challenge problem in the challenge (star) section; then we would consult the solution manual. It would not be acceptable for the standard material covered in the section; then we would have to reteach. Has never happened so far.

 

As far as specific resources, we love AoPS. DS is using Intro to Algebra. I know it is just right for him: on the material that is new, he sometimes spends an hour on 3 problems. I also know he gets it; on the material that has been mastered, he is racing through problems and does them correctly. So you have to watch carefully and monitor mastery and challenge.

[Kathy in Richmond]

I also like AoPS curriculum for math-loving students, and I like your idea to have her go through their Intro Algebra text next. It will definitely have some challenging problems, and I just think it's a good idea with young learners to follow up an easier algebra book with one that is more challenging.

 

About the end-of-chapter Challenge sets: I think it's super that she's getting 70% correct. Even Richard Rusczyk states that the goal on the Challenge sets is not 90%.:) I'm working through the AoPS precalculus text with a very gifted young man, and I pick and choose Challenge set problems for him to complete. At this level, several of the problems come from AIME or ARML contests, and I don't expect any kid, even top kids, would get them all right the first time around. They should puzzle over some of them, though. Many of these problems will take a longer time to solve. As regentrude said above, it's OK to peek at the solution manual if you've tried a problem without luck, though. What works for me and my students is to just read the first line or two of the solution, and see if that helps. If not, look at a little bit more of the solution, etc, till you catch on.

 

One idea for stretching your daughter might be to get her involved in MathCounts (grades 6 to 8, so next year perhaps) or Moems or AMC math olympiad contests. Both MC and the AMC-8 are appropriate levels for a kid who's mastered beginning algebra and geometry. Even if she doesn't care for the competition, she might still like to work in a group setting with other math-lovers. My math-devouring daughter loved being part of a team.:) And even if you don't go that route, the materials put out by MathCounts and the AMC folks could still be a nice supplement to her learning.

 

~Kathy

[nmoira]

I read something a few months ago on the boards to the effect of if you give a student the appropriate challenge in math, they may only get about half of the problems correct.

With younger kids, I gun for about 80% (not including trivial things like facts practice). Some texts/materials are a bit easier, others a bit tougher... but it's an overall thing. IMHO, children shouldn't be conditioned to expect "perfect" or even A's. If a child goes into some problem sets knowing x and would have to stretch to score 50% on a difficult set or handily score 100% on an easy one, under which of the two circumstances will the child likely learn more? I'm forever telling my children that "perfect" leaves no headroom for stretching and growing.

 

I expect the success rate to go down with DD the Elder once she hits AoPS. :D MEP and CWP are so far proving enough for DD the Younger.

[Halcyon]

Oh my. I have pretty much assumed my son needed to achieve about 95% in his work before we move on.

 

I might be overdoing this "thoroughness" thing. :confused:

[nmoira]

Oh my. I have pretty much assumed my son needed to achieve about 95% in his work before we move on.

 

I might be overdoing this "thoroughness" thing. :confused:

It depends. I adjust the level of difficulty to maintain about 80%.

[regentrude]

Oh my. I have pretty much assumed my son needed to achieve about 95% in his work before we move on.

 

I might be overdoing this "thoroughness" thing. :confused:

 

It really depends on the kind of problems.

For simple problems that practice a well established concept, my kids have to get every one correct; if not, they have to rework them.

For problems at the beginning of the chapter BEFORE the concept is introduced, they have to spend time trying and if necessary consult the solution. They will get plenty of opportunity to work similar problems in the practice set.

For challenge problems, they have to work on it, spend time, consult a parent or the solution manual and understand the solution before moving on, but I do not expect them to be able to solve them all without help.

 

Depending on how I select problems, I could make a test from a chapter that my kid must pass with 100% - or I could select problems where a 50% would be an outstanding achievement deserving an A.

[Dana]

With younger kids, I gun for about 80% (not including trivial things like facts practice). Some texts/materials are a bit easier, others a bit tougher... but it's an overall thing. IMHO, children shouldn't be conditioned to expect "perfect" or even A's.

 

This is what is tough for me.

 

I find the challenge problems in the IP books from Singapore are the ones that my son has to think about. I am expecting 100% once corrections are made in the text and workbook. We use the IP Challenge problems and it's SO HARD for me not to explain how to get the answer to him. Instead, when he's worked on a problem for a bit, we set it aside and return to it the next day. Some problems just need time to percolate.

 

But ending a day with a problem still unanswered - and letting him try again and not giving suggestions.... OH it's tough. I do believe that this is best for him though... to continue to try and to learn that he needs to continue to attempt a problem and return to it again.

[Halcyon]

This is what is tough for me.

 

I find the challenge problems in the IP books from Singapore are the ones that my son has to think about. I am expecting 100% once corrections are made in the text and workbook. We use the IP Challenge problems and it's SO HARD for me not to explain how to get the answer to him. Instead, when he's worked on a problem for a bit, we set it aside and return to it the next day. Some problems just need time to percolate.

 

But ending a day with a problem still unanswered - and letting him try again and not giving suggestions.... OH it's tough. I do believe that this is best for him though... to continue to try and to learn that he needs to continue to attempt a problem and return to it again.

 

 

It IS tough. Sometimes, for the very final questions in CWP or IP (the toughest ones) we'll work them together, and then, the next day, I have him go back and do them independently so I am sure he understood the explanation. This is what the HIG says to do (or maybe it's in the IP intro) when a child is truly stuck.

[Dana]

It IS tough. Sometimes, for the very final questions in CWP or IP (the toughest ones) we'll work them together, and then, the next day, I have him go back and do them independently so I am sure he understood the explanation. This is what the HIG says to do (or maybe it's in the IP intro) when a child is truly stuck.

 

And the dreadful part is figuring out if he's truly stuck or needs more time to play with it or if he's just delaying.

 

I've started doing the CWP problems so I can have the bar diagrams and give hints when needed (or say, "Draw the bar diagram before I answer anything").

 

I don't want ds to think that if he doesn't understand something it's okay to just wait for me to explain it. He needs to keep trying, ask questions, and then keep trying. But it's so tough not to answer.

 

On the plus side, I do think he's getting the idea that we think his attitude and work ethic is more important than what he knows or is able to do - so keep trying. And he did get an IP problem correct yesterday and ask to do a similar one :) Of course after that we tried one that he wasn't able to figure out - and I didn't give help - and we set it aside to try again later. So I did succeed in not explaining it which was good.

[Halcyon]

(or say, "Draw the bar diagram before I answer anything").

 

This is constantly on my lips too!!! LOL.

"Have you done the bar diagram yet?"

"No, I don't need to!"

"Oh good, then you must understand the problem!"

"But I need help."

"Draw the bar diagram first."

"But I don't need to!"....

 

and so on..

 

LOL.:tongue_smilie:

[regentrude]

This is constantly on my lips too!!! LOL.

"Have you done the bar diagram yet?"

"No, I don't need to!"

"Oh good, then you must understand the problem!"

"But I need help."

"Draw the bar diagram first."

"But I don't need to!"....

 

 

 

LOL.

I try to beat it into my college students that they must have a diagram, identifying all information and defining all symbols before they can start using equations on a physics problem. It drives me crazy every semester because they just refuse. It takes several weeks (and me taking off points every single time) for them to accept that they HAVE to do it.

What amazes me most is that they tell me that none of their high school teachers ever made them draw diagrams. Arrrgh!

[Halcyon]

LOL.

I try to beat it into my college students that they must have a diagram, identifying all information and defining all symbols before they can start using equations on a physics problem. It drives me crazy every semester because they just refuse. It takes several weeks (and me taking off points every single time) for them to accept that they HAVE to do it.

What amazes me most is that they tell me that none of their high school teachers ever made them draw diagrams. Arrrgh!

 

 

I hear you. And when he DOES finally draw a bar diagram, the answer just "magically" appears. He has yet to grasp the weakness of his approach. :lol:

And yes, on every question, I ask "And what does this number you've come up with represent?" (such as, the number of crayons Bob has remaining, or what have you). Because of course, with multistep word problems, he'll say "I solved it!" and I will say "What did you solve?" and he will respond "I got 43!!!" "43 what?" "Um....oh yea, wait a minute, I'm not done."

[Dana]

LOL.

I try to beat it into my college students that they must have a diagram, identifying all information and defining all symbols before they can start using equations on a physics problem. It drives me crazy every semester because they just refuse. It takes several weeks (and me taking off points every single time) for them to accept that they HAVE to do it.

What amazes me most is that they tell me that none of their high school teachers ever made them draw diagrams. Arrrgh!

 

I generally manage not to tell my students who whine about including units in their answer that I make my son write out a complete sentence when answering a word problem. :D