Gifted Issues Discussion homepage Forums Parenting and Advocacy requesting help with math advocacy

Three comments.

First, my heart goes out to 'Neato. It must be enormously painful to feel that your child's love of learning is being squashed by the very institution ostensibly devoted to engendering it. We are hopeful that our DS will have reasonable accommodations this year, but he is only 4 and I can well imagine this problem is not likely to get any easier.

Second, if you are looking for ideas about how to go deeper in even basic math, I think there are ways. Knowing about addition is not just knowing the addition tables. It could involve knowing the relations between numbers and sizes, numbers and shapes, arithmetic and geometry, and many other things. One good resource for developing these kinds of broad facilities is the old book "Family Math" by Stenmark, Thompson, et. al. (http://www.amazon.com/Family-Math-Equals-Jean-Stanmark/dp/0912511060) Tons of fun activities in there.

Finally, an interesting context in which to think about the issue of deep vs. fast is that of the emerging Math Circle communities that are sprouting up throughout the country. They are based on an Eastern European model, but much of what is special about many of them here is that they take as their central concern getting kids (and others - they are for adults as well) to enjoy the love of discovering math for themselves. This is inevitably slower, but the idea is that it the knowledge gained is more long-lasting. One of the first American Math Circles has a web-site at: http://www.themathcircle.org. Check the "Press" button to read various newspaper articles (linked at bottom).

BB

Under the circumstances, I completely agree that for your GS, doing the work assigned was important. I think there was a very specific, larger goal that you were trying to accomplish, and it was a vital goal for your GS's future success. Respecting authority is important and necessary, and if doing the drudge work while you advocated for more was helpful, then I'm all for it. You know your child, and every child is different.

For my situation, my child had always respected authority, but the drudge work was making him LOSE that respect. Not to mention making him think of himself as superior to others in very negative ways and at the same time, making him feel like he was a bad kid because he kept getting into trouble. It was NOT a positive experience for him, and letting it go on was not going to teach him any lessons that he needed to learn at the time.

Blanket rules about kids make me nervous. But if I were going to make a blanket rule in this case, I'd definitely err on the side of giving GT kids more challenge and less/no drudge work most of the time, especially while they're young. (Teens are a different story.) I agree that there are some cases where a certain child might get something they need from drudge work if there are special circumstances. But I don't believe that most young GT kids need to learn anything that boring repetition is likely to teach them, and in fact, I think it can often teach them some very bad things!

My kids do not skate by, and their lives are not pampered, sheltered parties all day long. I am very firmly the boss. I expect hard work. I don't let them give up on things willy-nilly--I've actually gotten some sideways glances about how firm I am with my kids about their trying things and not giving up. I just don't think that young GT kids in general are going to learn useful lessons from boring, too easy, repetitious school work. And except in isolated cases with a specific goal in mind, I don't see any reason to let that go on.

I think that explains both ways well. And also points out how Ania's advice to back away from the forum for 48 hours can be very useful. Advice & alternative viewpoints can be wonderful, but when it comes down to decisions about our own kids we know our goals and how to achieve them has to be tailored to our kids personalities.
Good luck 'neato.

What Kriston said! I totally agree, situations and personalities vary widely.

I think we had more a situation like yours. I am having to do some serious remedial work on respect issues, although we've come a long way this summer alone. DS7 is very much "you respect me, and we'll talk".

I love reading about the ability to go deep and wide in math, instead of just plowing through the material faster. We have been staring at the Calculus Trap (without knowing that it had a formal name!) for some time now. But I wanted to make a few comments.

In one of the gifted books that I have read in the last several months, (I can't keep them all straight now, but I think it may have been Karen Rogers?), the author describes the effect of math drudgery, or 'drill and kill", on the gifted student. She (if I am correct on the reference?) stated that mathematically-inclined gifted kids learn the concepts in math exceptionally fast, which is no surprise. But she then stated that with repeated drilling of the same topic, gifted kids actually unlearn the material. It was hypothesized that after the first or second time running through the same material, gifted kids stop paying attention and their scores for assessing accuracy of math facts go down rapidly. So drilling a gifted kid in math is in fact detrimental to their mastery of the subject.

That said, I would also argue that many of the parents on this board, myself included, have posted that their child would rather learn the big, abstract concepts in math rather than do the more mundane calculations that allow you to connect point A to point B. This is worrisome, at least to me with a fairly young kid (okay, at age 8 he is not as young as I think he is!). He needs to be able or willing to focus on the drudgery in order to do more advanced calculations later. Not all of math is built on these big, exciting leaps that seem to fuel the gifted brain.

The problem that I see is that you have to keep them interested enough in the topic by dangling the next big leap under their noses so that they are willing to do the drudgery that fills in the details. If they race from big idea to big idea, then they are missing the structure that holds the whole house of cards together. And if they get so stuck on the minute structure that they miss seeing the grand picture of the whole house, then they dig in their heels and lose that spark of learning.

I think with our kids the pitfall of missing the structure is much, much less than losing the spark. We know our kids and we know what they are capable of and how fast they can go. The schools are focused solely on the drudgery that fills in the gaps in the structure. Their achievement tests depend on the kids mastering the drudgery, their school report card (a la NCLB) depends on it, and frankly they can't imagine any instance where going over and over the drudgery one more time is not a good thing.

I guess the only way around this is to get the school to acknowledge that once the child has mastered the structure or details of a particular lesson, then it is in the best interest of the gifted child to be allowed to move forward. They need to do a certain amount of drudgery in order to make sure that they have mastered the material, as well as to build character and learn perseverance. But for goodness sakes, then they need to move forward!!

And if anyone knows of a way to get the schools to understand this rather simple concept, then please bottle it and sell it. I would be willing to purchase great, big jugs of it!

We are currently stuck with lots of instances of repeating the previous year's drudgery (as if 4th grade drill and kill wasn't bad enough... the teacher is repeating most of last year's drudgery, just to make sure that all of the kids have it.... yawn!), and balancing it with any afterschooling in math that I can get my hands on. (hence the post on Mandelbrots sets). This is surely a kluge job, and may not last for long. When (not if) DS reaches the end of his patience for the slow pace of 4th grade, we will have to start fighting for another solution.

I hear you, 'Neato, and will probably be in your shoes shortly. Any suggestions for the deep and wide aspect of math would be greatly appreciated, as it may stave off inevitable battle of subject acceleration.

I think ebeth's point is an important one: math concepts are great, but math skills are necessary too. Developing the skills shouldn't be particularly difficult for the HG+ kid, but it still requires a certain amount of practice. For some of our kids that process of acquiring and perfecting a skill is itself an exciting thing - I think our DS, for example, gets a real thrill out of getting the right answers. But perhaps this changes with age. Still, perfecting the skill is only the very first stage of real mathematical understanding; the deep and wide aspects are really much more important. (Terence Tao's father seems to have recognized this relatively early on, and he is a good advocate for the view.)

Not to pull the thread off-topic, but I would be interested to know if anyone has any experience with Math Circles. Properly done this seems the right place for developing deep and broad acquaintance with math, and there really are a lot of them sprouting up. DS is joining one in the Fall, and we have high hopes.

BB

Going deep could include working on physics and chemistry knowledge that is accessible with that level of math. Much of classical physics and most chemistry is workable with just a bit of Algebra. Finding a HS physics/chemistry text then working it mught be good. F=ma and pv=nrt are easy to grasp.

Learning how to do graphs and charts is another.

My approach (so far) has been to have DS do the easy "drudge" work such as coloring pages or math facts. I point out to him that he can practice writing his numbers neatly or get creative with the coloring. If he complains that his hand is tired I tell him that's good, it means that your writing muscles are getting stronger. If he complains that something is too easy, I tell him to see how quickly he can finish it. If he says it's too hard then I tell him it means he needs more practice. I really don't tolerate complaints of any type about homework. I want to teach my kids that in order to succeed, they need to do their assigned work and turn it in on time. I tell them that homework is their chance to "show what you know." Maybe they already know how to do something, but they need to show the teacher their mastery.

I think this approach really paid off. The fact that DS had done and turned in on time every scrap of homework ever assigned to him in Kindergarten was greatly in his favor in the eyes of the school.

Very good points. This is often the carrot that we choose to dangle under my "live and breathe science" kid. But my son would still prefer to race ahead to algebra, since that is where the cool and exciting ideas are. He sees calculus as something akin to Harry Potter's magic wand, and the faster he gets there (according to him), the better.

It is like DS8 is dreaming of running down the sidewalk to another place, when he is still learning to crawl in his own small yard. He can see down the street. He knows it is there, just waiting for him. And he doesn't understand why he can just get up and go. As a parent, you feel as if you are constantly trying to hold these kids back and slow them down. Yes, they have to master the finer details. But at what point do they just give up the dream of running free?

Just around his 8th birthday, DS was sitting and eating lunch, staring off into space. He then asked, out of the blue, "How do you calculate the volume of a cone?" And I responded, "Gee, I don't know. How do you calculate the volume of a cone?" He then preceded to tell me that if you know the area of a circle, which he does, then you could stack consecutively smaller circles upward to fill the volume. Or, he said, you could take a triangle and rotate it through a circle to fill in a cone. He is already doing the beginning steps of calculus, without any instruction at all. So much for the Calculus Trap! It is not determined by how fast the material is presented to them. It is determined by how quickly they invent the material all by themselves.

If you don't feed it along the way, it will die from neglect.

Things are very similar in our house. I regularly remind my kids about the importance of trying hard. My DS-then-5 used to say "Try hard, don't try easy!" With my kids, the results of standing firm can be impressive.

I'm also a big advocate of giving young GT kids more challenging work. Especially at this age, they need to learn how to solve problems that look too difficult at first. Ironically, the non-GT kids who have to work harder to get grade-level concepts get much more practice at this skill, which is probably very good for their future work habits. GT kids have a right to develop this skill too!

I think it's difficult for teachers to see the distinction between "working hard" on drudgery and "working hard" on challenging material. They aren't the same thing at all. A GT kid can do simple problems while watching TV or talking. He's not learning to focus his mind by doing the easy stuff. The ND kids are learning to focus when they do this stuff. GT kids should have this challenge as well.

Val