"Vertical" curriculum expansion is normally called "acceleration." It occurs when students study material that is part of the normal curriculum for older students. This can mean allowing the student to:

	move at his/her own pace through individualized course material
	test out of any unit with a high enough score on a unit pre-test
	take above-level coursework in the age-level classroom
	move to a higher grade-level class for one or more subjects
	skip one or more grades

From what I've seen of the research and commentary by people who study gifted kids, there is a consensus that enrichment is largely ineffective at reducing the percentage of gifted kids who become alienated underachievers and/or dropouts as they reach their teens. In contrast, virtually all research on acceleration, especially grade-level acceleration, indicates that it works well in both the short and long run for the majority of gifted students. These topics have been discussed at length on TAGFAM and GT-Families over the last few years, with anecdotes and arguments for and against each of the alternatives. It's worth a look through the web pages and archives.

IMHO, the thing that favors grade-level acceleration the most is that it is easily reversible. If the new teacher is supportive and the child wants to move ahead, the school can put the child ahead one year on a trial basis. If it works, that will be obvious to all within 8-10 weeks. If it doesn't work, the child just rejoins the lower class with no penalty.

On the other hand, from all we know about the many gifted underachievers and gifted dropouts, few of them have been accelerated to the point where they experience a reasonable challenge in their schoolwork. The penalty for failure to accelerate is often serious damage to the child's motivation, grades, and willingness to remain in school, none of which is easily or quickly reversible.

IMHO, what that means in terms of K and his school, is that "horizontal expansion" of the curriculum is high risk and low gain, while "vertical expansion" is lower in risk and much higher in potential gain.

You can learn much more about K's educational needs, and get more ammunition for your fight with the school, by having a private psychologist give him the 2nd grade achievement test. So-called "out-of-level" testing is much, much more accurate than the grade level scores derived from an on-grade-level test like the one K took. This is also a good time to get an IQ test done, but be sure that the psychologist has a great deal of experience with gifted kids.

In spite of the research, most teachers and administrators oppose acceleration and rarely permit it. From what I've seen and read, the reasons include:

	misplaced egalitarianism
	fear, resentment, and dislike of gifted kids (and anyone else who is much smarter than most teachers and administrators)
	ignorance of the research on GKs (Gifted Kids)
	the misinformation about GKs that is widely taught in ed schools and in-service training programs
	fear of alienating the next grade's teachers (as when a 1st grade teacher lets a gifted child study 2nd and 3rd grade math and the 2nd & 3rd grade teachers are furious at the 1st grade teacher for "creating" problems for them)
	the potential loss of high test scores if a student is accelerated through the grades in that school and "graduates" in less than the normal time
	reluctance to lose a year of student attendance (loss of ADA money for public schools, or tuition for private schools)
	general administrative rigidity ("If we make an exception for your child then we'll be besieged by parents who want special treatment for their children!")

As a result, most schools have a "don't confuse me with facts" attitude about acceleration. Others have written at length about how to get around this, so I won't, but the best starting point is the Hoagies' Gifted Education Page.

However, even if the research favors one course of action, there are still gifted kids in the minority who do not react well to acceleration, or who react very well to enrichment. It depends mostly on the personality and level of giftedness of the child and the attitudes and abilities of the teachers who are directly involved. Also, at K's age, handwriting may be a big factor, especially for a double jump. So your mileage may vary quite a bit from the norm.

Good luck!
Draper