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What subject tests would any of you suggest?
My 2 cents: portfolio including reading list and video tape of his analysis of what he read. Also anything mathy, and anything scientific/creative/building he may have done. If he fails to make academic progress and/or regresses, you may be glad to have evidence of his current performance level.

Have you considered applying to DYS ?

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I'd just like to see him more engaged and working on his level, but I don't think he's socially mature enough for grade acceleration. Thoughts? Thanks.
You may have read this previously on the forums... the Iowa Acceleration Scale (IAS) helps place a lot of issues on the table for discussion, which may not otherwise be considered.

Additionally, the landmark work on acceleration A Nation Deceived, which has served well for a decade, is now updated: A Nation Empowered. Web seminar (webinar) January 29, 2015.

The IAS is subtitled, "A Guide for Whole-Grade Acceleration K-8", therefore not addressed specifically to single-subject acceleration, (although single-subject acceleration is mentioned briefly in the Manual on page 104, and Planning Record page 3). Some schools may use the IAS to prepare a complete record of a student's scores and "thoroughly discuss the case and to consider other curricular options and recommendations for the student." (Manual page 34)

While an IQ of at least one standard deviation above the norm is considered one of several critical factors for whole-grade acceleration (Manual page 35; Form page 4), it is also stated that a student performing above the 50th percentile on above-level material may be ready for "more challenging material" (Manual page 120). Consideration is given to the student being successful under the expectations of the new environment and also being successful in the long term (Manual page 5).

Page numbers were provided above so that interested parties may read the selected statements in context.

To prepare for advocacy for single-subject acceleration, you may also wish to look at the book and forms by Dr. Karen B. Rogers.

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socially mature
You may have read this previously on the forums... Direct teaching of social skills can be facilitated, in some cases, with books/resources such as The Unwritten Rules of Friendship (which is geared for parents to read and digest so they may guide their children), The Gifted Kids' Survival Guide (which is geared for kids but parents may wish to read it first to prepare for meaningful and supportive conversations, following questions their kids may have when they read it), and Social Thinking (which discusses skills in perspective taking).

Many families also experience positive results from enrolling their kiddos in martial arts.