This is information from the Brooklyn School of Inquiry's brochure.
"Within our self-contained classes, you'll find enrichment and a variety of accelerated teaching styles geared toward children with superior intellectual potential."
Their Philosophy: "Brooklyn School of Inquiry believes gifted and talented students require a curriculum of diverse content and great depth to realize their full potential. We are committed to the whole child: our goal is to balance the social, emotional and academic development of our students in an environment that nurtures creativity and fosters divergent thinking. We believe parents play a crucial role in the daily life and long-term growth of their children's school. It is through this vital home/school connection that we will partner with parents to build a sense of responsibility in children about the importance of attendance, punctuality and homework. Together, we will create a community that values sensitivity and respect for others. We support the development of self expression through dance, theatre, music, painting and drawing. Collaboration with many New York City cultural institutions enables us to promote the arts both in and outside of our classrooms."
The Academic Curriculum: "differentiated integrated curriculum, infusing Science, Social Studies and Literacy into thematic studies shaped by the New York State Framework for Grades K-8. The studies will include independent and group hands-on projects to foster questioning and the development of critical thinking skills. Math inquiry will involve interpreting, organizing, and constructing meaning of situations using mathematical models to develop number sense. Homework is a logical extension of the school day and serves to reinforce the skills, techniques, and information learned during school hours."
Language Arts: reading in all genres, and "writing projects including poetry, realistic and historical fiction, feature articles, comic books, interviews, persuasive essays and literary analysis and criticism." Readers and Writers Workshop.
Mathematics: "The curriculum is aligned with the National Council of Teachers of Mathematics standards. The goal is to help students learn to apply mathematics to everyday life and the world around them and to become confident by communicating and reasoning mathematically, both verbally and in writing." City College Math in the City Contextual Investigations.
Social Studies: "Students explore their communities and study world and American history and culture, within thematic interdisciplinary units that integrate language arts, music and the arts."
Science: "Our hands-on discovery approach invites students to theorize, hypothesize, observe and draw conclusions using the F.O.S.S. differentiated kits."
Social and Emotional Curriculum: "our counseling program is designed to be preventative an developmental. Guidance counselors will see students on an individual basis as well as during classroom lessons where they'll teach skills and share information in small-group settings.
The program will also include:
Preventive and Developmental Social and Emotional Counseling Program, SENG Model (Gifted Parent Group), Technology Education, Chess Instruction, Arts Integration, Academic Intervention and Enrichment Program.
The description of the different subject areas is similar to the regular citywide curriculum, and programs that are present in many quality general ed schools in Brooklyn. The difference will probably come in the level of support (including developmental and emotional) and the method and rate of acceleration within these programs. If I get any more specifics I will pass them on.