It’s no controversy that education appears to be under par in comparison to what we might hope. I claim this has not only to do with home/environmental conditions for individual students and the ever omnipresent media (and lately, social networking media as well), but also with the curriculum in the classes they take–particularly math and language arts courses. What seems to be the case is that the math courses focus on topics that, while enhancing the mental discipline of students, fail to teach concepts that are readily applicable to everyday situations. Language arts courses emphasize composition (and in particular, stress the ability to make effective arguments) under the premise that students are already well-versed in the grammatical aspects of language (an assumption so far from the truth that the very idea of expecting them to write cogent argumentative essays is ludicrous).
I’d recommend keeping the middle school curriculum essentially the same (introducing key concepts of elementary algebra and geometry), but I’d vehemently oppose the idea of continuing this sort of curriculum for another four years. In 9th grade, students should be introduced to key concepts from set theory (set notations and operations, functions, equivalence relations, bijections and counting principles, and concepts from elementary number theory, including divisibility, prime numbers, and the fundamental theorem of arithmetic). With this collection of concepts in their inventory, they can spend 10th grade covering concepts from logic and proof writing–and applying them to concepts they learned the previous year (as well as everyday phenomena).
11th grade could then be devoted to a more serious algebra course–covering concepts of operations more thoroughly than the 9th grade course, identities, concepts like associativity and commutativity, matrices, inverses, basic definitions and examples of groups, rings, and fields, polynomials, and comparisons between integers, rationals, reals, and complex numbers, and the fundamental theorem of algebra. If students only took these courses and earned a C in them, I’d still argue they were better prepared for life than earning an A in the traditional courses.
An additional 12th grade class covering geometry more seriously could entail concepts of lengths, triangles, trigonometry, polygons, area of polygons, polytopes and hypervolume, axiomatic Euclidean, spherical, and hyperbolic geometry and basic properties of spherical and hyperbolic triangles, approximation of areas/volumes and method of exhaustion (leading up to a freshman course in real analysis (to replace calculus)).
I’d recommend middle school curriculum to focus a little more on grammar and sentence structure. A 9th grade course could solidify this with a rigorous treatment of the core concepts of language: parts of speech, morphology, syntax, and grammar. Concepts like word families, clauses (independent, dependent, subject, and predicate), transitive and intransitive verbs, and sentence diagramming should be emphasized.
A 10th grade course emphasizing argumentative writing would appropriately accompany the 10th grade math curriculum in logic and proof writing. I’d recommend abstaining from requiring students to read nontechnical works until the third year of language arts. This way, rather than getting distracted by a fiction or nonfiction story as a platform for an argument, emphasis is instead placed on the concept of argumentative writing itself. Smaller readings should be used in this course.
An 11th grade course could then more effectively do in one year what four years of language arts typically try to do. This course could focus on work-based and research-based extended essay writing.
Curriculum comparable to the AP English Literature course could make an appropriate optional fourth year class.