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Homeschooling Resources for Gifted Students of Mathematics:
Middle School
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Geometry by Harold R. Jacobs
- Jacobs' style has much appeal to the mathematically gifted learner. The book begins with a chapter on deductive reasoning, direct and indirect proof, and proceeds to develop a system of postulates and theorems. Jacobs gives careful proofs of his theorems, and the student gets lots of practice in writing his own. Delves into some interesting topics, such as cyclic quadrilaterals, Ceva's theorem and non-Euclidean geometry. Each exercise set includes a challenger problem.
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Introductory Logic by Douglas Wilson and James Nance
Intermediate Logic by James Nance and Paula Marston
- A logic course integrates nicely with the study of formal geometry. These books work well with the gifted middle-school student who enjoys abstract reasoning. The first volume covers statements and their relationships, syllogisms and validity, arguments in normal English, and informal fallacies. The second volume includes types of definitions, propositional logic, formal proofs of validity, and truth trees. (Note: written from a Christian perspective)
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Singapore Math(available at www.singaporemath.com )
- The official curriculum of the country of Singapore. The New Elementary Math (grades 7-10), and College Math (grades 11-12) series are more challenging than typical American school textbooks. New Elementary Math is a secondary school series, integrating Pre-Algebra, Algebra I, Geometry, Algebra II, and some Trigonometry into four volumes. Terrific problem solving, especially in geometry. Lacks any treatment of formal proof. College Math is a rigorous two-volume set covering Precalculus and Calculus.
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