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Most people think of Arithmetic as a program forming a core part of a modern K-12 curriculum. If we look back through history, we can rarely find anything written about Arithmetic in schools. We know that the ancients and that medieval Christians studied Arithmetic, but where was it in the curriculum?
The reality is that Arithmetic doesn't have to be a 13+ year study. It is such today simply because it's convenient when you take the K-12 system for granted. They take the body of Arithmetical knowledge, divided it by 13 years, add in lots of review and...voila!...a massive curriculum with textbooks, manipulatives, calculators and dozens of professional Arithmetic teachers.
In an academy setting, Arithmetic doesn't need to take 13 years. It's a single study to be mastered as any book would be studied....from beginning to end. In the CLAA, we present Arithmetic to our students systematically in a single course and then use two additional courses to cover topics in Arithmetic such as algebra, functions and so on. It's really pretty simple, so long as the instructor knows Arithmetic and the study materials are well organized and concise.
Fortunately, study materials are not difficult to obtain, since we have access to Arithmetic texts from before the advent of the K-12 school model. By restoring these texts and adding to them the benefits of modern teaching technologies, our students can study true classical Arithmetic suited to academy students.
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Introduction to Classical Arithmetic Preview
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Definitions, Axioms, and Theorems Preview
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Inventions I: Addition Preview
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Inventions II: Subtraction Preview
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Properties of Inventions I Preview
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Measuring Preview
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Classifying Numbers Preview
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Inventions III: Multiplication Preview
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Properties of Inventions II
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Putting it all together I
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Algorithms I: Addition
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Algorithms II: Subtraction
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Algorithms III: Multiplication
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Greatest Common Measure
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Ratios and Proportional Numbers
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Inventions IV: Division
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Solving Equations
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Note: If you desire an Arithmetic program based on this course, but in a K-12 format, see the CLAA Common School program. |
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OUR INSTRUCTOR
Dr. Daniele Arcara
Classical Arithmetic, Geometry
Dr. Arcara works as assistant professor of mathematics at St. Vincent College, in Pennsylvania and serves as the primary author of the CLAA's Classical Mathematics program. Born and raised in Italy, Dr. Arcara received more of a "classical" mathematics education than American students do and this has allowed him to bring together the benefits of modern mathematical resources and the wisdom of the ancients. He earned his Bachelor of Science degree in mathematics from the Universita di Torino, Turin, Italy in 1996. He earned his Ph.D. in mathematics in 2003 from the University of Georgia. Dr. Arcara is Catholic husband and father with children studying in the Classical Liberal Arts Academy.
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