An Intellectual Arithmetic, Upon The Inductive Method, With An Introduction To Written Arithmetic by James S. Eaton is a 19th-century educational treatise that grounds arithmetic teaching in Pestalozzian inductive principles. It emphasizes the development of reasoning and independent thinking through concrete, object-based lessons that gradually transition from mental to written computation. The work bridges Mental Arithmetic and Written Arithmetic, presenting a progressive sequence of topics—from basic counting and comparisons to the introduction of Arabic numerals, fractions, percentages, and practical applications such as interest and measurement. It includes detailed guidance for teachers in the Suggestions to Teachers section, outlining methods to engage learners, avoid rote memorization, and cultivate self-reliance and mental discipline. The contents cover arithmetic operations, fractions, ratios, percentages, and problem solving, with notes on pedagogy and the inductive method. The Preface and appended material emphasize active student participation, object teaching, and a logical, inquiry-based approach to learning mathematics.
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