Full Description
This book provides a focused socio-historical analysis of the secondary mathematics curriculum, revealing how science and cultural factors influenced the genesis of many core mathematical ideas. The authors explore why certain concepts became foundational and why their original intentions matter. While seemingly epic in scope, the history provided here is more accessible than one might suspect. Much of the curriculum has its genesis in a rather narrow piece of social history and culture: Europe in the 1600s and the Scientific Revolution. Why history? Because intentions matter in mathematics and education, especially when a mandatory curriculum is tied to high-stakes testing. The authors' historical research reveals mathematics as a powerful, utilitarian approach to science, technology, and engineering. By studying the genesis of mathematical knowledge, the authors identify pathways for both practitioners and researchers to redesign curriculum and instruction in secondary and post-secondary STEM education. By discussing how old ideas could become new again, the authors argue that educators can gain deeper insight into the nature of mathematical reasoning and problem-solving, providing clarity on the complex relationship between mathematics, its history, and the future of STEM education.
Contents
1. How Did We Get Here (and Where Should We Go)?.- 2. What Did Mathematicians in the 1600s Know?.- 3. Measuring the Immeasurable - Galileo and the Invention of Scientific Discovery.- 4. Flattening Apollonius.- 5. Euclid Fades Away - The Geometry of René Descartes.- 6. Algebra That Makes You Think -- The Code of John Wallis.- 7. On the Shoulders of a Giant -- The Rigorous Intellect of Isaac Newton.- 8. Gottfried W. Leibniz and the Future of Science.- 9. Coming Full Circle--The Science of Trigonometry and the Complex Numbers.- 10. Euler's Enduring Legacy -- From Practicality to Pedagogical Imperative.- 11. Reclaiming Mathematical Intentions -- Bridging History and the Modern Curriculum.
