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Mathematics education is in sore need of some serious analysis and revision: not with regard to how to teach mathematics, but rather with regard to what we teach! It is so important to not have a fixed idea about the optimal sequence of topics. Here we begin a discussion about alternative ways of teaching trigonometry, and geometry, to primary school students. We want to separate the study of triangles and circles. We want to let go of the need of using distances and angles for all our measurements. And we want a measurement system that is consistent with the Cartesian coordinate framework introduced in the 17th century. Quadrance and spread work within the Cartesian coordinate system, not against it! ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at / njwildberger Your support would be much appreciated. Here are the Insights into Mathematics Playlists: • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист Here are the Wild Egg Maths Playlists (some available only to Members!) • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист ************************