Calculus By and For Young People

I want my children to understand that there's more to math than arithmetic, and that math is truly an art, not just a "get the right answer, please" subject. For much of math is not coming up with one, correct answer; it is conceptual and interesting! However, what a child attains in the way of mathematical understanding is directly related to our expectations of what he can achieve. And the typical math curriculum for younger children reveals much about our expectations. In fact, when Don Cohen presents his program as appropriate for ages seven and up (yes, seven and up), your initial reaction may be that it's just for the gifted. Not so! Mark, at age seven, is ready for most of the concepts explored. In fact, the videos are aimed at 6- to 11-year olds. Don's admonition to "start important math early" is well-grounded in his own experience with young children, and advice we should consider. Young children are naturally fascinated by the "art" part of math. Iteration and infinite sequences, key concepts in calculus, are delightful to contemplate for a naturally curious six-year-old. Take this beginning example: start with a square, and keep filling in half of the remaining portion (Don supplies a nice gridded square in the Worksheets to illustrate this). Each time, cut the remaining section in half. You get smaller and smaller "leftovers," but you never fill it all in! Mark found this fascinating, and had no trouble understanding the concept. I found the whole idea behind Don's books and videos intriguing; concepts are presented in an understandable and thought-provoking way, encouraging the student to use hands-on exploration to "discover" many concepts foundational to calculus. It reminded me somewhat of Miquon, only with more involvement by the reader, and is well suited to questioning minds of all ages. The heart of the course is the brief, clear text, now only available in an electronic PDF format on the Calculus By and For Young People CD-ROM. Most of this material is repeated, in a more usable format for the investigator, on the Worksheets on CD-ROM (it is not necessary to purchase both). The worksheets are PDF files, and are large, making the program more accessible to the young reader, and the pages are uncluttered. Don truly has a knack for presenting these ideas and explorations in a way that children quickly become caught up and actively involved in deducing the principles he's leading them to uncover. He teaches techniques of discovery that will improve their ability to solve problems everyday, and not just in the area of math. In fact, several of the explorations include more than a bit of science, as orderly design is evident in creation. The chambered nautilus is studied, as are pineapple leaves, sunflower stalks, light reflection, and a ratio of surface area to volume of rods that leads to a discovery of why rats are nocturnal animals! I got absorbed in the book immediately, pondering his follow-up questions that take you past the immediate discovery, into uncharted waters! Calculus By and For Young People is empowering for anyone who has natural curiosity! As far as implementation, I would suggest using this course here and there throughout elementary ages (perhaps during summer months), and certainly before your student reaches calculus as a regular math course because it teaches the concepts behind the numbers so much better than traditional calculus books. Anyone who can read can be set loose with the Worksheets on CD-ROM with no adult intervention. Younger children can benefit from the videos. The Infinite Series video parallels chapter 1 in the text and would be a helpful for the teacher who is not confident about this type of math instruction. The Iteration to Infinite Sequences video parallels chapter 8. Please note that these videos are not available separately anymore; the material is only available on the Complete Set CD-ROM. Last is the Map of Calculus. The map is a large (15"x 18") flowchart which illustrates how ideas from each chapter connect to one another and contribute to the development of calculus. The Complete Set contains all of Don Cohen's Calculus for Young People materials, bundled into a CD-ROM set. Materials included on the CD are: the Calculus By and For Young People complete text, the worktext, the Infinite Series video, the Iteration to Infinite Sequences video, the Map to Calculus, Changing Shapes with Matrices, and the "On Thinking About and Doing Mathematics" poster. All print materials are in PDF format, and videos are Windows Media files.

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