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<body><div><br>Mathematics education author Alan Selby, Ph. D., has added a new section<br>"Secondary Mathematics for Ages 11+, a Practical Approach" to his website.<br>There is a link to it from the top border of every page. Its URL is<br><br>www.whyslopes.com/index.php/0400Secondary_Mathematics_-_A_Practical_Approach/<br> Section material provides a coherent guide to technical innovations in<br>other site sections aimed at simplify and easing the learning and teaching of<br>arithmetic and number theory practices, elementary and advance algebra, elementary and advanced<br>geometry. The new section descibes two calculus previews for inclusion</div><div>in secondary level mathematics as motivation for skills and concepts, or </div><div>for inclusion in a light calculus course, more descriptive<br>than deductive, introducing the key ideas in differential and<br>integral calculus. An appendix "Calculus with Proofs for the Keen or Gifted"<br>describes how to reform calculus, restrict it to Lipshitz continuous functions, all in<br>a manner that makes proofs simpler and more accessible for the keen and<br>gifted. The restriction is essentially without loss to the domain and range of calculus in </div><div>senior secondary and college level mathematics.<br><br>As of April 14th, the site has a new title "Logic and Mathematics Skill &<br>Concept Development" to better reflect its extent and intent. The site outgrew its original<br> title "Appetizers and Lessons for Mathematics and Reason" in use since<br>site birth in June 1995. The new section says how to employ site material, 1200 pages in 70 plus sections, in secondary<br>level skill and concept building in mathematics, logic and more generally quantitative<br>skill development upto calculus. The new section results from the study of topics European and American<br>mathematicians were considering in the 1960s for the preparation of university-bound students in commerce,<br>science and engineering. It further results from the somewhat ad hoc of a hundred plus<br>textbooks and exercise books in use from the mid-1960s to the present in primary and<br>secondary level instruction.. The new section and site as a whole is also the result of<br>the thought in my 1966 onward highschool and college days that words were missing<br>in the introduction of algebra. In the last four plus decades, I have<br>seen how to remedy most of the difficulties I saw, provide a more accessible</div><div>wordy introduction to algebra, and add multiple technical innovations, again</div><div>to ease and strengthen skill and concept development.<br><br>Initially, the aim was to reform modern mathematics curricula of the<br>period 1960-1990, the content of which essentially implies the content of today's secondary curricula<br>apart from the inclusion of more and more statistical methods in the last two decades. But<br>technical innovations including methods for the systematic development of algebra skills in<br>secondary mathematics and calculus as well, plis reflection on how to make mathematics instruction serve</div><div>the needs of more led to more practical, skill-oriented approach, one that may<br>be of service in home-schooling, in home-tutoring, and in independent schools with control over the<br>curricula they use. Finally, some pages are slow not to load, but to appear properly due to the use of<br>web-based LaTeX tools MathJax and its earlier form jsMath to dynamically typeset <br> formulas and equations. Bon Appetite. <br></div><div id="M2Signature"><div>-- </div><div>Alan Selby<br>www.whyslopes.com</div></div></body></html>