HomeschoolMath.net new design
My main math site, Homeschoolmath.net, has gotten a face-lift... with better NAVIGATION on the left sidebar. Hopefully you'll be able to find your way around better along all the articles, reviews, worksheets, and stuff there.
I especially want to draw attention to the ONLINE RESOURCES section. I used to have this on 9 pages... now I split it into 29 different pages, according to topic.
These pages feature the best online games, quizzes, tutorials, or websites on various math-related topics. Have your pick:
I especially want to draw attention to the ONLINE RESOURCES section. I used to have this on 9 pages... now I split it into 29 different pages, according to topic.
These pages feature the best online games, quizzes, tutorials, or websites on various math-related topics. Have your pick:
Comments
Maria
As a christian homeschool parent, I have been looking for ways to integrate math into our curriculum. Do you have any advice?
Also, are you familiar with the idea that Calculus is anti-Christian? (There is an article about this at thesuperba.com) Is this for real?
Newton and Leibniz were the first ones to formulate the basic ideas of calculus. However, many mathematicians after them have refined those ideas and written them in a more "presentable" form, which is different from how Newton wrote them. The ideas are the same, but the exact mathematical formulations have become more refined and exact.
The definition of a limit in modern mathematics does NOT rely on "infinitesimal" or anything of the sorts. Mathematicians themselves RECOGNIZED that relying on such notion was NOT rigorous. So finally in 1800s, Karl Weierstrass was able to provide a rigorous definition for the concepts of limit, derivative, and continuity that weren't based on infinitesimals.
This definition simply relies on the notion of "arbitrarily close" or "arbitrarily small". Basically it goes like this: let's say that the closer you get to number x, the closer the value of some function gets to y. Then, the limit of the function at x is y. This getting very close, getting arbitrarily close is expressed in precise mathematical language which avoids any idea of "infinitesimals". It only uses the ideas of a number, difference of numbers, absolute value, and less than. See it here: Precise definition of a limit.
I also quote from Wikipedia article on Calculus:
"In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but using ordinary numbers. From this viewpoint, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are easy to put on rigorous foundations, and for this reason they are the standard approach to calculus."
Someone objecting to calculus as a tool of the Devil would also have to throw out these areas of science: computer science, statistics, engineering, economics, business, and medicine. They would have to stop using computers, TV, and any electronic equipment, they'd have to stop traveling on bridges, airplanes, cars, and stop shopping in large malls or online stores, etc. because all those are based on calculus.
The fellow who wrote this strange article says, "His invention, Calculus, did seem to explain the way the stars and planets without God's help. But it also relied on the idea that the sun moves the planets all by itself in the same way that a tennis ball falls when you throw it in the air."
I would venture to say that God himself CREATED gravity to work the way it works; to pull a tennis ball back to Earth AND to make the sun pull on the planets so they go on elliptical paths around the sun. Calculus is simply the mathematics of motion and of change, and an extremely useful tool for mathematicians and scientists.
I have done homeschooling consulting and tutoring for the last 14 years as well as been the director of a satellite school. I am now pregnant with my second child so am taking some time off to spend time with my children. As a result I am selling the majority of my curriculum and have created a website to list it all. I am wondering if you would be willing to put it in your newsletter or as a link on your website so others can access it. Most of the items are in good condition and I am asking only about 10% of the original price. I also have many teacher editions and sets which include reinforcement activities and tests. The website is www.bricebargains.blogspot.com.
Thanks so much!
Janis Soule