Homeschool Math Blog

Recently I've been exchanging emails with Alexander Givental, who has translated the famous Russian book Kiselev's Geometry into English. He's raised some interesting points regarding answer keys. I will just quote him directly from his emails to me. The discussion concerns geometry problems (please see the earlier post for examples). "What is actually accomplished by supplying any solution at all? Ideally a student should be able not only to find a solution himself, but also be able to check that his solution is correct. With the aid of a written colution, the exercise is rendered useless for both purposes. Furthermore, a beginning student who finds a more complex solution (or may be even the same solution but eplained differently) may decide - incorrectly! - that his solution was wrong. So, comparing your solution with your classmate's, teacher's, or parent's one makes sense, but with the one written in a silent book - very little. That's why, I t...

Here's an example geometry problem from Kiseleve's geometry book that I blogged about earlier . This problem is not difficult and is a good example of problem where you need to prove triangles congruent. The reason I'm solving it here is simply to help those of you who will be homeschooling your child thru high school geometry. It helps enormously to be familiar with proofs and the type of reasoning before you actually need to write proofs yourself. Problem: 80. Prove that if two sides and the median drawn to the first of them in one triangle are respectively congruent to two sides and the median drawn to the first of them in another triangle, then such triangles are congruent. First draw a picture. We have two triangles with certain parts congruent, and we are supposed to prove that the triangles are congruent. We know that AB = A'B', AC = A'C', and BM = B'M' (givens). This proof in a nutshell is based on first proving that the two trian...

Just a reminder... the summer sale for my math e-books is ending soon. The offers are valid till end of July. The e-books are basically PDF files that you print on your own. All the books have been written as worktexts, with explanations and problems in the same text. Read what old customers say Visit the ebooks page here!

This blogpost is inspired and especially written for Homeschooling Carnival, as they are having a galaxy theme. Astronomy and mathematics have always been closely related. Astronomers have always been using the latest mathematical knowledge and theories. Many mathematicians in the past have also done research in astronomy. All sciences strive to help us understand the world we live in, but astronomy does it on the largest possible scale. I have always found astronomy fascinating, and so have multitudes of other people, too. But I just wonder if mathematicians might have even a little bit stronger fascination or interest in that direction; somehow those two just seem to fit together very well. It is part of well-rounded education, I feel, to know some basics of history of astronomy. And it sure is very interesting too! What I've written below is just some thoughts on the subject of planetary orbits. Greeks believed that planets go around the earth, in circular orbits. This view was...

Recently I received the following note, I would like to bring to your attention the following new geometry textbook: "Kiselev's Geometry / Book I. Planimetry" by A.P. Kiselev, ISBN 0977985202 Publisher: Sumizdat It is an English translation and adaptation of a classical Russian textbook in plane geometry, which has served well as to several generations of students of age 13 and up, and their teachers in Russia. The English edition is intended for those students, homeschooled or not, who want to achieve a good command of elementary geometry, and learn to appreciate for its intellectual depth and beauty. More information about the book and its author is available through the publisher's webpage: www.sumizdat.org . The book is currently available at: www.sumizdat.org and Singaporemath.com . I posted this note here because some of you might be interested - a classical Russian geometry book translated into English. You can browse quite many sample pages to get an...

I found Integer Jim's website two days ago, and I had to browse thru his whole website because it was quite interesting. Here we have a math teacher who is very enthusiastic and excited about what he is teaching (you can sense that by reading his website). Now, that is, I feel, one ingredient in what makes a good teacher: being enthused about your subject matter. I realize not every homeschooler feels that way about math; but don't despair if you feel teaching math is a drudgery. All that CAN change... Head for the Living Math website for starters. But back to Integer Jim. Besides being a math teacher, he's also an artist and has made some interesting projects with his students that tie art and math together. I wanted to highlight one: The Math Journal project . Jim says, The Math Journal is a comprehensive and in depth project. It requires a lot of time and effort on the part of the students. For that reason, I use it as the centerpiece of my curriculum; the textbook t...

... with interactive resources online. In my mind, geometry is lots of fun. It should involve lots of drawing, of course. But you can go beyond that: with modern technology, geometrical drawings can come 'alive' or dynamic. You can change one part of the picture and observe which things change with it, and which things don't. You can explore the situation, analyze, learn. The best of it is that you don't even have to buy geometry software since the various math websites already offer so much. I'd like to highlight today Mathsnet.net geometry section . This British site contains interactive courses and lessons for a wide range of geometry topics. In fact, the site is just HUGE. And, well-made too. They offer three very comprehensive courses (totally free): Constructions : You will build points, line and circles on-screen just as you would on paper with a ruler and compasses. These constructions are then dynamic - you can move the objects and see the construction ...