Homeschool Math Blog

Fifth Carnival of Homeschooling is up and going. Enjoy!

I asked you in my previous post if what I wrote was a proof (Click here to read my 'proof') . Well, yes and no. It IS a fine proof if it was SPOKEN to someone while pointing to the various parts of the picture. But it isn't the best proof if it was written in a book. You probably had to spend some time figuring what I meant by "this line" and "that angle". Proof needs to COMMUNICATE clearly your thoughts. That's why we use "line segment AB" or AB in text. Then the other is you need to CONVINCE - to be logical in your reasoning. Also it's not enough to convince a fellow student but any sufficiently educated rational person - like your parents, your math teacher, and a mathematics professor. But, the form of the proof is not the most important thing. Numbering your arguments is not the most important thing. In my opinion, students don't need to write proofs in 2-column format if they want to write them as plain text (prose). I want ...

Another obstacle in high school math are the proofs in the geometry course. What is proof? Certainly, two-column proofs are not the only kind. In fact, they are mostly popular in high school geometry textbooks. Mathematicians, most often, just write their proofs out in sentences, and that's called "paragraph" proof (well their proofs usually take many many paragraphs worth of writing). Keith Devlin says in his book , "... being a proof means having the capacity to completely convince any sufficiently educated, intelligent, rational person..." Proof is about COMMUNICATING in a CONVINCING way. Remember those things: you need to COMMUNICATE (not just write a jumbled mess of symbols and numbers) in a CONVINCING way. Is this a proof? PROBLEM: If E is the midpoint of BD, and AE is as long as EC, prove that the two triangles are congruent. "Look at this picture that I drew. It's not drawn to scale or to be accurate. See, this line is as long as this line. An...

Homeschoolers often wonder if they are capable of teaching algebra or high school geometry to their child. You know, maybe your own knowledge on those areas is a little shaky, so you're not so sure what to do when the time comes. I'd like to ease your worries: First of all, maybe you don't have to do all the teaching, after all. Quite recently, it seems, companies have popped up with products where you see an experienced teacher solving algebra or trig or geometry problems, from start to finish. You're watching little video clips on your computer but it's like sitting in a classroom, almost. There's HomeworkTV.com and MathTV.com . These would work as a supplement to your algebra book. And there's Math U See of course, a whole curriculum with videos. And, there exist online animated lessons of great quality, for example our current advertiser MathFoundation.com . Or, software that solves algebra problems for you . Then there are lots of online tutoring ser...

I hope everyone's teaching is going well; I guess this is a slower week for blogging for me. Maybe I'll share some of the questions asked on the site. Someone recently asked me about MY suggested scope and sequence for teaching math, based on the way I have organized my online resources list . Well I have never made any personal or suggested scope and sequence... Those pages are just categorized as elementary, middle school, and high school. The thing is, you can find as many different scopes and sequences as there are textbooks. It varies from country to country, from state to state (in standards), from book to book. People seem to have vary different ideas when it comes to when to teach which math topics. But in my mind, you could try get your child to start algebra on 8th grade or thereabouts. If you set that as a goal, then one should study pre-algebra topics such as integers, percent, ratio, proportion, square root, exponents on 7th grade. One could try set a goal of goin...

Have you ever had your youngster ask, "Why do I need to study math? Where do I need this stuff?" Well if not yet, you can expect the question when they get into algebra. But even before your students ask, take them into certain websites and show them! First, Math Careers Database at Xpmath.com. - it's not actually about careers in math, but instead a list of occupations/jobs and what kind of math topics are needed in that particular job. I've also written an article (earlier) touching on this topic and collected a few similar links. See Where do you need square roots or algebra? Why study math? - scroll down to the bottom to see the links. Categories: math

You know that Blogger doesn't support categories. But I found a way to add them by using del.icio.us bookmarking service. So I'm trying them out now on my blog.