Hi Everyone! 

Fall is here and cooler weather is on it's way.  It's time for me to clean out my inbox and share some of the links I've been gathering.  I haven't fully researched each site but I have glanced at them to see if they hold some potential.  Here are some Math links that you might find of some interest.

The Math Forum an internet Mathamatics Library

SpaceRef.com NASA Educational Materials available for downloads

NASA CONNECT integrating science, technology, engneering, and mathamatics... geared for 6th-8th grade.

We All Use Math from the TV show NUMB3RS (Use discretion)

Here are some fun NASA related Videos about airflow, Algebra and Geometry and such.  I love when math can be explained in a fun way.

And last but not least, Cyberchase.  This site is loaded with all types of fun learning not just limited to the subject of math.

Have FUN and learn!!

 There have been some great discussions going on in some of my homeschooling groups about just how a child learns math.  This is a discussion that is important to me as I still have one more child to educate.  Well, I can’t teach him as I don’t believe you can make anyone learn that which they don’t want to learn so I guess I should rephrase that as one more child to guide or facilitate along his journey. 

So what have my homeschooling groups been discussing?  Well, one topic is about the essay Just Do the Math excerpted from Have Fun. Learn Stuff. Grow. Homeschooling and the Curriculum of Love, by David H. Albert .  In this essay David Albert explains how a child can learn math in only eight weeks!  Now you will have to read the article for yourself to gain the full picture, but the basic gist is children learn quickly when they desire to learn.  

When my children were young, I remember taking them to the toy store and my spouse giving them a challenge.  He would give them a number amount that they could spend any way that they chose.  The only rule was they could not go over the amount.  If they did, they got nothing.  At some point, as they grew, he added in that tax was included.  Hmmm….  I find it interesting that Mr. Albert suggests this same type of real life math.  Oh.  The kids never failed to spend near the full amount not once going over, lol, better to be a little shy then to go over.

Another discussion is going on about simple verse complex math.  It seems that many parents of the gifted child are finding a great deal of trouble and frustration over trying to teach rote math.  The kids hate doing worksheets and multiplication drills. I was surprised I must say, at how many parents besides me, have decided to jump math levels!  It seems that many of these parents found that their children could understand the complex math and enjoyed the complex math before they wanted to bother with the simple math.  But that is what we did before my youngest hit school age. Once he was school age, we became traditional and sent him to school which ended in school at home which became unschooling and back to where we started with him learning in his own way.  Whew. 

Here is an excerpt from ‘Anna’ about her child’s journey:

We did the same thing (skipping ahead). Actually it wasn't my idea at all. My son insisted because he only can learn math through higher level conceptual thinking. He would make up little algebraic ways to learn arithmetic. Anything rote stumped him. Higher level stuff...no problem. I wonder how many kids learn in a similar way. If you're right than quite a few.

If I had tried to make him learn math "in order" he would have hated it. So I just let him do what he liked and skip the stuff that annoyed him.

Years later I don't think he is any worse for it. He can do "the annoying stuff' most notably long division and long multiplication problems. He doesn't usually make mistakes and he seems to know his times tables. I did make a point to eventually walk him through long division so he would understand it but the other stuff he picked up mostly from working with algebra.

Its interesting to read opinions on math education. The debate is so impassioned. It never fails to surprise me how invested people get. There are many educators out there that strongly believe that children need hours of drilling basic math in order to ever be mathematically literate.

I love this post!  I have found this so true of how my son is learning and it’s nice to hear that another child was successful in learning this way.

Katherine writes:

Seriously. Algebra should be part of math instruction from the beginning. Since it's *in there* anyway.

We included Algebra in early education.  We just didn’t call it Algebra.  Math is everywhere.  Would you like one cookie or two?  If I gave you three cookies and Dad gave you some cookies so you had five total, how many cookies did Dad give you?  My son learned acceleration and triangulation as practical knowledge when he was little.  He had a use for them so he learned them. 

Another interesting article I’ve come upon is The Teaching of Arithmetic I: The Story of an experiment by L. P. Benezet, Superintendent of Schools, Manchester, New Hampshire, 1929.  In this article Mr. Benezet tells of an experiment he conducted and the findings of this experiment.  Mr. Benezet in Part III  writes:

 ‘They saw what we were trying to do and were surprised at the ability to reason and to talk, shown by children whose minds had not been chloroformed by the dull, drab memorizing of tables and combinations.’

In this article, arithmetic wasn’t formally taught till seventh grade!  Instead, the teachers concentrated on teaching the children to "read, reason, and recite”.  When I read this, it made me think of some of the reading I’ve done about the Thomas Jefferson approach to education and the Charlotte Mason approach.  I’m not an expert at either of these approaches but from what I’ve gathered, they focus on literature and building up the character through these readings.  By teaching the child to think and reason, the child learns and can apply concepts to more areas of understanding.  Hmmm…That explains quite a bit about how my son is learning.

My youngest son’s unschooling math journey:

My youngest really didn’t enjoy the repetition system. He felt that once he read it, he had it.  I must say, that seemed to be the case.  My oldest was a firm believer in the repetition system as that’s how she learned.  I was tired of the fussing so I went looking for other ways.  At first, my spouse was adamant that I could unschool everything except math.  So I did what every practical Mom does and I turned that subject over to him!  He wanted it his way, so I let him at it.  That didn’t last long.  In fact, I don’t even think it went two consecutive days!  Being me, I wasn’t going to just ignore the situation so I went to the unschooling groups and learned some more. 

The Life of Fred series was suggested and since I love books, I went looking.  The books are suggested for about fifth grade and up so I had time.  I finally bought the complete series last year when my son, by age, would be considered fourth grade.  They sat on the shelf for a period of time after the initial interest and the opening giggles the Story of Fred creates.  Then one day, my son came to me and asked if he could just read them as a novel and skip the problems.  I told him of course!

He sat down with the first book and giggled his way through it.  Then he moved on to the next book and while reading that one, he went back on his own, and started re-reading the first one, doing all the equations along the way!  I must add, he got them all right, too!  He has since moved on to the third book ‘Beginning Algebra as serious as it needs to be’.   This book really caught his attention and he ran to me to share what he had just read:

Here in print, was EXACTLY how he was feeling about ‘normal’ math books!  WoW!  This author gets it!  So here I am, with an unschooling ten year old, who loves math!  He always DID love math but those redundant math books would have beaten the love of math out of him.  Do I assign him a certain amount of pages he must cover in a given day?  Absolutely not!  Why would I set limits?  Sure there are some weeks that he doesn’t open up a math book and that’s OK.  There are days he does.  Besides, just how advanced do I need him to be?  If without prodding, he is still learning at an accelerated rate, why would I interfere?  No.  I see my job as always being on the lookout for more interesting things that will continue to enrich his world.    

Vicki

OK, so I can get some sleep tonight, I'm going to share my final thoughts on triangulation and why it's important.    I am sure that I probably had some early learning of this math form as I come from a family of engineers.  I know I didn't study it in public school.  I know my brother used it to find the Bahamas when he took me there on his newly designed boat for it's maiden voyage.  Without a good concept of triangulation, one could miss the islands completely and find oneself lost in the middle of the Atlantic.  Not an experience I personally wanted.  But this isn't the situation that made the concept of 'triangulation' stick in my head.

Many years ago, I was a 911 operator for a small village in south Florida.  I worked the midnight shift.  One night, I received a few 911 calls about a boating accident that happened in the intracoastal waterway but in a wide section so it was hard to locate where exactly.  Thank goodness, the Sgt. on duty was educated.  He sent an officer to each of the locations that had called in the accident.  By doing triangulation, then "borrowing" a boat, he was able to get medical help to the victims rather quickly considering the location of the accident. 

I hadn't remembered this particular situation when I first posted of my son learning the concept to locate a small bird's nest in middle of twenty acres.  But tonight as I tried to get to sleep, this memory wouldn't go away.  So there it is.  We never know what we may some day need.  It also makes me realize that I have too many sad stories even if a rescue was accomplished.

God bless you all and I pray he keeps you all safe.

Goodnight.

Vicki

Click on the pictures for detailed explanation

Hope that helps!

So today I thought I'd post what my son learned this weekend as this is a homeschool blog, lol.  

Triangulation:  

1. 1. A surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry.
   2. The network of triangles so laid out.
2. The location of an unknown point, as in navigation, by the formation of a triangle having the unknown point and two known points as the vertices.

The reason this 'lesson' came about, was my ds (9) and my dh were out walking around our property and playing with the pets.  They came across a killdeer nest out in the open field.  Now if you've ever tried to locate a killdeer's nest, you'll know they can be very hard to find.  So my son wanted to mark the nest so we can protect it but also, so we can return to it to watch the eggs hatch!

My spouse took this time to explain triangulation and how to apply it.  So this afternoon, my son took me on a walk and using his new skill, located the nest quickly.  He was also able to point out the mother killdeer, who had wandered away to feed.