Yesterday I was thinking about blogging about some ways we could use time in order to have a feeling of accomplishment as we finish off the year. I will still blog about that, but meanwhile, last night, I suddenly realized this is not only the end of a year, 2009, but the end of a decade, the first decade of the 21st century. This idea led my thinking in a whole different direction, pondering these past ten years.

Of course, we laugh now as we think of how, in the months leading up to 2000, there was the big build-up to “Y2K”. For those reading this who may not have heard of it, Y2K was when, as we approached midnight of December 31, 1999, due to a problem with the calendars in many computers, it was thought that one minute into January 1, 2000, many computer systems would crash, causing worldwide disasters, including power outages. Fortunately, due either to frantic searching for solutions, or to this possibly being mostly hype, we survived and did not have to use our kerosene lamps and stockpiles of food and bottled water! (Some people had amassed months of emergency supplies, as the threat was made to sound quite real and serious.)

Although Y2K was basically insignificant, for a lot of people it began a decade in which tragic events occurred which caused many lives to be lost and many to be never the same again. Here are a few. The Gujarat earthquake of January, 2001. The attack on America on September 11, 2001. The Iraq war. The Afghanistan war. The European heat wave of 2003. The Indian Ocean tsunami of 2004. Hurricane Katrina, 2005. The Sichuan, China, earthquake of 2008. Cyclone Nargis, Burma, 2008. The economic downturn. (Click here for more info on natural disasters of this past decade.) I am sorry about the losses suffered by those affected by these (and other) events, and I hope that the new year and decade ahead will be a time of new hope and restoration.

What else have we seen in this decade? One thing is the continued increase of technological advances. The iPod. The iPhone. Lots of text messaging. Social networking. Facebook. Twitter. As this ABC News article states, “The ’00s have brought us blogs on every subject, random thoughts on Facebook and Twitter, 10,000 songs in our pockets and piano-playing cats on YouTube.” We can access and share information so fast now that it seems unbelievable. We can so quickly “connect” with so many people we have never met in real life. We can “add” them, “friend” them, and “block” them. Is all of this good? Is it bad? Or is it just different? Is our communication more effective with these tools? Perhaps so – or is it just faster? Is it shallower? Perhaps. I welcome your comments on this. What do you think? Interestingly, I just noticed that in writing the above sentence and question I am actually part of this “communication revolution” myself, lol! I am asking you, my readers, many of whom may be people I don’t know, to interact with me on a blog. This is new for me, but I’m thinking and hoping I will like it!

How has this decade been for me, personally? How have I grown, changed? It’s hard to summarize ten whole years without making this post longer than I want it to be, so I’ll focus briefly on just the last few years. I’m happy that I have become more “goal-oriented” in the last couple of years. Instead of merely making New Year’s resolutions, I have been writing down goals and developing the habit of thinking often throughout the weeks and months, about what I want to do, and what steps I’ll need to take to accomplish these goals. Reading a lot of articles about goal-setting and time management has really helped me to keep my goals in view. As a result, I have achieved at least some of them, starting this website being one.

Another significant development for me in this decade has been my renewed interest in art. Around 2007, while working in a call centre, I noticed some of my co-workers honing their drawing skills while waiting for calls. (We were allowed to do quiet activities like that, between calls.) Inspired, I decided to buy some felt pens and start making abstract designs. Since then I have been exploring being creative with pastels and acrylics. In 2009 I have been mainly using acrylics, and in October this year I displayed some of my paintings at a local coffee shop. In pondering this seemingly “new-found” art interest, I realized that I have had an “undercurrent” of interest in art for most of my life, but it was dormant. I used to draw cartoons occasionally (such as Fred and Wilma Flintstone, Dennis the Menace, and a few others.) Our family frequently visited our local art gallery on Sunday afternoons. I enjoyed these trips, and, in retrospect, I feel that these visits instilled in me an appreciation for art, although if you had asked me even five years ago if I was interested in art, I probably would have said, “No.” Isn’t it funny how these things can be deep inside, unnoticed, waiting to be awakened decades later? In me it’s like embers that are being re-kindled into flames, and I am excited about seeing where my art will lead!

How has this past decade been for you? What have you learned? How have you grown as a person? What are your hopes for 2010 and the new decade? I look forward to reading your comments. Let’s connect.

Fractals – Unit Study Ideas

Ever since I was a child, I have loved learning and been fascinated by information. That is why I decided, in Grade 12, to become a teacher. After university, I taught school for a year. Although my life and career path have taken me in other directions since then, I still love to research, learn, and impart to others what I am learning. Last night, my niece, Honey, and I, were discussing this, and she suggested that developing ideas and resources for unit studies for homeschoolers would be a good way for me to communicate about some of my interests. (Of course, the ideas could be used by classroom teachers as well, and anyone who wants to learn about whatever topic the ideas are about.) Since I love surfing the Internet anyway – let’s call this “research” – I found this idea very appealing and exciting!

Recently I have been getting interested in fractals, so I thought this would be a good topic for generating some good unit study ideas.

If you are not familiar with fractals, here is a pretty straightforward definition. I got it from Xaos – Fractal Zoomer, an application (fractal viewer) I downloaded a few days ago: “A fractal is a shape that is built from pieces each of which is approximately a reduced size copy of a whole. This process repeats itself to build the complete fractal.”

The word “fractal” was coined by Benoit Mandelbroit, who discovered fractals in the 1970s. Besides forming a new branch of mathematics (fractal geometry), fractals have a wide variety of other applications including art, economics, music, and many aspects of science.

As I have been looking at a lot of fractal art lately, I have been absolutely awestruck by their beauty, and this is the main thing I enjoy about fractals. To get a “taste” for the beauty of fractals, I recommend having a look at this video clip, which shows some fractals set to music. (More clips of fractals set to music will be included at the end of the post.)

Fractals to Music

Many examples of fractals can be found in nature, such as in broccoli, fern leaves, our lungs, forked lightning, clouds, mountain peaks, snowflakes, and coastlines. Here are two sites that show cool pictures and descriptions of fractals in nature

17 Captivating Fractals Found in Nature

Naturally Occurring Fractals

This site is a really good one for introducing fractals to kids. It is well-organized and has some cool activities. Questions and teacher notes are included.

A Fractals Unit for Elementary and Middle School Students

This comprehensive site includes information on different types of fractals, 36 famous fractals, and a lot more. It also provides a very good page of reference books about fractals.

Fractals Unleashed

This site has a fractal math lesson on it, lots of beautiful fractal pictures, and even a link to fractal jigsaw puzzles!

CoolMath’s Fractal Gallery

On this interesting website you will find some fractal art galleries, tutorials, a page of suggestions for software to make fractals, as well as a page with a lot of links about fractals.

FractalArts.com

I would say this is the “granddaddy” of fractal sites! If you want to go deep into the mathematical aspects of fractals, this is the place to see! It includes a section of lesson plans for middle school and high school levels. (To find the lesson plans, go to the left side-bar, and select #12.)

Fractal Geometry

At the above site, if you go to the left side-bar and select “3K – Fractals in Art”, and click on Decalcomania, you will find an interesting, fun activity – making fractal patterns in paint.

Here’s a cool fractal pop-up card to make:

Fractal Cut

As mentioned near the beginning of the post, here are some more video clips of fractals with music. I hope you enjoy them!

Apophysis 3D fractal animation … music Bach Badinerie BWV 1067

Fraktal Nr. 3

(This one is exceptionally beautiful – the fractals are spheres with exquisite designs on them!)

Fractal Crystal Spheres

I hope you have enjoyed looking at these websites, and that you find them useful. You may also find some helpful books about fractals at your local library or bookstore.  A few that I found in the library where I live are:

Fractals – by Hans Lauwerier

The Colors of Infinity:  The Beauty and Power of Fractals – with contributions by Ian Stewart, Sir Arthur C. Clarke et al.

The Fractal Geometry of Nature – by Benoit B. Mandelbroit

The Snowflake – winter’s secret beauty – by Kenneth Libbrecht;  photographs by Patricia Rasmussen

If any of you would like to recommend any other helpful resources, please mention them in the Comments. Thanks!

Fractals – Unit Study Ideas
Ever since I was a child, I have loved learning and been fascinated by information. That is why I decided, in Grade 12, to become a teacher. After university, I taught school for a year. Although my life and career path have taken me in other directions since then, I still love to research, learn, and impart to others what I am learning. Last night, my niece, Honey, and I, were discussing this, and she suggested that developing ideas and resources for unit studies for homeschoolers would be a good way for me to communicate about some of my interests. (Of course, the ideas could be used by classroom teachers as well, and anyone who wants to learn about whatever topic the ideas are about.) Since I love surfing the Internet anyway – let’s call this “research” – I found this idea very appealing and exciting!
Recently I have been getting interested in fractals, so I thought this would be a good topic for generating some good unit study ideas.
If you are not familiar with fractals, here is a pretty straightforward definition. I got it from Xaos – Fractal Zoomer, an application (fractal viewer) I downloaded a few days ago: “A fractal is a shape that is built from pieces each of which is approximately a reduced size copy of a whole. This process repeats itself to build the complete fractal.”
The word “fractal” was coined by Benoit Mandelbroit, who discovered fractals in the 1970s. Besides forming a new branch of mathematics (fractal geometry), fractals have a wide variety of other applications including art, economics, music, and many aspects of science.
As I have been looking at a lot of fractal art lately, I have been absolutely awestruck by their beauty, and this is the main thing I enjoy about fractals. To get a “taste” for the beauty of fractals, I recommend having a look at this video clip, which shows some fractals set to music. (More clips of fractals set to music will be included at the end of the post.)
Fractals to Music
Many examples of fractals can be found in nature, such as in broccoli, fern leaves, our lungs, forked lightning, clouds, mountain peaks, snowflakes, and coastlines. Here are two sites that show cool pictures and descriptions of fractals in nature
17 Captivating Fractals Found in Nature
Naturally Occurring Fractals
This site is a really good one for introducing fractals to kids. It is well-organized and has some cool activities. Questions and teacher notes are included.
A Fractals Unit for Elementary and Middle School Students
This comprehensive site includes information on different types of fractals, 36 famous fractals, and a lot more. It also provides a very good page of reference books about fractals.
Fractals Unleashed
This site has a fractal math lesson on it, lots of beautiful fractal pictures, and even a link to fractal jigsaw puzzles!
CoolMath’s Fractal Gallery
On this interesting website you will find some fractal art galleries, tutorials, a page of suggestions for software to make fractals, as well as a page with a lot of links about fractals.
FractalArts.com
I would say this is the “granddaddy” of fractal sites! If you want to go deep into the mathematical aspects of fractals, this is the place to see! It includes a section of lesson plans for middle school and high school levels. (To find the lesson plans, go to the left side-bar, and select #12.)
Fractal Geometry
At the above site, if you go to the left side-bar and select “3K – Fractals in Art”, and click on Decalcomania, you will find an interesting, fun activity – making fractal patterns in paint.
Here’s a cool fractal pop-up card to make:
Fractal Cut
As mentioned near the beginning of the post, here are some more video clips of fractals with music. I hope you enjoy them!
Apophysis 3D fractal animation … music Bach Badinerie BWV 1067
Fraktal Nr. 3
Fractal with own pictures
(This one is exceptionally beautiful – the fractals are spheres with exquisite designs on them!)
Fractal Crystal Spheres
I hope you have enjoyed looking at these websites, and that you find them useful. You may also find some helpful books about fractals at your local library or bookstore.  A few that I found in the library where I live are:
Fractals – by Hans Lauwerier
The Colors of Infinity:  The Beauty and Power of Fractals – with contributions by Ian Stewart, Sir Arthur C. Clarke et al.
The Fractal Geometry of Nature – by Benoit B. Mandelbroit
The Snowflake – winter’s secret beauty – by Kenneth Libbrecht;  photographs by Patricia Rasmussen
If any of you would like to recommend any other helpful resources, please mention them in the Comments. Thanks!

Posted: December 11th, 2009 under Uncategorized .
Tags: Art, Fractal Geometry, Fractals, Homeschooling, Math, Science, Unit Study Ideas
Comments: none

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I Do My Best – A Tribute to Mrs. Whittaker

There are times when one seemingly “small” act of kindness can powerfully impact the recipient’s life for years to come. Such was the case in late October, 1963, when my Grade One teacher placed a bookmark on my desk. Printed in felt marker below a little drawing of a smiling pumpkin, was this simple sentence: “I do my best.”

I do my best. Such powerful words. Evidently, my teacher, Mrs. Whittaker, saw that I was putting forth my best effort in my work, and decided to reward me with these words of affirmation. Through this simple action, she communicated to me that doing one’s best is what counts. What’s important in life is not — “Did you do the task perfectly? Did you get 100% on the exam? Did you win the game? Did you do something better than someone else?” – but, “Did you do your best?”

“I do my best” became my approach to life throughout my school years and beyond. I aim for “excellence”, but not necessarily “perfection”. I appreciate Michael J. Fox’s thought on this: “I am careful not to confuse excellence with perfection. Excellence I can reach for; perfection is God’s business.” Perfectionism generates anxiety and sets us up for disappointment and feelings of failure. Perfectionism is based on the misbelief that we can and must do everything right, all the time, which is impossible. If we put this type of expectation onto ourselves, we can feel that we have failed if we make even a small mistake, or if we get anything less than the highest possible score on a test. As a result we can be robbed of the satisfaction we could have had from enjoying what we did and simply knowing that we did our best.

An attitude of excellence, on the other hand, means saying to ourselves, “I will do the best that I can with the knowledge, ability and resources available to me .” If we choose excellence, it is not tragic if we make a mistake. We do not have to become stressed out if something we do does not turn out perfectly. If we make mistakes we can learn from them, and grow in character and ability. With an attitude of excellence, it really doesn’t matter if someone else can do something “better” than we can, because our focus is not on outdoing others, only on being and doing the best that we can. I have found that this attitude brings me a lot of contentment.

A couple of days ago, when going over my school report cards, I found the bookmark. It means so much to me, and I’m really glad I still have it. When I looked at it, I thought, “I would like to thank Mrs. Whittaker for how she influenced the direction of my life.” I don’t know how to contact her, so I got the idea that I could write this blog post and perhaps she will come across it someday. So, Mrs. Whittaker, if you are reading this, I say a big “Thank you!” to you for encouraging and challenging me to develop the lifelong habit of doing my best!

Michael J. Fox quote:

http://www.quotationspage.com/quote/3172.html

Interesting articles about perfection versus excellence:

http://www.medhunters.com/articles/fromPerfectionToExcellence.html

http://www.ivysea.com/pages/intrap_0701_2.html

http://simplemom.net/how-to-be-disorganized-unproductive-aim-for-perfection/

There are times when one seemingly “small” act of kindness can powerfully impact the recipient’s life for years to come. Such was the case in late October, 1963, when my Grade One teacher placed a bookmark on my desk. Printed in felt marker below a little drawing of a smiling pumpkin, was this simple sentence: “I do my best.”

I do my best. Such powerful words. Evidently, my teacher, Mrs. Whittaker, saw that I was putting forth my best effort in my work, and decided to reward me with these words of affirmation. Through this simple action, she communicated to me that doing one’s best is what counts. What’s important in life is not — “Did you do the task perfectly? Did you get 100% on the exam? Did you win the game? Did you do something better than someone else?” – but, “Did you do your best?”

“I do my best” became my approach to life throughout my school years and beyond. I aim for “excellence”, but not necessarily “perfection”. I appreciate Michael J. Fox’s thought on this: “I am careful not to confuse excellence with perfection. Excellence I can reach for; perfection is God’s business.” Perfectionism generates anxiety and sets us up for disappointment and feelings of failure. Perfectionism is based on the misbelief that we can and must do everything right, all the time, which is impossible. If we put this type of expectation onto ourselves, we can feel that we have failed if we make even a small mistake, or if we get anything less than the highest possible score on a test. As a result we can be robbed of the satisfaction we could have had from enjoying what we did and simply knowing that we did our best.

An attitude of excellence, on the other hand, means saying to ourselves, “I will do the best that I can with the knowledge, ability and resources available to me .” If we choose excellence, it is not tragic if we make a mistake. We do not have to become stressed out if something we do does not turn out perfectly. If we make mistakes we can learn from them, and grow in character and ability. With an attitude of excellence, it really doesn’t matter if someone else can do something “better” than we can, because our focus is not on outdoing others, only on being and doing the best that we can. I have found that this attitude brings me a lot of contentment.

A couple of days ago, when going over my school report cards, I found the bookmark. It means so much to me, and I’m really glad I still have it. When I looked at it, I thought, “I would like to thank Mrs. Whittaker for how she influenced the direction of my life.” I don’t know how to contact her, so I got the idea that I could write this blog post and perhaps she will come across it someday. So, Mrs. Whittaker, if you are reading this, I say a big “Thank you!” to you for encouraging and challenging me to develop the lifelong habit of doing my best!

Posted: December 11th, 2009 under Uncategorized .
Tags: Excellence, Motivation, Personal Development
Comments: none

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