The beauty of homeschooling is that you can do so much more than in school, and in a much more fascinating way - use it!
By Julia Brodsky, homeschooling mom, NASA engineer and math educator at Art of Inquiry, LLC http://www.artofinquiry.net/about-us-2/.
We are not going to discuss the accelerated math courses here – rather, we will explore how young homeschoolers can do some math on their own. Some of them involve teaching younger children, writing and translating math books, and doing other projects that involve math, such as robotics and computer science. All these types of projects worked extremely well for my kids, keeping them motivated to explore more math, learn math terminology, and find more people to talk to about math. Socializing and math is a very effective concept, which rarely presents itself in school setting, but may be fully implemented in homeschool environment.
To keep children motivated to explore deep math concepts, many parents turn to math circles. A lot of homeschooling parents are interested in starting their own math circle – and we are seeing more and more resources to help with that. Books by Maria Droujkova and Anna Burago are a wonderful place to start.
For older kids, doing something for the community may be highly stimulating and meaningful. This year, my daughter was invited to teach math to 4-5 year olds at private day care. Here is her blog, Tricky Pre-K Math http://trickyprekmath.blogspot.com/. Not only she had to think of the topics that may keep the attention of younger crowd, she also had to present the problems in both meaningful and entertaining way. Overall, her experience was very successful. Little ones loved to be taught by an older child; parents were happy that their little ones were learning about fractals, infinity and other deep math concepts; and she herself had to go over tons of math books to find suitable problems, learning a lot on the way. This year, she plans to teach "in-school field trip" classes in the local elementary school on a monthly basis.
The older students may enjoy teaching a math circle or math contest prep club on their own. Many of you shared that students work as coaches for MOEMS and Mathcounts. By doing so, they learn math, contribute to the community, and serve as role model for younger kids. Not only that, the math club leaders learn how to deal with groups of people, how to organize a class, how to develop a lesson plan, how to present the material in clear way - all of these being so valuable skills, both in college and in life overall.
Another way is to contribute to the citizen science projects in math and development of math resources http://www.moebiusnoodles.com/2013/06/problemsolvingminimooc/.
Students may contribute to rating math videos in Khan academy https://www.khanacademy.org/, developing courseware and math videos for fellow students, translating math books, textbooks and articles for American Mathematical Society http://www.ams.org/home/page and other math book publishers, and providing suggestions to math games developers ( such as Lure of the Labyrinth MIT math game http://labyrinth.thinkport.org/www/). Some students may build and share their own math games online.
With math skills being quickly computerized, students will benefit from developing higher-level skills, such as math modeling and math software skills. Many young students love building graphs and exploring relationships in Excel. Older students may enjoy Insight Maker https://insightmaker.com/ system dynamics tool, Matematica http://www.wolfram.com/ and Matlab https://www.mathworks.com/.
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