Living Math


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Recording

Full recording: voice, chat, web tour, ebook sharing.

Select quotes from the event are here. I took two big action items home. First, as a community, we need to figure out a way to make tens of thousands of messages on the Living Math Forum more available and searchable. Second, we need to find a way to "virtually visit" math clubs, circles, and family activities of others. Stories are great for many things, but we need to see and hear, as well. - Maria Droujkova

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How Living Math came to be
  • I wanted to create the resource that I wished I'd had trying to change the way I approached my son's education. There wasn't a central place where you could find a lot of resources.
  • Ten years ago I haven't even heard about the term "math reader." There was Marylin Burns, John Scieszka, "The Number Devil," but there was no place where you could go and say, "These are readers, resources that worked well for my child and that you could try." People would share titles with me individually.
  • Montessori had the reputation of being too elementary. Saxon Math was still the one that had the biggest reputation, we did not even have Singapore Math, and Miquon was considered the most holistic at the time. But my son did not do well with workbooks.
  • When I was teaching classes, I was chatting about the classes, and people wanted to do the same thing in their homes, families, cooperatives. That's how my books started. I know some schools bought them, as well.
  • The more I was doing it, the more I ran into the same questions on different email lists. I am a member of San Diego Home Ed, Latin Classical Ed Books, Charlotte Mason Homeschool Community, Thomas Jefferson Ed. People would ask a question, and I would pose an answer, and the same question would come up again, with a slightly different twist. I would pose the same information again and again. The Living Math forum was an attempt to consolidate that: let's put it all in one place.

Future plans
  • There is a lot of information now in the Living Math Forum that I would like to migrate and make available, because it may be hard to find in archives.

Changes of the last decade
  • So much have changed in the last ten years. Because of the demand, the number of the resources is increasing exponentially.
  • Six years ago, when we started the Living Math forum, book closeouts listed great math books, but after a period of two or three years, they dried out. The demand in higher. We may have made an impact on it.
  • On Amazon, the number of new titles is increasing year by year. There are publishers that popped up, making titles like a funny story about division of fractions based on Rumpelstiltskin.
  • There are more people joining from other countries
  • There are more educators. At the beginning there were all homeschoolers.
  • When I started this, I had absolutely no thought that it would go beyond homeschooling. Not that I have given up on public education, but frankly, it seems like such a massive problem for undertaking. I still have four kids at home and I can't be much of an activist. At some point in my life, I won't be as involved in parenting, and I hope to do something like this.
  • I started thirteen years ago, and homeschooling evolved in a tremendous way. Before, when people homeschooled, their only interaction was with those they happened to bump into or manage to make connections with face-to-face. The internet has created many opportunities for people to network, to hook up with others, and to share information and resources.
  • It's how I set up my classes - I posted it on the San Diego HomeEd list: "I am opening it up, would you like to join?" That's how I filled my classes, that's how I formed a cooperative, that's how I formed science clubs.

Math is for all ages
  • Archimedes' principle of exhaustion is pretty complex, but it can be modeled and explored with young kids.
  • As a homeschool parent, working with many people expanded my horizon. I opened my home to others, and was rather ambitions to teach three levels of classes, because I had three levels of kids. I had a very young class for my daughters. We were working with the same ideas in lockstep in each class, but at different levels. For example, with the very youngest, we used beans and broken spaghetti to model Mayan numbers and just play with it. At the level of my middle son, we were more abstract. We were able to use the reading they did in-between for the activities. And with the twelve to fourteen year olds, we went even farther.
  • We built a proof of the Pythagorean theorem with Cuisinaire rods. I was able to do it with the youngest and the oldest, because it was a new way of thinking to them. Even teens wanted to actually get their hands on these activities.
  • There are a lot of math ideas not specific to an age group. For example, exponential growth: a five-year-old can experience that! With the chessboard story. An upper elementary child can experiment with how many times you can fold a paper onto itself.
  • With the youngest, when we read a story about negative numbers, we are not looking for them to fully master negative numbers and jump into algebra. It's like a hook: they will remember the stories years later.
  • I went through the whole "The Man Who Counted" with my daughter over a four or five months period, chapter by chapter. She did not initially have the algebra skills for it, but through drawing out, diagramming and thinking it through, she could engage with many problems that are in the story form. Now that she is doing algebra as a class, she is flying through, because she was doing algebra all along.
  • For my kids, the more ways they learn something, the better they retain the information. We read about it, we talk about it, we do an activity about it, and watch a movie about it, and it sticks.

The role of history
  • One of the "From Five Fingers to Infinity" quotes I absolutely love says that one can invent mathematics without knowing much of its history, you can use mathematics without knowing much, if any of its history, but one can't have a mature understanding of mathematics without a substantial knowledge of its history.
  • The humanizing piece of historical stories adds interest. But there is another aspect. We often take for granted ideas that seem simple. Homeschooling parents ask, "Why can't my kid remember place value?" Archimedes, one of the greatest minds in history, would have discovered calculus as he was very close, but lack of the place value system held him back. It isn't that simple of an idea. This idea is a revolutionary invention.
  • A lot of the big trouble areas for people today - negative numbers, fear of variables, exponents - those were all, historically, ideas that mathematicians had most trouble with. These kind of abstract ideas took a long time to become accepted, and you get an appreciation of that when you study history.

Bridges between family learning and institutional learning
  • The other thing is the creation of so many different hybrid options for schooling that incorporate class elements and homeschooling. Before, it was either hundred percent school or hundred percent homeschooling. There's an explosion of charter schools, independent study programs. These part-time options cause homeschooling to grow. Now it's not as much homeschooling as alternative, blended schooling. The lines are blurred, so to speak.
  • About the feedback I get from "professionals"... There are times I feel shy a bit, and inclined to keep it within the homeschool community, because that's where I feel competent. And it's interesting when you guys reach out to me and tell me what's being said here and what's being developed has relevance to you, it builds a bridge. It even builds some confidence on my part that yeah, it has relevance beyond the homeschooling community.
  • Early on, as a parent, when you are willing and brave enough to experiment, you are worried about messing up your kids. My oldest is turning eighteen in a week. We talked extensively about how his education unfolded. He ended up going to a traditional high school. He never regretted earlier homeschooling: he learned to approach math in holistic ways, how to problem-solve, he understands math and he's never had trouble with it. He is going to college this year. For me, the job is done. I look at the results with my own kids, and the results people share on the Living Math forum, which is really important to me. It's not just my kids it works with! When I tutored and taught classes, I've never had someone say, "Oh, you stirred me wrong, you took me down the wrong path and now I regret it."


About the event


All Math 2.0 events are free and open to the public. Information about all events in the series is here:http://mathfuture.wikispaces.com/events

Saturday, May 15th 2010 we will meet in the LearnCentral public Elluminate room at 11am Pacific /2pm Eastern time.
https://sas.elluminate.com/m.jnlp?password=M.FCAF787B38E30D58F943EB7232EE27

Living Math is a tight, active community of several thousand family educators learning mathematics through stories. Here is some information from the LivingMath.net site.

LivingMathLogo1.JPG


"Beauty in mathematics is seeing the truth without effort." -George Polya

~ Insisting a child must be taught traditional, scope-and-sequence arithmetic to learn mathematics is like saying one must learn classical notes and scales before one can learn music. You might get there, but you miss out on the inspiration of beautiful music created by the masters along the way. We need not master all the "basics" before being able to experience the appreciation that carries us through the hard work of learning. Think of applying living math principles as developing a "mathematical ear" while working toward the mastery of basic theory. ~
This site is dedicated to sharing resources for learning, exploring and enjoying math in a dynamic and holistic manner, for all ages.
I want to build a bridge. I'd like to close the gap between math and history, science, literature and humanity created by the isolated way we traditionally approach math education.
In teaching my own children, tutoring and furthering my own self education, I've seen the results of early exposure to real mathematics in natural settings, without requiring mastery of arithmetic on a set timetable - this has been a key to the ease with which my kids attain mastery when the time is right for them. I've also found that math literature and history humanizes math, makes it come alive, and provides a context to enjoy and retain learning. Patricia Kenschaft of Math Power refers to a goal of preserving the "rage for learning" that every child has inside of them. I believe that the way we isolate mathematics learning with the contrived, unrealistically applied arithmetic our children are traditionally taught, without real context and the human drama that created it, has caused much of the math phobias and illiteracy ("innumeracy" to use John Paulos' term) our generation of educators, whether in home or classroom, experienced and pass on, as they know nothing else.

On Topic E-List - The Living Math Forum: http://groups.yahoo.com/group/LivingMathForum/ Dedicated solely to discussion related to living math and science methods and materials. See Articles for some topics. The Forum concentrates discussion related to non-traditional math methods and resources in one location. The archives are extensive and searchable by key words.
You may join via the web address, or send a blank email to LivingMathForum-subscribe@yahoogroups.com and respond with a brief description of your purpose for joining.
Book Recommendations: I am an unabashed book junkie, as you can see from my Math Reader Listings. I encourage you to use your local library, but if you decide to build a home library, using my links supports this site, and allows me to preview more books for you :o). I also review new listings on Bookcloseouts periodically on the LivingMathForum list.
Family Math History course: I'm developing a series of lesson plans with materials for all ages. These lessons have been used in our homeschool and cooperative classes. It is currently being published via .pdf file with notifications via email as additions are published. The material will eventually be incorporated in a 2 to 4 year guide for those wishing to apply this approach to their homeschool or group learning experiences. More info.

Event Host

Julie_Brennan.jpgI am a homeschooling parent of four, and work on this site in my spare time. We live in sunny San Diego, and take advantage of the weather and sites to actively learn in our environment :o)

Julie Brennan
San Diego, California

Julie's story of what Living Math is all about


“Reading math” is really a more central idea to Living Math than mathematics history. History became more of an offshoot of the reading approach to learning math. It was through my oldest son’s growing aversion to math, but intense love of reading, that we discovered this path to learning math could be very effective. Inevitably that led to learning the history of mathematics.

Living Math Through History ideas simply evolved from my own personal interest in the history of mathematics, which I found natural to share with homeschool parents who were humanities-oriented and who struggled with interest in math. I saw that even with myself having a math background as a professional CPA for many years, I struggled to find a way to communicate math in an interesting way to my children if they didn’t have the interest in the more traditional presentations, which were all I knew how to teach myself, or the ability yet to understand the financial context I understood math best in. When we discovered the books, Mathematicians Are People, Too, I found myself intensely intrigued that math had a very human history. I was frankly amazed that I went through so many years of schooling and never knew this fascinating history existed. I also saw my oldest son go from feeling apathetic toward math, to enjoying and having interest in math.

After a year of reading the books and doing many activities surrounding the individuals we read about, my oldest son went so far one day as to say he thought he might like to be a mathematician! I saw that for kids and/or parents who connect with biographies and history more than math itself, this approach could open doors of interest and enthusiasm that traditional approaches could not. This led to teaching homeschool co-op classes. As I described the classes on homeschool lists, I was asked to write up the plans for others. That’s how the plans that are on the website developed.

The reading and/or history approach is not for everyone, and it may not be a long term study for everyone. For kids that love math, learning its history can be fun and provide a deeper relevance, even as it will not usually take center stage. Kids who dislike reading will benefit from being read to, but may never take off and read stacks of math readers on their own. But over the years I’ve found there are many uses in between, from using material for math relevance and context to kids, to providing a math and science history course separate from math that can be stretched out over years. Parent teachers thought they disliked math find they can enjoy it for the first time and begin to even understand math as a cohesive, logical outgrowth of human activity over thousands of years.

The depth of the study can vary a lot as well; it can be something to kick-start interest at one level, which then leads to a more enthusiastic interest in math on a traditional path. We’ve all seen how one experience can light a fire that ignites a life long interest in a topic in ourselves or others. While my oldest son “read” math and learned non-traditionally in this way until 9th grade, my middle children have been more interested in the math itself, and thus have read less, and done more actual math. My 8th grader enjoys the math history stories, but he would rather work through his algebra text step by step than graze for many hours on middle school level quirky math readers, he is not a voracious reader like his older brother was. My daughters are split as well, one is clearly reading oriented and has already embarked on much the same math education path her oldest brother took, spending countless hours immersed in math readers and much more limited time on arithmetic instruction, while her older sister enjoys doing math and does not choose to read math readers beyond her years spent with math picture books. But to comment on the nearly-universal appeal of Mathematicians Are People, Too book series, all four of my children and all the kids I have taught have greatly enjoyed it, and had it read aloud and/or read to themselves many times over.

I believe the study of math history is vital and meaningful, particularly to the majority of us who study mathematics but will never become mathematicians. If one does not have an inborn drive to study mathematics, the infamous question, “What will I ever need this for?” is best answered by studying the history of mathematics, which highlights how pervasive mathematics are throughout science, music, art and nature. The critical role math has played in mankind’s development, both in practical and philosophical terms, cannot be communicated in tiny marginal insets in a textbook, the only way most traditionally-educated students ever get exposed to this history. The depth and breadth of a study of mathematics history can vary greatly, and it used to be the case that one didn’t have much access to readable materials unless they were a graduate student. But the wealth of materials becoming available to us that brings even some complex mathematical ideas in their historical context down to a level even a early elementary child can understand makes it possible to communicate the beauty of math, and the human role in discovering and developing it, to our own children. And we as homeschool parents benefit from the side-by-side study with our children, when many of us would not have read a scholarly text on the history of mathematics in our lifetimes.