How do your kids learn math?

I get asked a lot of questions about homeschooling and unschooling.  One question I've been getting more recently is, "How do your kids learn math?"  And, "What about things like algebra and calculus?"  Honestly, I have no idea about algebra and calculus.  I never took calculus and algebra never seemed like a big deal - it was a different way to figure things out in the world, but it didn't seem especially difficult.

As far as math in general is concerned, that's hard to describe.  I could describe things we do that are math, or require some figuring, but we obviously don't follow a linear curriculum.  I would consider the picture above to be about math - Julian was inventing different bugs that lived in an underground world (much like a particular Minecraft mod).  When Julian and Oliver organized their stuffed animals in piles of big, medium and small - that was sorting, and that's math.  The patterns that Oliver is always making on paper, with Legos, with K'nex, in his head, with the hose water on the side of the house, those things are all math because patterns are math.  When my kids listen to music, they are, in a way, listening to math.  You can't learn how to read music without also learning patterns, fractions, and probably more that I can't think of right now.
Of course, there's also the regular counting of things to make sure they both got the same amount, or figuring out how to divide things up so they get both get an equal share, or figuring out how many of what chores they'll have to do to earn enough money to buy their next "Mixel."
This all happens "naturally," but it doesn't just happen.  As an unschooling parent, one has to see life as learning - it's all learning, there is no summer break, and no cramming for finals (unless you decide to go to school).  You are learning all the time.  So when my kids ask a question, a lot of times I don't just give an answer and leave it at that.  Most of the time I try to show them the answer, walk them through my thinking processes to illustrate how I got there.  Unless I see their eyes starting to glaze over, in that case I quickly shut up and give them the answer.  There's no point, I know they'll get it when they actually want or need to know it.  I know this because this has happened over and over again.
At this point maybe I should be asking people, "How would my kids not learn math?"

Whoa! We bought a house!

So, we bought a house about a week and a half ago, and it's been fun. Busy and confusing and tiring and even emotional, but also fun. Amid the mental chaos that accompanied the processes of buying and moving into our house I kind of forgot to go running or ride my bike for a few weeks. Or I was exhausted from thinking about buying a house, wondering what some of the piles of papers were that  I just signed, even though they made perfect sense at the time.
What happens when I forget to run or ride my bike? A dullness takes over my body and mind. Does that even make sense? A dullness? It's more like all the cells in my body feel heavier and slower and sadder and angrier. But it creeps up on me, so I don't notice it right away, until one day I'm wondering why everything is so hard and why I don't like my life anymore.
So I'm running again.  It's hard because I don't want to at first, but then again I don't want to do anything, so why not do what I know will help me feel better?

We went to the river with our friends Niko, Deva and Emily this morning!  It was perfect.  Everyone got more wet than they intended to - Julian fell in up to his neck.  He was not happy about it. 

 Oliver throwing mud balls into the river.

 Deva instructing her assistants - Niko and Emily.

Julian sloshing around.

It's mornings like this that I'm so glad we get to homeschool.  

Grossology

There is an exhibit at the New Mexico Museum of Natural History and Science called Grossology, apparently based on the book.  Oliver pronounces it Gross Algae.  These are pictures of a giant version of Operation.  Not pictured are the squeeze bottles of stink.  You squeeze a smell into your face and guess what the smell is from.  Choices include: armpit, feet, mouth and anus.  I smelled one, saw the options, and decided not to find out what I had smelled or ever smell another squeeze bottle again.  

Mac-n-cheese Dominoes

Ollie spent a long time using the Mac and cheese boxes like Dominoes, only after he accepted the fact that we would not be cooking all of them at once.  Later water was involved and I had to relocate the contents of some of the boxes to ziplock bags.  

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An Inquiry Into Unschooling In Our Home

This is part of a qualitative inquiry I did last year on unschooling, as it applies to our family!  

I'll post more interesting stuff next time!  (I think!)

O and J are making paper train tracks.  J has superior cutting skills, so he takes on that job. O supervises and explains how he wants the paper train tracks to look.

Inquiry question:

    How will Julian’s focus and understanding grow without the use of shaming methods to manipulate his behavior and by allowing him to be in control of his learning and time?

Sub-Questions:

·      What will he decide to focus on?

·      What will his learning look like?

·      How deep will his understanding be, and will it be measurable?

·      Will I be able to step back fully and trust him to learn on his own?

Once I developed my wonderings, I began voraciously reading homeschool accounts by homeschooling parents and students.  I learned many different ways people homeschool, and how their methods worked, or didn’t, for them and their children.  These sources included books by homeschooling families, books about homeschooling with anecdotes from homeschooling parents and children, and blogs about homeschooling written by both parents and children. 

Through my readings, I quickly learned how diverse the homeschooling population is.  Some essentially have “school at home” while others are devout “unschoolers” – a term coined by John Holt in the 1970’s in an attempt to describe “learning and teaching which does not in any way resemble school and which does not necessarily have to take place in one’s home”  (Farenga, 2003, p. 61).  John Holt was at first a proponent of school reform, but after many years of frustration with a public education system that seemed to only give lip service to what he considered to be positive change, he decided the best way for children to learn would be in the home, no matter how good the schools were.   

I have been encouraged when reading anything by Holt, as this inquiry is, in a way, an inquiry into unschooling as it applies to our family, and specifically to Julian.  But there were some materials that I read that didn’t support what I was attempting.  As I read Looking Backwards: My Twenty-Five Years as a Homeschooling Mother by Joyce Swann (2011), I honestly sank deeper into my chair and took faster and deeper breaths out of shame for wanting to let my kids learn whatever they wanted.  Swann begins by chronicling how she began homeschooling her oldest child, developing her own curriculum at first, with her children eventually using schools that gave accreditations and degrees through correspondence distance learning.  All of her children had Masters degrees by age 16.  Their family basically did school at home.  Swann (2011, p. 3) says, “If you are going to have a successful homeschool, you must understand that without clearly defined school hours, your school will fall short.”  However, it is assured and broad statements like these that have always been troubling to me.  That was true for her family’s homeschooling, but when I thought about changing our homeschooling style to something rigid and mandatory, it sounded dreadful, like everyday would be a chore to get through. 

Most of the homeschooling books I read didn’t specifically espouse a structured homeschooling environment, but described different environments that many homeschooling families find to be effective.  Some of these books include Homeschooling 101: The Essential Handbook by Mark and Christine Field, The Homeschooling Option: How to Decide When it’s Right for Your Family by Lisa Rivero, and The Homeschooling Book of Answers: The 88 Most Important Questions Answered by Homeschooling’s Most Respected Voices by Linda Dobson.  

Closer to the other end of the spectrum (if there is a homeschooling spectrum) might be someone like Penelope Trunk.  On her homeschooling blog - http://homeschooling.penelopetrunk.com/ - she often talks about how her kids do almost whatever they want, and how great it is for them.  On one of her most recent posts, High Achievers Have lots of Playtime, Trunk (2013) states

So often people tell me that I need to force my kids to learn stuff they hate and I need to force my kids to sit still for long periods because this is what adult life requires. But I think it's the opposite. You need to make sure your kids have enough play time so they grow up and are early risers because they know the importance of having time for self-expression.

The idea that children (and even adults) need time to play to be healthy, productive members of any society isn’t new.  In the article The Play Deficit: Children Today Are Cossetted and Pressured in Equal Measure. Without the Freedom to Play They Will Never Grow Up in Aeon Magazine, an online publication, Peter Gray – a psychologist and research professor at Boston College - cites Karl Groos, a noted philosopher.  In 1901, after writing The Play of Animals, Groos wrote The Play of Man, documenting how humans play and how it is vital to their proper development.  Groos talked about the role adults should take in children’s play saying, “Adults have three important tasks in this direction which are imperative – namely, general incitation to play, encouragement of what is good and useful, and discouragement of injurious and improper forms of play,” (1901, p. 402). 

Essentially, he says to mind your children.  They should be playing, but they are still very young and will need some reminders of what is ethical in their society.  Gray (2013) declares, “Play deprivation is bad for children. Among other things, it promotes anxiety, depression, suicide, narcissism, and loss of creativity. It’s time to end the experiment” (The Play Deficit).

While it was encouraging to read Groos and Gray’s work, I really loved reading the blog I’m Unschooled.  Yes, I Can Write.  The author, Idzie Desmarais, is a self-declared “unschooling vegetarian animistic green-anarchist feminist hippie child.” She grew up being unschooled and is now a well-spoken, intelligent, informed young adult who finds satisfaction following her passions.  

Some of the literature supporting our homeschooling life discusses unschooling within a school setting.  Examples are in the towns of Reggio Emilia, Italy and Matamoros, Mexico.  These cases will be examined further in the Trusting the Child section of this paper.

Unschooling?!

Sometimes it is so hard to unschool.  It sounds too easy to be true, just drop forced curriculum, learn what ever you want to, live as a cohesive family unit.   But as soon as I try, I'm bombarded by all the voices in my head telling me, "You're doing it wrong…"  "Your kids will end up failures…"  "They won't be happy with their lives and it's all because you thought they should be treated like humans and live free, democratic lives…"  Or worse, "They won't know the difference between there, their and they're…"  

And then my kids want to spend the majority of a day playing video games.  And even though we're all feeling sick, it still feels like I shouldn't be letting them just play video games for hours at a time.  

But then they start asking questions about the video games that I never thought of.  Like, "Is this really what Tokyo looks like at night?"  "Where is Japan?"  "Why do the Japanese and Chinese like dragons so much?"  "What's a Yin Yang?" "What's a ninja?"  What's a samurai?"  

Then we get to look up the answers to all these questions (or the beginnings of the answers) and talk about them.  We look up answers on several different sites to cross reference.  

And then it feels like, "Of course you should play video games all day."

Mario Candopoly!

J and O made up their own board game today, a mixture of Monopoly, Candy Land and Mario Party (using Diggity Dogs from a different board game).  The discussion about rules and how to play and the point of the game was extensive.  Just an excerpt:

O says, "When you get to a question mark anything can happen."  

J says, "Yeah, anything."

"If you get a shape, something will reappear.  It will give you 3,000 coins and $6,000."

"There is no way to have $6,000."

"Yeah, it just makes you have $6,000.  The ground will sink if you get a square."

We were actually able to play for quite a while.  We started out with 10 coins each.    I bought Tito's Peanuts, and tried to sell peanuts for 4 coins each.  J bought Senor Tucan's Gumdrops and sold gumdrops for 5 coins each, O bought Benny's Peppermints and sold Peppermint sticks for 4 coins each.  
No one bought peanuts from me, so I think I lost.  Oh well, when life gives you peanuts, make peanut-aide!

Why My Children Learn at Home

Chameleon Monsters "blending in" with the couch.

I am a homeschooling mother, which means I am my sons’ teacher.  I have two boys, one is three, and the other is six.  As a family we didn’t plan to homeschool.  I am currently working towards a Masters in Elementary Education and had planned on working in a school once both of our kids were of school age.  Now that we are homeschooling, we want to continue for as long as we can. 

There are many issues and inadequacies in public schools today that I have observed during my time spent in my son’s classroom in the Fall of 2012 and through informal talks with friends in the teaching profession.  These include mandated curriculum, high stakes testing (and the classroom culture that it creates), developmentally inappropriate time and classroom structures, and the punitive and shaming method for behavior management.  This – the punitive and shaming method of behavior management witnessed in my son’s classroom– was, for me, dismaying.

When our six year old, Julian was in Kindergarten he was constantly getting into trouble.  Every day after dropping him off at school we would not only wonder, but worry about the day he was having.  Is he getting in trouble?  What will the teacher talk to me about after school?  How pitying will the teacher look at me as she describes his unacceptable behavior?  Why was it I could take him to a grocery store without being embarrassed, but it seemed to take all of his will power to stay within the acceptable parameters of a kindergarten classroom? 

So, my husband and I each took time to observe and help in his classroom, to see what was going on.  Maybe there were certain triggers we could identify or certain times of the day that were problematic. 

What we discovered was the way the school day was structured was developmentally inappropriate for five and six year olds, in that there was a lot of sitting and writing.  The sitting and writing was mandated to the children from the teacher (which was mandated to her from the government).   No one had a choice in what to learn, and those who did best were those who wanted desperately to please the teacher, not necessarily those who best understood the content. 

How does a teacher get students to behave in a developmentally inappropriate way?  From what my husband and I saw, they shame them. This particular school uses construction paper circular faces of red, yellow and green.  Green is good, yellow means you had some trouble that day, and red means the teacher and parent must talk.

At first, I thought these circular faces were meant as an easy way to communicate to parents about how their child’s day went.  While observing in the classroom, I learned these colored faces are used to get children to behave.  As in, “You don’t want your mom to see that you got a yellow face, do you?”  Or, “If you can sit quietly and write your numbers I’ll take you off of red for today.”  Of course, the only children this reliably worked for were those eager to please the teacher, and even then it didn’t create lasting change, it was only in the moment. 

When we decided to homeschool our children – Julian 6 and Oliver 3 - we excitedly left these problems behind.  We also brought upon ourselves new problems that cannot occur in the public school setting, as it exists today.  Problems, such as: What do I teach my children?  How do I teach it to them? And generally, what do we do all day?

This got me thinking about how, in public schools, children are made to learn certain things, whether or not they have any interest in it.  I also began to catalogue all the things I learned in school that I have needed in my life, which led me to think about all the things I’ve needed in life that I didn’t learn in schools. 

Before homeschooling, I thought that a teacher should force a student to do their work no matter what, because it was “good for them.”  But after having children, and being witness to and participant in our wonderful, open and trusting relationship, I can more clearly see how poorly students are treated in schools.  It is evident that forcing children to do their work “no matter what” flies in the face of their humanity.  They are required to learn what is dictated to them, in the way it is dictated to them.  Not only are they not expected to have (or be capable of having) passions, they are not given any time to pursue nor develop them.  They are learning content and subjects that are said to make them “well rounded,” but some kids have “sharp edges.” 

When we began homeschooling, out of fear my child would fail in his life because he wasn’t going to school, I attempted to recreate a sort of school at home.  It wasn’t all day, but it consisted of me sitting Julian down at the dining table to do number drills, practice writing letters or words, reading something specifically because I thought it was educational, and even doing workbooks when I felt we weren’t being “academic” enough. 

This felt awkward because I was acting (or trying to act) like a teacher during “school time” and like mom during the rest of the day.  My son hated it, so of course I hated it.  He would refuse and I would entice, he would refuse and I would cajole, he would refuse and I would threaten.  Threatening usually worked, at first.  After a while it stopped working too.  So I began to shame him, just like his teacher had.  This only sometimes worked, but it always felt horrible.  It felt like I had broken the most important promise I had ever made to at least help him grow into himself with compassion, patience and love.  I can’t do everything, but can’t I at least be strong enough to give him space and time to be human?

Realizing that I was using shame to shape my son’s behavior led me to wonder, “Is the end result worth it?”  And, “What end result would have to be guaranteed to make me feel ok with doing what ever it takes to get my son to do well in his schooling?” 

After a lot of thinking and journaling, I realized that the end result would have to be my children knowing themselves well enough to know how to make themselves happy or satisfied, and having the tenacity to make that happen.  So then I began thinking about how to do that.  

So how does a child with “sharp edges” learn “what he needs?”   After assimilating everything I had read and recorded about our journey, I realized that before Julian went to school he was an eager learner and he absorbed everything easily without any formal instruction (at least not planned).  So I began to step back, to watch.  It seems like he has more intense and longer periods of focus when what he is working on is his idea, when he is working his way, at his pace.  It also seems that his learning and understanding are deeper when his project is fully his.  In light of these insights, I began to wonder how far this could go.  

Drawing a story.