Math Question

Paradise Found asked the following question in her blog:

How is it possible that a child can understand and complete the process of long division one day, and have forgotten how to do it by the next day?

I immediately opened the post from bloglines and started writing an answer. Then I thought that others might be interested in reading it:

The problem most kids have with math is they learn the mechanics of it but don’t understand why the mechanics of it solve the problem (in this case division). Long division is a repetitive process of the repetitive process of multiply-compare until the right number is found and then subtract.

If I haven’t pointed it out yet, after a certain point in math, almost everything reuses the simple math that was learned in the early years. So, it is by nature repetitive. The issue with learning something like long division is that a child who knows how to multiply, compare and subtract can follow the mechanical process of long division without learning a thing other than they have to do more of stuff they already know how to do.

I believe that is the reason most kids who start having problems with math at ages 8-12 have problems. It isn’t that they aren’t capable of it, but that they see no reason for it. They are just doing the same things in different ways to different numbers. And it’s boring.

I did a homeschool workshop a little over a year ago. During the workshop we got onto the subject of math and a one mother mentioned her child having problems with math. I responded, “He’s what, 9 or 10?” She was speechless. Because I was able to see all the faces in the audience, there were a few other mothers there who had had the same issue at the same age at some point.

What we did was use real problems. Packages of items that contain X items costs Y. How much did each X cost? This package contains 18 items. That one contains 24. Which one is less expensive per item? Opportunities for real math are all around us 🙂

An unheard voice

A week ago Joanne posted Unschooling Voices #1. The question for the July edition was, “How did you and your family come to unschooling?” Because of the schedule I’ve been running, I didn’t have the opportunity to answer the question in time for the July edition. But I do think it is a question worth answering. Before I get to that…

The optional August question is, “Do you extend the principles of unschooling (trust, freedom, etc) into any other areas of your child’s life?”. (Details on submitting blog posts)

The simple explanation of how our family came to unschooling is that it was all a matter of time. But that doesn’t really say very much. TBH, I have known for years that there was a single moment at which I stepped onto the path that through many twists, turns and dead ends eventually lead to unschooling.

A little over 10 years ago, our oldest was in his third year of school. At the time, we were still somewhat following a school-at-home program. He was doing math that he had originally learned two years before. In the course of helping him with it, I came to the startling realization that even though he knew how to do the math, he had no idea as to why he was doing it beyond that was the way it was done. What I wanted to say next was some estimate of how long it took me to get over that. I spent about 5 minutes thinking about it. I have a sneaky suspicion that I haven’t gotten over it and that I probably never will. In any event, I spent the next week or two helping him understand why we borrow when we subtract.

I could write pages and pages describing hundreds of things that happened between then and now. I can summarize it somewhat tangentally. All of my teenage children are excellent at math because the only interest I had in teaching them was that they understood what it was for, what purpose it served and why it works the way it does. If you ask them a question that involves math it is unlikely that any of them will reach for a pencil in paper. They do math in their head. If you are wondering what approach we used in planning and adjusting over the years, the simple version would be that if it didn’t work, we threw it out. No preconceived idea/assumption or ‘proven method’ was exempt from the possibility that it was erroneous.

There are times, of course, when most of us second guess ourselves. But unschooling is not something about which I second guess. When you are standing on the side of the road in the dark and your child is tangled up in a bent up mountain bike describing the symptoms of his injuries, you don’t have alot of time to decide what is important. What you think about in the hours and days that follow define that for you. Speaking from experience, whether your child can list off the political leaders of your country through history is not important. Being able to compose a paper conforming to APA standards does not make or break a life (and is, in fact, worthless to you in a situation like that). Given the amount of the typical child’s life that is invested in school, I believe our society has a serious priority problem.

IMHO: Rote learning is worthless. Sitting a child at a desk and giving him or her a sheet of math questions to do which serves no purpose to the child beyond proving to you that that the child is capable (or demonstrating that in those circumstances he or she can’t or chooses not to) is a hideous offense to another life which is every bit as valuable as your own.

In refering to the accident above, I hope I haven’t suggested that prior to it we spent alot of time second guessing what we were doing because that wasn’t the case. There are things that come along in life which are gateposts from which there is no turning back.

(For readers who have joined since we started this blog, in the Fall of 2004, because of the glare of headlights from oncoming traffic, Addison hit a washout on the shoulder of the road, flipped his mountain bike and broke 4 vertabrae in his neck.)

The value of expression

There was a heretofore unmentioned little sidebar project I was working on for the last few days. Hopefully, in the next month or so I’ll be able fill you in on what that sidebar item was. Anyway, in the course of working on that I got to thinking about the human need for expression. In some ways this relates back to my post on freedom of speech. To an extent it is in the sense that they are both aspects of the same thing.

In some posts prior to that Andrea and I address some difficult subjects. They were difficult in the sense that, in a number of ways for subjects such as those, there simply are no words which will articulate how you feel. Second to that is the challenge of being articulate with a subject which weighs so heavily with you. In some ways it would be easy for me to get off into that subject again, but I want to focus primarily on the positive side of expression and how I’ve observed it playing out in children. And how I’ve transformed that learning through reflecting on things I’ve observed throughout my life and things I’ve found through examining my own behaviour. I included this paragraph in the post because the whole subject of that form of parenting was the one which had me thinking about expression and children.

We are often complimented on how articulate Emma is. Few use the word articulate, but when it comes down to it that quality is what they are refering to. Many adults we encounter are astounded by her. The reason she is so articulate is amazingly simple: practice. She has had years of experience of talking and listening where the ‘big people’ around her took her seriously and conversed with her. I (on the cell phone) had the following conversation with her:

Em: Hello.
me: Hi sweetheart.
Em: Daddy!… What are you doing?
me: I’m driving.
Em: Are you making your way home?

I know from reading some of your blogs that it’s not a great exception by any stretch. The thing is that it doesn’t read like it was said by a 5 year old. What it illustrates is something I’ve seen in many children: the desire to speak like an adult. The larger question is what is behind that desire or what drives that desire?

Over the years, I have had an interest in understanding what it was that made me tick. There were things, (ok, there are still a few things) that were seemingly insignificant that pushed my buttons. There were other things that I was (am?) somewhat compulsive about. For my own sanity and well-being, it was necessary that I fathom some of those things out. One of the ways I worked toward that was by observing my kids.

What I believe is the answer to the above question is the need (or want) to express oneself and to have that expression understood. In a child, that means that framing what they have on their mind in the language of an adult is the best avenue to having an adult understand it. When I am in front of the computer writing a post, most of the thinking that goes into a post is not about what I want to say but in how to say what is on my mind in a way that it is unlikely to be mistaken for something different. The sort of person who I’ve found to be the poorest communicator is one who promptly blames the person on the other end of the conversation for any misunderstanding. That’s because they don’t give a thought to what they might be doing that is causing it and therefore don’t get any better at it.

From birth, most children express themselves. When they are newborns, they only have one means of communication and that is to cry. Later they learn to coo, make noises and smile. But the drive to be understood is clearly evident. Every year the number of blogs on the internet doubles. I don’t believe that the need to express oneself dimishes with maturity. I do believe that a person will not feel fulfilled (or happy) unless they have avenues of expression. Even though our society makes great talk of freedom of speech, it provides few opportunities or avenues for expression. And that is what I believe fuels the blog explosion because an avenue of expression is what blogs have created.

For all of the talking that I’ve done, what I’m really trying to encourage you to do is to provide your children with avenues of expression. Talk to them as though they were another person. Debate and discuss issues with them. Allow them to disagree with you on those issues. Assume that they things they say to you are serious and legitimate and important from their perspective. Your children will benefit from this far more than any instruction/training you will provide them with.

Standing Tall or Copping Out

Today there was an unamed and unlinked (at least here) carnival posted. At least one of the posts features in the carnival had objectionable content. One author who had also contributed a post to the carnival asked to have their post removed. The owner of the blog where the carnival was hosted contacted the coordinator of the carnival to get permission to remove the link from their own blog.

Other readers objected in the comments of the carnival to the link to the objectionable post. The owner of the blog where the carnival was posted replied in the comments:

I have no control over whose blog entries are in this Carnival

christine: That is a cop out. The terms of service of that blog service clearly state that the owner of the blog is responsible for the content. And, you agreed to those terms. You are responsible for every single letter and every single link. I realize that you did not write the other post and based on what else I see in your blog, you don’t agree with it. But you linked to it.

There is an appointed time for everything, and a time for every affair under the heavens.
A time to be born, and a time to die; a time to plant, and a time to uproot the plant.
A time to kill, and a time to heal; a time to tear down, and a time to build.
A time to weep, and a time to laugh; a time to mourn, and a time to dance.
A time to scatter stones, and a time to gather them; a time to embrace, and a time to be far from embraces.
A time to seek, and a time to lose; a time to keep, and a time to cast away.
A time to rend, and a time to sew; a time to be silent, and a time to speak.
A time to love, and a time to hate; a time of war, and a time of peace..


This week would be the week for another unschooling carnival. For this carnival I’m asking you to consider writing a post (and leaving a comment on this one) about one of two subjects:

  1. Unschooling feels, sounds or appears like a good philosophy to follow, but ________ prevent me (or make me hesitant to) follow through with it.
  2. Unschooling my child(ren) has enabled me to see ________

If you can spare the time to write a post on one of those 2 subjects, it would be great. Both subjects would allow us to share the 2 sides of the coin and perhaps we can help one another see our way through one difficulty or another.

Elevated Comment Question

Joanne has asked the following question in her comment on the Yet another Adventure post:

Will there be any kind of moderation on your end in terms of parenting philosophy that is endorsed? I don’t expect a complete lack of punishment or spanking. Just protection from the culture of abuse being embrace by more and more Christians.

I’ve had a few hours to consider this question. I think mostly that I am saddened by the fact that moderation may be necessary for something other than a spam blog or link farm blog. It isn’t as though Andrea and I had not discussed this more than once in the months leading up to getting the domain and space to run it. In fact, we had talked about the homeschool journal site before we started this one. And we have always understood and agreed that removing an offensive blog might be necessary.

But, offering homeschoolers a place to blog where they didn’t have to advertise or promote something was worth that risk. The story of Sean Paddock (see below) may mean that an ‘if’ has turned into a ‘when’.

Andrea and I set up to allow homeschooling families to talk about homeschooling. I would personally like our society to have the opportunity to see that we are not all nut cases.

What was done to Sean Paddock had nothing to do with homeschooling. Not all children who endure such treatment, or other forms of abuse, die and if the statistics are reliable, the vast majority of those children are not homeschooled. I would expect a parent might talk about parenting philosophy because it does play a part in home education. I talk about parenting philosophy in this blog. What I would not expect is a set of instructions for crime and punishment under the guise of ‘discipline’. One of the reasons I was satisfied with the name homeschooljournal is that the name creates a line in the sand.

Doing this is a new adventure for both of us. Perhaps, I’m really trying to address 2 questions: Do I want to ‘moderate’ a blog? No. Would I? Yep.

Chatting & Creativity

Before I get into the subject of tonight’s post, I must confess I feel the urge to talk a bit about the past. Shortly after we started this site, I briefly recounted our history of homeschooling. The thing I wanted to remind you of is that we were not always unschoolers. All 3 of the older children started out with an out of the box curriculum. So, many of the things I talk about are lessons that have been learned the hard way. Probably the main reason I am able to write with the surety that I do is that I’ve already tried the alternative. But, the main reason I take the time to write is to share our experience, so that anyone reading will not be as alone in this as we were for many years. And that, in the last few years, I’ve come to realize that the experts really know very little about what they are talking about in many instances.

Since I’ve been away during the week, Andrea and I have been using Google Chat to talk at night to allow for longer (and more convenient) conversations and save on long distance charges. In the first week, occasionally, Andrea would send a message for Emma. But the next week, Emma wanted to sit on Andrea’s knee and watch. The first thing you know, I’m getting messages typed by Emma. Some of them are something like ‘asfadflkfdj;sdlfndmcn,smcniowafhewoude’, others resemble things she would say. One of those is ’emmatodade’ (Emma to Daddy) followed by ‘iloveyou’. And once, she sent me a ‘fune’ (funny) in reply to something I sent her. Since then, she has taken to counting with me, ‘12345678910’ and then I say ’11 12 13 14 15 16 17 18 19 20′. Then she giggles hysterically.

This week she did, ‘123456789100’. When I got home last night she wanted to know if I thought it was funny that she ended with one hundred. That’s the number we count to when I’m tucking her in for the night (she always has to say 100). She has also caught onto a number of the ascii ‘smiley’s that the chat turns into a graphic. Of these, her favourite is <3 which rotates counter-clockwise and into a heart. What Andrea did this week was set her up with her own profile on a second computer so she can chat with me on her own. She loves it. Mom is close by if she needs help, but otherwise, she can do it independently.

I realize that circumstances have created a situation which has heightened the interest in learning something. I’m sure the experts would argue that the chatting doesn’t support unschooling because of the extenuating circumstances. But, that couldn’t be further than the truth. This is a perfect illustration of both how and why unschooling does work. The how is really simple. If children are interested in something, they will invest the time and energy into learning it. The whole point of unschooling is that if children are interested they can and will learn. If you eliminate all the situations in a child’s life which heighten his or her interest in learning what you are likely to be left with is, …well, something pretty much like a classroom.

The second half of the title relates to Emma’s growing investment in creativity. To step back in history again, we had abandoned alot of the structured element of the older children’s education by the time Emma was born. The transformation I went through involved me realizing that alot of the things that I had formerly assumed about children were not necessarily true. Having been graced with her, I had (and have) an opportunity to discover and learn about children. And so, I’ve done a great deal of observing and making mental notes. One of the things I’ve watched along the way is the development of her ability to exercise her creativity.

One of the things I’ve done with Emma has been respond to her motor skills being unable to keep up with her creativity differently than I did with the older children. When they got upset that they couldn’t do something because of a lack of coordination or fine motor skills, we used to try to comfort them by telling them it was ok. With Emma, what I’ve done is hug/hold her and ask her if she’d like me to help her. Sometimes she accepts and sometimes she refuses. The thing is, whether you are 2, 5, 10 or 50, when you can’t do something you really want to do, it’s not ok, it’s frustrating. I don’t want to give the impression that I think she is more creative than the older kids. But, that I think responding in a different way has allowed me to be more involved in her creativity and she is more willing to allow me to help her by hurdles.

Having said that, this week she made a car out of a cardboard box. Essentially, she drew alot of the details found in a car on appropriate locations on the box including a rearview mirror. In the rearview mirror you can see the sun, an ice cream stand and a car parked in front of the stand (because the driver is buying ice cream). It has an ignition and keys, a gas tank with fill cap, gauges and controls, etc. It’s very elaborate. She put alot of time into it. At the same time, you can tell it’s the artwork of a child.

When I was teaching at the college, this was the time of year where I taught the first year students their first language specific programming course. Likely, in the last few weeks, I would have discussed the course workload (very heavy compared to the other courses they had) and that the reality they were up against was that programming was like riding a bike. You can watch all the videos about riding bikes that you want and you can talk about bikes all you want, but you will never learn to ride a bike that way. The way to learn to ride a bike is to get on one and ride it. And that’s what creativity is like. It’s learned and developed through exercising it.

That’s one of the reasons I’m not really a fan of alot of early educational materials. Many of the materials out there in common use are intended to develop ‘skills’ but provide very little exercise outside of that. An example of that is a colouring book. The only real creativity involved in colouring a predrawn picture is choosing the colours. (We don’t prevent her from having such things. We just don’t limit her to those.) I guess what I want to say is that, wanting children to be able to produce a picture that looks as though it could have been done by an adult is a poor excuse for depriving them of the opportunity to develop the ability to create a picture they can call their own. I would rather be able to sincerely faun over 10,000 real drawings that undeniably show the development of real talent, imagination and expression than the best of the colouring competitions.

Jung Typology Profile

Tim at Making It Up is responsible for this post 🙂

We discussed the Jung Profile in my first Adult Ed course. I always find these things interesting whether or not I agree with them. Of course, I’d love to dig into the guts of the thing and see how it scores. Since I can’t do that, I’ll just tell you that I profiled as a Counselor Idealist (iNFj). What do you think? Does it fit me or not?

You can try for your own profile here.

12 Keys to homeschooling

Witin the next month or so, we’ll be celebrating our 12th anniversary of homeschooling. Last week Andrea and I discussed the possibility of doing he said/she said posts in recognition of Valentine’s Day. We wanted to reflect back on things we learned over the years. I thought to myself, ‘Surely I can come up with one significant thing that I’ve learned for each year of homeschooling.’ I’m not going to present these in the order in which they were learned. I’d rather present them in what I consider to be the order of importance.

There are an abundance of ‘keys to’ books out there. So, I’m expecting that everyone in familiar with the ‘keys to’ concept. In a way, you can look at my list as a set of morals. In presenting these, I recognize that I won’t be telling you anything that has not been told before.

  1. When you wake up each day, before you get out of bed, forgive your children, in advance, for anything that they might do during the day. Don’t be discouraged if in the course of your day you fail to keep your original intent. Tomorrow is a new day in which a fresh start can be made.
  2. Love unconditionally.
  3. Be humble. Be gentle. Be patient. You were a child once.
  4. Listen to your children.
  5. Trust your children.
  6. Don’t underrate your children.
  7. Don’t control. Set an example instead.
  8. Don’t be afraid to tell your children you were wrong.
  9. It’s okay to say, ‘I don’t know.’
  10. Reinvent the wheel. You may get a new wheel.
  11. Look forward to experiencing new things.
  12. Every invention is the result of someone going where no one has gone before.

Like all moralists, I am not really telling you anything new. I’m just reminding you of things that other moralists have said for thousands of years. When I initially jotted down this list, I started to come up with explanations for each. But, as I write this, I don’t see that any explanation is necessary. And so, I offer none.

Carnival of Unschooling #3

A very small carnival this month, but some excellent reading therein.

First up, we have David, making the case for unschooling, which he does quite well, I might add. Loads of good stuff in the many comments as well.

This, and the events going on in our own lives, lead me to thinking about how wonderfully adaptive unschooling is. Just looking at a typical day from Joanne at A Day in our Lives you can see how unschooling doesn’t necessarily mean a day full of disorganized chaos. Even for a family of younger children, like at Patch of Puddles, you can see how their typical day (in pictures even) is at once similar but distinctly different, geared just for them.

Topic can be grabbed on the fly, as they occur, delved into with the child’s interests, with life. See specifically how Homeschooling Mami explores Black history month with her child, and how it is just a part of their lives, appreciating all their friends year round.

I admit, though, there is often a steep learning curve for the parents, as we navigate the uncharted waters. Over at Tricotomania, she talks about our need to plan for things and how sometimes we need to just let go.

The hard parts that go along with that are noted by Janine, on a day where she’s had to wear too many hats.

This gives me pause for reflection, and an urge to dig out an older post of mine from two whole years ago, Homeschooling and the ADD Mom, where I bemoan my sorry state and declare we just can’t unschool. But just look at how far we can come, what our children can do, if only we adapt our thinking and get out of their way.

Note: The Carnival of Unschooling has move to Unschooling Voices.