Tuesday, April 29, 2014

Field Trip to a P.E.I. Sugar House

A week ago, the boys and I went on a field trip with our local homeschool co-op to Woodlands Maple Syrup in Woodville Mills, PEI. We had been trying to go for a couple of weeks, but somehow between rain and other circumstances, we ended up going on the very last day of the maple syrup season (a season that only lasts a few weeks, depending on weather.).

Woodlands Maple Syrup sugar house

Our guide began our tour by taking us outside to an old maple tree of over 150 years old. (Most of their trees are not this large.) We all got to taste the sap from the tree. It tasted like sweet water, with a slight plant-like aftertaste.

He drew our attention to the tiny holes in the bark, made by sapsuckers (a type of woodpeckers). He speculated that First Nations people first discovered the sweetness of maple sap because of the insects that were attracted to the sap that came from these holes.

Even MM was interested, and he loved the taste of the sap!

With three children to keep an eye on in the crowd, I didn't hear everything our guide said, but I looked the process up later in my Handbook of Nature Study.
"The starch which is changed to sugar in the sap of early spring was made the previous season and stored within the tree. ...During the latter part of winter, the stored starch disappears, being converted into tree-food in the sap, and then begins that wonderful surging up and down of the sap tide. ...The ideal sugar weather consists of warm days and freezing nights. This change of temperature between day and night acts as a pump." (Handbook of Nature Study, p.630)
Next, our guide gave us all a taste of maple syrup in our little cups. My boys did not enjoy this as much...they found it too sweet to drink straight!

He explained to us that the first maple syrup of the season is very light-coloured, and it gets darker as the season progresses. He didn't explain why, but my trusty Handbook of Nature Study explained that  "During the first part of a typical sugar season, more sap comes from above down than from below up; toward the end of the season, during poor sap days, there is more sap coming up from below than down from above."

At Woodlands Maple Syrup, they use the time-honoured tap and bucket system, and go around with their tractor and collect the sap from all their buckets into a larger holding tank. From the holding tank, a hose carries the sap to their wood-fired evaporator inside the sugar house.

Inside the sugar house

The evaporator has three compartments. The first one is the largest. It is wide and shallow. Once enough water has evaporated, the sap goes into the second, then is finished in the third compartment. When the right temperature is reached, the tap is opened and the syrup is strained into a collection container. From there, it is taken and tested to make sure it meets the Canadian standards for concentration. It can take forty litres of sap to make one litre of syrup!

We bought a half-litre bottle of maple syrup, and had it on our whole wheat pancakes for supper that evening.

I will be sharing this post with Nature Study Monday at Fisher Academy International for their May link-up.

Sunday, April 27, 2014

Charlotte Mason and Preschool Priorities 2: Habits

I have been sharing how Charlotte Mason has encouraged me as a mother of preschoolers. One of our priorities as parents of preschoolers is to help them form good habits. To Charlotte Mason, "Education is a Discipline." In other words, this habit formation is essential to our children's education...as essential as the atmosphere of our home, and as all the living books they learn from.

I must admit, I find the "discipline of habit" one of the most challenging aspects of Charlotte Mason's philosophy of education. It doesn't help that I don't quite agree with some of what she says about habit in Volume 1.* However, on the whole, her thoughts have been very helpful to me as a mother of preschoolers, and I am still learning and growing...and practicing!
"This relation of habit to human life--as the rails on  which it runs to a locomotive--is perhaps the most suggestive and helpful to the educator; for just as it is on the whole easier for the locomotive to pursue its way on the rails than to take a disastrous run off them, so it is easier for the child to follow lines of habit carefully laid down than to run off these lines at his peril. It follows that this business of laying down lines towards the unexplored country of the child's future is a very serious and responsible one for the parent. It rests with him to consider well the tracks over which the child should travel with profit and pleasure; and along these tracks, to lay down lines so invitingly smooth and easy that the little traveller is going upon them at full speed without stopping to consider whether or no he chooses to go that way." (p. 109, Vol. 1: Home Education.)
"In the first place, whether you choose or no to take any trouble about the formation of his habits, it is habit, all the same, which will govern ninety-nine one-hundredths of the child's life:... "As for the child's becoming the creature of habit, that is not left with the parent to determine. We are all mere creatures of habit. ...If it were not so--if we had to think, to deliberate, about each operation of the bath or the table-- life would not be worth having; the perpetually repeated effort of decision would wear us out... What we can do for them is to secure that they have habits which shall lead them in ways of order, propriety, and virtue, instead of leaving their wheel of life to make ugly ruts in miry places." (p. 110-111, HE)
I'd just like to share one very little way making a habit has made a difference in our home. I used to get up, make breakfast, feed the boys, have devotions, and then try for the rest of the morning to pry them from their play to get dressed. I often found myself threatening and cajoling, and it was always a bit of a circus. I decided that we would form the habit of getting everyone dressed before breakfast. If everyone wasn't dressed, it wasn't breakfast time yet. (I know, some of you super organized people are thinking, "Really?" right now. Things like this always seem obvious to people who already do them.) We stuck with it, and now it takes no effort at all on my part to convince them to get dressed in the morning. It is simply habit. It would feel wrong to them to sit down to breakfast in their pajamas. The choice is gone now, and that aspect of our morning, at least, is on "smooth and easy lines."

And speaking of "smooth and easy," I'd like to direct you over to a free e-book called Smooth and Easy Days from Simply Charlotte Mason. This little e-book is a great introduction to what Charlotte Mason says about habit formation, and I highly recommend it for all mothers of preschoolers!


*Charlotte Mason seems very optimistic about the power of habit to change human nature, and I don't quite share her confidence. I believe in our need of redemption through the cross of Christ, and in the power of the Holy Spirit to change sinful hearts. But this is only Volume 1, and I feel I need to read more before I critique. She does speak of "Divine grace" (p. 104), so I fear (hope) I may be being unfair here. And while I may not have as high confidence in the results of habit formation, I nevertheless do believe in habit formation itself...it is "training up a child in the way he should go." If you've read more Charlotte Mason than I have, I'd welcome your comments on this!

Thursday, April 24, 2014

April 2014 Favourite Read-Aloud Roundup

For several weeks in a row this month I didn't manage to get out to the library, so I don't have a lot of books to share today. However, the one I do have is absolutely wonderful, and it has gone onto my to-buy list.

Eric Knight's Lassie Come-Home is rewritten by Rosemary Wells and beautifully illustrated by Susan Jeffers in this picture-book edition. My boys were enthralled by both the story and the pictures. They also loved the map at the beginning of the book that showed the route Lassie came back home. This was more of a heart-wrenching story than I have read to my little ones before (aged five and three), but they were okay with it (it does have a happy ending!). However, parents should use their discretion as to whether their children are ready for it or not. It may not be a good choice for a sensitive child.

My second choice this month is not one I read aloud, but one SA read and loved. He'd be reading along, then stop to look at me and grin (it's a very cute, gap-toothed grin right now...), then go on and do it again. I think this was his favourite book out of the forty-nine that he has read so far. JJ enjoyed listening as well, and asked me to read it to him again today. For you moms with early readers, this is classified as Level 2 in the I Can Read series.


Since I told you a while ago that I wasn't a big fan of Rosemary Wells' illustrations, both of the books I'm sharing today have some of her work. Lassie Come-Home was rewritten by her, and Emmett's Pig had the original illustrations by Garth Williams done over in watercolours by her as well. So. I do appreciate some of the things she has done. (Not to mention that I do enjoy the Max and Ruby stories as well...)

I'm sharing with Read-Aloud Thursday at Hope is the Word. Click through to see more great read-aloud recommendations.


I'm also sharing with Book Sharing Monday at Life on a Canadian Island. (edit 28/04/14)

Monday, April 21, 2014

Charlotte Mason and Preschool Priorities 1: The Outdoor Life for the Children

I've been outlining the ways Charlotte Mason has been a blessing to me as a mother of preschoolers. Last time I wrote about how she has encouraged me to be the best mother and educator I can be. This time I want to begin to share how Charlotte Mason has helped me set my priorities in my day-to-day life with preschoolers. There are a few areas where she has helped me with this, but one of the most significant has been her emphasis on "the out-of-door life for the children."

"In this time of extraordinary pressure, educational and social, perhaps a mother's first duty to her children is to secure for them a quiet growing time, a full six years of passive receptive life, the waking part of it spent for the most part out in the fresh air." (Vol. 1: Home Education, p. 43)

The "extraordinary pressure" Charlotte Mason talks about is certainly no less now than it was in her time. Preschool children all around us are doing more, and better...they must know their alphabet and their phonics sounds before ever beginning Kindergarten, they must count to 20, they must develop their fine motor skills by creating paper crafts using scissors and glue, and on and on it goes. It can be easy to go along with these expectations if your child is able to do all these things, or feel guilty and inadequate if your child is not achieving as well as your neighbour's preschooler. Charlotte Mason gives us permission to leave all these pressures and expectations behind. (Though she does leave us with another set of expectations, but it is a much more delightful one, I promise!)
"Never be within doors when you can rightly be without." (HE, p. 42)
What are the benefits of all this outdoor time? Here are some of the ones Charlotte Mason mentions:

1. Gladness and joy. She urges mothers to make it their goal "that every [hour] shall be delightful." This does not mean that mothers need to entertain their children outdoors. It has more to do with the fact that in taking their children outdoors, mothers are introducing their children to things so interesting that they never have any reason to be bored.

2. Health. A healthy body is very important to Charlotte Mason's philosophy of education. She makes much of the benefits of fresh air and sunshine.

3. Time and space for children to wonder and grow. Children should be left to themselves a good deal so they can explore, or observe quietly, or play vigorously.

4. First-hand knowledge of the world around them. This direct observation and handling of things is the foundation of the "Science of Relations" that education is, and is worth far more than learning the alphabet at age three. "Set the child to definite work by all means, and give him something to grind. But, pray, let him work with things and not with signs--the things of Nature in their own places, meadow and hedgerow, woods and shore." (HE, p. 55-56)
"Now is the storing time which should be spent in laying up images of things familiar. By-and-by he will have to conceive of things he has never seen: how can he do it except by comparison with things he has seen and knows? By-and-by he will be called upon to reflect, understand, reason; what material will he have, unless he has a magazine of facts to go upon?" (HE, p. 66)

5. Opportunity for training children in habits of careful observation and attention. "Consider, too, what an unequalled mental training the child-naturalist is getting for any study or calling under the sun--the powers of attention, of discrimination, of patient pursuit, growing with his growth,  what will they not fit him for?" (HE, p. 61)

6. Development of a sense of beauty. Charlotte Mason quotes a Dr. Morell saying, "All those who have shown a remarkable appreciation of form and beauty date their first impressions from a period lying far behind the existence of definite ideas or verbal instruction." (HE, p. 68)

7. Natural opportunity for learning science, geography, weather, astronomy, measurement, finding direction, making maps, and speaking a second language. Charlotte Mason gives specific methods to introduce your children to all these ideas without talking too much. "..an occasional 'Look!' an attentive examination of the object on the mother's own part, a name given, a remark--a dozen words long--made at the right moment, and the children have begun a new acquaintance which they will prosecute for themselves;..."

8. Training in "pluck, daring, and resource" (provided, of course, that mothers do not hover, and do allow their children to try risky things like climbing trees.)

I really love Charlotte Mason's balance for mothers of "masterly inactivity" (letting the children alone to play and explore) and purposeful (but gentle) method in introducing children to nature. It provides some variety in our outdoor time as well. We still do not spend as many hours outdoors as Charlotte Mason recommends (our winter climate is slightly more extreme, for one thing...), but we have begun, and I see this as a long-term goal. We spent time outdoors almost every day last winter, many times more than an hour. Before Charlotte Mason, I was more of a hibernator. She has really challenged me, and our home is the better for it. I am planning to work up to reaching her recommended four to six hours every fine day as the weather grows warmer.

Thursday, April 17, 2014

Tuesday, April 15, 2014

Palindromes: Our Best Math Lesson Ever!

SA and I did this math activity together last term, and I've been intending to share it ever since. It was the best week of math we've ever had. I could see and hear the learning happening, and we both enjoyed every minute of it. We worked away at it every day, and often SA would ask to just do a bit more after our 10 minutes was up.

I have to be honest and tell you that I didn't put a lot of thought or planning into this lesson. I opened up one of my math game/activity books as I do every Monday morning (in this case Family Math). The purpose of the activity was to provide "many hours of highly motivated addition practice." Because SA had just learned how to add and carry, I thought it might work for us. So I printed off 100 Charts for SA, JJ, and myself (though I noticed, revisiting it, that Family Math called for a 0-99 Chart. It will work either way.).

Maybe you've heard of palindromes before, and you're thinking, "I thought they were words or sentences that spell the same thing forwards and backwards." And you would be right. The number variety also "spell" the same forwards and backwards: 44, 121, 1111. 

Our first step was to find all the palindromes. We found and coloured 11, 22, 33, 44, 55, etc. with one colour. Those were the 0-step palindromes. 

Next, we started to turn the non-palindromes into palindromes. We flipped the numbers and added them together. For example, we added 12 + 21 = 33. Aha! A palindrome. That one just took one "flip and add." We coloured the "one-step palindromes" with a second colour, and started making a colour key at the bottom of the page. Some numbers took longer: 19 + 91 = 110, 110 + 011 = 121. That was a two-step palindrome. There were even a couple that we didn't solve (I'll let you find them. You're welcome.). We ended up making a separate colour for numbers that still hadn't turned into palindromes after ten "flip and adds." After a while we started to see an interesting pattern on our pages.

We did not duplicate each other's work, even though we each had our own pages. SA would figure some of them out, and I'd figure others out, and then we'd both colour our numbers according to what the other person figured out. JJ (3) would just copy our colours.

After we were working on it for a while, SA began to notice certain patterns. The first one was after doing number 30. 
"Mama!" he said excitedly. "40 is a one-step palindrum, and 50, and 60, and 70, all the way to 90!"
"Palindrome," I corrected. "And why is that?"
"30 is 33, so 40 is 44, and 50 is 55." He was busily colouring them all blue.
"Why, you're right!" I exclaimed, and got busy colouring all of mine as well.

A little later, I noticed that 12 + 21 = 21 + 12. (In other words, we should be able to colour them the same colour without doing the sum all over again.) I tried and tried to get SA to notice this. If he added up 23 + 32, I would add up 32 + 23 beside him. But he did not get it, even when I drew lines between them to connect them. Then suddenly, two days later, he suddenly found it himself, and he was so excited about it. I had to laugh. 

Later in the process, he realized that any two-digit number that adds up to eleven is a one-step palindrome, and any two-digit number that adds up to ten is a two-step palindrome. (See his paper below. He likes drawing arrows between things when he makes these realizations.) In other words, 92 is a one-step palindrome because 9 + 2 = 11, and 82 is a two-step palindrome because 8 + 2 = 10.  

Today, while I was writing this post, he said "44 is blue and green." In other words, according to his colour scheme, 44 is both a zero-step palindrome and a one-step palindrome.

I think you can see by now why I thought this was our best math lesson ever

- SA was completely engaged. Each addition problem was not "drill and kill"...he was genuinely interested in what each sum would be and whether it would turn out to be a palindrome. 
- This was a long project that he had to persist in to find the pattern. I sometimes worry he doesn't have enough opportunity to build persistence in math, since it often comes so easily to him.
- It gave him a chance to explore and make his own connections in math. I know that any discoveries that come to him this way are truly learned. 

I highly recommend this math activity for any child who knows how to add and carry. It will provide lots of practice, and may pave the way for some real math discovery!

Saturday, April 12, 2014

Saturday Funnies

My children have a habit of waking up early every morning. We don't let them get up until Stephen's alarm rings at 6:45, though. The problem with that is, until the alarm rings, I hear "What time is it now, Mama?"
"6:35, SA. Still 10 more minutes."
"What time is it now, Mama?"
"Mama, when it's 6:45 on your watch, it will be 6:42 on Papa's phone."
(Hmmm...somebody has noticed that my watch is a little ahead! It's my strategy for getting anywhere on time.)
"...and it will be 6:45 on the clock on the stove."
(Yep, it enhances the effect when all the clocks in the house are a few minutes ahead. But he noticed that the time on the cell phone is different, and by how many minutes.)

The charger for our laptop computer was not working very well for us this week, and we noticed it was getting hot as well. "Does that mean it's toasted?" asked SA.

We have been trying to get our time outdoors up again with 1000hoursoutside.com, and so we made a couple trips to the playground at the local elementary school this week. As we were walking back on Friday, SA was talking about how it was too bad he'd missed his "screen time" that day.
"That's OK," I said. "I will let you have 15 minutes of screen time while I get supper ready."
JJ was very excited. "I have an idea! We could go on the X-Box and play a two-player game!"
SA clearly had other intentions for his screen time, but he wasn't giving them away.
"That's a thought," he replied noncommittally (and diplomatically!). And said nothing more.

Monday, April 7, 2014

{My CM Journal} Encouragement for Mothers of Preschoolers

"It is a great thing to be a parent: there is no promotion, no dignity, to compare with it."

I have a good mother. I grew up believing in the value of my mother's work, as she stayed home and raised us and educated us. When I had children, there was never a question in my mind as to what I would do once the maternity benefits ran out. How could I, in Charlotte Mason's words, "make over [my] gravest duty to indifferent persons"? I believe to the depths of my being that what I'm doing as a mother is the best and most important career I could possibly undertake.

I know not everyone is like me. For many women, coming home is a great sacrifice, and the decision is made through a painful struggle. And even for me (and probably every other mother of preschoolers) the daily round of diapers, dishes, laundry, and child training can occasionally feel like an endless cycle of futility. We can all benefit from a little bit of encouragement once in a while.

One of the joys of reading Charlotte Mason as a mother of preschoolers has been her affirmation of the value of motherhood. She doesn't stop with affirmation, but also challenges mothers to think, to learn, and to dedicate themselves wholly to be the best mothers and educators they can be.
"Mothers owe 'a thinking love' to their Children.--'The mother is qualified,' says Pestalozzi, 'and qualified by the Creator Himself, to become the principal agent in the develpment of her child;...and what is demanded of her is--a thinking love. ...God has given to thy child all the faculties of our nature, but the grand point remains undecided--how shall this heart, this head, these hands, be employed? to whose service shall they be dedicated?'" ... "'Maternal love is the first agent in education.'" (Vol. 1: Home Education, p. 2)
"We are waking up to our duties, and in proportion as mothers become more highly educated and efficient, they will doubtless feel the more strongly that the education of their children during the first six years of life is an undertaking hardly to be entrusted to any hands but their own. And they will take it up as their profession--that is, with the diligence, regularity, and punctuality which men bestow on their professional labours." (Vol. 1: Home Education, p. 2-3)
One thing I don't quite agree with Charlotte Mason on is her elevation of the mother's role above the father's role in the young child's life, though I do agree that mothers usually have the most active role in the daily routines. The consequences of the growing fatherlessness of our culture today are making me more aware of the value of faithful fathers, however hands-on they may or may not be in day-to-day parenting of young children.

I could share more, but since my aim is to inspire you to take up Charlotte Mason's works yourselves, I will leave it at that. You can actually read her works online for free at Ambleside Online, and they have a modern English version as well if you find Victorian English a bit challenging.

Saturday, April 5, 2014

Saturday Commonplaces 11

Math Notebook:
Fibonacci Sequences are amazing! I can't remember learning about this in my youth. ("Score one for public school," says Stephen. That's okay...his children will learn about this.)

Nature Notebook:
Last week's two storms brought the accumulated snowfall for the winter to over four meters in Charlottetown. Here's a neat little chart showing how much we got. (Please note that this chart does not include April's snowfall.)

Despite the fact that it is not unusual to get a bit of snow in April, this does feel like a lot. I think because we got so much in December, and it is still not gone, it really is feeling like a long winter. We were glad to get outside for hours three days in a row once the stormy weather was gone. We made a snowman, had snowball fights, played fox and geese, shoveled snow, and walked over to the school playground to play.

Homeschooling Notebook:
It surprised me this week what a difference there can be in ease of memorization between different passages. After spending more than six weeks on the Beatitudes and the boys still could not say them, we moved on to a parable (Build Your House on the Rock). After just one week of repetition, both SA and JJ surprised me by reciting it from beginning to end. Why is this?

I love the way SA attacks problems. We started making a multiplication chart this week with the times tables from 1-10. He filled in the 1 times table first, because it was easy. Then he started working away at the 2's. He noticed the 5's next, and filled them out. Then he started working on the 10's column. He noticed the 50 and the 100 at the bottom of the 5 and 10 columns, and realized he could count by 10's across as well. So he filled that row in. He was thrilled that they were the same across and down. Then he knuckled down and started figuring out some of the harder numbers. We actually got about half-way through filling in the chart that day. (He didn't want to stop.) It makes so much sense to attack it this way! Me, I would have started at one corner and worked methodically through the whole chart until it was done. He does the easy stuff first, and there is very little left to actually do the hard work on.

I know JJ said something awfully cute this week, and for the life of me I can't remember what it was. Oh well, I'm sure he'll come out with something else next week.

Have a good week, everyone!

Thursday, April 3, 2014

Musings on Math

This post is just an unloading of thoughts onto a page. I've been thinking too much, and sometimes the only way to steer a clear path through all these thoughts is to write about it. So I warn you, this is going to be long, intense, and possibly tangled, and I might change my mind on some things in the future. This "thinking love" we have for our children is a long-term process. I fully expect to make mistakes and learn from them.

Let me tell you about my son SA. He is five and a half, and he has a special love for numbers and math. He seems to see the world through math-coloured glasses. 

- When we first began our poetry teatimes half a year ago, he spent weeks (months?) creating math equations out of the food on his plate. The strips of cheese were made into plus and minus signs, the slices of apples and crackers were added and subtracted. Similarly, if he has a stick at the beach, or sidewalk chalk on a sidewalk, he is making math problems for himself to figure out.

- He is always asking math questions and making math observations. My approach to this has always been to ask questions back to him to see if he can figure things out himself. He often can. If the question seems beyond the math building blocks he's already assimilated, I'll answer truthfully and make some comments about the process I used to get to the answer. 
For example, he was in the back seat of the car one day when I handed Stephen three $20's. 
"Here's $60," I said. 
SA had noticed the $20's. 
"How many 20's makes 60?" he wondered out loud.
"How many do you think?" we asked him. 
"Three," he said.
He thought for a couple more minutes. "60 is 20 3's," he said next.
Then his mind seemed to go to the number 23, (it sounds like 20 3's) because his next announcement was, "23+27=60."
"No, that's not right," we said. "Can you try again?"
It took him a few minutes, but he figured it out. 23+37=60.
This type of conversation is not untypical with him.

- He almost always understands the math concepts I've taught him immediately, without frustration. Now don't be thinking he's a genius...I still mean easy elementary school concepts. Borrowing and subtracting was the latest one. But hey, I distinctly remembering having considerable frustration with that concept...in grade two.

Charlotte Mason's insistence on a method, not a system, is making more and more sense to me. (See Volume 1, Home Education, p. 6-10) What is the difference, you ask? 

System implies:
- following a path of definite rules in order to achieve precise results.
- does not take the child into account as a self-acting, self-developing being.
- focuses on the development of a skill set, or subject matter, rather than the whole person.
- easier (and lazier) to contemplate for the parent.

Method implies:
- a way to an end
- step by step progress in that way
- begins with a vision of the end result
- is natural and easy, yet careful and watchful use of every circumstance in the child's life to bring him to the goal.

There is always the danger that a method (even a good method) can become a system.

Practically, this concept has meant more to me in this (seemingly) gifted area of my son's life than in any other area. 
- It means that I make my goals for his math development, and every curriculum, every game, every math activity I use serves that end.
- It means that I use the curriculum in ways that serve my son, even if that means using it differently than it was intended, or speed through things that he already knows intuitively. 
- It means that math is taught consecutively, in a logical order, but once it is mastered, we do not drag it out. 
- It means that I try to provide activities that give him the space to allow him to have his own "aha" moments, his own connections.

So far, in Kindergarten, this has been fairly "natural and easy." I introduce a new math game or activity every Monday. I do not choose these in advance, but try to either match them to something he's interested in at the time, or to something in his regular lessons. From Tuesday to Thursday, I aim to make our daily Miquon math lesson about 10 minutes long. We use manipulatives to introduce any concept, but I do not insist on their use for every problem if he doesn't need them. I do not necessarily have him do worksheets for every lesson. Friday, for variety, we do a worksheet from MEP Math (a program that emphasizes mental puzzles/problem solving, rather than manipulatives.). He also often does lessons from Khan Academy during his daily "screen time." I'm not sure yet how I feel about that (and yes, it's my fault he discovered it). Positively, it gives him a sense of how BIG the world of math is, and how much there is to learn. Also positively, it motivates him to become more fluent at the things he already knows. (It's practice drill, in other words.). 

It sounds like I'm very sure of myself, doesn't it? But I'm actually questioning myself all the time.
- Am I holding him back? I feel this especially in our daily math lessons, which are all very easy for him. My intuition tells me not to skip any foundational steps. But when he started playing with Khan Academy, within a day he had discovered adding and carrying, which before then I had no plans to teach him for a while yet. (I made sure to demonstrate with Cuisenaire rods.) As with all his math so far, he understood it immediately, and made no mistakes in his practice problems. Does this mean I should skip ahead?
- How much practice work should we do to gain fluency? When does it become useless busywork?
- Am I challenging him enough? I've read a lot on math, and one of the great values of math is supposed to be training to "try, try again," learning to persist even when problems are hard. But nothing has been hard yet. Does that even matter in Kindergarten? Will he eventually hit something that's challenging for him, or do I need to move through the material faster so we get there sooner?

And then I question myself because I'm questioning myself. I mean, lady, your boy likes math. What a problem to have! He's in love with it. He enjoys everything, even the things that are too easy. He is not bored (yet.).

I think all my struggling with this is because I'm a planner. I would like to be able to see precisely the steps and the speed and the direction I'm going. I like systems a bit too much! :) Lazy ol' me would like to find the perfect math program that I could plug him into and let him go. I have some goals, though. They may yet change, but they give direction to my methods for now.

At the end of all his learning at home, I want SA to have:
- A sense of awe and wonder in mathematics as the language God built into the universe. (I'm thinking of this quote from Galileo: "Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.")
- The foundational tools he needs to build on to figure out any math problem he wants to figure out.

- An attitude that is conducive to problem solving, especially persistence and determination.
- A big picture, an understanding of the historical context of the study of math. (Please note that I understand that my goals may be less lofty for another child, but because of the intense interest SA has in math, I feel this goal would be important for him.)

There. I feel a little bit better now that my thoughts are written down. I feel a little hesitant about posting this. Strangely, it would be much easier to write about real problems my child is having. But I've decided to put it out there in case anyone has any wisdom or experience to share with a young homeschool mom. Believe me, non-problem that this is, it has consumed a lot of my thoughts and energy in the last year and a half.

(Edit. I should make clear that Charlotte Mason would not have recommended math lessons this young. I'm just in a situation where withholding the knowledge his mind craves would be unkind. This child too is a born person. Charlotte Mason was also quite accommodating to mothers who wanted to begin teaching reading at a very young age, as long as it was done gently and naturally (no pressure), so I don't feel she was inflexible. Second, she was critical of the concept of Kindergarten. When I speak of him being "in Kindergarten," I'm simply referring to his age of five and a half.)