Friday, January 15, 2010

Grade 4, Winter Term, Long Division Block Week 2 ~ We Celebrate a Birthday

T-Guy is 11 today. Do you remember when I wrote about him turning 10? He is still every bit as wonderful as he was a year ago. He is a child who comes running to the car when I've been to the market, carrying in heavy bags without prompting. He remembers to put his clothing in the hamper and to close the door behind him. He even puts the cap back on his tube of toothpaste! He offers his help consistently and rarely grumbles when given a chore.

More than all of these little things, he is a child who loves life and is grateful for all it offers. He never fails to see the beauty in a sunset. He loves the dogs fiercely. Whatever he is given is enough; he is a child who sees the positive, never the negative. When he is interested in something he vibrates with passion; currently, his passion is baseball and we are entering our first foray into Pony Baseball, with baseball camp starting tomorrow, baseball practices beginning in February, and finally competitive games starting in March. He is unable to contain his joy at such prospects.

He was a baby who smiled, a child whose view of the world was one of abundance and goodwill. This optimism means that he doesn't always understand why others don't act their best day in and day out. He has immense trust in the sincerity and goodness of others. When he was younger it meant that he didn't get the joke most of the time, or understand teasing, but now he is able to laugh along with others.

I am so happy to have him at home with me, to serve him in the role of teacher as well as mother, and sometimes even as friend. ("They" warn you against that, but really, how can you have a close loving relationship with your child and not have it spill into friendship? You just have to remember that you are a parent first.)

P.S. That child up there? That is his 10 1/2 year-old self; this year the hair came off. I do miss it, but 10 and 11 year-old boys aren't always very good at caring for their hair, and he would no longer sit still for me to comb it.

P.P.S. That isn't our house, it's the neighbor's house. We move cars out of the driveways and let the guys practice catching across several yards.

Thursday, January 14, 2010

Grade 4, Winter Term, Long Division Block Week 2 ~ More Thoughts on Introducing Long Division

Having been through the process this week of bringing long division to my boys I would say that the most important thing is that the parent/teacher not approach math and long division as a scary thing. Long division is simply fast subtraction, and we all know that subtraction isn't hard.

Indeed, the boys and I took some time to work a couple of long division problems as slow subtraction, and they could see how much easier it is to divide rather than subtract. This is an easy thing to bring to children if they already have a sense of multiplication as fast addition.

Working with just the three of us I take the boys through the steps of long division, and then they each had a couple of turns doing the same. I don't bother with a black board; we each have a grid paper lesson book and we work the problems as the person who is talking us through it speaks out loud. This actually gives me a lot more information than I would get if I simply corrected problems that they had done themselves.

We'll still be working long division next week; I intend to look at our Miquon books and see if there are any supporting math lab materials that we can use. We're also going to start factoring and averaging. It should be fun!

Wednesday, January 13, 2010

Grade 4, Winter Term, Long Division Block Week 2 ~ Double Digit Divisors

I thought it would be hard for the boys to grasp long division with double digit divisors, but I was happily proven wrong. Indeed, I would say that it brought them deeper understanding of the entire division process. It moved away from What multiplication fact am I supposed to remember? and took us to How many times does this number go into that number? In some ways they are the same question, but the understanding was different.

Children understand division on a very practical level. How many x do we have, and how many y do we have to share it between? They may apply it to cookies, slices of bacon, play silks, or wooden blocks. There is a strong desire for things to be divided in an even and fair manner. Written division takes this process from the concrete to the abstract. When we worked simple division and division with remainders we used manipulatives and then a bridge to bring it from the concrete (rocks in our hands) to the abstract (numbers and symbols written on paper).

When talking about long division with the boys, even with two digit divisors, I often bring the abstract problems back into the practical by asking the question the same way I would if I had 10 pieces of bacon for 4 people; only the numbers get bigger. I have 169 wooden blocks and 13 children to share them. There are 1248 M&Ms and 48 children to share them. Talking this way makes the problems something that the child can understand.

Again, using grid paper is very helpful with long division, as the columns stay nice and tidy. We also use a sticky note to cover the parts of the equation that we aren't working with. Together these help the child see the problem clearly and work the steps in order.

Tuesday, January 12, 2010

Grade 4, Winter Term, Long Division Block Week 2 ~ Day 2

Today we worked more with long division using single digit divisors. I think the boys are getting the concept, but it is somewhat slow. I have to remind myself that this is the block where the material is introduced and not expect mastery.

While discussing multiplication tables a member of the Waldorf at Home Forum (a paid membership forum) reminded me to do more than just oral practice with the boys, and also to work similar tables together. Today we worked 4s and 8s and I had the boys fill out a blank multiplication table. For T-Guy this is truly practice for mastery, but J-Baby is still working on his rote memorization. Already he has made great practice with his 4s now that I am asking him to recite them alone.

Now that I can see that our basic rhythm is working well I need to bring back guitar and regular hand work and other afternoon lessons.

Monday, January 11, 2010

Grade 4, Winter Term, Long Division Block Week 2 ~ And We're Off!

Today we started long division. I used the examples in A Little Garden Flower's math book but didn't bring a story to it. I wanted to write one, but left it to the last minute and found myself struck with the flu yesterday (I still feel rather cruddy today).

I did, however, purchase a copy of Live Education Grade 4 yesterday, and it should be here Wednesday or Thursday. That will give me more guidance, and perhaps even a story. I was very impressed with what I saw in the LE G5 materials I bought last month that I decided to bite the bullet and get LE G4 to finish out our school year.

The boys aren't sure what to make of long division. They don't want to believe that it is hard, but it isn't exactly intuitive, either. I wish I could remember what I thought and felt when I learned long division myself; obviously I wasn't traumatized by it as I still like math and I don't even recall how old I was or in which grade I was taught. My own mathematics learning was rather all over the place because of the gifted label bestowed upon me and various schools' attempts to keep me from utter boredom (I'm glad that they tried), plus changing schools each grade until 4th. In 1st grade I did my math with 2nd graders in a combined 1st/2nd grade class. In 2nd grade I was sent to do math with a 3rd grade class. In 3rd grade I was in a combined 3rd/4th grade cluster class for gifted students and again worked well above "grade level". In 4th grade I took math with the 6th graders. After that my elementary school couldn't help me; I took 6th grade math again in 5th grade and 6th grade, and then finally I took pre-algebra in 7th grade and had a challenge again. All of that being a very wordy way to say that I may have been learning long division at age 8.

Our power was out all morning and for the first half of the afternoon, and it didn't affect our learning in the least. There is enough natural light in the family room that we rarely turn on the lights on sunny days anyway. We don't use the computer or anything else electronic for our learning.

We sang.
We wrote.
We discussed homonyms, contractions, and the differences between there/their/they're.
We said our multiplication tables.
We reviewed long multiplication and how to figure area.
We had our main lesson on long division.
The boys did their independent reading.

Saturday, January 9, 2010

Saturday Focus on Simplicity ~ Why Stress Is Bad

I have been reading a wonderful book entitled Simplicity Parenting; it is a book with a Waldorf view that addresses the complexity and choice in our children's lives and how we can simplify things and make our lives together smoother and happier.

One of my favorite ideas from the book is that all children (and indeed all adults) are quirky. We are not automatons and we really don't all want to be the same; quirks are one of the things that make us different. But the author of Simplicity Parenting introduced the idea that quirky + stress = syndrome. Wow ~ I love it! The author conducted a study that took children who had been evaluated and labeled as having ADHD and they educated the parents and teachers on how to simplify, and after time they retested and most of the kids did not meet the criteria for ADHD any longer. To me that is very powerful.

To bring a very female slant to this, I think of PMS, or pre-menstrual syndrome. Menstruating women have a pre-menstrual phase of their cycle, during the luteal phase post-ovulation. Progesterone production ramps up and then drops off if an egg has not been fertilized. Many of us feel the effect of the progesterone drop and find ourselves feeling physical and emotional tension.

Bear with me here. All women menstruating women experience the physical changes of the luteal phase, but not all women report PMS symptoms. Indeed, in some cultures the idea of PMS is non-existent. While I have seen some conjecture that increase in PMS in our North American culture is do to hormones in our food I think in fact that we might look to the stress in our culture. Not that being menstruating female is a quirk, but it is something that makes us different from men, babies, children, pregnant women, and menopausal and post-menopausal women.

Technically I am not a menstruating female as I do not bleed, but neither am I a menopausal or post-menopausal female. I have cycles just as other menstruating women do, and I have the potential for the second half of the luteal phase to manifest as PMS. It often does, too, because of the stress in my life. I would conjecture that luteal phase + stress = PMS. My body feels different, my hormones are different (have you ever noticed how great and unshakeable you feel when you are ovulating?), and I just don't have as much resilience. Most of the time I manage just fine, but throw in some stress and I become a very easily irritated woman.

If you can't relate to PMS perhaps you can relate to how it is to have to function in pain. As adults we attempt to tune out pain signals and continue with the tasks of our daily lives but we aren't always that good at it. My mom got so good at reading this that when my dad was really grumpy she would ask him where it hurt, because chances were good that he had a toothache or pulled muscle.

Apply this same thinking to our children. Some children don't transition well; they love the dependability of routine and comfort of familiar surroundings and objects. This child may be labelled as shy when put in a new situation. A child who doesn't like loud noises is going to struggle with the stress of a loud situation.

It isn't only situations that are stressful; environments can be stressful as well. Do you feel a sense of calm and peace when your home is tidy and clean? I know that I do and conversely the visual chaos of cluttered environments translates into mental chaos for me. Do you feel impatient when you have to wait in a long line at a noisy grocery store?

I can't address every syndrome that a child might be diagnosed with, but I can talk about my own experiences with sensory overload. When I am cold I find it hard to function; I have to be aware and keep myself warm. Likewise I find it nearly impossible to think with a lot of background noise; I don't do mental work to the sound of music or TV in the background. Papa loves to listen to NPR while working in the kitchen and it nearly drives me crazy (he knows this and will either shoo me out of the kitchen so he can work and listen or he will let me know that it is fine if I turn off the radio).

Sensory Processing Disorder (SPD) is a newer diagnosis that children are given these days; I would never claim that SPD isn't real; I live with sensory challenges and I understand how frustrating it might be for parents with highly sensitive children to navigate an overstimulating world. I know that some children become so sensorially defensive that they require professional intervention. But I do think the term is overused and that many people don't know that sensory overload is something they can work on. Being sensitive to sensory stimuli is my quirk, and because I am 40 years old it was always considered a quirk and not a disease or disorder. Indeed, I don't see it as a disorder; I am different, yes, but everyone is different. Some are faster or have quicker reflexes. Some hear music in their heads and put it on paper. I ~ I am aware. I see more light, hear more sounds, feel more temperature and texture. I smell more scents and I taste more flavors. All of my senses are heightened.

Lack of sleep causes stress and for me that makes me very sensitive to noises.

Friday, January 8, 2010

Grade 4, Winter Term, Long Division Block Week 1 ~ Friday Free Day

Our rhythm so was so solid and effortless all week that I almost forgot that Friday is a free day. I was ready to sing and write and figure. Instead I prepared our home for the major weekly cleaning and we got ready for our homeschool park day. (I did sneak in some singing, as California Here I Come is just so catchy!)

The boys were loathe to create a mess in their room that they would have to tidy right away so they spent the morning building and drawing. Keva Planks are a favorite toy as they offer endless possibility and they are very easy to put away. They have good drawing paper, Stockmar crayons, and Prismacolor pencils available to them at all times and they can also put those away quickly and into their proper places.

We couldn't have asked for a more beautiful day at the park; the weather was typical of January with sun, blue skies, and gorgeous views of the mountains. The afternoon started quite warm and then cooled as the wind began to blow. The children spent more than an hour building fairy houses out of sticks, twigs, leaves, and small branches. Okay, maybe they weren't fairy houses; that is what I call them but several of the girls were populating their houses with Littlest Pet Shop figures.

The moms (we haven't had any dads attending lately, although one came as we were wrapping things up) chatted and several of us worked on our knitting. I finished an alpaca blend hat for T-Guy as his head is often cold now that he had his hair cut. I had my double-pointed needles out and was able to show a new knitter how to switch from the circular needle to the dpns.

Thursday, January 7, 2010

Grade 4, Winter Term, Long Division Block Week 1 ~ Bringing It Together

Today we took what we learned in measurement and combined it with long multiplication to figure the area of a rectangle. Not just random rectangles, however ~ we used our house and the rooms in it and then the boys designed their own houses on grid paper and figured the area there as well. They had so much fun with it! Of course, each boy made a huge bedroom for himself and an itty bitty one for his brother, which is funny as they share a room. T-Guy gave himself a bathroom but said that J-Baby had to go outside, and he gave me my own bathroom as well (I have my very own half-bathroom in our house that I don't have to share with anyone).

The week was so successful. Morning chores were accomplished with a minimum of fuss. The bedroom was easy to keep clean. The boys were engage in what we were doing and they also very much enjoyed their assigned reading of James Harriot's Treasury For Children. Indeed, assigned reading is something that I wasn't sure I would stick with but it is a great way to bring new (never read before) books and new sub-genres of books to the boys. We've been keeping up with the Oak Meadow G4 reading materials so we can still do activities with our OM4 friends (not that we have, but we can, LOL).

Wednesday, January 6, 2010

Grade 4, Winter Term, Long Division Block Week 1 ~ Another Aha Moment

Today J-Baby multiplied a 4 digit number by a 4 digit number and got the correct answer, which really pumped him up! I love seeing a child go from thinking that multiplying large numbers is hard to knowing that it just a series of steps involving multiplying smaller numbers and adding the products of those sums.

In observation I noticed that J-Baby is leaning on us for help with oral multiplication work by watching our mouths and giving his answer just a second after we do, so we took turns today rather than saying them in unison. I have him go last so he has heard them twice before it is his turn. He really does seem to have a harder time remembering some things, but letting other people remember for him isn't going to help him.

Tuesday, January 5, 2010

Grade 4, Winter Term, Long Division Block Week 1 ~ More Multiplication

One great thing about learning at home with my children is that I really get to see their strengths and challenges. For example, T-Guy has his multiplication facts down pat but is struggling with the order of steps in long multiplication. J-Baby has the opposite problem; he gets long multiplication but not knowing his multiplication facts causes errors.

The order of the morning:

Active Math: Bean Bag Multiplication Tables
Singing: California Here I Come
Copywork: California Here I Come (the boys write one line of the song each day and then decorate the page)
Review Concepts (from previous day)
Main Lesson Work
Assigned Reading

I'll need to bring in spelling at some point, and we'll return to journal writing (vs. copywork) in a couple of weeks.

Sunday, January 3, 2010

Grade 4, Winter Term, Long Division Block Week 1 ~ A Great First Day

We had an amazing first day of our winter term; I thought it might be a trifle difficult to ease back into rhythm but I am so glad I was wrong.

We began the day with the familiar pattern of waking, eating breakfast, doing morning chores, and accomplishing morning hygiene (if the boys brush their teeth and their hair it is an accomplishment). Papa is the foundation of our morning rhythm; he must wake and go to work and so we wake with him and begin our day at home.

We gathered in the family/learning room and recited several multiplication tables; I will add the bean bags in and we can switch off who answers and who calls out the mental math problem.

Using the Live Ed grade 4 book as a guide I decided we would learn a song for part of our morning gathering. I selected the chorus of California Here I Come as I am certain I learned it in 4th grade and I figured it will pertain to our later study of state history. We went through the song several times and the boys were joining in by the third run through. The boys then copied the first two lines into their social studies main lesson books (I had written them in chalk on a small slate) and then decorated the page.

(Eventually we'll get back to journalling; this was a nice way to ease into writing again.)

We reviewed some of the things we had learned in our previous blocks; the basic parts of speech, the various geographical areas in Southern California, and a few others.

Our math main lesson this month is long division, but the block begins with long multiplication, or multi-digit multiplication. We reviewed carrying numbers in multiplication and then delved into the main lesson material. The boys really seemed to get what we were doing. I must say that using arithmetic books from Paper Scissors Stone was a big help; the grids are perfect and I find myself wondering why we never used grid paper for these types of problems when I was in school.

We're using A Little Garden Flower's Math ebook for our current block, typically long division in Waldorf grade 4, but also encompassing the aforementioned long multiplication, plus averaging and prime factoring. I'm still debating writing a math story for long division; luckily we start that next week.

I often think of early mathematics as bringing language and order to concepts the children have already internalized. Teaching long multiplication (or multi-digit multiplication) is simply teaching a child how to write out a longer multiplication problem and how to solve it in a systematic way; Papa says it is the first algorithm a child learns. A simple example would be 12 X 12; my boys know that one way to solve this problem is to multiply 12 X 10 and add that product to 12 X 2. (Another way would be to memorize the multiplication tables, and we're still working on that.) Doing it that way is common in mental math, but unwieldy in written math, and so we introduce standardized ways to write and solve problems.

I think it is important to understand the why of written math to help avoid the idea that math is something that few people use in their everyday lives. Written math helps us figure problems efficiently and correctly, yes, but we do have calculators and once we are past schooling we usually use them for the more difficult multiplication and division problems. No, written math is also about communicating; math is a universal language and is also the language of science. We need to know the fundamentals of written math to progress to more difficult equations and complex ideas.