Planning Math Lessons

The greatest unsolved theorem in mathematics is why some people are better at it than others. ~Adrian Mathesis

The mind works of a child—and just one child! Can you imagine teaching a classroom full of individual thinkers? I used to think I wanted to be a teacher—I was very young—now I realize I much prefer being a tutor of a few. Learning how one thinks and molding that to its greatest potential, now that is a challenge I enjoy. A classroom of children, with which I cannot really connect, is too similar to throwing each child out in the water and then expecting me to teach them swimming techniques while while standing on the dock. I just cannot imagine it.

As every other child in the world, my daughter has a unique mind, different from mine and yet we have so much in common. I have to say, though, that our differences are most striking in math. I knew I was going to be challenged with her when she was learning coins. You see, my daughter is a people person, so much so that when she was four years old she could not pick out a penny amongst silver coins, but if I asked her to find the coin with Abraham Lincoln, the child found it and then proceeded to tell me everything she knew about the man and the coin itself, even saying that it was a "penny" worth one cent and that it was the only coin that was made of copper which turns brown. I then would place the penny back with the other coins (all silver) and ask her to find the "penny," she just could not do it. She progressed by learning the people on all the coins and then surprised me with not only her ability to count money but to add it. It came so easily to her!

Subtraction was and still is an obstacle. 5-3=__ I showed her multiple ways of getting the answer, including turning it around to an addition problem because she did so well with addition, but her brain just could not process any equation with a minus sign, even when she knew the word problem required a subtraction equation and she had written it out herself. I finally asked her if she had five pieces of candy and she gave one piece to each of three friends how many would she have left, without any hesitation at all, as if she was a whiz at math, she said "2." Then I would show her the equation on paper 5-3=__ ....blank stare! It took some time to teach her to talk out each equation, using her interesting thinking processes, so it was a story with friends in it. She finally got to the point that she could just look at the equation and get the answer using more traditional math thinking processes. However, now that she is into regrouping, she has had more difficulty with it again, but she does much better when the equation is about money...?

So this is how it works with the Princess:

• She gets addition, simple multiplication, and simple division, but struggles with subtraction.
• She does better with any 3 or 4 digit numbers used in subtraction if we convert them to money.
• She gets word problems, but zones out with a page of simple equations.
• She likes teaching math to her friends (dolls, Sunday School class, etc.) but she doesn't like math lessons herself.
• She can do most math mentally, but she does not like writing it out.
• She will make up her own math problems and solve them, but does not like to write out equations when required.

It is challenging for me, because at her age I well remember how I loved writing out math equations, having equations in neat columns and rows to see how neat I could keep my paper and how fast I could solve them, and memorizing math tables, but I had more difficulty with mental math and struggled some with word problems. We are nearly polar opposites when it comes to math, but it seems that her math mind-works come from her father, who always amazed me how he could just look at the groceries we were buying and guess within a few dollars the total cost. I would have to tally as I go so I would not embarrass myself in making an estimate, if one could call it that, but he could quickly calculate it all in his head at a glance. That describes what I see with the Princess.

Presently, the Princess is finishing the last couple of weeks in my lesson plan for the present level and I have stacks of books and papers piled on my desk to combine together in a tailor-made curriculum for the Princess as I am planning the next level. I am still using Singapore's Primary Mathematics as our spine with Miquon and a few other resources. Singapore is a logical sequential approach from concrete to pictorial to abstract. Miquon, by contrast, is more focused on encouraging observation, investigation, and the discovery of patterns. Neither alone would have been sufficient and I must continually teach the math as she is not ready to do it on her own, except when it is multiplication, of course.

~ My Lord, I ask that You continually guide me while I am teaching my daughter, particularly in math. ~

Confessions of a Nonconformist

Whoso would be a man would be a nonconformist. ~Ralph Waldo Emerson

We all have our differences, but I have come to the conclusion that some differences are more tolerable than others. I see this when we are in any group situation, even in my church. There are times what seems in vogue for others is just not for us.

I take into consideration that change is inevitable throughout every one's life and no one really likes change unless it is his own idea. I would also add that one's ability to adapt to change is an indication of age, not physical age but mental age, so someone who is willing to take on new challenges cheerfully, even with some reservations, is often considered young at heart. That is why I carefully examine if something is a matter of principle for me or just a habit that would be uncomfortable to change, as I do not want to become too set my ways. On matters of principle, I believe one should stand firm despite what other people think or are doing.

We have made some life choices that are a matter of principle for us. I believe these choices make other people far more uncomfortable with us than we are with them.

One uncommon custom we have that seems to bother other people is that we eat organic foods. That is not to say that we expect anyone to go out of their way to serve us organic foods when we are guests, nor does that mean we will refuse their food or that we don't eat out or that we never eat conventionally-raised produce and meat. It merely means that we believe in the health benefits associated with limiting the amount of toxins we consume and support those who farm organically because it is hard work and a commitment to improving our environment as well as their own health.

Homeschooling is a huge wedge between us and most families. Perhaps some think we do it to shelter our daughter and, quite frankly, that is one of the advantages or disadvantages depending on the circumstances and your perspective. The bottom line is we homeschool because God had guided us to do so. This is not a judgment on other families who have their children in schools—my only concern there would be that they were led by God as to where and how they should educate their children, not just because it is free or everyone does it or even because it is the default method of education. If they know it is God's will for them, that is all that needs to be said. If God was never asked, then perhaps He should be...?

I fast one day a week and I fast for longer periods regarding spiritual matters as I am called upon to do so by my Lord. Compared to other places in the world where food scarcity is more common, fasting has become an uncommon religious practice in the more developed, civilized countries where food is abundant, oddly. We read about our spiritual forefathers in both the Old and New Testaments of the Holy Bible, including Jesus Himself, whom we are to strive to be like, and yet our churches do not train or even encourage us about fasting. It is a shame, really, that this is considered unusual in our present times.

There is another thing that I dance around, trying not to offend others or bring too much attention to our family in its regard, but I also believe that the church has become a victim of society's expectations. Families are basically split up whenever they go to church, usually according to age. I accept this for Sunday School, but I don't agree with it for services. In the last few churches we attended, this was not a problem because there was no children's church offered, but that was more due to inconveniences than philosophy, because it would be offered should the church acquire a pastor and space for a separate service just for the children.

Now, for me, I homeschool so I am with my daughter much of the time and we read Bible stories and have devotions nearly every day, so it is not like she has learned anything new in Sunday School, but it is good reinforcement from other teachers and children. However, my husband has often been gone from Monday to Friday, even before this job he worked long hours being on call on nights and weekends with catching up on sleep during the day when he could, so being together on Sundays for worship has always been quite important to us. Hence, we have opposed the now popular idea of "children's church."

I probably am going to step on some toes with this one, but I honestly think it should be important to every family to worship together as a family, particularly when the children are in schools all week. The church seems be trying to mimic an "educational institution" too much, thereby perpetuating separation of the family members, instead of advocating the importance of family members worshiping together in practice. It is particularly important because, according to statistics, family worship in the home rarely happens beyond prayers at meals and bedtime.

One of the changes in my church, which I hoped would not happen, is that we have begun having children's church every Sunday. Apparently, this began while we were in Florida as we missed two Sundays. Last Sunday, my daughter left the service with the other children as my husband did not know for what they were calling the children and I was ill at home. We have discussed this and we are still in agreement about the Princess remaining with us for services. After having been a youth leader for years and seeing the effect on families who go their separate ways as soon as they enter the church doors, I am sadden, but then I knew it was likely to happen.

I think our opinion on this will not be the popular one at our church, but it is just another in a list of things about us that seem to make other people uncomfortable with us. It is not just a matter of resisting change for us, but a matter of principle. I have seen too many families going their separate ways in life. With work, school, extracurricular activities, and, yes, now even church, too many parents do not have time with their own children to parent them. Worse, some prefer even less time with their children than they have. It saddens me so much.

~ My Lord, I pray that You continue to guide the leaders of our church and that only Your will is served in the direction our church is taking. I also pray for the families of my church, that we all grow in knowledge and understanding of You, Our Father, so that we can be the parents You wish for us to be to our children. ~

My Lord Keeps His Promises

God never made a promise that was too good to be true. ~Dwight L. Moody

I have so much for which to be thankful to my Lord. Two years ago my husband lost his job the first week of December. When things like that happen, I tend to worry, but also I wonder what my Lord has in store for us; I ride up and down the roller coaster of tearful fear to joyful anticipation. As I usually do for such things, I fasted and prayed often for the following weeks. I prayed for three things in particular: That my husband would get another job before his severance pay ran out. That he would make enough that we could live off of it and I could continue homeschooling. Plus, not just a job, but one that he would love and also where he would be recognized and promoted.

The Lord answered me quite specifically also. We knew that his former boss, the one who had to fire him against his wishes, was working out the details of changing jobs himself and was interested in hiring my husband at soon as that might be possible, supposedly in the mid summer. When I prayed about this, my Lord told me that my husband would be hired before the severance ran out, but not by his former boss; He told me it would be the former boss' boss and that my husband would be promoted within two years. He also told me not to bother looking for a job for myself as it was not in His plan that I should work at that time. I was to continue homeschooling and trusting Him.

Well, I did apply at a few places even so, but I was not called at all, so I continued homeschooling and trusting Him. This was all against what I thought the responsible thing to do would be. If someone had asked my advice, I would have told them that both people should be looking for a job, any job. Worse, this was the advice everyone else was giving me, even people I know who pray and listen to the Lord. This probably was the most difficult part of all for me, but during that time, my Lord reminded me that even the Christians I trust the most may not have prayed about this specifically and may not be speaking His words, but advising me with limited human understanding. I was to rest on His promise.

The week we received my husband's last severance paycheck, I saw the sign for which I had been asking for months. I asked to see a hawk from my back deck just within feet of me and that same week a hawk's cry called me out to the back deck and then it swooped down within just a few feet of me. I just knew the time had come. My husband was asked to be interviewed for a job for which he had not even applied, and he was offered the job at that one and only interview. And...he was hired by his former boss' boss, just as my Lord had told me months before.

Although he makes less than he used to do, we have managed to live on it: all the bills get paid, we are able to afford the necessities, and still are working on paying off our debt, although slower than we hoped. We don't have much extra and it would be easier having a second vehicle, but we have been comfortable and have worked out getting by with the one minivan for two years.

This job also answered a prayer my husband had for some years, which was to visit Israel (something I thought was impossible financially for years into the future, if ever). He has been required to go to Israel for training and he has since been there a few times and will be going again. He travels quite a bit with this job and that is a hardship, but we manage it well.

Now the time has come that my husband has been recognized and he has been promoted to a specialist job that surprisingly skipped a few levels. He will still be traveling, perhaps not as often, but perhaps more internationally. He was again hired by the same manager, who first hired him and had been moved up to manage this higher level of specialists.

I don't doubt my Lord, but I doubt myself. I wonder sometimes if I really am hearing my Lord, and more often if I heard Him correctly, which is why I ask for specific signs at times. I often feel undeserving—very undeserving—but still I beg things of Him and how gracious He is to give me the things for which I ask. No, I have no doubts at all that He spoke to me about these things and then He did what He promised. I just wish I would not worry and just rest on Him. He is so close.

~ My Lord, so many people think You are so far away and that You don't talk to each one of us. I pray those who visit this blog will know that You are not only hearing them when they cry out to You, but are near to them and their concerns, ready to guide and show Your love, ready to make promises and fulfill them. Thank you for not only keeping the promises You gave me, but for giving them to me so that I would know that is was You, Who provided them. ~

Let It Snow, Snow, Snow!

We build statues out of snow, and weep to see them melt. ~Sir Walter Scott

Settling back in on the home front, we had an interesting change in the weather.



Before we left home to pick my husband up on Friday, the Princess had made snowmen on our back deck.



It would continue snowing most of the night. The day before, we were warned that computer models were not matching up so we could get any thing from one to six inches. It looked as though we actually got about four.

On Saturday morning, I was reminded how beautiful winters were in my home state of Ohio and I drank it in. I don't think the pictures truly illustrate the splendor just outside our windows.






Here, though, the real problem is that at night when the temperatures would go way below freezing, causing ice on the roads, but thankfully the days have been warm enough to clear off the roads. As I write this, two days later, it all is almost gone...and even the snowmen are nearly forgotten lumps.

Still, she will remember....

~ Thank you, my Lord, for the beauty of the seasons and for this sweet glimpse at a winter wonderland in Georgia. ~

Space Coast

A man who has been in another world does not come back unchanged. One can't put the difference into words. ~C.S. Lewis, Perelandra

While in Florida, we found out a Space Shuttle lift-off was planned around 4:30 AM on Sunday before we were going to leave, so my husband decided that we might like to go the the Kennedy Space Center, about an hour's drive, on Friday, even though the weather report warned that rain was expected. We could not choose the tour we wanted because they were readying for the lift-off, but we had a great day and it did not even sprinkle until near closing time. I so wish we had not stopped in the shop to look for a souvenir because that is when it began to pour and we left with not one but four souvenirs, one astronaut Barbie-like doll and three rain ponchos with the NASA logo, which did not save our shoes and feet as we made our way to the van.

Of the different displays there, the Princess was mesmerized by an animated display of illustrating how they planned to update and integrate designs of an Apollo-like command module atop a rocket similar to the one that boosts the shuttle to return to the moon. However, our current president is against the moon proposal, which could affect a number of companies with government contracts, therefore jobs, in the Space Coast area. What was a booming area with a fast-growing population contributing to research and technology twenty years ago is obviously not what it was. In fact, there are only four more scheduled shuttle missions and the direction for NASA afterward seems to be in question.

The take-off of Endeavor on Sunday morning was scrubbed in the last ten minutes due to low cloud cover. It was rescheduled for Monday morning around 4:15 AM. Yes, we, including the Princess, were up both mornings to watch the launch on TV and then run outside to see the fire in the sky from 50 miles away. Even at that distance it was still spectacular. There was one place at the Kennedy Space Center with plaques of every one of the missions and the number truly amazed me. This launch was STS-130, which stands for the 130th mission of the Space Transportation System.

I remember being just my daughter's age when the first manned Apollo mission launched and orbited the earth for eleven days. I will never forget less than a year later watching Neil Armstrong, a fellow Ohioan from a little-known town called Wapakoneta (Native American roughly translated "clay river"), being the first man to step on the moon and uttering this ever famous saying, "That's one small step for man; one giant leap for mankind." That step from the last rung to the ground, by the way, was not that small! In fact, on the second mission to the moon, Pete Conrad remarked, "That may have been one small step for Neil, but it's a long one for me!"

There is a lesser known story about one astronaut. James Irwin of Apollo 12 was the eighth person to walk on the moon and the first to drive the lunar rover. While looking at Earth teaming with life compared to the barren moon, he had a religious awakening and later decided to search for Noah's Ark.

~ My Lord, it is amazing what people desire to do and how they can develop the means to do it. That men have reached out to touch the moon over 200,000 miles away is a testament of the spirit You have breathed into us. ~

February in Florida

February, when the days of winter seem endless and no amount of wistful recollecting can bring back any air of summer. ~Shirley Jackson

I would add to the quote above: unless you go to Florida.

You may be wondering why I have not posted lately. We went to Florida to visit and help my husband's parents. Dad is legally responsible for his 99-year-old aunt, who is currently in a nursing home. It has been decided that her home needs to be sold and we had to get it cleaned out so it would be ready to place on the market. Her place is about a two-hour drive for them, too long for either of my husband's parents to drive nowadays. The plan was to clean everything out in just one day, which we did, but we had no time left over to visit the aunt at the nursing home. So, we made plans to go back days later on Saturday. Even though her memory is not good, she seemed to recognize my husband, remarking on his beard. She is such a sweet lady, truly one of social graces with a loving heart for Christ.

I brought home a few things, really just a few, but I have yet to unpack them, so they are waiting for me, cluttering the art/craft room I just cleared out a few weeks ago. I have not had the energy to go through them yet. My husband's parents are also trying to get us to take things we would like from their home also, for which we really have no room at this time.

Florida's weather ranged from cool to nearly too warm for what we brought to wear, but the humidity is the real difference. I had forgotten what it was like, but now I remember why my hair took all day to dry naturally when we lived there!

We studied this Red Shouldered Hawk sitting on a wire just across the street from the house. I saw a hawk there often when I stayed there the summer before last helping out while my husband's mother was in the hospital and nursing home, but I never got a really good photograph of that one. Perhaps it is the same hawk. I caught it just as it turned to consider me.

We arrived back home on Tuesday evening and unpacked only the necessities, food and bathroom things, as we would be getting up early the next morning to drive to the airport. My husband had to be in Chicago for work the rest of the week. I took that Wednesday off myself, but unpacked the clothes. Thursday was for errands and Friday back to lessons and the airport.

~ My Lord, please watch over our family in Florida and thank you for providing us the opportunity to help them. ~