Thursday, May 5, 2016

The Three Kings Lesson is Very Cool!

This spring has just flown by. And now we are in warm-weather mode. The kids got in the pool today!! (They got in the pool with all of their clothes on when the babysitter was here. And then she got them all showered before releasing them back to mommy. We have a smart babysitter.) We are plugging along and I am spending most of my free time planning for next year. 

Plans are flexible. With that in mind, I intend to be crazy busy, on and off, during June and July, and then get back into school mode in August. I would have liked to have had the opportunity to school during the summer, but our schedule ended all chopped up and we don't have a free chunk that is longer than a week and a half. So, we will just stop school and then start again when our schedule is clear. I think it is better for my stress levels for me to just "let it go" and not expect to get anything done during the summer months.

The "big change" I was alluding to in the last post is that we are going classical with our homeschooling. I am kind of turning the sock inside out, if you will. I plan to use classical theory for our foundation and then insert pieces of the Montessori curriculum into our science and math sequences. The Well-Trained Mind, written by Susan Wise Bauer and Jessie Wise, says something like, "pick a math program." Okay, I am picking the Montessori materials and sequence for our math program. And to beef-up the science curriculum, that I feel is a bit lacking in the classical model, I am going to insert some of the Montessori presentations as a jumping-off point for further book work. I also plan to give each child a Montessori inspired first-impression when possible. I am introducing the parts of speech to D using the Montessori lessons, but I plan to review them with him, over, and over, and over using text-book methods.

I plan set aside the Montessori theory that I believe isn't working in our homeschooling classroom. I will turn to more text and book learning and will focus more on language, reading, and writing. I will be using off-the-shelf curriculum to reinforce areas like grammar, spelling, and sentence analysis, and to develop areas like writing and history. And the kids will start studying Latin and T will begin studying logic next year. 

In the Montessori sequence, it didn't matter so much which grade you chose for your child. But as I am selecting text books I am finding that everything is organized by grade level. I am also finding that publishers consider my kids to be way ahead in some subjects and so very far behind in others. Finding the right "level" for them has been a challenge. 

I am re-assigning our grade-levels internally, but am keeping the kids at age-grade level for PR purposes. I will be teaching D at a grade-1 or grade 2 (or sometimes grade 3) level. My target grade for D is grade 1. To the outside world he will be a 5-year-old kindergartner. S will be herself, actually. She is of 3rd grade age, 8 years old, and I have chosen 3rd grade texts for her. T will turn 10 this summer, and his target grade will be 5th grade in all subjects except for math. (I suspect he will start pre-algebra or algebra in about a year.) To the outside world, we held him back a year, so, we will call him 4th grade for PR purposes. 

Why classical? There are so many reasons I chose to switch. A few of the biggest are:

  • There are many classical-style curriculum texts that present a straight-forward, easy to prepare and implement, and rigorous lesson plan. I am looking forward to thinking about what to implement, less.
  • It is one of my homeschooling requirements that my children learn how to write well. The classical model very much supports written expression. And since this is an area I feel I am unable to "teach" alone I am happy that there are a plethora of Classical-style writing programs that can help me out.
  • I am training the kids to be able to go to college. Specifically, I am training them to be able to get into a college and then not flunk out of said college, or university (as in T's case.) In college, students learn largely from lecture and texts. I feel the classical method focuses on these methods of instruction. Therefore, I feel that using the classical method of instruction will help enable my children to learn what they want to learn in the traditional classroom setting.
  • I feel that the Montessori theory does not produce the responsible, enthusiastic, independent child that loves learning, that Montessori observed, when it is employed in a homeschool setting. (I am sure that there are others who will disagree, but I am not entertaining a debate at this time.) There is, of course, the fact that I my not being a formally trained directress and my faulty implementation could have affected my sub-par results. But, observing that my children lacking in these areas, I am seeking another approach to help them develop these character qualities I feel will most help them succeed in life. 
As I type this, I am surrounded by text books, reference materials, and planning papers. I plan to put forth more on this topic soon.

But now, on to Montessori math.
T is nearly done with the cubing sequence.
Here T is cubing a trinomial using numerical values. 
His problem is (5+4+3)^3 = 1,728.

Again, there is an album presentation that goes with this, but I can't tell you what it is. T just did this on paper with a pencil and I wasn't involved very much.
This is the story of the three kings. In other lessons, the prisms on the table are the terms that comprise the trinomial cube. 

The story summarized and re-told by me: 
There were once three kings: red, blue, and yellow. Each guy had six men that were the same color as their king. In addition, each king had two all-black bodyguards. Everyone marched around in this formation, with the big red king leading the way.

One day the blue king decided he was going to make some mischief and take over the red king's men. Some of the blue king's men jumped on the red king's men and sat on top of them.
Immediately everyone's bodyguards surrounded the blue king and said, "there is a rooster in your britches." (That last part was made up.)
Then the yellow king's men trounced on the blue king's remaining men to keep them from creating further chaos. 
And then the yellow king slipped around back so that he could see the entire spectacle without missing a bit of it. It is written in the album, that the red king was so fat and happy, in front of the line, that he didn't know what was going on behind him.

Then I told T that the whole reason the blue king instigated this re-arrange was that they all had marched pass the kingdom of the decimal.

I named the red king, hundreds-cubed, and put a "h^3" ticket by him. Since 100^3 is a million, we renamed the red king the 1,000,000 cube. The prisms to his right are all "h^2*t" or 100,000 prisms. The next two columns of prisms are all "h^2*u" or 10,000 prisms. The blue king was named the tens-cubed king and he got a "t^3" ticket by him. We renamed him 10*10*10, or 1,000. The black bodyguards were "h*t*u" prisms and we named them 100*10*1, or 1,000 prisms. The next two columns of prisms are "t^2*u" and "u^2*h" or 100 prisms. And lastly the yellow king was named the unit-cubed king and he got a "u^3" ticket by him which translates to 1. (The album says to have prepared tickets which probably could have been a good idea. But, in this instance, we didn't need them because T just wrote all the tickets out himself, after figuring out what was going on, in the middle of the lesson.) 

Then I asked, "what if each category could be colored a single color? What would that look like?" And THEN I brought out the algebraic trinomial cube (or the hierarchical trinomial cube.) T's face light up with absolute delight at the sight of a new material and he switched out all of the prisms as you can see above. In the algebraic cube, all of the prisms and cubes are the same dimensions as the trinomial cube, but each prism and cube is colored according to category.

Who knew that someone could derive so much happiness and delight from a trinomial cube.
The kids have been playing around with this algebraic trinomial cube for many months now, and T finally unlocked the lesson and found out just how we use that cube.
You can see the "values" we assigned to the cubes and prisms here.

I plan to circle back around and finish up the squaring sequence before doing the final cubing lesson, cubing a decimal quantity

More later!