Matzoh Ball Math and More!
A Jewish homeschooling friend of mind - the psychologist and writer Dr. Jeffrey Fine (Jeffrey specifically asked me to identify him and his family by name) with an almost eight-year-old son - Kessem - just went a life-threatening disease episode. He was in a coma, and the doctors said he was within hours of death, but through something akin to a miracle, coupled with spectacular advances in medical science, Jeffrey's own extraordinary willpower, and perhaps a little prayer thrown into the mix, he is well on the road to recovery.
During this episode, which lasted for a period of almost half a year, his wife Dalit enrolled their son in Kumon math. They both felt their son needed to be doing something at least vaguely academic, and perhaps add a little bit of regularity to a situation that was totally out of his control. They asked for my blessing, as if they really needed it (well, to be fair, they probably did), and I readily gave it. I wasn't so concerned about what Kessem was actually going to learn, if anything, but rather that there be a bare semblance of normality in his life, and that his parents didn't feel any extra burden of guilt on top of what was already an extraordinarily trying situation.
Kumon math does a pretty good job, for what it is. Most families find their way there when the kids are doing "poorly" in school, not "keeping up", or "falling behind" (all those quotation marks are deliberate), and are being stereotyped, picked on, scapegoated, or ignored accordingly. Needless to say, many of the kids lose self-esteem in the process, feel stupid, and often either lash out or withdraw as a coping mechanism to deal with the injuries being dealt to them in the process of their "education".
So what Kumon does, first and foremost, is work to raise children's self-esteem. And they do so by requiring only "work that is easily completed". The idea is never to give a child work at which she won't be successful. So instead of, as is usual in most educational theory, providing assignments at the proximal level of a child's development so that she may learn either through teaching or through a process of error and correction, the only work required is that at which the child is sure to succeed. "Success from the start" is Kumon's motto, and ensuring there is no frustration is the key. In other words, if a child is ready for "two plus two", the "self-motivated learning model" will have the child writing her numbers. All material must be completed with a perfect score within a prescribed period of time before the child is allowed to progress on to anything more difficult. Daily worksheets are provided that must be completed until they are mastered in the required amount of time before moving on. If it works, self-esteem is restored, and the child will be able to transfer the self-knowledge that success is possible back to the location of the original insult and humiliation.
It didn't take long, however, for Kumon to chafe on poor Kessem. He couldn't see any reason to work on worksheets containing information he already knew for 20 minutes when he could do it in 10, especially as no new learning was taking place. His mother asked me for ways to get him to "concentrate", and all I could find myself doing was trying to assure her that Kessem had already proven that concentration wasn't the problem.
The point being of course that if you get all the answers right, powers of concentration aren't at issue. Your self-esteem might increase for awhile (until you figure out you are being patronized, and look for ways to non-cooperate), but you probably wouldn't be learning anything, except that no one ever really cared about the worksheets once you had completed them, perfect and all. Kessem wasn't suffering from lack of concentration; he was suffering from growing lack of interest.
This morsel being hard to stomach raw, I reached for my trusty "that reminds me of a story" approach, which I borrowed some quarter of a century ago from the great anthropologist and systems thinker Gregory Bateson.
Bateson used to tell a story about a learning experiment with a dolphin he conducted and observed in Hawaii. The experimental protocol involved a number of repetitions with a hoop that any experienced dolphin trainer would have warned would be boring, so the animal would break the sequence by tossing the hoop off to the side. "Funny," said Gregory's assistant, "every time he does that he gives a little chuckle." Gregory asked her if she wrote the chuckle down, but there was no place to record it. All that was recorded was that the dolphin had failed to demonstrate successful learning. Hmm.
This seemed to hit the spot, if not so much with Dalit, at least with Jeffrey, who recognized this other form of frustration from his own school days. "What do we do now?" he asked.
"Hold a graduation ceremony for Kumon, and move on to something that is now a big part of your and Kessem's world. I suggested. What's up for you?"
Jeffrey thought a minute. "Well, I never thought I'd live to see another Passover. And the Angel of Death seems to have passed over our house, at least for now. (The word "Passover" refers to the Biblical story that the Angel of Death passed over the houses of the Israelites and killed all firstborn males among the Egyptians, resulting in the expeditious exit of the Israelites from Egypt.) So we are doing it up big. Grandma is coming from Israel for several weeks to help out, and we expect around 20 people for the Seder (the ritual Passover meal)."
"All right. And Kessem knows the Four Questions?" (The youngest participant at a Seder gets to ask four ritualized questions, preferably in Hebrew, which the rest of meal (that can take up to six hours or longer, depending on how thorough one is), is set up to answer.)
"He's got those down," Jeffrey said proudly.
"Well, then I've got just the thing, but grandma will have to get in on the action. Matzoh Ball Math."
Back up. Matzoh is a kind of unleavened cracker, eaten during the eight days of Passover (there are folks who eat it all year round) in remembrance of the haste with which the Israelites left Egypt, so quickly that they didn't have time to allow the bread to rise in the oven. For some folks, one of the great treats of Passover is matzoh ball soup, chicken soup (vegetable soup for vegetarians is of course acceptable) eaten with a kind of round dumpling made with matzoh meal, eggs (unless cholesterol free), and various and sundry kinds of extras. There are matzoh ball connoisseurs, and there are various factions prepared to do battle for seasoned or unseasoned, with schmaltz (chicken fat) or not, onions/no onion, firm or feathery, traditional or light textured, gluten-free or cajunfusion. (You can find a terrific selection of recipes at Ellen's Kitchen - I've posted a simple, traditional one at the end of this article.) In my extended family, we have members of both the sinker (prefer the matzoh balls on the bottom of the soup) and floater persuasions. [My wife and I are both floaters. It is said that flotation can be ensured by not peeking in the covered pot during cooking - this could be a subject of scientific inquiry (it may be folklore, simply an old wives' tale designed to keep nosey husbands out of the kitchen;) I prefer simply adding a little seltzer to the recipe.]
Matzoh Ball Math is something that can be done over a period of years, to match a child's interest and mathematical readiness. There's no need to do it all at once (and certainly not in order, even if the name for the Passover meal - Seder - means "order"), and for those who celebrate the holiday, it can be incorporated a bit more at a time each year, a new "ritual" grafted onto the old.
The first lesson, of course, is simply in the making of the matzoh balls themselves. (I suggest that children be provided with separate materials for their own pot of matzoh balls. That way one is sure to have enough for consumption, without having to be concerned about the ultimate fate of the objects of mathematical inquiry. Of course, you'll want your children to be able to make good ones so that even if they don't turn out to be math whizzes, they'll have a sense of what it is to be a good cook!)
Equipment (besides the basic food stuffs needed for the recipe, normal cooking utensils, and a good pot with a tight lid): two scales (one which can weigh an entire pot full of stuff, one that can weigh small amounts of ingredients, or an entire cooked matzoh ball); teaspoon and tablespoon measures; marked measuring cups and pitcher; a small ruler; string; butcher paper; eight small colorfast buttons (two each of four different colors); and a set of calipers. Oh, and of course, a handy white board with colored markers.
Ready? The first thing for a child to learn is measurement, and in doing so, about bases. (I am presuming that she has already learned the basics behind base 10.) So start playing with matzoh meal. How many teaspoons in a tablespoon? Make sure to put the results on the board. Write equations: draw three small spoons = 1 tablespoon. Write it out in words - words are in fact a form of algebraic expression, where the words substitute for the thing itself. Then turn it into more formal algebra. (I am convinced, by the way, that most kids are prepared to handle basic algebra by age 7 or so.) Let Teaspoon = A; let Tablespoon = B. 3A=B. 6A=? Show her the symbols for greater than ( > ) and less than ( < ). 4A>B. Some kids are going to like the writing part best; others, playing with the spoons - you'll quickly find out whether yours is a writer or a spooner.
You get to do this with all kinds of measurement. How many ounces in a cup? (If you have an ounce measure, actually perform the operation to find out rather than simply reading the side of the liquid measure.) How many cups in a pint? Pints in a quart? Quarts in a gallon? How many ounces does the four-gallon pot hold? Write out all the equations: in pictures, in words, in algebraic symbols. (This will all pay off later when you start reading recipes together.)
Same with grams, ounces, and pounds. Ah-oh. There are two kinds of ounces - how are we going to write the symbols so we don't get confused? Do liquid ounces of various different substances weigh the same amount? Try it out - with water, oil, and flour. Write the results on the whiteboard, and use the less than/greater than symbols.
If you do this all backwards, working from the largest measures to the smallest, you will have learned fractions. The rest is just a writing exercise (which you should do, in the equation format.)
Now one needs to know how to read the ruler. All of sudden we have fallen into a world of fractions, and base 12! The calipers, too. With the ruler, start measuring the kitchen world. The diameter of the pot; the radius of the pot (show how you can get the same result using the ruler or the calipers; the height of the scale and the measuring cup. Length, width, and height. Make a couple of "LWH" charts, and begin to examine the relationships of the measures.
Wow - that made me all hungry. Time for some gefilte fish. Those of you who like to fish can go in quest of the giant Gefilte. Boy, do I have stories for you! (you can look up many of them on-line).
* * * * *
Two thousand words, and we haven't cooked anything yet! Time to roll the matzoh balls. Make them about an inch across. About 15 of them should do.
What are different ways you can measure the diameter? One way is simply to leave them on a flat surface of butcher paper, and use a ruler to measure them end-to-end. Another way is use the calipers. A third way is to cut one in half, and measure the diameter on the open face. See if you come up with the same answer all three ways. write it on the board - D = 1. What about "r"?
Now let's make things interesting. Let's name four of the matzoh balls: "Abraham", also known as "Matzoh Ball A", "Benjamin - B", "Chaim - C", and "Daniel - D". Let them represent the four brothers who traditionally are said to ask questions at the seder - the wise son, the simple son, the wicked son, and the one who is too young to ask. Figure out together how you might determine how "long they are around". In other words, the circumference. Use a string or thread, and take a measure of the girth. Take the amount of string required to go around the middle, and measure it with the ruler. Now do it to three or four more. Write down the results in a little chart for A, B, C, D. Let's see: 3 1/2, 3 1/8, 3 1/4, 3. (Abraham was a little lumpy; Daniel was kind of small.) On the white board, write out their relative sizes using the "<" and ">" symbols, and scramble the order. Now on another line on the chart, list the diameters of each. What is the ratio between the diameter and the circumference?
Sooner or later, you'll be singing the Pi Day Song, which will make the exercise truly ecumenical. (We sing it in my office, as the price of slice of pie, every March 14th). It's to the tune of "Oh Christmas Tree":
Oh Number Pi
Oh, number Pi
Oh, number Pi
Your digits are unending,
Oh, number Pi
Oh, number Pi
No pattern are you sending.
You're three point one four one five nine,
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.
Oh, number Pi
Oh, number Pi
You are a number very sweet,
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There's 2 Pi r and Pi r squared,
A half a circle and you're there,
Oh, number Pi
Oh, number Pi
We know that Pi's a tasty treat.
(Words by LaVern Christenson, Windom, Minnesota)
Now it's time to weigh the four matzoh balls (in grams), and put their uncooked weights on the chart.
Then we are going to cook them in a covered pot for 40 minutes or so (40 is a very important Biblical number, as in "It rained for 40 days and 40 nights", Moses went up to Mount Sinai for 40 days, or the Israelites spent 40 years in the desert. Forty years is another way of saying "a very long time", as is 40 minutes for many seven- or eight-year-olds.) Follow the recipe. A vexing question arises: how are we going to distinguish Abraham, Benjamin, Chaim, and Daniel from each other when we take them out of the pot? This question vexed me, too, so I consulted two Quaker experts, neither of whom had ever made matzoh balls, but one had made plum pudding, and the other was a preschool teacher. We all agreed that we could try to dye them each a different color, but most of the color might likely wash out, leaving all the matzoh balls an unappetizing gray. Not a good move. So we came up with another method, though you and your child might come up with a better one. (Write me). Get eight small colorfast buttons, two each of four different colors, and assign a color to each matzoh ball. Make sure to put the assigned colors on the chart. Tie the two similarly colored buttons together with a string, with about a one-inch space between them. Stick one button in the middle of the matzoh ball, and let the other dangle on the outside. (We also thought of fancy-colored toothpicks that are blunt on one end, but we feared they might stick to another matzoh ball.)
Carefully measure the amount of water being placed in the pot. Then, when the water comes to a boil, carefully drop all the matzoh balls in the water, including the four brothers. Cover the pot, weigh the whole thing, and don't look! (As already noted, there are people who believe that uncovering the pot turns floaters into sinkers - this, as noted, could be the subject of some more advanced experimentation. I haven't had the time.)
When cooked, carefully remove the matzoh balls with a slotted spoon. Weigh the total for the matzoh balls, and the water that remains in the pot. Add the two weights together. Has any weight been lost? Where did it go? Measure out how much water is left in the pot, and compare with the amount put in. You could use this as the beginning of an exercise in understanding percentages.
Now separate out the four brothers. Weigh them individually. Measure their girth. Find the diameter and radius. Expand the chart: now there is a "Before" and "After".
There is so much more than can be done. The volume of the spheres. The volume of cylinders. The ratio between weight and volume (density). Exercises to calculate the rate of change at various temperatures (in other words, a matzoh ball curriculum in calculus and organic chemistry.) All of this can wait for future years.
And there will be questions! Plenty of them, more than could possibly be generated by just the four sons - and we have daughters, too! You will have become matzoh ball scientists.
But you can't do any of this without a recipe! Here's a relatively simple one:
3 tablespoons chicken fat (vegetable oil will work)
½ teaspoon salt
3 tablespoons hot water or chicken soup (I also believe in a spritz of seltzer water)
¾ cup matzoh meal
Separate the eggs (that is, the whites from the yolks!)
Beat the yolks until they are thick
Add the salt, fat/oil, water/soup/seltzer.
Beat the whites until stiff but not too dry, and fold in.
Fold in the matzoh meal. Put in refrigerator for an hour.
Roll into balls.
Carefully drop the balls into two quarts boiling salted water or soup.
Cover and cook for 25 minutes. DON'T LOOK!
If cooked in water thus far, transfer to soup for another 15 minutes.
Well, I think I gave Jeffrey, Dalit, Kessem, and grandma more than they were likely to handle this Passover. That's fine, as it will give them plenty to chew on (though matzoh balls should melt in the mouth), and there will be plenty more Passovers to follow. In the meantime, I suggested that they not save one of the traditional Jewish blessings exclusively for the lighting of Passover candles, but they could use it to inform every day of their homeschooling lives:
"Blessed are You, Ruler of the Universe, who has given us life, sustained us, and brought us to this very special occasion."