Bottom Up Top Down Analogy

January 1, 2008

This morning I “Stumbled upon” Rick Garlikov’s essay
describing his impressively successful experience teaching, by means of questions alone, binary arithmetic to a third grade class. Throughout the entire session Rick made no categorical declarations and, apparently, the children came to understand binary arithmetic by means of their own answers to Rick’s questions.

As I have some experience teaching children, the piece invoked in me plenty of comment material. I am not arguing against anything Rick says in his piece; his piece is far more descriptive than prescriptive.

My central point in this post is a simple one: a good teacher must constantly tailor his teaching method to fit the subject matter and the level, aptitude, and attitude of his students. No one method can ever suffice.

The methods of teaching employed by a teacher for the benefit of student can be divided, generally, into
two classes, each with it’s own advantages. I shall call them Bottom Up and Top Down, respectively. A good teacher, I insist, will employ a mixture of both, even, most often, in the same teaching session.

Bottom Up: Basically, what Rick did in the session described in his post is a perfect example of this method in its most extreme manifestation. The teacher brings his students (bottom) up to the level of the information. The advantage is obvious; the students
really get it; in fact, they got to it ‘themselves’; the students now hold at the level of the concept.

Top Down: Basically the teacher brings the concept down to his students. The advantage is simple: the ceiling of Bottom Up is mainly determined by the current level of the students, while
the ceiling of Top Down is mainly determined by the level of the teacher; the better the teacher the further he can bring concepts down. Thus, a teacher can give to his students what they are not at the level yet to arrive at themselves.

(Relatedly, it’s a safe bet that almost all of the answers offered by the students to Rick’s questions were, rightly, transmitted to them, originally, through a top down method.)



December 30, 2007

In the midst of Moshe’s famous encounter with G-d at the burning bush, Hashem reveals to him the purpose of the upcoming exodus: “After you take the nation out of Egypt, You shall all serve me on this mountain [you shall receive the Torah].

The Hebrew letters forming the word Mitzraim (Egypt) are the same as those forming the word Maitzarim (limitations or restrictions), the only difference between them lying in their respective pronunciations. Thus, Torah tells us, freedom from Egypt is, in a grander sense, the true freedom of the Jewish people from all that had hitherto limited and restricted it.

Every entity has its own freedom:

While the plant is free when it is afforded the opportunity to grow unrestrictedly, an animal can not be free under similar conditions; it must also be afforded the opportunity to roam without limitation.

Higher is Man: A man who is afforded all his physical needs, but not the opportunity to learn and acquire wisdom, is not free.

Different is the Jew: Endowed with a soul that is a “part of G-d’, a Jew cannot be free without the opportunity to engage in Torah and Mitzvos.; “No one is free other than he who engages in Torah and Mitzvos.” (Pirkei Avos)

(Adaptation of a letter written by the Lubavitcher Rebbe.)

The Function of the Messianic Monarch

December 24, 2007

A partial translation of Ezekial 37:21-25: (See the whole thing here.)

[G-d instructs Ezekial saying,] Say to them, So says the Lord God: Behold I will take the children of Israel from among the nations […] I will gather them from all around, and I will bring them to their land […] I will purify them, and they shall be to Me as a people, and I will be to them as a God […]

(verse 24) My servant, David, shall be king over them […] and they shall walk in My ordinances, observe My statutes and perform them […] They shall dwell on the land that I have given to My servant, to Jacob, wherein your forefathers lived; and they shall dwell upon it, they and their children and their children’s children, forever.

(verse 25) […] And David, My servant, shall be a Nasi unto them forever.

The Lubavitcher Rebbe points to several differences between the prophecy’s two descriptions of the awaited Jewish monarch (verse 24 and 25, respectively):

In 24 the Monarch is described as “Melech”, or “king” in the English, while in 25 he is described as “Nasi”, a term not only connoting Kingship, but also Wisdom. Indeed, the title Nasi was conferred on the leader of the Sanhedrin who, in the words of the Rambam, “stands in the place of Moshe our teacher”.

In 24 the King is described as being over the people–“ shall be king over them”–while in 25 the Nasi is described as relating to the people–“shall be a Nasi unto them.”

While verse 25 says explicitly that he shall be a Nasi unto them forever, 24 makes no such statement regarding his being King over them.

The Rebbe explains how all the differences can be accounted for when bearing in mind the dual nature of the role of the awaited Monarch:

The Rambam, in his “laws of Kings”, speaks of two functions of the Messiah:

1. The Messiah as a King, who “will force Israel to go in the ways of the Torah…..” , “ wage the wars of G-d”, “build the Temple in its place and gather in the dispersed Jewish people” and “bring the entire world to serve G-d together.”

2. And The Messiah as Sage, prophet and teacher of Torah to the people: “that King… from the seed of David, will be more wise than Solomon and a prophet close in stature to Moses our teacher. Therefore, he shall teach the entire nation and show it the way of G-d. And all the nations shall come to learn from him”.

The two verses speak of these two roles, respectively.

Referring to his role as sovereign, verse 24 speaks of the Messiah as “King”, characterizing his kingly relationship with his subjects as one of exaltedness and distance–he “shall be king over them”. Referring to the Messiah’s role as teacher, verse 25 describes him as Nasi–the title held by the head of the Sanhedrin–characterizing his standing as being unto his subjects, as a teacher who must bring knowledge down to the level of his students.

Indeed it is only this relationship that is described as persisting forever. For while Messiah’s role as King over the people is mainly relevant to the beginning of the messianic era, when the children of Israel need be “forced” to go in the way of the Torah and “the entire world” need be “brought” to serve G-d together, the Messiah’s role as prophet and teacher is eternal.

We want Moshiach Now!

Sage Prescriptions For a Strong Torah Marriage; a translation of Rambam 15:19-20

December 19, 2007

Law 19:

Likewise our Sages commanded: that a man honor his wife more than he honors himself; that he love her as he loves himself; that if he is a man of means, he provide for her welfare in accordance with those means; that he not cause her to fear him excessively; that he speak to her gently; and that he not act nervously (depressed?) nor be easily made angry.

Law 20:

They [the Sages] likewise commanded upon the woman: that she honor her husband excessively; that she be in awe of him; that she tailor all her actions to be in accordance with his will; that he be in her eyes as a ruler or king, conducting herself in the ways of his heart, and distancing that which he hates.

And this is the conduct of the holy and pure children of Israel in their unions. And through this conduct, their dwelling will be beautiful and praiseworthy.

Do we all worship the same G-d?

December 18, 2007

The truth is that the question is a non-starter; what does one mean by the same G-d?

There is only one G-d. So when you direct your attentions to G-d, it is at him you are aiming.

Let’s look at it in another way:

There is G-d; and there is our conception of Him.

Let’s say G-d ‘is’ Light (as it were) and our conception of Him is the vessel in which that light is ‘contained’ and expressed.

If part of a man’s conception of G-d is true, then G-d(ly) light is contained and expressed in that vessel. If part of the conception/vessel is false, then there is no light contained and expressed in that part. The light is the same light nonetheless.

Accordingly, the more ‘pure’ the vessel, the more expressed the light; the less pure, the less expressed the light. Same light, though.

If a person has vessels within vessels within vessels, the light is less manifest; especially if the exterior vessels are false, then the light is concealed. But expressed or not, concealed or not, the light is there the same. Matter of fact, even a pure vessel, though expressing light, obscures or directs attention from the light which cannot be contained, and of course from the essence of G-d which is not light, which is G-d, simple and undefined.

Thus the advantage of relating to G-d through simple faith, accepting that he is beyond conception, not just our conception, but any conception, even infinite conception. Sorta like trying to physically touch an idea.

The reason why we must try to understand-it is the very first commandment according to the Rambam-is because G-d wishes to fill the person; his mind, then his heart; then his thought, speech and action. Indeed that is why he chooses to manifest himself also in a finite way; alas, just as G-d isn’t limited to the finite, so he is not limited to the infinite. But the light is the light is the light. There is one G-d. G-d is one.

This dynamic holds for all theistic attentions.

Here is the difference: Torah says about itself that it is one with G-d; thus Torah vessel and G-dly light are utterly one.

The Heart of the IDF

December 16, 2007

Art is a tremendous medium for communication, and I have yet to see anything better convey the heart of the Jewish army than the combination of images and music in the clip that follows.

Though most attention is payed to the hands, which are “the hands of Eisov”, what’s critical is the heart: the voice of Ya’acov.

The chorus of the song, rendered in English, is,

We are believers, children of believers; we have no one upon whom to rely; except for our father–our father in heaven.

The most striking image is 1.15 minutes in; the wall is the Eternal Western Wall; The men in green are our soldiers.

The Place of the Altar: Rambam; Laws of the Temple, Chapter 2, Law 2

December 9, 2007

Through our tradition, it is well known to everyone that the place in ‘Goren Aravna’ on which David and Shlomo (Solomon) built the altar is the very place on which Avraham built the altar on which he bound his son Yiztchak (Isaac). It is the very place on which Noach (Noah) built [his altar] after leaving the Ark. It is the very place on which Kain and Hevel (Cain and Abel) offered [their respective sacrifices]. And in this very place Adam offered his sacrifice after he was created.

From this place he [Adam] was created; Our Sages said, “From the place of his atonement, Man was created”.