Last year, we celebrated Yom Ha’atzmaut (Israel Independence Day) with a discussion of Israel’s many winners of the Nobel Prize. This year we will focus on just one of them, the economist Joshua Angrist.
Joshua Angrist.
Angrist was born in 1960, grew up in Pittsburgh, and from 1982-1985 he served in the Israel Defence Forces as a paratrooper. He then came back to the US where he earned a PhD from Princeton. (His thesis was on the Vietnam Draft Lottery.) He returned to Israel as a lecturer at the Hebrew University, and in 1996 he was appointed MIT's Ford Professor of Economics. He holds dual US-Israeli nationality, and has spent most of his career analyzing the economics of schooling and the effect of class size on academic achievement. One of his papers looks at the “Maimonides Rule,” named for, well, Maimonides, who apparently noted a correlation between class size and student achievement.
The Maimonides Rule
Angrist noted that the Talmudic sage Rava limited the size of a class of students to twenty-five. Any more than that, and the school must provide a second teacher:
בבא בתרא כא, א
וְאָמַר רָבָא סַךְ מַקְרֵי דַרְדְּקֵי עֶשְׂרִין וְחַמְשָׁה יָנוֹקֵי וְאִי אִיכָּא חַמְשִׁין מוֹתְבִינַן תְּרֵי וְאִי אִיכָּא אַרְבְּעִין מוֹקְמִינַן רֵישׁ דּוּכְנָא וּמְסַיְּיעִין לֵיהּ מִמָּתָא
Rava said: The maximum number of students for one teacher of children is twenty-five children. And if there are fifty children in a single place, one establishes two teachers, so that each one teaches twenty-five students. And if there are forty children, one establishes an assistant, and the teacher receives help from the residents of the town to pay the salary of the assistant.
This ruling was later codified by Maimonides:
משנה תורה, הלכות תלמוד תורה 2:5
עֶשְׂרִים וַחֲמִשָּׁה תִּינוֹקוֹת לְמֵדִים אֵצֶל מְלַמֵּד אֶחָד. הָיוּ יוֹתֵר עַל עֶשְׂרִים וַחֲמִשָּׁה עַד אַרְבָּעִים מוֹשִׁיבִין עִמּוֹ אַחֵר לְסַיְּעוֹ בְּלִמּוּדָם. הָיוּ יוֹתֵר עַל אַרְבָּעִים מַעֲמִידִין לָהֶם שְׁנֵי מְלַמְּדֵי תִּינוֹקוֹת
[A maximum of] 25 students should study under one teacher. If there are more than 25, but fewer than 40, an assistant should be appointed to help him in their instruction. If there are more than forty students, two teachers should be appointed.
Angrist noted that Maimonides’ ruling leads to smaller class sizes and a lower student-teacher ratio, and that “this rule induces a nonlinear and non-monotonic relationship between enrollment size and class size.” Angrist used this rule as a basis for an investigation between the class size of fourth and fifth graders in Israel and the scores of their tests in math and reading. His work which you can read here, showed that reductions in class size induced a significant and substantial increase in reading and math scores.
“Besides being of methodological interest and providing new evidence on the class size question, these findings are of immediate policy interest in Israel where legislation to reduce the maximum class size is pending.”
Who would have thought that the Rava’s ruling as codified by Maimonides would play a role in the awarding of a Nobel prize to an Israeli ex-paratrooper?
