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I recall reading that their is a pesak/teshuvah/report by a major posek, perhaps an early "later" Acharon, (Rabbi Akiva Eiger zt"l) which noted that at least elementary arithmatic or mathematics was traditionally taught in cheder. I did not make note of the makor, however. Is anyone able to provide the source?

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I believe there is a Teshuva given by Rabbi Masliah Mazuz HY"D that permits learning math in a synagogue. This probably doesn't help you though. –  Hacham Gabriel Dec 26 '11 at 2:50
    
I would still like the makor :) –  Yirmeyahu Dec 26 '11 at 3:02
    
Legacy of Leaders Vol. II written by Yehuda Azulai (section about Rabbi Masliah Mazuz). I don't believe it is published in his Seforim. –  Hacham Gabriel Dec 26 '11 at 3:05
    
Question... how can you teach gematria without basic arithmatic? –  avi Dec 29 '11 at 9:36
    
@avi I don't think that's the question. Because if you want to learn Gimtarya, all you have to do is learn some math WHILE you are teaching Gimtarya. Any secular studies that are included in the Torah are certainly permitted to learn in order to understand the Torah. –  Hacham Gabriel Jan 1 '12 at 2:39
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3 Answers 3

Sefer Sheeris HaNachala mentions in the name of the Sefer HaItim that Rav Hai Gaon said that it is permitted to teach children Arabic and mathematics in order to assist them in learning Torah.

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And R' Ovadya Yosef shlita has a responsum to the rabbinate of Argentina, in which the only way their Jewish educational system may work would involve teaching math and Spanish in the beis medrish, where he references this allowance of R' Hai Gaon. –  Shalom Dec 26 '11 at 23:48
    
Very nice sources –  Yirmeyahu Dec 27 '11 at 4:10
    
@Yirmeyahu While a great source for the general concept, are you looking for Cheder (the european mode of teaching) specifically, or to young children in general? –  avi Dec 29 '11 at 9:38
    
Yes, it would have been a European posek speaking about it being part of the standard curriculum. –  Yirmeyahu Dec 29 '11 at 16:59
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@HachamGabriel, Yabia Omer 7: Orach Chaim 21. –  Shalom Dec 30 '11 at 14:59
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Yaskil Avdi (vol. 1 Orah Haim siman 7) permits it (he was asked by Rabbi Masliah Mazuz). As well as Sis Eliezer (vol. 9 siman 15). See the aforementioned Yabia Omer 7:21.

I found in Yalkut Yosef vol. 2 pg. 255

אין לערוך הרצאות של חול בבית הכנסת, וכל שכן לערוך שם קונצרטים וכיוצא בזה. אלא אם כן ההרצאה כוללת גם דברי חיזוק ועידוד לשמירת התורה והמצוות (כגון עריכת ''סמינרים'' לקרב רחוקים לצור מחצבתם).‏

He prohibits lectures about non-Torah things in a Shul except for Kiruv and Hizuk.

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