To our great delight on Rosh Chodesh Adar our children all walked in with a creatively designed משנכנס אדר מרבים בשמחה. To my initial dismay I was sure that all our well meaning teachers may have transgressed a Gemoro (Temurah 14b). The Gemoro learns from psukim in the Torah that one may not 'write' the oral part of our torah - תורה שבעל פה אסור לכותבם. The phrase משנכנס אדר מרבים בשמחה come from a Gemoro (Taanis 29a) and is part of תורה שבעל פה, it would therefore seem to be ossur to write it.
The Gemoro concludes that based on a possuk in Tehilim (119 126) - עת לעשות לה' - one may write even the oral part of Torah, the reason behind this is that since writing the תורה שבעל פה is an integral part of its survival it is preferable that it should get written. In the times of the Tanoim when they had the minds and clarity to remember everything by-heart there was no risk to the Torah being forgotten even though it wasn't written. However, the last Tanoim [approximately 2000 years ago] realized that this was changing, and that the learners no longer had the capacity to remember everything by-heart, they understood that Hashems desire was to start writing done even the oral part of the torah. Hence the Mishnah, and afterwards that Gemoro was written and accurately passed from one generation to the next.
However, does this allowance have any limitations?! It must be noted that the Shulchan Aruch makes no mention of the initial issur, nor any limitations to the permission we have to write the oral torah.
 The Taz (YD 183 1) writes that the heter of עת לעשית לה' is only כדי להתלמד בו when done for the purpose of torah learning (see also Mishnah Berurah 638 24). [There may be a possibility that the Taz only said this referring to details pertaining to the teaching of תורה שבכתב that we don't find an explicit heter of עת לעשות. However regarding writing תורה שבעל פה, that the Gemoro explicitly writes the heter of עת לעשות it may possibly be more lenient].
The Rebbe of the Chasam Sofer - Harav Noson Adler - had a phenomenal memory, which never failed him, and from a very young age he never forgot anything he learnt. Harav Adler held that since he didn't need to write his chidushei torah to prevent him forgetting them, he never wrote any of them down, for fear that he is transgressing the issur of writing תורה שבעל פה. [This is not a ruling which was given for the public, and if this would have been a halocho, it would have to have been brought in the Shulchan Aruch]. According to the Taz one can debate whether making a Rosh Chodesh decoration is indeed a "need" for which to use the exemption of עת לעשות לה'.
 The Rambam (Responsa 5) writes that כתב אשורית - the letters as they are written in a sefer Torah - is holy and should not be used for mundane matters. The Remoh (Responsa 34) wonders why our seforim are not written with the Ashuris alphabet. The Remoh [quoted in Magen Avraham (334 17)] explains that the previous generations developed a new alphabet in order to write chidushei torah with. The Remoh suggests that the main issur of דברים שבעל פה אין לכותבם is against writing with the Ashiris letters, but with other letters it is somewhat more lenient. Hence, after the Gemoro told us that due to עת לעשות לה', they could write the oral torah, it become mutter with a non-Ashuris alphabet only. According to the Magen Avraham it seems that any תורה שבעל פה not written in Ashuris is muttar. Accordingly the משנכנס אדר signs are ok.
 Many Poskim hold that since the Gemoro allowed writing תורה שבעל פה, it is muttar irrespective of what one is writing for.
According to these Poskim obviously we would have no reason to challenge the kindergarten teachers.
 One teacher suggested to me that the don't mean to write a part of תורה שבעל פה rather they are simply writing that at the start of Adar one should increase ones level of simcha. [This sounds a bit of a weak excuse, since they are choosing the very wording of the gemoro].
 If you look carefully you will even find some people who write משנכנס ... מרבים בשמחה which is not a complete phrase [3 words may be called a phrase] in-order to avoid the issue of תורה שבעל פה אין לכותבם.