It depends.
Yes, some schools teach it, some don't, and in varying ways.
First, some context. The word Nakba has a variety of uses. To some people, it refers specifically to the expulsion of mostly Arabs from Palestine in 1948 (seemingly the usage in the question, and what I'm following here). To others, it is synonymous with the founding of Israel itself. Some Palestinian activists consider it an ongoing state rather than a one-time event, whereas some Israeli activists have argued for consideration of the expulsion and voluntary flight of Jews from Arab countries to Israel as a form of Nakba. As such, the various quotes in the answer might define the word slightly differently.
One major reason this distinction is relevant is because one might imagine that a school might accurately represent the expulsion and killing of Palestinians carried out during the founding of Israel, but not portrary it as something negative. Indeed, at least as of 2011, this was a common portrayal of the Nakba in schools, at least according to at least one academic:
The killing of Palestinians is depicted as something that was
necessary for the survival of the nascent Jewish state, she claims.
"It's not that the massacres are denied, they are represented in
Israeli school books as something that in the long run was good for
the Jewish state. For example, Deir Yassin [a pre-1948 Palestinian
village close to Jerusalem] was a terrible slaughter by Israeli
soldiers. In school books they tell you that this massacre initiated
the massive flight of Arabs from Israel and enabled the establishment
of a Jewish state with a Jewish majority. So it was for the best.
Maybe it was unfortunate, but in the long run the consequences for us
were good."
That said, at least one textbook apparently omitted the subject altogether:
The history textbooks for high school approved by the Ministry of
Education do not present a uniform narrative. In fact, one textbook
omits the subject altogether while another treats it in a superficial
and biased way.
History and Memory in the Israeli Educational System: The Portrayal of the Arab-Israeli Conflict in History Textbooks (1948-2000)
However, according to Wikipedia, newer textbooks tend to be somewhat more balanced:
From the late 1970s onward, many newspaper articles and scholarly
studies, as well as some 1948 war veterans' memoirs, began to present
the balanced/critical narrative. This has become more common since the
late 1980s, to the fact that since then the vast majority of newspaper
articles and studies, and a third of the veterans' memoirs, have
presented a more balanced narrative. Since the 1990s, also textbooks
used in the educational system, some without approval of the Ministry
of Education, began to present the balanced narrative.
As one of the sources referenced noted, some later Israeli textbooks (closer to the 2000s) took a more critical view:
The years 1998–1999, however, witnessed the publication of a new
generation of textbooks, written according to a new history
curriculum, which differ substantially from previous textbooks. The
textbook for junior high does not elaborate on the issue but it states
that “during the battles many of the country’s Arabs were expelled.
Some ran away before the arrival of the Jews to the village or to the
Arab neighborhood in the city, and some were expelled by the occupying
force.” It also adds that “more than 600,000 Arabs were uprooted from
their places in the country and were settled in refugee camps.”79 The
teacher’s guide for this textbook is more explicit, instructing the
teacher to emphasize that “in this war over the home and the land
there were acts of expulsion by the victors. When the [Jewish] forces
conquered the mixed cities and Arab villages, Arab Palestinians were
expelled on more than one occasion. This is why the Arabs call this
period al-nakba (the disaster or holocaust).” Another junior high
textbook explained that in certain areas, where good-neighborly
relations existed between Jews and Arabs, there was an “explicit order
not to expel Arabs,” but “the expulsion of the Arab population of
Lydda and Ramla was confirmed by the political leadership.” This
depiction stands in sharp contrast to the narrative of the first- and
second-generation textbooks.
History and Memory in the Israeli Educational System: The Portrayal of the Arab-Israeli Conflict in History Textbooks (1948-2000)
Relatively recently, some prominent Israeli educators have also advocated for schools to teach it:
Former education minister Shai Piron said Monday he believes students
at Israeli schools should be exposed to varied and even opposing views
regarding the establishment of the State of Israel, including the
Palestinian “Nakba” narrative, according to which the founding of the
Jewish state in 1948 is considered a national tragedy.
Speaking at a conference in Tel Aviv, Piron, a Yesh Atid party MK,
said that “political education” requires of teachers to expose their
students to a wide range of different narratives and opinions,
according to Army Radio.
The statement by Piron broke a long-standing taboo in mainstream
Israel, which has traditionally downplayed the Nakba narrative. Recent
legislative efforts by nationalist lawmakers have attempted to pull
funding from schools that mark the Nakba.
However, a countervailing current has promoted the opposite trend, downplaying the expulsion in textbooks:
Israel's education ministry has ordered the removal of the word nakba
– Arabic for the "catastrophe" of the 1948 war – from a school
textbook for young Arab children, it has been announced.
The decision – which will alter books aimed at eight- and
nine-year-old Arab pupils – will be seen as a blunt assertion by
Binyamin Netanyahu's Likud-led government of Israel's historical
narrative over the Palestinian one.
So overall, I would say that:
- Israeili schools generally teach about the Palestinians who were killed or expelled during the 1948 conflict, but often present it as justified or positive.
- However, this is not universally true: some textbooks encourage recognizing the Nakba as negative; conversely, others gloss over it altogether.