It seems natural for an Ethiopian citizen - and more boradly in the context of African history - to give a special weight to the battle of Adwa. After all, it ensured the independence of Ethiopia for another forty years.

Its place in the history of Italy is much less prominent.

It's hard to provide you with sources on how things are thought though; I have found something online but nothing on a higher education level. I'll also use the Italian names of a few places because they are the ones familiar to me.

Italian colonialism was not a successful endeavor; it didn't left the lasting social or economical impact of other "colonialisms", it didn't result in the establishment of a lasting administrative structure; it didn't last long in short. Despite the claims of the Fascist Regime, the belated Empire established with the conquest of Ethiopia was in no way comparable to its British model. For those reasons comparatively little attention is paid in general to the process of Italian colonialism.

Most text book cover it only to the extent of acknowledging its existence, briefly establishing its questionable methods (the use of concentration camps in Lybia and asphyxiating gases in Ethiopia) and exploitative nature. When more details are given, it is often in the context of establishing the "social features" of colonialism as a broad phenomenon (on page 53 you will find an example of integrative activity for students 12-13 years old dealing with European Colonialism: they are expected to know which countries were colonies and which ones colonists - that a small excerpt is given concerning "British" India), with special chapters creating paths through different forms of exploitation: slave trade - forced labor - segregation. Of course these get more in depth depending on the age of the students. It's pretty rare though, to see a more modern approach, that tries to establish the point of view of the exploited people; and the use of local sources is to my knowledge almost non existent.

That's beacuse, despite being a minor event in Italian history, the battle of Adwa has already its place in the context of interior politics, that contributes to make it more than a footnote; but shifts the focus on it from colonialism to that troubled period that was the sunset of the Crispi era that opened what is generally referred to as "crisis of the end of the century".

The Italian expansion in Africa, first the establishment of footholds in Massaua and the surrounding area, then the economical penetration in the area of Tunis and the crisis of relations with France, than the attempt to establish a "strong protectorate" over Ethiopia, later the conquest of Lybia, all must be understood as reflections of the Italian internal politics. From the rising steel/navigation blocks in the 1880s to the unbalanced growth of investments capital in the age of tariffs, the extension of granary tariffs in 1887, to the social crisis that peaked around the fasci revolt in Sicily in 1893-94.

Of course, the local populations couldn't care less about Italian internal politics; yet the Italian establishment never seemed to look at the Italian colonial adventures as a value in themselves. Or to consider those regions and people as "equal" political subjects. Thus an analisis of those events is somehow driven by this kind of outlook and the Italian colonialism is seen through the eyes of Italian colonialism. I can see the issue here - unfortunately it is also fair to say that there isn't probably enough to warrant an "Italian colonialism" unit in school texts - as I assume might be the case for other nations - unless use of local sources is expanded in historiography (it is possible that more recent works exist that I am unaware of and teachers have a bit of room to expand if they choose to, but there would be little to draw upon).

It is certainly true of the defeat of Adwa. Without going into too many details, the government of Francesco Crispi was pressed by growing social conflict and coming out of a reactionary turn that had brought the old Garibaldine to pass special legislation against the socialists and proclaim the state of siege in large swaths of the nation. Meanwhile the colonial process - that Crispi had never really cared for (he believed that very little was there to be gained and he held no favorable impression of the men who had started it) - was lagging behind with Italy failing to gain anything of substance. Crispi, who had by then accepted the process as something that was going to happen no matter how, thought that, if something had to be done, it was better doing it right - and it might have been possible to turn a colonial victory into a prestige boost for Italy and its government.

Of course, Crispi had very little knowledge of the State of things on the Somalian border, so his impulse to the initiative was limited to push for advance. The resulting tensions with the Ethiopians brought to the eventual diplomatic crisis and beginning of military operations.

As I mentioned, Crispi was busy with the end of the fasci revolt and Italy had probably sent more soldiers to Sicily that it had to Ethiopia; so there was a tendency to push for results while witholding support. General Oreste Baratieri, understanding that after the Amba Alagi defeat the strategic position of the Italian forces wasn't as solid as he hoped for, wanted to keep a defensive position. Crispi pushed him forward - even refusing Baratieri's resignation and encouraging him to advance. Baratieri obliged, compounding the strategig mistake with a series of tactical blunders he shared responsability with his officers for. The resulting defeat and peace treaty marked the fall of Crispi (that usually gets his own Chapter in history books) and the rise of the other political leader to have his name in the chapter title: Giovanni Giolitti.

The events of the first Italian attempt in Ethiopia did leave a certain impact though, as toponyms show, even if the history behind them is mostly obscure. Wandering around in some periferic neighborood you'll find the names of Adua, Amba Aradam, Amba Alagi, Dogali, Massaua, Makallè, Coatit; they are often placed appropriately not far from the name of Francesco Crispi and other Italian politicians of the late XIX Century. Of course those names were not given to remember the Italian defeats but the victorious conquest of 1935-36 that avenged that half forgotten shame.

I have touched upon the issue in this old post but feel free to ask for clarifications if you think it necessary.