I was sent to a boarding school in Bloemfontein when my father was working in Maseru back in the mid 1970s, and was taught much the same things. Whether you accept that the first use of "concentration camps" was by the British against the Boers during the Second Boer War (1899-1902), depends largely upon your definition of the term "concentration camp".
The camps constructed by the British in South Africa were certainly not the first use of internment camps for civilian populations. They had been used at least as early as the 1830s when the United States used them to contain native American populations and black slaves prior to relocation under the terms of the Removal Act of 1830. Later, they were to be used by the Spanish as a military tool in Cuba during the Spanish American War in 1896-97 (known as "Reconcentration Camps").
The camps in South Africa during the Second Boer War actually started out as refugee camps. They had been set up by the British Army to provide refuge for civilian families that had been forced to abandon their homes due to the war. Conditions at that point were nowhere near as bad as they would become later.
When Kitchener took over in late 1900, he introduced new tactics, borrowing from those used to great effect during the US Civil War (for example by General Sherman in Georgia), in an attempt to break the guerrilla campaign. As Thomas Packenham observed in his book, The Boer War, Kitchener initiated operations to ...
... flush out guerrillas in a series of systematic drives, organised like
a sporting shoot, with success defined in a weekly 'bag' of killed,
captured and wounded, and to sweep the country bare of everything that
could give sustenance to the guerrillas, including women and children
... It was the clearance of civilians - uprooting a whole nation - that
would come to dominate the last phase of the war.
-- Packenham, 1979, p493
Not surprisingly, the influx of civilians to the camps grew dramatically as a result of these operations. It was at this point, that the British began to refer to the camps as "concentration camps", which might be the first use of the term. A total of 45 tented camps were built for Boer internees (and a further 64 for black Africans).
The camps were poorly administered, hygiene was poor and sanitation inadequate. Contrary to popular belief, there was never a policy of deliberately starving Boer families to death (although it is certainly true that there was a two-tier allocation policy, whereby families of men who were still fighting were routinely given smaller rations than others). Internees were issued the same (appalling) food rations as those provided to the British Army at that time.
The overcrowding in the camps led to endemic contagious diseases such as measles, typhoid and dysentery. These were the cause of the majority of the 26,000 civilian deaths in the camps.
In December 1901, partly as a result of the death toll in the camps, and partly in response to political pressure resulting from the outcry against the camps back in the UK, Kitchener stopped placing women and children in the camps and issued orders that they should be left with the Boer guerrilla fighters. Obviously, this policy had the additional strategic benefit of further hampering the enemy in the field.
Notwithstanding what others have said, there is no evidence that the Boers were "not considered as fully human" by the British. In fact, the public outcry in the UK when the news of the concentration camps broke suggests just the opposite.
The paper British Concentration Camps of the Second South African War by John L. Scott examines the question of the concentration camp in South Africa in some detail. It is rather long, but is well worth reading.
The British National Archives hold an extensive collection of records relating to the Second Boer war, including records of the camps. Although relatively few are available online, all are available to view in person at Kew.