She taught at home with the support of the then Highland Region. Then when the children went to secondary school in Perthshire, Mrs Klemm, a German graduate of St Andrews University, enrolled at Northern College in Dundee for a year's postgraduate course.
Her daughters are now at university and she believes she is repaying the council's investment in her family by ploughing back her unique experience as head of the school. Last term five-year-old Anna joined her brother Calum on the roll, bringing it to five. There are two babies in the area.
Mrs Klemm says the children have an unusual ability to relate the curriculum to their day-to-day lives. Mark, aged six, adapted a lesson on floating and sinking to understand why the Spanish John, the estate's legendary landing craft, can be made of steel and yet not sink. He could even explain how it righted itself after an unfortunately loaded truck almost caused its capsize.
Although technically on the mainland, Inverie has island status because its nearest neighbour is a fair-weather 45-minute boat trip away in Mallaig. Information technology and art feature in the school's development plan. Following an invitation to participate in a European Comenius project, there are now links with island schools in Feoy, Norway, and Lyo, Denmark. Contact time via the computer is in three sessions a week, each of 150 minutes. Since many of the 28 children involved are in the early stages of reading and writing, drawings and computer-generated imagery are used, as well as voice links. The main language is English, but by swapping television programmes, the pupils familiarise themselves with the sounds of other languages.
Funded by the Central Bureau for Educational Visits and Exchanges, Mrs Klemm went to Norway last July to help develop the programme. The topics on which the children have worked include, not surprisingly, the weather. Children record changes in wind direction and strength, cloud coverage, rainfall and times of sunrise and sunset.
Other topics were children's games followed by the exchange of recipes. A common dictionary is being compiled on a framework made by the Norwegian project co-ordinator, who is an artist.
The attempt by Knoydart's residents to control their own future is given practical backing by the Inverie children. They have designed and printed a tea-towel depicting life through their own eyes. Profits from tourists will make a modest contribution to the #163;1 million needed to buy the estate.
Mrs Klemm travels for an hour each day from home to school by foot and four-wheel drive. On occasion she stops to view porpoises, golden eagles, otters, badgers or red deer. Even in such a setting she has a nagging problem - how to realise the ambition of eight-year-old Stephanie, who wants the school to acquire its own clarsach.