David Renfrew White was born in Edinburgh, Scotland, on 21 June 1847, the son of James Wilson White, a carpenter, and his wife, Agnes Renfrew. He moved to Van Diemen's Land (Tasmania) with his family in 1853, settling first in Launceston, then in Hobart. Here he attended Chalmers Presbyterian church school, winning prizes in algebra, Euclid, drawing, English grammar and geography in 1861. After arriving in Dunedin with his family on 10 June 1862 from Hobart on the Tamar, White worked as a seedsman, baker's bookkeeper and builder's labourer for his father.
From 1866 to 1868 White mined for gold in Hokitika, returning in 1869 to Dunedin to continue his education. He studied for the entrance examination to the University of Otago from 1869 to 1872, and passed his first teachers' examination in 1872. White was appointed sole-teacher at St Leonard's School, West Harbour, Dunedin, in July 1872, joined North Dunedin School (later called Union Street School) in 1874 as junior assistant, and became first assistant in 1878 at William Street School. In 1878 he was elected first secretary to the Educational Institute of Otago, formerly the Otago Schoolmasters' Association.
In 1879 White began study at the University of Otago, and in 1880 he returned to the Union Street School as first assistant. He graduated BA in 1883, and in 1884 gained his MA with second-class honours in political science and a prize in mental and moral philosophy. He was first secretary to the New Zealand Educational Institute (NZEI) from 1883 to 1885, was elected president for 1890, and became the first teacher to be awarded an A1 teachers' certificate by the Department of Education. He married Ida Macfarlane Spedding, a primary school teacher, at Dunedin on 2 April 1884.
In March 1895 White was appointed principal of the training college. In this position he introduced several reforms to teacher training in Otago which were to be subsequently adopted in other provinces. He succeeded in drawing the Normal School, associated schools and the Dunedin Training College closer together, and established a model infant room and a kindergarten at the college. White firmly believed that a close association between training colleges and universities was necessary to help teaching become a fully fledged profession. Professionalism was possible, he concluded, only when teachers could gain degrees, when they received their theoretical training at a university, and when colleges were practical schools placed under university and not Department of Education jurisdiction.
The relationship between training colleges and the university became closer from 1904 when education was introduced to the university curriculum, although the colleges remained under the jurisdiction of the Department of Education. White was appointed the first lecturer in education at the University of Otago in 1904. His work as an outstanding educator was recognised when he was appointed to the university's first professorial chair in education in 1909, a position he held until his retirement in December 1912.
In retirement White continued his involvement in the educational affairs of Dunedin. He became a member of the Free Kindergarten Association Advisory Board, and for three years examined students on their kindergarten work. He lived in England from 1913 to 1914, attended the 1913 conference of teachers from overseas dominions in London as a New Zealand Educational Institute representative, and returned to Dunedin in 1915. White was elected vice chairman of the Astronomical Branch of the Otago Institute in 1917, appointed chairman of the Education Court of the 1925–26 New Zealand and South Seas International Exhibition held in Dunedin, and was guest speaker at the 1933 NZEI jubilee celebrations in Dunedin. He died in Dunedin on 28 October 1937 at the age of 90, survived by his wife, three sons and a daughter.
David Renfrew White was a dark, fragile-looking man with a 'keen intellectual face'; short and bald, he had a dark beard and a baritone voice. He had lifelong interests in gardening, amateur astronomy and singing – he had been trained by Carmini Morli, a Dunedin-based Italian opera singer, in the early 1870s. As one who knew the value of embracing change and initiating reform, he warned fellow educators against complacency, and stressed that enthusiasm in their work was essential to progress. Such attitudes, formed by long experience, led him to play an important part in the professionalisation of teacher training in New Zealand.