**Thomas Turner Tate** (1807–1888) was an English mathematical and scientific educator and writer. Largely self-taught, he has been described as "a remarkable pioneer of science and mathematics teaching".^{ [1] }

Born at Alnwick on 28 February 1807, he was son of Ralph Tate, a builder; his mother's maiden name was Turner, and George Tate was his brother. Initially expected to take up his father's business, he studied under an architect in Edinburgh.^{ [3] }

After his father's death, Tate changed direction from 1830. He lectured to local evening classes.^{ [4] } In 1835 he was the appointed lecturer on chemistry to the medical school in York.^{ [3] } York Medical Society was founded in 1834; the Medical School in fact was founded formally in 1838, and then lasted for about three decades.^{ [5] }

In 1840 Tate became master of the mathematical and scientific department at the Battersea teacher training college; this was a private venture founded in 1839–40 by James Kay-Shuttleworth.^{ [6] } Kay-Shuttleworth recruited Tate and two Scots, William Horne and Walter McLeod, to launch what was a new initiative in training, and textbook writing. Tate went on to write educational works on mathematics, mechanics, drawing, and natural science. His *Principles of Geometry, Mensuration, Trigonometry, Land Surveying, and Levelling* (London, 1848) was translated into Hindustani.^{ [1] }

In 1849 Tate obtained a similar post at the Kneller Hall training college. Its foundation was an initiative of the principal Frederick Temple, but the staff were few: Francis Turner Palgrave was vice-principal, Tate taught mathematics and science, and James Tilliard languages, geography and music.^{ [7] } The mission was to instruct teachers for paupers (i.e. those in workhouses).^{ [8] } For a period Temple led discussion at Kneller Hall of radical education reform, with his friend Ralph Lingen and others.^{ [9] } The flow of visitors there was closely linked to Balliol College, Oxford, and also literary circles.^{ [10] }

With Temple, Tate worked to select chemical and electrical equipment for school science teaching, and a government grant was made available to subsidise its sale.^{ [11] }

Tate was elected fellow of the Royal Astronomical Society on 14 March 1851.^{ [3] } During the 1850s his approach to teaching through the "science of common things" became fashionable: Tate's reaction was that he had been using it for two decades. He traced the pedagogic tradition in which he stood as Locke, Pestalozzi, the object lesson, David Stow and Samuel Wilderspin.^{ [2] } He had taken advice from Henry Moseley in his days at Battersea, and through Kay-Shuttleworth was influenced by the ideas of Richard Dawes. The thinking was to tackle the needs of a working-class education.^{ [12] }

The college was closed down in 1856, and a pension was given to Tate.^{ [3] } The institution had run into problems on the political front, where the Derby administration of the early 1850s disapproved, and also because it admitted some nonconformists as trainees.^{ [13] } *John Bull* had called it a "godless college" and complained of the cost in 1849.^{ [14] }

Tate died at his residence, 51 Catherine Street, Liverpool, on 18 February 1888, and was buried on the eastern side of Highgate Cemetery.^{ [3] }

Tate was twice married; his second wife Lavinia survived him. Three children were living at the–date of his death: of those Ralph Tate was his son by his first wife, Frances Hunter, and George Tate (1858–1933) the chemist was another son.^{ [15] }^{ [16] }^{ [17] }

Tate was the author of numerous educational works on mathematics, mechanics, drawing, and natural science, all tending to promote intellectual methods of instruction. His 'Principles of Geometry, Mensuration, Trigonometry, Land Surveying, and Levelling' (London, 1848, 12mo) was translated into: Hindustani.

His 'Philosophy of Education' (London, 1854, 8vo) reached a third edition in 1860; it showed Tate's debts to Francis Bacon, John Locke, Johann Pestalozzi and faculty psychology; it is noted for its advocacy of the inductive method.^{ [15] }^{ [18] } From 1853 to 1855, with Tilliard, he edited the *Educational Expositor*, a work designed to assist schoolmasters and teachers.^{ [3] }^{ [19] }

From 1853 to 1855, in company with James Tilleard, he edited the 'Educational Expositor,' a work designed to assist schoolmasters and teachers. In 1856 he began to publish 'Mathematics for Working Men,' London, 8vo, but only one part appeared.^{ [15] }

At York, Tate wrote a mathematical column for the *York Courant*.In 1856 he began to publish *Mathematics for Working Men*, London: only one part appeared.^{ [3] } In mathematical pedagogy, Tate favoured the teaching of estimation at an elementary level.^{ [20] }

In experimental science and engineering, Tate contributed to the * Philosophical Magazine *, With William Fairbairn, he was the author of memoirs in the * Transactions of the Royal Society *, on the vapour-tension of superheated steam, the strength of materials in relation to the construction of iron ships, the strength of glass tubes, and the elasticity of sulphuric acid. He was the inventor of a double-piston air-pump that was known by his name.^{ [3] }

*Exercises in arithmetic for elementary schools,*1844*Principles of Geometry, Mensuration, Trigonometry, Land Surveying, and Levelling*(London, 1848)*Educational Expositor,*with James Tilleard (eds.), 1853 to 1855*The principles of mechanical philosophy applied to industrial mechanics: forming a sequel to the author's "Exercises on mechanics and natural philosophy,*1853.*Philosophy of Education*(London, 1854)*Mathematics for Working Men,*London, 1956.*An elementary course of natural and experimental philosophy,*1856*The principles of the differential and integral calculus, simplified,and applied to the solution of various useful problems in practical mathematics and mechanics. By Thomas Tate,*1863

- Works about Thomas Tate

- Peter Hinchliff (1998).
*Frederick Temple, Archbishop of Canterbury*. Oxford, Clarendon Press. ISBN 0198263864. - David Layton (1974).
*Science for the People: The Origins of the School Science Curriculum in England*. Science History Publications. ISBN 978-0-88202-028-0.

The **history of mathematics** deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.

**Alexander Bain** was a Scottish philosopher and educationalist in the British school of empiricism and a prominent and innovative figure in the fields of psychology, linguistics, logic, moral philosophy and education reform. He founded *Mind*, the first ever journal of psychology and analytical philosophy, and was the leading figure in establishing and applying the scientific method to psychology. Bain was the inaugural Regius Chair in Logic and Professor of Logic at the University of Aberdeen, where he also held Professorships in Moral Philosophy and English Literature and was twice elected Lord Rector of the University of Aberdeen.

**Allan Kardec** is the *nom de plume* of the French educator, translator, and author **Hippolyte Léon Denizard Rivail**. He is the author of the five books known as the Spiritist Codification, and the founder of Spiritism.

**Science education** is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process, some social science, and some teaching pedagogy. The standards for science education provide expectations for the development of understanding for students through the entire course of their K-12 education and beyond. The traditional subjects included in the standards are physical, life, earth, space, and human sciences.

**William Whewell** was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge. In his time as a student there, he achieved distinction in both poetry and mathematics.

**Isaac Todhunter** FRS, was an English mathematician who is best known today for the books he wrote on mathematics and its history.

In contemporary education, **mathematics education** is the practice of teaching and learning mathematics, along with the associated scholarly research.

**Jeremiah Day** was an American academic, a Congregational minister and President of Yale College (1817–1846).

**Edward John Routh**, was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics and reaching its modern form with Leonhard Euler (1748).

**Trigonometry** is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.

**Methodios Anthrakites** was a Greek Orthodox cleric, author, educator, mathematician, astronomer, physicist, and philosopher.

**James Wood** was a mathematician, and Master of St John's College, Cambridge. In his later years he was Dean of Ely.

**Oliver Byrne** was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering. He is best known for his 'coloured' book of Euclid's *Elements*. He was also a large contributor to *Spon's Dictionary of Engineering*.

**De Volson Wood** was an American civil engineer and educator. He invented a steam rock drill and an air compressor and designed an ore dock. Wood was a professor, an author of multiple monographs on mathematics and engineering, vice-president of the American Association for the Advancement of Science and the first president of the American Society for Engineering Education.

**Sir Thomas Percy Nunn** was a British educationalist, Professor of Education, 1913–36 at Institute of Education, University of London. He was knighted in 1930.

A **mathematical exercise** is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.

**John Radford Young** was an English mathematician, professor and author, who was almost entirely self-educated. He was born of humble parents in London. At an early age he became acquainted with Olinthus Gilbert Gregory, who perceived his mathematical ability and assisted him in his studies. In 1823, while working in a private establishment for the deaf, he published *An Elementary Treatise on Algebra* with a dedication to Gregory. This treatise was followed by a series of elementary works, in which, following in the steps of Robert Woodhouse, Young familiarized English students with continental methods of mathematical analysis.

**Enoch Lewis** was a mathematician. He early exhibited a talent for mathematics, at the age of fourteen was usher in a country school, and at fifteen became principal. In the autumn of 1792 he removed to Philadelphia, studied mathematics, teaching half of each day to earn his support, and in 1795 was engaged as a surveyor in laying out towns in western Pennsylvania under the direction of Andrew Ellicott.

**Katherine Puckett Layton** is an American mathematics educator and the author of mathematics textbooks.

This article incorporates text from a publication now in the public domain : Lee, Sidney, ed. (1898). "Tate, Thomas". * Dictionary of National Biography *. Vol. 55. London: Smith, Elder & Co.

- 1 2 Layton, p. 77.
- 1 2 Layton, pp. 122–3.
- 1 2 3 4 5 6 7 8 Lee, Sidney, ed. (1898). .
*Dictionary of National Biography*. Vol. 55. London: Smith, Elder & Co. - ↑ Great Britain Privy Council Committee on Education (1857).
*Minutes of the Committee of Council on Education*. Clowes. p. 32. - ↑ Katherine A. Webb (1 January 1988).
*One of the Most Useful Charities in the City: York Dispensary, 1788–1988*. Borthwick Publications. p. 14. ISBN 978-0-903857-32-1. - ↑ Gary McCulloch; David Crook (26 November 2013).
*The Routledge International Encyclopedia of Education*. Routledge. p. 337. ISBN 978-1-317-85358-9. - ↑ Hinchliff, p. 71.
- ↑ Neil J. Smelser (3 September 1991).
*Social Paralysis and Social Change: British Working-Class Education in the Nineteenth Century*. University of California Press. p. 56. ISBN 978-0-520-91154-3. - ↑ Hinchliff, p. 33.
- ↑ Gillian Sutherland (15 April 2013).
*Studies in the Growth of Nineteenth Century Government (Routledge Library Editions: Political Science Volume 33)*. Routledge. pp. 1845–6. ISBN 978-1-135-02637-0. - ↑ College of Preceptors (1866).
*The Educational Times*. p. 248. - ↑ Layton, p. 82 and p. 111.
- ↑ Hinchliff, pp. 49–50.
- ↑
*The English Review*. Francis and John Rivington. 1849. pp. 110–. - 1 2 3 Howson, Geoffrey. "Tate, Thomas".
*Oxford Dictionary of National Biography*(online ed.). Oxford University Press. doi:10.1093/ref:odnb/26987.(Subscription or UK public library membership required.) - ↑ A. R. Alderman, 'Tate, Ralph (1840–1901)',
*Australian Dictionary of Biography*, Vol. 6, MUP, 1976, pp. 2434 - ↑
*Journal of the Chemical Society*. The Chemical Society. 1934. p. 1480. - ↑ Edward J. Power (January 1996).
*Educational Philosophy: A History from the Ancient World to Modern America*. Taylor & Francis. p. 116. ISBN 978-0-8153-1971-9. - ↑ Great Britain. Committee on Education (1852).
*Minutes of the Committee of Council on Education Correspondence, Financial Statements, Etc., and Reports by Her Majesty's Inspectors of Schools*. p. 23. - ↑ Thompson, Ian (1 June 2010).
*Issues in Teaching Numeracy in Primary Schools*. McGraw-Hill International. p. 5. ISBN 978-0-335-24153-8.

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