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“Set Them to the Cyphering Schoole”: Reading, Writing, and Arithmetical Education, circa 1540–1700

Published online by Cambridge University Press:  14 July 2017


During the late sixteenth and seventeenth centuries, English men and women replaced their existing oral and object-based arithmetical practices with literate practices based on Arabic numerals. While the adoption of Arabic numerals was incentivized by continental commercial developments, this article argues that England's increasing literacy rates and the development of vernacular arithmetic textbooks enabled changing arithmetical practices. By exploring the qualities of printed books, analyzing marginalia in arithmetic textbooks, and examining changing educational advertisements and curricula over time, we can demonstrate the importance of literacy and literature to early modern arithmetical education.

Copyright © The North American Conference on British Studies 2017 

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14 High-profile examples of the survival of other symbolic systems include the use of tallies in the British exchequer until the beginning of the nineteenth century as well as the continuing use of Roman numerals in regnal titles and to paginate the prefaces of printed books.

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22 Cressy, Literacy, 142–56.

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34 Watt, Tessa, Cheap Print and Popular Piety, 1550–1640 (Cambridge, 1991), 6 Google Scholar; Spufford, Small Books, 66.

35 English Short Title Catalog (hereafter ESTC), Exact numbers are not possible to calculate due to the loss of sources over time and occasional difficulties distinguishing between editions printed in the same year. At least an additional seventy editions of basic accounting books were also produced during this period. Yamey, Basil S., Edey, H. C., and Thomson, Hugh W., Accounting in England and Scotland, 1543–1800: Double Entry in Exposition and Practice (London, 1963), 202–8Google Scholar. For more on mathematical publishing in general, see Harkness, Jewel House, 104. For the canonical work on early modern English mathematicians and their publications, see Taylor, E. G. R., The Mathematical Practitioners of Tudor and Stuart England (Cambridge, 1954)Google Scholar.

36 Harkness, Jewel House, 104–5; Meskins, “Mathematics Education,” 152; Simon Schaffer, “Science,” in Raymond, ed., Oxford History, 1:398–416, at 399.

37 Worsop, Edward, A Discouerie of sundrie errours and faults daily committed by Lande-Meaters, ignorant of Arithmetike and Geometrie (London, 1582), A2vGoogle Scholar. While Keith Thomas's reference to this passage carries with it a strong implication that arithmetic is too difficult to learn, the context of the full list makes it clear that Worsop is referring to Recorde's far less heralded geometry textbook, The Pathway to Knowledge. Thomas, “Numeracy,” 118.

38 Schaffer, “Science,” 399–400.

39 Egmond, Van, Practical Mathematics, 6; An introduction for to lerne to recken with the pen or with the counters (London, 1539), A1rGoogle Scholar.

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42 The arte and science of arismetique (London, 1526), 1rGoogle Scholar.

43 For further analysis of the influences, structures, and authorships of these early arithmetic textbooks, see Williams, “Earliest English Printed,” 164–84.

44 These new arithmetics included bestsellers by James Hodder, Edmund Wingate, and especially Edward Cocker.

45 Didactic books, in general, often had long “afterlives” in the early modern period. Natasha Glaisyer, “Popular Didactic Literature,” in Raymond, ed., Oxford History, 1:510–19, at 514.

46 21793, fol. 2v, Huntington Library, San Marino (hereafter HEH).

47 Harkness, Jewel House, 118.

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51 Recorde, Robert, The Ground of Artes Teachyng the Worke and Practise of Arithmetike (London, 1543), 8r–vGoogle Scholar. The work was officially dedicated to a landowner and royal official named Richard Whalley, who had at least five children of an age to be learning arithmetic at that time. Alan Bryson, “Whalley, Richard (1498/9–1583), administrator,” ODNB,

52 Recorde, Robert, The Grounde of Artes, ed. Mellis, John (London, 1582), A2vGoogle Scholar.

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54 Mellis's accounting textbook was also a newly revised edition of an earlier book, Profitable Treatyce by Hugh Oldcastle, but in this case the original is no longer extant. Yamey, Edey, and Thomason, eds., Accounting, 155–59; Oldcastle, Hugh, A Briefe Instruction and maner how to keepe bookes of Accompts after the order of Debitor and Creditor, & as well for proper Accompts particle, &c., ed. Mellis, John (London, 1588)Google Scholar.

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57 Harkness, Jewel House, 133. For more on early modern instruments, see Bennett, Jim, “Early Modern Mathematical Instruments,” Isis 102, no. 4 (December 2011): 697705 CrossRefGoogle ScholarPubMed.

58 Cab Lib g, Society of Antiquaries, London.

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61 X513 W72p 1630, University of Illinois, Urbana-Champaign Special Collections, 3r; C.175.d.34, British Library (hereafter BL), 2v; 1607/500, BL, 1r; 8532.aa.24, BL, 2r; Adams.8.65.35, Cambridge University Library (hereafter CUL), 1r; Vet.A3, fol.1247, Bodleian Library, Oxford University, 2r; and 313383, HEH, 1r.

62 Clavell, Catalogue, 43.

63 646/A, Wellcome Library, London; 8506.aa.34, BL; M.6.58, CUL; and C.115.n.43, fol. A2r, BL.

64 Watt, Cheap Print, 263; Thomas, “Numeracy,” 120.

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69 For an example of book ownership versus book reading, see Gingerich, Owen, The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus (New York, 2004)Google Scholar.

70 For an example of a manuscript arithmetic textbook, see MS HA School Exercises Box 5, Folder 1, HEH, which is an educational commonplace book dating to 1623. The book also contains extensive notes on geometry and rules of measurement, as presented by the London mathematical tutor, John Speidell.

71 Sherman, William, Used Books: Marking Readers in the Renaissance England (Philadelphia, 2008), 3 Google Scholar.

72 [DeM] L.1 [Cocker] SSR.1700, fol. 3r, Senate House Library, University of London (hereafter SHL).

73 Ibid., 5–6, 9.

74 512 K47e, fol. K1v, American Philosophical Society Library, Philadelphia.

75 They do have library markings, including notes on acquisition and rebinding, which generally date to the twentieth century. For example, the subset of arithmetic textbooks from the Senate House Library were largely acquired in the nineteenth century by Augustus De Morgan, and most contain notes in his hand.

76 For more on the breakdown of textbooks by libraries and first author, see the appendix.

77 Wingate, Edmund, Arithmetique Made easie, In Two Bookes (London, 1630), 4v–A1rGoogle Scholar.

78 Wingate, Edmund, Mr. Wingate's Arithmetick, ed. Kersey, John (London, 1658), A4r–A5rGoogle Scholar. These changes were likely made possible by Edmund Wingate's death in 1656. Taylor, Mathematical Practitioners, 205; Bertha Porter, “Wingate, Edmund (bap. 1596, d. 1656), mathematician and legal writer,” rev. H. K. Higton, ODNB,

79 BL Add. MSS. 4239, fol. 18r. The inclusion of Hill in this list is curious, as the ESTC only records one edition of his arithmetic textbook, as opposed to Recorde and Baker's frequently reprinted textbooks. It is possible that other editions have been lost to the historical record or that Martindale had personal experience with Hill's arithmetic that made him highly value the book despite its failure to be reprinted. Hylles, Thomas, The arte of vulgar arithmeticke (London, 1600)Google Scholar.

80 Martindale, Adam, The Countrey-Survey-Book: or Land-Meters Vade Mecum (London, 1692), M3rGoogle Scholar. Martindale was not the only one to begin writing an arithmetic textbook, but he never make it to publication. For example, BL Add. MSS. 4473, fols. 24–27, contains the partially completed textbook of “William Senior professior of the Mathematiques 1641,” who taught mathematics out of his house.

81 Baker, Humfrey, The Wellspring of Sciences (London, 1564), A1rGoogle Scholar.

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83 Recorde, Robert, The Grounde of Artes, ed. Dee, John and Mellis, John (London, 1607), A1rGoogle Scholar.

84 Robert Norton had previously translated a Dutch treatise on decimal arithmetic and published it in 1608. Stevin, Simon, Disme: the Art of Tenths, or, Decimall Arithmetike, trans. Norton, Robert (London, 1608)Google Scholar; Recorde, Robert, The Grounde of Artes, ed. Dee, John, Mellis, John, and Norton, Robert (London, 1615), A1rGoogle Scholar.

85 Recorde, Robert, The Grounde of Artes, ed. Dee, John et al. (London, 1631), A1rGoogle Scholar.

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88 Ruth Wallis, “Cocker, Edward (1631/2–1676), calligrapher and arithmetician,” ODNB, See also the auction advertisement pasted inside the back cover of [D.-L.L]L2[Cocker]SR, SHL.

89 Wingate, Edmund, Arithmetique Made Easie, ed. Kersey, John (London, 1650), 462–65Google Scholar; Ruth Wallis, “Kersey, John, the elder (bap. 1616, d. 1677), mathematician” and “John Kersey the younger (b. c. 1660, d. in or after 1721),” ODNB,

90 Hodder, James, Hodder's Arithmetick, ed. Mose, Henry (London, 1683), A8vGoogle Scholar.

91 Martindale, Countrey-Survey-Book, M3r.

92 For an excellent, recent discussion of these issues, see Green, Ian, Humanism and Protestantism in Early Modern English Education (Burlington, 2009)Google Scholar.

93 For more on the universities’ resistance to any new institutions of learning—regardless of proposed curriculum—that might challenge their supremacy, see Feingold, Mordechai, “Tradition versus Novelty: Universities and Scientific Studies in the Early Modern Period,” in Revolution and Continuity: Essays in the History and Philosophy of Early Modern Science, ed. Barker, Peter and Ariew, Roger (Washington, 1991), 4559 Google Scholar.

94 Feingold, Mathematicians’ Apprenticeship.

95 Hoole, Charles, The Petty-Schoole, Shewing a Way to Teach Little Children to Read English with Delight and Profit, (especially) According to the New Primar (London, 1659), 2 Google Scholar.

96 Jewell, Helen M., Education in Early Modern England (New York, 1998), 17 CrossRefGoogle Scholar.

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98 ESTC, record no. 006176804.

99 Clement, Francis, The Petie Schole with an English Orthographie (London, 1587), A1rGoogle Scholar.

100 Ibid., 65, 71–85.

101 Hoole, Petty-Schoole, 30.

102 Schoolmasters’ licenses rarely survived in full, as they were kept by individual schoolmasters in their private records. Instead, most instances of licenses come from ecclesiastical visitations, where the contents of licenses were summarized for the visitation record. Cressy, David, Education in Tudor and Stuart England (New York, 1975), 32 Google Scholar.

103 In this usage, accidence signifies the “branch of grammar which deals with the inflection of words, grammatical morphology.” OED, s.v., “accidence, n 2”; Cressy, Education, 33–34.

104 Cressy, Literacy, 36.

105 Ibid., 35–41.

106 Wase, Christopher, Considerations Concerning Free-Schools as Settled in England (London, 1678), 33 Google Scholar.

107 Charlton, Kenneth, Women, Religion and Education in Early Modern England (London, 1999), 146 Google Scholar.

108 Jewell, Education, 95.

109 Lawson, John and Silver, Harold, A Social History of Education in England (London, 1973), 107 Google Scholar; Robert Ashton, “Leman, Sir John (1544–1632), merchant and mayor of London,” ODNB,; Charlton, Women, Religion and Education, 151, 148; Plumley, N., “The Royal Mathematical School within Christ's Hospital: The Early Years—Its Aims and Achievements,” Vistas in Astronomy 20 (1976): 5159, at 58CrossRefGoogle Scholar.

110 Charlton, Women, Religion and Education, 147.

111 Cressy, Literacy, 30; Charlton, Women, Religion and Education, 149.

112 Coote, Edmund, The English School-Master (London, 1651), A2r, H2rGoogle Scholar.

113 See, for example, The ABC with The Catechisme: That is to say, an Instruction to bee taught and learned of euery Child, before he be brought to be confirmed by the Bishop (London, 1633)Google Scholar, which was reprinted at various times throughout the seventeenth century.

114 White, John, The Country-Man's Conductor in reading and writing true English … and some arithmetical rules to be learnt by children, before or as soon as they are put to Writing (Exeter, 1701), A1r, A5vGoogle Scholar.

115 White, Country-Man's Conductor, A1r.

116 Thomas, “Meaning of Literacy,” 102–3.

117 Jewell, Education, 85–86.

118 Brinsley, Ludus Literarius, 25.

119 Jewell, Education, 84.

120 Although the grammar school was teaching Arabic numerals and ciphering as early as 1597, the school's various accountants used Roman numerals to record monetary entries and sums until 1669/70. Stocks, George Alfred, ed., The Records of Blackburn Grammar School, Remains, Historical and Literary, connected with the Palatine Counties of Lancashire and Chester, n.s., 66 (Manchester, 1909), 1:73Google Scholar.

121 Ibid., 1:74.

122 Cressy, Education, 65.

123 Lilly, William, Merlini Anglici Ephemeris: Or, Astrological Judgments for the year 1677 (London, 1677), F8vGoogle Scholar.

124 Mellis advertised his school in the versions of Recorde's The Ground of Artes that he edited, from 1582 until 1607. His advertisement also appeared in the 1610 edition, “now lastly corrected by John Wade,” but was replaced by N. Physhe in the 1615 edition. Recorde, Ground of Artes (1607), Mm8r; Recorde, Ground of Artes (1610), A1r; Recorde, Records Arithmeticke (1615), Oo3v.

125 Ruth Wallis, “Hodder, James (fl. 1659–1673), arithmetician,” ODNB,

126 Ruth Wallis, “Cocker, Edward (1631/2–1676), calligrapher and arithmetician,” ODNB,

127 Cocker, Edward, Cocker's Arithmetick, ed. Hawkins, John (London, 1680)Google Scholar.

128 Lilly, Merlini Anglici Ephemeris, F8v.

129 Sarah Powell and Paul Dingman, “Arithmetic Is the Art of Computation,”

130 Green, Humanism, 310.

131 Minns, Chris and Wallis, Patrick, “Rules and Reality: Quantifying the Practice of Apprenticeship in Early Modern England,” Economic History Review 65, no. 2 (May 2012): 556–79, at 559CrossRefGoogle Scholar; Wallis, Patrick, “Apprenticeship and Training in Premodern England,” Journal of Economic History 68, no. 3 (September 2008): 832–61, at 836CrossRefGoogle Scholar.

132 Willis, Arthur J. and Merson, A. L., eds., A Calendar of Southampton Apprenticeship Registers, 1609–1740 (Southampton, 1968), 19 Google Scholar.

133 John Rigges, apprenticed in 1611 to his uncle, was to be instructed in his uncle's trade and “alsoe to be enxtructed in all other trades or sciences as the said Frauncis Rigges shall use during the said terme.” Ibid., 2.

134 Vanes, Education and Apprenticeship, 21.

135 Willis and Merson, Calendar, 86.

136 Ibid., 38.