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

  • Jessica Otis
Abstract

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.

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1 Fauvel, John and Gray, Jeremy, eds., The History of Mathematics: A Reader (New York, 1987), 316–17; Meli, Domenico Bertoloni, “Wallis, John (1616–1703), mathematician and cryptographer ,” Oxford Dictionary of National Biography (hereafter ODNB) (Oxford, 2004), http://www.oxforddnb.com/view/article/28572. The Wallis family's choice to send the elder son to university and to set up younger sons to earn their livings through trade was common among early modern gentry. Wallis, Patrick and Webb, Cliff, “The Education and Training of Gentry Sons in Early Modern England,” Social History 36, no. 1 (February 2011): 2046 .

2 For an analysis of the hyperbole in Wallis's autobiography, see Feingold, Mordechai, The Mathematicians’ Apprenticeship: Science, Universities and Society in England, 1560–1640 (Cambridge, 1984), 8688 .

3 Van Egmond, Warren, Practical Mathematics in the Italian Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to 1600 (Florence, 1980), 912 . The canonical work on late medieval commercial expansion is Lopez, Robert S., The Commercial Revolution of the Middle Ages, 950–1350 (Englewood Cliffs, 1971). For more recent sources, see, for example, Ormrod, David, The Rise of Commercial Empires: England and the Netherlands in the Age of Mercantilism, 1650–1770 (Cambridge, 2003); and Ogilvie, Sheilagh, Institutions and European Trade: Merchant Guilds, 1000–1800 (Cambridge, 2011). For more on late medieval Italian accounting practices, see Robert H. Parker and Basil S. Yamey's collection of post-Second World War British essays, especially Geoffrey A. Lee, “The Oldest European Account Book: A Florentine Bank Ledger of 1211”; W. T. Baxter, “Early Accounting: The Tally and the Checker-board”; Christopher W. Nobes, “The Gallerani Account Book of 1305–1308”; and Yamey, Basil S., “Balancing and Closing the Ledger: Italian Practice, 1300–1600,” in Accounting History: Some British Contributions, ed. Parker, Robert H. and Yamey, Basil S. (Oxford, 1994), 160267 . On accounting history more generally, see also Littleton, Ananias Charles and Yamey, Basil S., Studies in the History of Accounting (New York, 1978); and Oldroyd, David and Dobie, Alisdair, “Bookkeeping,” in The Routledge Companion to Accounting History, ed. Edwards, John Richard and Walker, Stephen P. (New York, 2009), 95119 .

4 Harkness, Deborah E., The Jewel House: Elizabethan London and the Scientific Revolution (New Haven, 2007), 101 .

5 The general shift from oral to literate technologies of knowledge has been well explored by scholars such as Burke, Peter, Popular Culture in Early Modern Europe (New York, 1978); Ong, Walter, Orality and Literacy: The Technologizing of the Word (New York, 1982); and Fox, Adam, Oral and Literate Culture in England, 1500–1700 (Oxford, 2000). For more on the specific shift from oral and object-based to literate forms of numeracy—and the consequences of these changes—see Glimp, David and Warren, Michelle R., Arts of Calculation: Quantifying Thought in Early Modern Europe (New York, 2004); and Jessica Otis, “By the Numbers: Understanding the World in Early Modern England” (PhD diss., University of Virginia, 2013). For an analysis of numeracy and systemic changes more generally, see Chrisomalis, Stephen, Numerical Notation: A Comparative History (Cambridge, 2010) as well as the canonical study of Hill, George Francis, The Development of Arabic Numerals in Europe Exhibited in Sixty-Four Tables (Oxford, 1915).

6 For more on print and the dissemination of knowledge in England, see, for example, Eisenstein, Elizabeth, The Printing Press as an Agent of Change (Cambridge, 1979); Johns, Adrian, The Nature of the Book: Print and Knowledge in the Making (Chicago, 1998); and Peacey, Jason, Print and Public Politics in the English Revolution (Cambridge, 2013).

7 Oxford English Dictionary (hereafter OED), 2nd ed., s.v.v., “numeracy, n.” and “numerate, adj.2”; Butterworth, Brian, What Counts: How Every Brain Is Hardwired for Math (New York, 1999); Dehaene, Stanislas, The Number Sense: How the Mind Creates Mathematics (New York, 1997); Thomas, Keith, “Numeracy in Early Modern England: The Prothero Lecture, Read 2 July 1986,” in Transactions of the Royal Historical Society, 5th ser., no. 37 (London, 1987), 104–5.

8 Thomas, “Numeracy,” 120. For more on the popular numerical practices of early modern England, see also Cohen, Patricia Cline, A Calculating People: The Spread of Numeracy in Early America (Chicago, 1982); Howard, Geoffrey, A History of Mathematics Education in England (Cambridge, 1982); Denniss, John, “Learning Arithmetic: Textbooks and Their Users in England 1500–1900” in The Oxford Handbook of the History of Mathematics, ed. Robson, Eleanor and Stedall, Jacqueline (Oxford, 2009): 448–67; Harkness, Jewel House; and Otis, “By the Numbers,” 45.

9 For an example of a multiplication table included in a book with wax tablets, see Stallybrass, Peter et al. , “Hamlet's Tables and the Technologies of Writing in Renaissance England,” Shakespeare Quarterly 55, no. 4 (Winter 2004): 379419, at 397.

10 Arabic and Italian mathematicians used the dust board for Arabic-numeral arithmetic until pen and paper began to supplant it in the fourteenth century. Warren Van Egmond, “The Commercial Revolution and the Beginnings of Western Mathematics” (PhD diss., Indiana University, 1976), 343. Wax tablets continued to be produced and used for a variety of purposes, including calculation, throughout the early modern period. Stallybrass et al., “Hamlet's Tables,” 402–3. While women did not perform calculations with their embroidery, they did reproduce letters and numbers on their samplers, and many surviving instances of women's handwriting show the clear influence of embroidered letters. Hubbard, Eleanor, “Reading, Writing, and Initialing: Female Literacy in Early Modern London,” Journal of British Studies 54, no. 3 (July 2015): 553–77, at 565.

11 Wardley, Peter and White, Pauline, “The Arithmeticke Project: A Collaborative Research Study of the Diffusion of Hindu-Arabic Numerals,” Family and Community History 6, no. 1 (May 2003): 517, at 6. More extensive data and reports from the Arithmeticke Project are available online at http://www.rw007a7896.pwp.blueyonder.co.uk/

12 Meskins, Ad, “Mathematics Education in Late Sixteenth-Century Antwerp,” Annals of Science 53, no. 2 (1996): 137155, at 154.

13 Otis, “By the Numbers,” 57–66.

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.

15 Arbuthnot, John, An essay on the usefulness of mathematical learning, in a letter from a gentleman in the city to his friend in Oxford (Oxford, 1701), 27 .

16 Thomas, “Numeracy,” 119. For more on eighteenth-century popular numeracy, see Wardhaugh, Benjamin, Poor Robin's Prophecies: A Curious Almanac, and the Everyday Mathematics of Georgian Britain (Oxford, 2012).

17 Menninger, Karl, Number Words and Number Symbols: A Cultural History of Numbers, trans. Bronner, Paul (Cambridge, MA, 1969), 422 ; Ifrah, Georges, From One to Zero: A Universal History of Numbers, trans. Bair, Lowell (New York, 1985), 481 ; Smith, Eugene and Karpinski, Louis Charles, The Hindu-Arabic Numerals (Boston, 1911), 132 .

18 Cressy, David, Literacy and the Social Order: Reading and Writing in Tudor and Stuart England (Cambridge, 1980), 142–56.

19 Barry, Jonathan, “Popular Culture in Seventeenth-Century Bristol,” in Popular Culture in Seventeenth-Century England, ed. Reay, Barry (London, 1985), 62 ; Fox, Oral and Literate Culture, 18.

20 Hackel, Heidi Brayman, “Popular Literacy and Society,” in The Oxford History of Popular Print Culture, vol. 1, Cheap Print in Britain and Ireland to 1660, ed. Raymond, Joad (Oxford, 2011), 88100, at 93.

21 For more on the multiplicity of early modern literacies, see Thomas, Keith, “The Meaning of Literacy in Early Modern England,” in The Written Word: Literacy in Transition, Wolfson College Lectures 1985, ed. Baumann, Gerd (Oxford, 1986), 97131, at 99.

22 Cressy, Literacy, 142–56.

23 Hubbard, “Reading, Writing, and Initialing,” 568–69.

24 Van Egmond, Practical Mathematics, 6–7.

25 Van Egmond, “Commercial Revolution,” 72, 320–22, 341, 596; Tucker, John V., “Data, Computation and the Tudor Knowledge Economy,” in Robert Recorde: The Life and Times of a Tudor Mathematician, ed. Roberts, Gareth and Smith, Fenny (Cardiff, 2012), 165–88, at 171–72.

26 Van Egmond, Practical Mathematics, 30–31.

27 Swetz, Frank J., Capitalism and Arithmetic: The New Math of the 15th Century Including the Full Text of the Treviso Arithmetic of 1478, trans. Eugene, David Smith (La Salle, 1987), 24 .

28 Van Egmond, “Commercial Revolution,” 105–6; Meskins, “Mathematics Education,” 140.

29 Barnard, John and Bell, Maureen, “Appendix 1: Statistical Tables,” in The Cambridge History of the Book in Britain, vol. 4, 1557–1695, ed. Barnard, John and McKenzie, D. F. (Cambridge, 2002), 779–85.

30 D. F. McKenzie, “Printing and Publishing, 1557–1700: Constraints on the London Book Trade,” in Barnard and McKenzie, eds., Cambridge History, 4:553–67, at 556–58.

31 R. C. Simmons, “ABCs, Almanacs, Ballads, Chapbooks, Popular Piety and Textbooks,” in Barnard and McKenzie, eds., Cambridge History, 4:504–13, at 504. For more on early modern almanacs, see Capp, Bernard, Astrology and the Popular Press: English Almanacs, 1500–1800 (Ithaca, 1979); Feist, Timothy, The Stationers’ Voice: The English Almanac Trade in the Early Eighteenth Century (Philadelphia, 2005); Chapman, Alison A., “Marking Time: Astrology, Almanacs, and English Protestantism,” Renaissance Quarterly 60, no. 4 (Winter 2007): 1257–90, at 1269–70; and Curth, Louise Hill, English Almanacs, Astrology and Popular Medicine, 1550–1700 (Manchester, 2007).

32 Fox, Oral and Literate Culture, 16; Spufford, Margaret, Small Books and Pleasant Histories: Popular Fiction and Its Readership in Seventeenth Century England (London, 1981), 101 .

33 Thomas, “Meaning of Literacy,” 112; Peacey, Print and Public Politics, 59; Fox, Oral and Literate Culture, 15.

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

35 English Short Title Catalog (hereafter ESTC), http://estc.bl.uk. 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), 202–8. 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).

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), A2v. 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), A1r.

40 Meskins, “Mathematics Education,” 152; Simmons, “ABCs, Almanacs, Ballads,” 505.

41 Vanes, Jean, Education and Apprenticeship in Sixteenth-Century Bristol (Bristol, 1982), 2122 ; Williams, Travis D., “The Earliest English Printed Arithmetic Books,” The Library: The Transactions of the Bibliographical Society, 7th ser., 13, no. 2 (2012): 164–84, at 175.

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

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.

48 Brinsley, John, Ludus Literarius: or, the Grammar Schoole; shewing how to proceede from the first entrance into learning, to the highest perfection required in the Grammar Schooles (London, 1627), 26 .

49 Swetz, Capitalism and Arithmetic, 24. For more on Recorde's career as a physician and royal administrator, see Williams, Jack, Robert Recorde: Tudor Polymath, Expositor and Practitioner of Computation (London, 2011); idem, “The Lives and Works of Robert Recorde,” in Roberts and Smith, eds., Robert Recorde, 7–24; Taylor, Mathematical Practitioners, 15, 167, 313; and Stephen Johnston, “Recorde, Robert (c. 1512–1558), mathematician,” ODNB, http://www.oxforddnb.com/view/article/23241. For more on Baker, see Taylor, Mathematical Practitioners, 172, 318; and Anita McConnell, “Baker, Humphrey (fl. 1557–1574), writer on astrology and arithmetic,” ODNB, http://www.oxforddnb.com/view/article/1123.

50 For more on the use of dialogue in pedagogical texts, see Burke, Peter, “The Renaissance Dialogue,” Renaissance Studies 3, no. 1 (March 1989): 112 ; Green, Ian, The Christian's ABC: Catechisms and Catechizing in England, c. 1530–1740 (Oxford, 1996), 1721 ; Schaffer, “Science,” 401; and Glaisyer, “Popular Didactic Literature,” 513. On the blurred line between oral and literate knowledge in early modern England more generally, see Fox, Oral and Literate Culture.

51 Recorde, Robert, The Ground of Artes Teachyng the Worke and Practise of Arithmetike (London, 1543), 8r–v. 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, http://www.oxforddnb.com/view/article/29161.

52 Recorde, Robert, The Grounde of Artes, ed. Mellis, John (London, 1582), A2v.

53 Recorde, Robert, The Grounde of Artes, ed. Mellis, John and Wade, John (London, 1610), Mm8r. For more on Mellis, see Thompson Cooper, “Mellis, John (fl. c. 1564–1588), writer on arithmetic and bookkeeping,” ODNB, http://www.oxforddnb.com/view/article/18529.

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).

55 Recorde, Robert, The Grounde of Artes, ed. Dee, John, Mellis, John, and Hartwell, Robert (London, 1623), 596 . Recorde, Robert, The Ground of Artes, ed. Dee, John, Mellis, John, and Hartwell, Robert (London, 1632), 611 .

56 Recorde, Grounde of Artes (1623), Rr8v.

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 .

58 Cab Lib g, Society of Antiquaries, London.

59 Dane, Joseph A. and Gillespie, Alexandra, “The Myth of the Cheap Quarto,” in Tudor Books and Readers: Materiality and the Construction of Meaning, ed. King, John N. (Cambridge, 2010), 2545 ; Clavell, Robert, A Catalogue of All the Books Printed in England since the Dreadful Fire of London in 1666, to the End of Michaelmas Term, 1672 (England, 1673), 43 .

60 Simmons, “ABCs, Almanacs, Ballads,” 506; Adrian Johns, “Science and the Book,” in Barnard and McKenzie, Cambridge History, 4:289.

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.

65 Hodder, James, Hodder's Arithmetick: or, That Necessary Art Made Most Easie (London, 1667), a4v–5r.

66 Ruth Wallis, “Hodder, James (fl. 1659–1673), arithmetician,” ODNB, http://www.oxforddnb.com/view/article/13416.

67 Mayne, John, Arithmetick: Vulgar, Decimal, & Algebraical (London, 1675), A3r; R. B., An Idea of Arithmetick (London, 1655), A1r.

68 Cocker, Edward, Cocker's Arithmetick (London, 1678), A2v–A3r.

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).

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 .

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–A1r.

78 Wingate, Edmund, Mr. Wingate's Arithmetick, ed. Kersey, John (London, 1658), A4r–A5r. 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, http://www.oxforddnb.com/view/article/29732.

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).

80 Martindale, Adam, The Countrey-Survey-Book: or Land-Meters Vade Mecum (London, 1692), M3r. 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), A1r.

82 Baker, Humfrey, The Wel Spring of Sciences (London, 1591), A1r.

83 Recorde, Robert, The Grounde of Artes, ed. Dee, John and Mellis, John (London, 1607), A1r.

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); Recorde, Robert, The Grounde of Artes, ed. Dee, John, Mellis, John, and Norton, Robert (London, 1615), A1r.

85 Recorde, Robert, The Grounde of Artes, ed. Dee, John et al. (London, 1631), A1r.

86 Baker, Humfrey, Baker's Arithmetick, ed. Phillippes, Henry (London, 1670), A1r.

87 Moore, Jonas, Moore's Arithmetick (London, 1650), A1r.

88 Ruth Wallis, “Cocker, Edward (1631/2–1676), calligrapher and arithmetician,” ODNB, http://www.oxforddnb.com/view/article/5779. 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), 462–65; 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, http://www.oxforddnb.com/view/article/15474.

90 Hodder, James, Hodder's Arithmetick, ed. Mose, Henry (London, 1683), A8v.

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).

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 .

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 .

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

97 DeMolen, Richard, Richard Mulcaster and Educational Reform in the Renaissance (Nieuwkoop, 1991), xviii.

98 ESTC, record no. 006176804.

99 Clement, Francis, The Petie Schole with an English Orthographie (London, 1587), A1r.

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 .

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 .

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

108 Jewell, Education, 95.

109 Lawson, John and Silver, Harold, A Social History of Education in England (London, 1973), 107 ; Robert Ashton, “Leman, Sir John (1544–1632), merchant and mayor of London,” ODNB, http://www.oxforddnb.com/view/article/16420; 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 58.

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, H2r.

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), 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, A5v.

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), 1:73.

121 Ibid., 1:74.

122 Cressy, Education, 65.

123 Lilly, William, Merlini Anglici Ephemeris: Or, Astrological Judgments for the year 1677 (London, 1677), F8v.

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, http://www.oxforddnb.com/view/article/13416.

126 Ruth Wallis, “Cocker, Edward (1631/2–1676), calligrapher and arithmetician,” ODNB, http://www.oxforddnb.com/view/article/5779.

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

128 Lilly, Merlini Anglici Ephemeris, F8v.

129 Sarah Powell and Paul Dingman, “Arithmetic Is the Art of Computation,” http://collation.folger.edu/2015/09/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 559; Wallis, Patrick, “Apprenticeship and Training in Premodern England,” Journal of Economic History 68, no. 3 (September 2008): 832–61, at 836.

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

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.

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