Skip Navigation

Teachers College, Columbia University
Teachers College
Columbia University
International Journal for the History of Mathematics Education

Algebra
From Pierre de la Ramée, Algebra 1560

International Bibliography

USA/Canada

  • Amy K. Ackerberg-Hastings, Mathematics is a Gentleman's Art. Analysis and Synthesis in American College Geometry Teaching, 1790-1840 (2000 Ames/Iowa. Iowa State Univ. Diss. Thesis).
    • The study presents a detailed analysis of key persons as mathematics professors and as textbook writers at American colleges (Jeremias Day, John Farrar, Charles Davies) and their respective context.
  • Nadine Bednarz, Teaching mathematics -- why and to whom?. "Pourquoi et pour qui enseigner les mathématiques?. Une mise en perspective historique de l'évolution des programmes au Québec au XXème siècle ». (French) Zentralblatt für Didaktik der Mathematik, 2002, 34(4): 146-157.
    • The history of reform in the teaching of mathematics in Quebec since the start of the 20th Century has been strongly influenced by a social and political context that gives meaning to its particular orientation. In this paper, we attempt to trace the important moments in the evolution of the teaching of mathematics through the roles and missions that successive governments have given to schooling and subsequent curricular reforms. Our analysis shows that the teaching of mathematics has evolved from an essentially practical role, prior to 1945, to a double role that is both practical and cultural, in the 1950s, with the balance tipped in favor of the practical role. In the 1960s, the political will for universal education and, more recently, the concern over forming persons who can adapt to a constantly evolving society, are gradually pushing the Quebec curricula towards major changes. Mathematics is presented as a powerful tool that gives one a handle on reality, a complement of culture and an important language that is essential to the communication of ideas. Throughout the various reforms, these two finalities - the practical and the cultural - are constantly present, varying in importance and meaning with the successive roles attributed to schools. Our analysis shows a strong pragmatic anchoring of the first mathematics programs in Quebec, one that has not disappeared over time. The gradual curricular changes show, however, a progressive integration of the cultural formation role of mathematics.
  • James K.Bidwell, Robert G. Clason, Readings in the History of Mathematics Education (Reston,Va.: National Council of Teachers of Mathematics, 1970).
    • Substantial excerpts from major documents spanning the period 1831-1959 in the US.
  • Eileen Frances Donoghue, The origins of a professional mathematics education program at teachers college (1987 New York, Columbia Univ., Teachers College, Diss., 1987).
  • Eileen Frances Donoghue,  "History of Mathematics Education in the United States", Encyclopedia of mathematics education, ed. Louise S. Grinstein (New York: Routledge Falmer , 2001), 323-330.
  • James T. Fey, "Change in Mathematics Education since the late 1950's  - Ideas and realisation (An ICMI Report). U.S.A.", Educational Studies in Mathematics, 1978, 9: 339-353.
  • Hartzler, Stanley James: Secondary algebra textbooks in the United States 1806-1982 : selected descriptions and historical trends (Austin, Tex., Univ. of Texas, Diss., 1982).
  • Keith Hoskin, "Textbooks and the Mathematisation of American Reality: the Role of Charles Davies and the US Military Academy at West Point ", Paradigm 13 (1994), 11-41.
    • The period 1830 to 1860 marks the emergence of American colleges and high schools as institutions providing differentiated curricula, in a classroom setting, following a regular progression over a number of years. These developments owe much to the work of Charles Davies at West Point.
  • Phillip S. Jones, and Arthur Coxford (eds.), A History of Mathematics Education in the United States and Canada (Reston,Va.: National Council of Teachers of Mathematics,1970). 1970 Yearbook
    • Emphasizes curricular and methodological changes in the elementary and secondary schools, and the issues and forces causing the changes. Extensive bibliography.
  • Jeremy Kilpatrick, [The reform of the school mathematics curriculum in U.S. after 1900: reality and imagination.] "La riforma dei programmi di matematica negli stati uniti a partire dal 1900: realtá e immaginazione". (Italian; English) L'Educazione Matematica, 1994, 15(2): 117-131.
    • French original: "Réformer les programmes de mathématiques aux U.S.A. depuis 1900 : realité et imaginaire", eds. Bruno Belhoste et al., Les sciences au lycée: un siècle de réformes des mathématiques et de la physique en France et à l'étranger  (Paris: Vuibert, 1996), 247-258.
    • The varied history of efforts regarding reforms of mathematical education in the United States of America, including the development of mathematical didactics as a scientific subject is presented. It is, however, portrayed in simplified terms that a pragmatic trend dominated: the school lesson was more regarded as a technological problem ("find out what is wrong and replace it with something that works") than a problem of human communication and human values. 
  • Paul Lavoie, "Enseigner les mathématiques au Québec (1800-2000): l'émergence d'une spécialité, Bulletin AMQ, 2004, 44, 14-38.
    • Separate printing of Chapter 7 in the handbook : Stanic, Kilpatrick (eds.), A History of School Mathematics (NCTM 2003).
  • Stephen B. Maurer, Harold B., Leo J. Schneider, "The American High School Mathematics Examination: a 50 year retrospective" Mathematics Competitions. Journal of the World Federation of National Mathematics Competitions, 2001,14(2): 45-66.
    • On February 9 1999, students across America participated in the American High School Math Exam. The first such exam was given in 1950. Thus, the 1999 version is the 50th. Perhaps this is a good time to look at the history of the exam, its sponsorship, and its evolution-and important changes to begin in the year 2000. We conclude this article with a Special Fiftieth Anniversary AHSME, which includes one question from each of the first 50 editions of the AHSME. The AHSME is constructed and administered by the American Mathematics Competitions (AMC) whose purpose is to increase interest in mathematics and to develop problem solving ability through a series of friendly mathematics competitions for junior (grades 8 and below) and senior high school students (grades 9 through 12). As you read below how the AMC exams have evolved, you will see that they have moved towards greater participation at many grade levels, much less emphasis on speed and intricate calculation, and greater emphasis on critical thinking and the interrelations between different parts of mathematics. (Introduction)
  • L. Poirier, [Evolution of the importance of mental arithmetic in Quebec syllabuses]. "Evolution du rôle et de l'importance du calcul mental dans les programmes d'études quebecois ». Bulletin AMQ. (May 1990) v. 30(2) p. 5-10.
    • The role of mental arithmetic in Quebec syllabuses and textbooks of the years 1872 until today is investigated.
  • Susan Ross, Mary Pratt-Cotter, "Subtraction in the United States: an historical perspective". (English) The Mathematics Educator (Athens). An Official Publication of the Mathematics Student Association, University of Georgia. (Sum 1997) v. 8(1) p. 4-11.
    • This is a review of the historical development of subtraction algorithm used in the United States. The algorithms used to teach subtraction today have changed very little since the 1940's. However, significant changes occurred during the late 1800's and early 1900's (Brownell, 1939; Brownell & Moser, 1949; Wilson, 1934). Different algorithms were used and developed that had a major impact on the way subtraction is taught today, as will be discussed later. By going back and exploring other algorithms, we may rediscover different ways of teaching subtraction that might benefit some of today's students.
  • Sharon L. Senk, Denisse R Thompson, "School mathematics curricula: Recommendations and issues", eds. Sharon L. Senk, et al. Standards-based school mathematics curricula. What are they? What do students learn?. (Mahwah, NJ: Erlbaum. 2003), p. 3-27
    • In this chapter the authors provide some historical background to place the current curriculum reform efforts in perspective, and a summary of recommendations to reform school mathematics made during the 1990s. They also discuss issues that arise when conducting research on student outcomes.
  • George Milan Alexander Stanic, Why teach mathematics?: A historical study of the justification question (1983 Madison, Wis., Univ. of Wisconsin, Diss.).
  • George Milan Alexander Stanic, " The growing crisis in mathematics education in the early twentieth century."  Journal for Research in Mathematics Education, 1986, 17(3):190-205.
    • This article is based on a dissertation completed at the University of Wisconsin-Madison, 1983. An earlier version was presented at the annual meeting of the American Educational Research Association, Apr 1984.
    • The place of mathematics in the American school curriculum was challenged during the early years of the twentieth century. Specifically questioned was the requirement that all high school students take mathematics. By the 1930s, mathematics educators were speaking of the situation as a crisis. The crisis had grown in the context of major social changes arising from intense urbanization, industrialization, and immigration around the turn of the century; America's involvement in World War I; and the Great Depression. Along with significant growth in the school population had come a perceived decrease in the quality of that population. It was within this historical context that mathematics educators responded to suggested changes in the curriculum. Some of their responses may have exacerbated the crisis about which they were so concerned.  
  • A History of School Mathematics, eds. George M. A. Stanic and Jeremy Kilpatrick, 2 vol.s, (Reston/Va.: NCTM, 2003).
    • Its 38 chapters deal mainly with the history of mathematics education as an academic discipline, there are, however, also chapters on mathematics teaching, e.g. analysis of 19th century textbooks and of 20th century (by K. M. Michalowicz and E.F. Donoghue), too, and of mathematics teaching in the second half of the 20th century - thus being a follow-up study to the 1970 NCTM Yearbook.