# Book Review: NCTM’s *Compendium*: finding a balance between historical details, contemporary practices, and future resources. Jinfa Cai (Ed.) (2017) *Compendium for research in mathematics education*

The chapters of NCTM’s Compendium read as texts from the minds of experts, explicating, expanding, and sometimes dissecting the minutae of their respective mathematics education subfields. That said, detailed information about all aspects of research in the field simply cannot be covered in a single volume, even one with over 1000 pages.

I begin this review by asking the question: Does the Compendium live up to the expectation that it be a standard reference work which should be consulted by all mathematics education researchers? I will conclude this review with an answer.

## Structure of the book

### General characteristics of the book

This weighty *Compendium*(2.3 kg) has five sections, with 38 chapters written by 93 authors—47 female and 46 male—from 11 countries. It has a well-constructed 27-page subject index. No author index is provided. The large paper-back version, with its small font size and dense formatting, is cumbersome to handle. The e-book format is likely to be the more...

## References

- Brooks, E. (1859).
*The normal mental arithmetic. A thorough and complete course by analysis and induction, with a treatise on mental algebra*. Philadelphia: Sower, Barnes & Potts.Google Scholar - Brooks, E. (1889).
*Normal methods of teaching containing a brief statement of the principles and methods of the science and art of teaching, for the use of normal classes and private students preparing themselves for teaching*. Philadelphia: Normal Publishing Company.Google Scholar - Butler, N. M., & Smith, D. E. (1898).
*Held in the David Eugene smith professional papers collection. Rare books and manuscript library*. New York: Columbia University.Google Scholar - Clements, M. A., Keitel, C., Bishop, A. J., Kilpatrick, J., & Leung, F. (2013). From the few to the many: Historical perspectives on who should learn mathematics. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.),
*Third international handbook of mathematics education*(pp. 7–40). New York: Springer.CrossRefGoogle Scholar - Colburn, W. (1830). Teaching of arithmetic. In J. K. Bidwell & R. G. Clason (Eds.),
*Readings in the history of mathematics education*(pp. 24–37). Washington, DC: National Council of Teachers of Mathematics.Google Scholar - Ding, M. (2016). Developing preservice elementary specialized knowledge content knowledge for teaching fundamental mathematical ideas. The case of thee associative property.
*International Journal of STEM Education, 3*(9), 1–19.Google Scholar - Drijvers, P. (2012). Digital technology in mathematics education: Why it works (or doesn’t). In
*Proceedings of the 12th International Congress on Mathematics Education*(pp. 485–501). Seoul: ICME.Google Scholar - Dunkel, H. B. (1970).
*Herbart and Herbartianism: An educational ghost story*. Chicago: University of Chicago Press.Google Scholar - Ellerton, N. F., & Clements, M. A. (2012).
*Rewriting the history of school mathematics in North America, 1607–1861*. New York: Springer.CrossRefGoogle Scholar - Guildford, J. P. (1959). Traits of creativity. In H. H. Anderson (Ed.),
*Creativity and its cultivation*(pp. 142–161). New York: Harper & Brothers.Google Scholar - Hardy, G. H. (1940).
*A mathematician’s apology*. London: Cambridge University Press.Google Scholar - Harris, W. T., Draper, A. S., & Tarbell, H. S. (1895).
*Report of the Committee of Fifteen*. Boston: New England Publishing.Google Scholar - Husén, T. (1967).
*International study of achievement in mathematics: A comparison of twelve countries*. Hamburg: International Project for the Evaluation of Educational Achievement.Google Scholar - James, W. (1899).
*Talks to teachers on psychology: And to students on some of life’s ideals*. New York: Henry Holt and Company.CrossRefGoogle Scholar - Joyce, B., & Showers, B. (2002).
*Student achievement through staff development*(3rd ed.). Alexandria: Association for Supervision and Curriculum Development.Google Scholar - Kanbir, S., Clements, M. A., & Ellerton, N. F. (2017).
*Using design research and history to tackle a fundamental problem with school algebra*. New York: Springer.Google Scholar - Krutetskii, V. A. (1976).
*The psychology of mathematical abilities in schoolchildren*. Chicago: University of Chicago Press.Google Scholar - Loewus, L. H. (2015).
*Gender gaps at the Math Olympiad*:*Where are the girls*? http://blogs.edweek.org/edweek/curriculum/2015/07/gender_gaps_at_the_math_olympiad_where_are_the_girls.html. - National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010).
*Common core state standards for mathematics*. Washington, DC: Authors.Google Scholar - OECD (Organisation for Economic Co-Operation and Development). (2014).
*PISA 2012 results: Creative problem solving: Students’ skills in tackling real-life problems*(Vol. 5). http://www.oecd.org/education/pisa-2012-results-volume-v.htm - Page, D. P. (1877).
*Theory and practice of teaching: The motives and methods of good school-keeping*(90th ed.). New York: A. S. Barnes & Company.Google Scholar - Siemon, D., Horne, M., Clements, D., Confrey, J., Maloney, A., Samara, J., … Watson, A. (2017). Researching and using learning progressions (trajectories) in mathematics education. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.),
*Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education*(Vol. 1, pp. 109–136). Singapore: PME.Google Scholar - Sinclair, N., Pimm, D., & Skelin, M. (2012).
*Developing essential understanding of geometry, for teaching mathematics in grades 9–12*. Reston: National Council of Teachers of Mathematics.Google Scholar - Smith, D. E. (1900).
*The teaching of elementary mathematics*. New York: Macmillan.Google Scholar - Thomas, G. (1997). What’s the use of theory?
*Harvard Educational Review, 67*(1), 75–104.CrossRefGoogle Scholar - Thorndike, E. L. (1906).
*The principles of teaching based on psychology*. New York: AG Seiler.Google Scholar - Thorndike, E. L. (1917).
*The Thorndike arithmetic: Book one*. Chicago: Rand McNally & Company.Google Scholar - Torrance, E. P. (1966).
*Creativity: Its educational implications*. New York: Wiley.Google Scholar - Travers, K., & Westbury, I. (1989).
*The IEA study of mathematics I: Analysis of mathematics curricula*. New York: Pergamon Press.Google Scholar - Westbury, I. (1980). Change and stability in the curriculum: An overview of the questions. In H. G. Steiner (Ed.),
*Comparative studies of mathematics curricula: Change and stability 1960–1980*(pp. 12–36). Bielefeld: Institut für Didaktik der Mathematik-Universität Bielefeld.Google Scholar