# ELEMENTARY SCHOOL TEACHERS’ UNDERSTANDING OF THE MEAN AND MEDIAN

Article

First Online:

- 458 Downloads
- 3 Citations

## Abstract

This study provides a snapshot of elementary school teachers’ understanding of the mean and median. The research is presented in light of recent work regarding preservice teachers’ understanding of the mean. Common misconceptions are identified which lead to potential implications for teacher preparation programs. One of the primary concerns regarding increasing the standards expected of students to learn statistics is teachers’ preparation to address those standards. Exploring issues with teachers’ understanding of two of the most prominent concepts in the enacted curriculum provides a glimpse into the need to adequately prepare teachers to teach statistics.

## Key words

content knowledge mean median statistics education teachers’ preparation## Preview

Unable to display preview. Download preview PDF.

## References

- Batanero, C., Cobo, B., & Diaz, C. (2003). Assessing secondary school students’ understanding of averages.
*Proceedings of CERME 3*, Bellaria, Italia. Online: www.dm.unipi.it/~didattica/CERME3/. - Batanero, C., Godino, J. & Navas, F. (1997). Concepciones de maestros de primaria en formción sobre promedios (Primary school teachers’ conceptions on averages). In H. Salmerón (Ed.),
*Actas de las VII Jornadas LOGSE: Evaluación Educativa*(pp. 310–340). Granada, Spain: University of Granada.Google Scholar - Biggs, J. B. & Collis, K. F. (1982).
*Evaluating the quality of learning: The SOLO taxonomy*. New York: Academic Press.Google Scholar - Cai, J., & Gorowara, C. C. (2002) Teachers’ conceptions and constructions of pedagogical representations in teaching arithmetic average. In B. Phillips (Ed.),
*Proceedings of the Sixth International Conference on Teaching Statistics*. Cape Town, South Africa: International Statistical Institute and International Association for Statistical Education. www.stat.auckland.ac.nz/∼iase/publications. - Cai, J. & Moyer, J. (1995). Beyond the computational algorithm: Students’ understanding of the arithmetic average concept. In L. Meira (Ed.),
*Proceedings of the 19th Psychology of Mathematics Education Conference*(Vol. 3, pp. 144–151). Recife, Brazil: Universidade Federal de Pernambuco.Google Scholar - Callingham, R. (1997). Teachers’ multimodal functioning in relation to the concept of average.
*Mathematics Education Research Journal, 9*, 205–224.CrossRefGoogle Scholar - Cobb, P. & Bauersfeld, H. (Eds.). (1995).
*The emergence of mathematical meaning—interaction in classroom cultures*. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M. & Scheaffer, R. (2007).
*Guidelines for assessment and instruction in statistics education (GAISE) report*. Alexandria, VA: American Statistical Association.Google Scholar - Friel, S. N. & Bright, G. W. (1998). Teach-STAT: A model for professional development and data analysis for teachers K-6. In S. Lajoie (Ed.),
*Reflections on statistics: Learning, teaching, and assessment in grades K–12*(pp. 89–117). Mahwah, NJ: Erlbaum.Google Scholar - Gal, I. (2004). Statistical literacy: Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.),
*The challenges of developing statistical literacy, reasoning, and thinking*(pp. 47–78). Dordrecht, The Netherlands: Kluwer.Google Scholar - Garcia, C., & Garret, A. (2006). On average and open-end questions. In A. Rossman & B. Chance (Eds.),
*Proceedings of the Seventh International Conference on Teaching Statistics*. Salvador (Bahia), Brazil: International Association for Statistical Education. www.stat.auckland.ac.nz/∼iase/publications. - Gfeller, M. K., Niess, M. L. & Lederman, N. G. (1999). Preservice teachers’ use of multiple representations in solving arithmetic mean problems.
*School Science and Mathematics, 99*, 250–257.CrossRefGoogle Scholar - Groth, R. E. & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode.
*Mathematical Thinking and Learning, 8*, 37–63.CrossRefGoogle Scholar - Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert & P. Lefevre (Eds.),
*Conceptual and procedural knowledge: The case of mathematics*(pp. 1–27). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Jacobbe, T. (2007). Elementary school teachers’ understanding of essential topics in statistics and the influence of assessment instruments and a reform curriculum upon their understanding. Online: www.stat.auckland.ac.nz/~iase/publications.
- Leavy, A. & O’Loughlin, N. (2006). Preservice teachers understanding of the mean: Moving beyond the arithmetic average.
*Journal of Mathematics Teacher Education, 9*, 53–90.CrossRefGoogle Scholar - McGatha, M., Cobb, P., & McClain, K. (1998). An analysis of students’ statistical understandings.
*Paper presented at the Annual Meeting of the American Educational Research Association*, San Diego, CA.Google Scholar - National Council of Teachers of Mathematics (1991).
*Professional standards for teaching mathematics*. Reston, VA: NCTM.Google Scholar - National Council of Teachers of Mathematics (2000).
*Principles and standards for school mathematics*. Reston, VA: NCTM.Google Scholar - Russell, S. J. & Mokros, J. R. (1991). What’s typical? Children’s ideas about average. In D. Vere-Jones (Ed.),
*Proceedings of the Third International Conference on Teaching Statistics*(pp. 307–313). Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Scheaffer, R. (1986). The quantitative literacy project.
*Teaching Statistics, 8*(2), 34–38.Google Scholar - Shaughnessy, J. M. (1992). Research in probability and statistics: reflections and directions. In D. Grouws (Ed.),
*Handbook of research on mathematics teaching and learning*(pp. 465–493). New York: Macmillan.Google Scholar - Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. K. Lester (Ed.),
*Second handbook of research on mathematics teaching and learning*(pp. 957–1009). Charlotte, NC: Information Age.Google Scholar - Teach-STAT (1996a).
*Teach-STAT: Teaching statistics grades 1–6: A key for better mathematics. The University of North Carolina Mathematics and Science Education Network*. Palo Alto, CA: Dale Seymour.Google Scholar - Teach-STAT (1996b).
*Teach-STAT for statistics educators. The University of North Carolina Mathematics and Science Education Network*. Palo Alto, CA: Dale Seymour.Google Scholar - Watson, J. M., Callingham, R. A., & Kelly, B. A. (2007). Students’ appreciation of expectation and variation as a foundation for statistical understanding.
*Mathematical Thinking and Learning, 9*, 83–130.Google Scholar - Watson, J. M. & Moritz, J. B. (1999). The developments of concepts of average.
*Focus on Learning Problems in Mathematics, 21*, 15–39.Google Scholar - Watson, J. M. & Moritz, J. B. (2000). The longitudinal development of understanding of average.
*Mathematical Thinking and Learning, 2*, 11–50.CrossRefGoogle Scholar - Zawojewski, J. S. & Heckman, D. J. (1997). What do students know about data analysis, statistics, and probability? In P. A. Kenney & E. A. Silver (Eds.),
*Results from the sixth mathematics assessment of the National Assessment of Educational Progress*(pp. 195–223). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Zawojewski, J.S., & Shaughnessy, J.M. (1999). Data and chance. In P.A. Kenney & E.A. Silver (Eds.),
*Results from the seventh mathematics assessment of the National Assessment of Educational Progress*(pp. 235–268). Reston, VA: National Council of Teachers of Mathematics.Google Scholar

## Copyright information

© National Science Council, Taiwan 2011