ELEMENTARY SCHOOL TEACHERS’
COMPREHENSION OF DATA DISPLAYS

 

TIMOTHY JACCOBE

University of Florida

jacobbe@coe.ufl.edu

 

ROBERT M. HORTON

Clemson University

bhorton@clemson.edu

 

ABSTRACT

 

This study investigated elementary school teachers’ comprehension of data displays. Assessment, interview, and observation data were analyzed to determine their level of comprehension. Results revealed that the teachers were proficient at “reading the data” and computation types of “reading between the data” questions, but were unsuccessful with questions that assessed higher levels of graphical comprehension. Many of the difficulties exhibited by the teachers appear to be attributable to a lack of exposure to the content. Implications for teacher preparation, professional development, and curricula development are discussed.

 

Keywords: Statistics education research; Content knowledge; Graphical displays; Teacher preparation

 

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Statistics Education Research Journal, 9(1), 27-45, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), May, 2010

 

 

REFERENCES

 

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.

Begg, A., & Edwards, R. (1999, December). Teachers’ ideas about teaching statistics. Paper presented at the Joint Conference of the AARE and NZARE, Melbourne.

Bertin, J. (1983). Semiology of graphics (2nd ed., W. J. Berg, Trans.). Madison: University of Wisconsin Press.

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: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.

[Online: http://www.stat.auckland.ac.nz/~iase/publications/1/2c1_cai.pdf]

Callingham, R. (1997). Teachers’ multimodal functioning in relation to the concept of average. Mathematics Education Research Journal, 9(2), 205-224.

Carswell, C. M. (1992). Choosing specifiers: An evaluation of the basic tasks model of graphical perception. Human Factors, 34(5), 535-554.

Cobb, P., & Bauersfeld, H. (Eds.). (1995). The emergence of mathematical meaning: Interacting in classroom cultures (studies in mathematical thinking and learning). Hillsdale, NJ: Lawrence Erlbaum.

Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382-393.

delMas, R. C. (2004). A comparison of mathematical and statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 79 - 96). Dordrecht, The Netherlands: Kluwer.

delMas, R., Garfield, J., & Ooms, A. (2005). Using assessment ítems to study students’ difficulty reading and interpreting graphical representations of distributions. In K. Makar (Ed.), Proceedings of the 4th International Research Forum on Statistical Reasoning, Thinking, and Literacy. University of Auckland.

[Online: https://app.gen.umn.edu/artist/articles/SRTL4_ARTIST.pdf]

Espinel, M. C., Bruno, A., & Plasencia, I. (2008). Statistical graphs in the training of teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (eds.), Joint ICMI/IASE Study Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 Conference and IASE 2008 Round Table Conference. Monterrey: ICMI and IASE.

[Online: http://www.stat.auckland.ac.nz/~iase/publications/rt08/T2P11_Espinel.pdf]

Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M. et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report. Alexandria, VA: American Statistical Association.

Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32, 124–158.

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(5), 250-257.

Greer, B., & Ritson, R. (1994). Readiness of teachers in Northern Ireland to teach Data Handling. Proceedings of the Fourth International Conference on Teaching Statistics, Vol. 1, pp. 49-56, Marrakech, Morocco.

Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), 427-437.

Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37-63.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Jacobbe, T. (2008). Elementary school teachers’ understanding of the mean and median. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (eds.), Joint ICMI/IASE Study Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 Conference and IASE 2008 Round Table Conference. Monterrey: ICMI and IASE.

[http://www.stat.auckland.ac.nz/~iase/publications/rt08/T2P13_Jacobbe.pdf]

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. Unpublished doctoral dissertation, University of Kentucky.

[Online: www.stat.auckland.ac.nz/~iase/publications/dissertations/dissertations.php]

Konold, C., & Khalil, K. (2003, April). If U can graff these numbers—2,15,6—your stat literate. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

Leavy, A., & O’Loughlin, N. (2006). Preservice teachers’ understanding of the mean: Moving beyond the arithmetic average. Journal of Mathematics Teacher Education, 9(1), 53-90.

McKnight, C. C. (1990). Critical evaluation of quantitative arguments. In G. Kulm (Ed.), Assessing higher order thinking in mathematics (pp. 169-185). Washington, D.C.: American Association for the Advancement of Science.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.

Moss, D., Diaz, D., Lashley, E. Moss, W., & Sanders, S. (2005). Developing algebraic thinking: Plotting and growing, Teacher’s manual, Third Grade. Burlington, NC: Carolina Biological Supply.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Russell, S. J., & Mokros, J. R. (1990). What’s typical? Children’s ideas about average. In D. Vere-Jones (Eds.), Proceedings of the Third International Conference on Teaching Statistics (pp. 307-313). Voorburg, The Netherlands: International Statistical Institute.

Saderholm, J., Ronau, R., Todd Brown, E., & Collins, G. (2010). Validation of the Diagnostic Teacher Assessment of Mathematics and Science (DTAMS) Instrument. School Science and Mathematics, 110(4), 180-192.

Scheaffer, R. (1986). The quantitative literacy project. Teaching Statistics, 8(2), 34-38.

Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.

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). Reston, VA: National Council of Teachers of Mathematics.

Shaughnessy, J. M., Garfield, J., & Greer, B. (1996). Data handling. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 205-237). Dordrecht, The Netherlands: Kluwer.

Wainer, H. (1992). Understanding graphs and tables. Educational Researcher, 21(1), 14- 23.

 

Timothy Jacobbe

School of Teaching and Learning

PO Box 117048

2403 Norman Hall

University of Florida

Gainesville, FL 32611