Statistical versus Mathematical Literacy

Students and teachers should recognize that quantitative literacy is only a small component of statistical literacy. Statistics is not branch of mathematics but is rather a distinct discipline within the liberal arts (Moore, 1998; Cobb & Moore, 2000). Students who get entrenched in the idea that statistics is all about math may find themselves frustrated at the complexity and messiness of data. Gordon (1995) found that students who enter a statistics course with previous coursework in mathematics often tend to use surface approaches to learning, which are ineffective when attempting to learn statistics. Indeed, Ben-Zvi and Garfield (2004) asserted that a focus on formulas, equations, and computations does not lead to the development of statistical literacy, thinking or reasoning skills.

The teaching of mathematics is metaphorical in nature (delMas, 2004). Students learn mathematical ideas and then apply these ideas to a range of problems. delMas and others argued that statistical reasoning operates on a similar plane but is essentially different for several reasons. First, statistics is dependent on data. Data are often indeterminate compared to the more precise nature of mathematics (Chance, 2002; delMas, 2004; Gal & Garfield, 1997; Moore, 1998). Second, context shapes statistical inquiry (Cobb & Moore, 1997; Gal & Garfield, 1997; Moore, 1998; Wild & Pfannkuch, 1999). Researchers cannot separate the processes and reasoning involved in statistical inquiry from the content and context of that inquiry. Students need to be aware of the reasons and justifications for their methodological and analytic choices and recognize that there may be more than one approach or solution to a problem. Third, mathematics is simply a set of procedures in statistics, which researchers largely compute through technology (Gal & Garfield, 1997; Nicholson, Ridgway, & McCusker; 2006). Finally, the goal of a statistics education is for students to be able to reason about research questions and data as opposed to computing a set answer (Gal & Garfield, 1997). All too often, teachers provide students contrived data sets that negate the development and practice of underlying reasoning skills. Students need to learn that statistics involves the interplay of the abstract and the concrete. They need to recognize the similarities and difference in approaches when applying statistical processes to real-world problems.

References

Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 3-15). Dordrecht, The Netherlands: Kluwer Academic.

Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3). Retrieved July 31, 2007, from http://www.amstat.org/publications/jse/v10n3/chance.html

Cobb, G., & Moore, D. S. (1997). Mathematics, statistics and teaching. The American Mathematical Monthly, 104, 801-823.

Cobb, G. W., & Moore, D. S. (2000). Statistics and mathematics: Tension and cooperation. American Mathematical Monthly, 106, 615-630.

delMas, R. C. (2004). A comparison of mathematical and statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 79-95). Dordrecht, The Netherlands: Kluwer Academic.

Gal, I., & Garfield, J. (1997). Curricular goals and assessment challenges in statistics education. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 1-13). Amsterdam, The Netherlands: IOS Press.

Gordon, S. (1995). What counts for students studying statistics? Higher Education Research and Development, 14, 167-184.

Moore, D. S. (1998). Statistics among the liberal arts. Journal of the American Statistical Association, 93, 1253-1259.

Nicholson, J. R., Ridgway, J., & McCusker, S. (2006). Reasoning with data—time for a rethink? Teaching Statistics, 28, 2-9.

Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67, 223-265.