Staff Says

Text: Fulya Kula

From a Semantic Theory to Teaching Statistics

Theories are vital to the scientific profession in bringing order to complex phenomena to comprehend, clarify, and anticipate. Inferentialism is one of the theories that attract attention in statistics education. The semantic theory, of inferentialism, formulated by Brandom (2000) locates inference at the core of human knowledge and fits well with the idea of statistical inference. In general terms, Brandom privileges inference over-representation. According to him, the ability to represent anything depends on human reasoning practices. According to the representationalist view, we can reason once we can represent. This view was criticized in learning statistical inference, to assume without foundation, that if students know the essential representations of statistics they can reason statistically (Bakker and Derry, 2011). As a consequence of the representationalist view, for instance, the statistics curricula have an atomistic approach, mean, median, mode, and standard deviation are studied singly. To overcome these pitfalls, Bakker and Derry (2011) introduced three points: (i) statistical concepts should be predominantly comprehended in infer- ential terms, (ii) a holistic approach should be prioritized over an atomistic one (e.g., introducing mean and standard deviation together with the idea of distribution), and (iii) the illustration of an inferentialist approach in teaching statistics.

In statistics teaching, the idea that supports inferentialism is that statistics is not decontextualized wisdom but a discipline that imports statistical ideas and techniques in a conceptual context while connecting them to concrete conditions. In my opinion, inferentialism proposes a valuable theoretical lens that can brighten how students can learn to contextualize and integrate statistical and contextual considerations. A way to teach statistical inference, in line with inferentialism, is to teach statistical inference by starting with the population and picking up samples from this population (Kula and Kocer, 2020). We propose a new model to introduce statistical inference and name this as the direction of construction, as opposed to many sources in statistics that teach in the direction of application.

Inferentialism and representationalism can be better understood by the metaphor of using a microscope: doing statistics is like using a microscope to comprehend the anatomy of bacteria. One should be aware of the fact that the microscope magnifies the things it is directed to and the relative size of the object is changed. The representationalist view, in this metaphor, would let students see the bacteria for the first time through a microscope without comprehending how the microscope works with rather a distorted idea of the exact size and anatomy of the bacteria. On the contrary, inferentialism would leastways let students be conscious of the fact that the microscope amplifies the object that it is directed to and the magnification process changes the relative size of the object concerning the rest of the reality.

References:

Bakker, A. & Derry, J. (2011). Lessons from Inferentialism for Statistics Education. Mathematical Thinking and Learning. 13(1):5-26. 10 .1080/10986065.2011.538293. Brandom, R. (2000). Articulating reasons: An introduction to inferentialism. Cambridge, MA: Harvard University Press.

Kula, F. & Koçer, R. G. (2020). Why is it difficult to understand statistical inference? Reflections on the opposing directions of construction and application of inference framework, Teaching Mathematics and its Applications: An International Journal of the IMA, 39(4), 248–265, https://doi.org/10.1093/ teamat/hrz014