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]]>However, stacking the data that are the “same” as in my example can do more to reduce this idea. This is nothing new as Cobb, McClain, and Gravemeijer and their team at Vanderbilt University, Nashville, USA and Arthur Bakker from the Freudenthal Institute in Utrecht (Netherlands) pointed to this practice. Both studies clearly showed that by using computer software data that are manipulated as “stacked” data is better in the development of the understanding of these concepts. (See references below.)

Bakker even suggest that it may even be a good idea to even continue this “stacking” approach and super impose it on box-and-whisker diagrams to continue the development of seeing the “bump-effect” in distribution. It supply far more support for learners in the development of their diagrammatic reasoning about the distribution.

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht: Freudenthal Institute.

Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003, Jan/Feb). Design Experiments in Educational Research. Educational Research, 32(1), 9-13.

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]]>It is a curricular misconception rather than a learner misconception.

An easy way to protect learners against (naturally) forming this misconception when confronted with “mean, median, mode” before they have had sufficient experiences with distributions of different kinds, is to simply hold “mean, median. mode” back till grade 10 or even later.

I think it is wise, when dealing with misconceptions, to always first ask “did curriculum teaching possibly cause this misconception” and if so talk to the teachers/curriculum-makers.

To be currently practical with respect to those grade 10’s:

Just let go of “mean, median, mode” for three lessons and let them compare data sets by just ordering he data from smallest to biggest. By that time median and mode will be natural self-constructed ideas, if the data sets were well chosen.

There are two fundamentally different ways of trying to get a sense of how the data in a set is distributed:

A. To group the data into intervals of equal width (histogram)

B. To group the data into bags with the same number of data items in each bag (e.g. quartiles or centiles or whatever choice about the number of bags with equal numbers of data items you choose, you can also have twintiles, octiles or pentiles or hextiles for example)

In the case of A, the percentages of the total number of data items that are in each interval gives you a summary picture of how the data is distributed.

In the case of B the intercentile (or interquartile, or interoctile or twintile what have you) points provide a quick picture of the nature of the distribution.

The median is a thing which belongs to tile-analysis (B) of distributions and makes little sense outside that context.

Including it earlier in the curriculum gives rise to a lot of completely crap questions being dished up to learners.

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