Math Stats vs. Applied Stats

Hello All,

I did something I seldom do. I took some time off this summer to tend to family,  my garden; I even started exercising. One of the foci of my attention has been my children, including my high school son who took his first college class, math statistics.

He had a fantastic professor who was very dedicated to his learning. Yet, when my son came home to talk about something exciting in the class, it wasn’t the math that excited him as much as hearing how the professor applied statistics to answer questions in his own personal research. I always knew from watching students in class that students enjoyed examples of research that fellow faculty members at my school or I conducted even more than trendy current research but to have a teenager whose typical comment to the question, “How was school?” be … “fine,”  explain about research the professor conducted with enthusiasm (at 10 PM) really drove home the point of how critical it is for us to put statistics into an applied concept for our learners.

So, what activities or examples didn’t work for my son? Any kind of gambling, card, or dice example was just lost on him. In fact, there were times he mastered a concept before understanding the example!

Piaget, the child developmental psychologist, spoke of the ability of children to learn as beginning with requiring concrete information and experience, going toward semi-concrete (like illustrations or pictures), and finally to the abstract. Statistics affords us the opportunity to start with concrete examples, and though I only have a sample of 1 in this example, I have to say that the use of cards, dice, or any gambling example is in the realm of semi-concrete, and not as effective as starting with a concrete hypothesis, and gathering data to test it.

Nonetheless, at the basis of statistics is mathematics, whether our students like it or not, and by watching my son learn statistics this summer, I also have a new found respect for the importance of teaching math concepts well to aid students in the greater learning of applied statistics. I have included a blog on the teaching of specific math concepts. At the current time, the example is on statistics.  http://sk19math.blogspot.com

So, even while I spent a bit more time focusing on my family this summer, I ended up with a different perspective of how to maximize students’ learning in statistics.

Tips:

(1) When ever possible, keep examples concrete and show how to apply the use of statistics even before getting into the calculations … the calculations truly are the easy part and should take up the least amount of class time.

(2) Just because people have been using certain examples since the dawn of time (e.g., gambling, dice, cards), does not mean that students will see such examples as concrete, and thus their benefit to the students may not be as  great as you think. Informally assess the usefulness of your examples while teaching.

(3) Though in applied statistics, the mathematics underlying the statistics may take a back seat … they still belong in the car. Issues like probability, Central Limit Theorem, Order of Operations, and other  purely mathematical concepts need to be not only understood by the professor teaching the class, and their importance in statistics, but they must be formally taught to students, otherwise statistics will look like magic to them, thus weakening the conclusions one could extract from statistical results.

As we start this new semester, I hope that your students get as excited about your applied statistics classes as my son was excited about his this summer.

Teach well. Have fun!

Bonnie

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1 Comment

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One response to “Math Stats vs. Applied Stats

  1. Hi. I totally agree about gambling examples. The ubiquitous urns and balls I would put in the same category. I promised my students in business stats that there would be no mention of dice, coin-tossing or similarly artificial elements, and it was well received. I remember being totally mystified (some decades ago) at the use of poker hands in teaching probability.

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