Concrete or Abstract?

Concrete examples or abstract examples? I have struggled with this issue in lectures and in writing. Usually, I opt for concrete example first followed by the more general, abstract case.

My rationale for this approach has been the results from the Wason Selection task. That logical problem (If P then Q, if Not P then Not Q is the solution to both cases) is solved much, much more often in its concrete form (~75% of the time) than in its abstract form (~5% of the time). Here is a site that explains this problem.

However, recent research from the Ohio State University (as reported in the New York Times) in mathematics education suggests that teaching the abstract first is far superior to teaching the concrete first in mathematics problems. This research was recently reported in the journal Science. The authors are Jennifer A. Kaminski, Vladimir M. Sloutsky, and Andrew F. Heckler.

To me, the discrepancy between the Wason Selection data and the Kaminski et. al data indicates that further research is needed. I agree that flying by the seat of one's pants is not a good idea here. It would be nice for teachers to know, once and for all, which strategy is best.

By the way, I sometimes use an abstract first strategy. Recall my earlier post on the Mastermind game. There I use an abstract first-first strategy to teach about main effects and interactions.

Seven Myths from Medicine

In a recent article, Vreeman and Carroll expose seven medical myths:

• You should drink eight glasses of water a day.
• You only use 10% of your brain.
• Your hair and fingernails grow on after you die.
• Shaving your hair causes it to grow back darker and coarser.
• If you read in dim light, you will ruin your eyes.
• Eating turkey makes you sleepy.
• Using a mobile phone in a hospital can affect other equipment

They go on to debunk each of the myths above. Interestingly, these myths persist despite evidence to the contrary. I wonder if similar myths exist in psychology.

Meta-analysis

In chapter 2 we introduce meta-analysis, a statistical procedure for examining the results of a large number of similar studies.

A large meta-analytic study was recently released by the World Cancer Research Fund. That study found links between body fat and six types of cancer. They are: cancer of the esophagus, the pancreas, the colon, the womb, the kidney, and the breast (post-menopause).

The study looked some 7,000 published research reports published since the 1960s (out of a possible half-million articles). Dr. Michael Marmot, an epidemiologist, directed the project.

The report recommends:

• ham, bacon, and other processed meats should be eaten rarely
  
• no more than a pound of cooked red meat should be eaten weekly
• drinking no more than a small glass of wine (or equivalent) per day
• mothers should breastfeed for at least six months because that lowers their incidence of breast cancer
• exercising at least 30 minutes per day and working up to 60 minutes per day
  
• minimizing salt use
• drinking water instead of drinks with sugar
• eating fruit, vegetables and fiber

Meta-analytic studies strive to see the "big picture" created by many smaller and narrower empirical studies. To see the full report from the World Cancer Research Fund click here.

The value of undergraduate research

The Chronicle of Higher Education (August, 17, 2007, by Lila Guterman, ) has two articles : What good is undergraduate research anyway? (p. A12) and Research on undergraduate research (A14) Most teachers assume that having undergraduates conduct research is a good way to teach. So, it's refreshing to see some researchers asking themselves whether that assumption is warranted.

The article, Research on undergraduate research, looks at three separate research projects, one at the University of Colorado at Boulder (N = 76), published in Science Education, another at Grinnell College (N = 1,135), published in Cell Biology Education, and still another at SRI International (N = 8,000+). The report of the SRI research can be found by clicking here.

The longer article, What good is undergraduate research anyway?, provides some analysis and commentary. The results of the study above support the assumption that undergraduate research is a good way to teach. Interestingly, it looks like conducting undergraduate research convinces some, but not many, additional students to change their previous career plans and attend graduate school instead. Some students learn that research does not suit them.

On the other side of the coin, results indicated that "authentic" instead "mundane" undergraduate research experiences were more valuable, educationally. Faculty note that teaching via undergraduate research experiences takes more time than teaching in other ways.

We can agree on both the worth and the cost of supervising undergraduate research. Our text reveals our bias toward undergraduate research (we hope).