Most discussions about teaching often assume that the learning outcome is the important variable (compare evaluations, discussions about clickers, discussions about syllabi, etc.).

However, I find that there are teaching methods that I would not employ for either long-term or even ethical reasons. For an extreme example, let me point to the novel "The Wave" where the effective discipline would probably improve learning outcomes for many types of content but has certainly unethical implications and would hinder goals that are less easy to measure. For another example, on the recent thread on clickers, someone commented that they would not want to use clickers to remove peer-pressure because at some point, students have to learn to deal with peer-pressure, anyway.

Do you know any books or other resources that offer an analysis or a terminology for this problem?

I am only aware of people trying to make the more ephemeral goals (like "critical thinking") also measurable which might be quite hard for "maturity" and similar things. However, in a discussion it might already be helpful to be able to point to some studies on this issue that teaching focussed on measurable short-term goals does not provide the best long-term outcomes.

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    $\begingroup$ Mind if I ask what you have in mind as peer-pressure they will be encountering and if possible to give an example mentioned in said novel? $\endgroup$ – Mark Fantini Apr 28 '14 at 1:38
  • $\begingroup$ For the clicker/peer-pressure discussion see the comments on the question matheducators.stackexchange.com/questions/1940/… $\endgroup$ – user11235 Apr 28 '14 at 15:28
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    $\begingroup$ In the novel The Wave, a history teacher tries to teach his students how the Nazis could have established their dominance by introducing them to Nazi-style discipline: A common slogan, military-style discipline for addressing the teacher, standing up, chanting together, etc. The experiment goes much "better" than planned in the sense that many students like to be part of a movement that looks down on others and do not deviate from this opinion after being told about the experiment. $\endgroup$ – user11235 Apr 28 '14 at 15:32
  • $\begingroup$ en.wikipedia.org/wiki/The_Wave_%282008_film%29 Here is a link to the film site, because the novel wikipedia site seems to be corrupted. $\endgroup$ – user11235 Apr 28 '14 at 15:32
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    $\begingroup$ I think that Skemp's great article gives a great general idea of how "teaching focussed on measurable short-term goals does not [necessarily] provide the best long-term outcomes". In my experience, rote-learning is used in UK secondary schools for short-term, performance-boosting results which isn't an effective way to learn mathematics in the long run. Skemp doesn't provide any statistics but his 1972 book does, and is an excellent read. $\endgroup$ – Shai Apr 30 '14 at 0:18

Fawcett did a year-long experiment teaching high school geometry with the explicit aim of, not only teaching the content of geometry, but also transferring to students a new life-long behavior of considering propositions in all life arenas in terms of definitions, undefined terms and so on. Harold P. Fawcett, Ph.D. The Nature of Proof: The thirteenth annual yearbook of the National Council of Teachers of Mathematics, Teachers College, New York, 1938. 146pp.

Cut-the-knot has a write up of the book, and I have written a few notes about it too.


One of the best discussion of this in the Math Ed literature is Alan Schoenfeld's wonderful (1988) article "When Good Teaching Leads to Bad Results: The Disasters of 'Well-Taught' Mathematics Classes." From the abstract:

This article describes a case study in mathematics instruction, focusing on the development of mathematical understandings that took place in a 10-grade geometry class. Two pictures of the instruction and its results emerged from the study. On the one hand, almost everything that took place in the classroom went as intended -- both in terms of the curriculum and in terms of the quality of the instruction. The class was well managed and well taught, and the students did well on standard performance measures. Seen from this perspective, the class was quite successful. Yet from another perspective, the class was an important and illustrative failure. There were significant ways in which, from the mathematician's point of view, having taken the course may have done the students as much harm as good.

The "harm" Schoenfeld refers to has to do with what I would call mathematical dispositions, certain attitudes about what mathematics is that are out of sync with the values of mathematicians. These dispositions are very difficult to measure empirically, and there does not even seem to be a consensus that they are important to measure. So while the class in his case study was successful in terms of "measurable outcomes", that success seems to have come at a cost.

Schoenfeld presents his case study as a cautionary tale -- the moral seems to be "beware, just because everything looks good on conventional measures does not mean that all is well" -- but a more cynical reading of his evidence could be that these "disasters" are an inevitable consequence of teaching students to perform well on conventional measures; in other words, the cost of teaching "well" (as it is commonly assessed) might be that we have to distort the discipline along the way. Schoenfeld does not go there, and I don't really think that's the case, but sometimes we all have our dark days when it seems like there is a trade-off that cannot be avoided.


"Ethical and Professional Dilemmas for Educators" are the focus of this document from Connecticut. It presents and analyzes several examples, e.g. on p. 36:

Ms. H teaches ninth grade English. She gives the class directions for a writing assignment that is to be completed by the end of the period. Josh isn’t paying attention and missed the directions.... He asks for the directions to be repeated. The other students in the class begin to make fun of Josh....


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