Degradation
Mathematics educators using problem solving for evaluation have an issue phrased by Alan H. Schoenfeld:
- How can one compare test scores from year to year, when very different problems are used? (If similar problems are used year after year, teachers and students will learn what they are, students will practice them: problems become exercises, and the test no longer assesses problem solving).
The same issue was faced by Sylvestre Lacroix almost two centuries earlier:
- ... it is necessary to vary the questions that students might communicate with each other. Though they may fail the exam, they might pass later. Thus distribution of questions, the variety of topics, or the answers, risks losing the opportunity to compare, with precision, the candidates one-to-another.
Such degradation of problems into exercises is characteristic of mathematics in history. For example, describing the preparations for the Cambridge Mathematical Tripos in the 19th century, Andrew Warwick wrote:
- ... many families of the then standard problems had originally taxed the abilities of the greatest mathematicians of the 18th century.
Read more about this topic: Mathematical Problem
Famous quotes containing the word degradation:
“The three great problems of this century, the degradation of man in the proletariat, the subjection of women through hunger, the atrophy of the child by darkness.”
—Victor Hugo (1802–1885)
“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
—Anna Howard Shaw (1847–1919)
“Gradually we come to admit that Shakespeare understands a greater extent and variety of human life than Dante; but that Dante understands deeper degrees of degradation and higher degrees of exaltation.”
—T.S. (Thomas Stearns)