I have just received a copy of the new book `Teaching Mathematics' written by several authors.
Much might be said about this book, but I want to concentrate on pages 295-296 where the authors write inter alia:
``One research study analyzed problems, looking in particular at the context used for the problem along with the mathematical model used, if any. The conclusion was that problems provide little value as far as convincing students of the usefulness of mathematics... It seems ironic that problems changed little over many years with studies showing little appeal to students. How can we justify continuing in the same mode?..
Often a procedure is established for the student to follow as the problem is worked. These procedures are beneficial to completing the assigned task of doing a problem, but they are damaging in that the student is almost programmed to follow a routine... Procedures and organization such as this lead to some difficulties for some students. Essentially, they become specialists in a given problem type for the time it is being studied. After the test is given, another problem type may be discussed and developed. After a few days of dealing with the second problem type, the first is forgotten...
Sticky Question: Should problems be solved when teaching mathematics? Isn't it better, considering all the reserach data, give up this practice that leads to so many failures?''
Andre Toom Department of Mathematics email@example.com University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153