Do Problems 1 - 97...the Odds By Monday!
As homework, a mathematics teacher can assign Problems 1 - 97...the Odds. But, what are the odds that they will be done? Also, what are the odds that the mathematisc teacher has carefully looked at what is being explored in each problem?And, what are the odds that any learning will occur as a result of the homework?
In a book, articles, and conference talks, Cathy Vatterott offers what she considers the "five hallmarks of good homework." Her claim: "Homework shouldn't be about rote learning. The best kind deepens student understanding and builds essential skills."
Her five "hallmarks of good homework" are as follows:
Vatterott is a former middle-school teacher and currently an education professor at the University of Missouri-St. Louis. But, I doubt she has ever taught mathematics.
- Each task needs to have a clear academic purpose, such as practice, checking for understanding, or applying knowledge/skills
- Each task should efficiently demonstrate learning on the part of the student
- Each task should promote ownership by offering choices and being personally relevant
- Each task should instill a sense of competence, i.e. a student can successfully complete it without help
- Each task is aesthetically pleasing, i.e. it appears enjoyable and interesting
Though her five "hallmarks" are commendable, I am having trouble forcing a square circle into a round hole. More specifically, I can accept #1 and #2 and part of #3...having trouble with idea that every homework task needs to be "personally relevant." If a task gets at exploring a neat idea in mathematics but perhaps makes no personal connection, should it not be assigned. Plus, can you imagine a poor math teacher sitting there trying to devise a set of homework problems every night, ensuring that every assigned problem task is "personally relevant" when that teacher faces about 150 students daily?
I have more of a problem with her last two criteria. In #4, why does it have to be "without help"? That seems to deny the idea of challenging problems, open-ended explorations, and doing more than mindless review of skills. And in #5, I am lost as to the implications of finding problem tasks that are aesthetically pleasing, enjoyable, and interesting? If only life as a mathematics teacher was that easy.
And that is why I have trouble with content-generic advice, such as that given by Dr. Vatterott. Until she has walked in a mathematics teachers' shoes....!
Finally, in response, I am open to readers sharing their "hallmarks for good homework" specific to mathematics. I would be glad to share them via this website....so send me your ideas.
Source: C. Vatterott's "Five Hallmarks of Good Homework," Educational Leadership, Spetember 2010