Homework Tips for Beginners by Elizabeth McLean
            for Dr. Millman's "Writing in Mathematics" class in 1990
      Homework exercises  can often be  exercises in frustration, both  for the
 instructor and for the students.  The students do not know what the instructor
 really wants and do not  agree with the grades they get,  while the instructor
 can not understand why students communicate so little in their work.  But with
 a little care, homework can enrich our students and educate us.  
      The first thing that we must do is to make the homework an important part
 of the  course.    Homework assignments  should be a  significant part  of the
 total  grade.   If we tell  our students  that homework will  be used  only to
 decide borderline course  grades, or that it will  be counted as some  type of
 minor extra credit at the  end of grading period, many of them will not bother
 much with the  assignments, feeling that they are  not worth the effort.    We
 should decide  how much  the homework will  be worth (e.g., percentage  of the
 total  grade), and  then let  students  know its  worth in  advance.   If  the
 students feel  that not doing the homework will hurt them,  they are much more
 likely to work consistently on the exercises.  Unfortunately, most students do
 not realize that they will  not learn the material without doing the homework.
 They need to be motivated by having homework be a part of their grade.  
      Secondly, we must take care when we draw up assignments.  Assigning every
 problem at the end of  the section may not be the thing to do.   Repetition is
 not necessarily a good learning tool, and can sour students' attitudes.  If we
 expect students  to work every  single exercise in the problem  set, we should
 grade  every  one.    Otherwise,  if  we  are  going  to  grade  five  or  six
 representative exercises, why assign forty?   We need to choose problems which
 will  expose  the  students  to  different aspects  of  the  current  area  of
 discussion, or to different methods  of computation.  By making the assignment
 reasonable in terms  of time, relative to what  we want the students  to learn
 and  what we  plan to  grade, students  are much more  likely to  complete the
 assignment.  
      Thirdly, we must  make the standards  very clear and precise  and discuss
 them in  advance.  Many  instructors complain about how  poorly students write
 mathematics, but how many students have studied any work other than their own,
 or have ever  been told how better to  write mathematics?  This is,  I feel, a
 major problem, but the cure  is simple, if demanding.  We, teachers, must work
 very precisely and completely at the chalkboard, and tell the students that we
 expect the  same in  the homework.   That is,  we expect  them to  rewrite the
 problem as stated in the book (except, say, in the case of word problems).  We
 expect them  to write their  steps clearly, one  line after an- other;  not in
 scattered columns, but  neatly across the the  page so their reasoning  can be
 followed.   Their  computations are  to  be complete;  their steps  are  to be
 connected with  grammatically correct  English sentences.   Answers are  to be
 marked as such (by boxing,  underlining, "Ans." etc).  Then grade accordingly.
 If a student gives "#3. 42" for an answer, points should be taken off, even if
 the answer is actually 42; the students  will not take our standards seriously
 if we  do not.  Point  out to them that properly  worked-out homework problems
 are good study helps at test time.  Certainly  they will complain for a while,
 but once  they become  accustomed to the  new standards, the quality  of their
 work will pick up considerably.  
      The only  requirement remaining is  consistency.  We must  maintain these
 standards for the entire grading period, including quizzes and tests.  When we
 do this, not  only will we be better  able to help our students,  since we are
 getting  more communication  from  them  through the  homework,  but also  the
 students  will  gain some  measure  of  dis- cipline  and  a comprehension  of
 mathematics that otherwise they might not have.  
      Make the homework important.   Give assignments that will teach students.
 Tell them  what we want,  and penalize if we  dot not get it.   Repeat for the
 entire grading  period.  These  four requirtements can be  time-consuming, but
 the reward in  improving our students' depth of  understanding and performance
 is well worth the effort.        

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