Rationale Behind Selected Procedures and Policies in Many Math Courses

1.  Returning of Tests:  In a good “Test and Measurements” course, it is pointed out that tests are given for one of two reasons, to evaluate or to teach.  Unfortunately, these two purposes oppose each other.  When a test is first constructed it probably has technical problems that cause the test to be “unfair”, such as being too long, too short, too hard, too easy, typo errors, and poor wording.  As the test is administered, these problems are discovered and addressed, and the test is adjusted.  If the test is returned to students to keep, then we cannot use the same items again, and we will continuously be making unfair tests.

It is actually better for the student when a personal follow-up is attempted, such as seeing a tutor or some personal study of topics missed on the test, to not deal with the actual items on the test, but instead restudy the concepts that were involved with the missed items.  Something we observe every year when we give a diagnostic arithmetic test at the first of Algebra One are several students that get common denominators on multiplication and division of fraction problems.  This is caused by following up on missed items on previous tests.  Many students will have problems with fraction addition and subtraction when first learning fraction operations and miss those problems on a test.  These students take this test to a tutor and the tutor works the missed problems with that student.  On the next test the student suddenly gets a common denominator on all problems.  The tutor only needed to know that the student was having trouble with common denominators and the tutor should have discussed all operations with the student, with an emphasis on addition and subtraction.  The tutor or student did not need the actual items on the test, and in fact focusing on the actual tests instead of the difficulty was harmful.  In addition, many students feel that if they put in time covering the missed items that their difficulties are fixed, when in reality the student must address the concepts behind the problems.

I have observed some classes where teachers return tests for students to keep and thus make new tests each time and have seen extremely angry students because they saw the test as unfair, for the technical reasons stated earlier.  When I saw the test, I could see their point.  The potential for unfair tests is very disturbing to students, because they feel they have no control over their grade.  Therefore, the math department decided many years ago that we give exams to evaluate, not teach.  However, in most courses, students will receive a printout of there grade after every test (usually the next day).  In most classes, teachers will analyze the performance on the test and will address difficulties with the students.  This follow-up could include general discussions on topics that occurred with many students and board work for topics difficulties that involved fewer students.  In other words, we do follow-up on the test, but in the classroom setting, not by allowing the student to take the test home and as discussed above the student really does not need the exam to do an excellent personal follow-up.  Also, we often have many make-up tests to administer, so we usually cannot return test quickly.

2.  “Math Discussions – Board work”:  As discussed elsewhere in this package, all of our math courses are abstract in nature and not concrete memorization.  The only way to learn how a person is thinking is to ask them what was behind the work they did on a problem.  Therefore, in many of the math courses, especially the department courses of Algebra One, Geometry, and Algebra II/Trig, there will be a lot of board work and math discussions.  Often these discussions are driven by performance on quizzes.  Since quizzes and tests are given in a testing environment, we are relatively sure the concepts that are being used are the students understanding of the concepts and not a tutor’s or another student’s that might show up on homework.  At first students may be uncomfortable doing so much board work, but once students realize many of the students are called to the board and that all that is happening is math concepts are being discussed, they get comfortable with this process.  This is really a math seminar.

3.  Student Responsibility:  Most of our students will take advanced placement test and do well on them.  In order to do well on these exams the student must be individually in control of the material.  The student will not have a tutor, parent, or teacher with them.  Therefore, by a student’s junior and senior year, the student must be academically aggressive and in charge of their academics without excessive outside influence.  Starting in Algebra One we try to treat the student with the idea they are mature enough to be a responsible student.  We do this by communicating with them directly and holding them personally responsible for their learning.

4.  Pencil:  We require students to use pencil.  This is an example of a policy that sometimes looks like it is just picky.  However, like all of our policies, there is an important reason for this policy.  An example may illustrate.  In observing some younger students do long division, we see students do a large number of multiplications to determine the digit to write in the quotient.  This is sometimes caused by using ink in earlier grades.  They were afraid to “miss this digit”.  In reality, there is a need to erase in math, and when ink is used the work gets messy.  This has a psychological effect in making math look “trashy” and “disorganized”.  Using ink sometimes reflect that the student is not doing work in a timely manner and are rushing some work before class or copying problems and are using ink because they do not have a pencil.  In fact, teachers notice that students that are using ink are tending to make the lower grades.  It is very rare that we ever see the top students use ink.  In a related issue concerning class materials, we observe students that do not bring material to class and are borrowing paper and pencils for quizzes and tests are also students that are making lower grades.  If a student will not even take care of the simple task of bringing material that is obviously a part of being a student, then why would they take care of accomplishing the more challenging task of learning concepts?