Teaching Assistant Workshop

1
Teaching Assistant Workshop

• Problem Solving Approach
• Test Writing

2
Pres. G. B. Hinckley

• This institution is unique. It is remarkable. It
  is a continuing experiment on a great premise
  that a large complex university can be
  first-class academically while nurturing an
  environment of faith in God and the practice of
  Christian principle.
• You are testing whether academic excellence and
  belief in the Divine can walk hand in hand.
• And the wonderful thing is that you are
  succeeding in showing that this is possible. Not
  only that it is possible , but that it is
  desirable and the products of this effort show in
  your lives qualities that are not otherwise
  attainable. BYU Devotional Oct 13, 1992

3
BYU Department of Mathematics Shared Vision

• Teach mathematics and mathematical thinking.
• Extend the frontiers of knowledge in pure and
  applied mathematics.
• Build a unified and collegial atmosphere.

4
Teaching and Learning Mathematics

• A goal more important than teaching a set of
  theorems is to develop in students the ability to
  understand and manipulate the concepts of
  mathematics.
• Mathematics can be learned only by doing.
• Dont expect to read mathematics the way you read
  a novel. If you zip through a page in less than
  an hour you are probably going too fast.
• Linear Algebra Done Right
• by Sheldon Axler

5
Solving Linear Systems of Equations

• Homogeneous
• Fundamental Questions
• a) Is it possible that Ax0, has a
  non-trivial solution?
• b) How many non-trivial solution can it have?

6
Theorem

• A (NxN) matrix
• The homogeneous system Ax0 has only the trivial
  solution if and only if det(A) is different than
  zero.

7
Existence and Uniqueness Theorem

• Initial value problem
• yf(t,y), y(to)yo
• Theorem If f and df/dy are continous in a
  rectangle R containing the point (to,yo). Then in
  some interval (to-h,toh) contained in R, there
  is a unique solution yh(t) of the initial value
  problem

8
Existence and Uniqueness Theorem

• Application
• Does the IVP
• (t-3)yln(t)y2t, y(1)3
• has a unique solution around the point (1,3)?
• 2) y1(t)(2/3t)(3/2) and y2(t)0
• are solutions of the IVP
• yy1/2,
• y(0)0.
• Why the uniqueness theorem is not contradicted
  by this example?

9
Test Writing

• Tests are generally used to determine students
  grades. What else are tests useful for?
• Help students recognize their strengths and
  weaknesses in the subject.
• Help you to access the quality of your teaching
  and make corrections as you go on.
• Determine different levels of learning of your
  students.

10
Common Students Complaints

• For hours I studied material that was hardly
  covered on the exam!
• I didnt know that was going to be on the exam!
• The test had nothing to do with the classes!
• The test required more skills than those taught
  in class!

11
Learning Cycle
(Learning Activities)
12
Test Plan

• What objectives do you want to cover?
• How difficult should you make the test?
• Who is taking the exam?
• How much time has been provided for testing?
• How many questions should you have on your test?
• What type of questions should be in the test?

13
Test Difficulty

• Try to construct challenging but not impossible
  tests.
• From one of my syllabus
• If you are able only to do problems similar to
  those you have seen before, you are doing an
  average work. To earn a better grade you need to
  understand the derivation and application of the
  numerical methods and be able to solve more
  interesting problems.
• Best advise 1 Corinthians 1013
• God is faithful, who will not suffer you to be
  tempted above that ye are able but will with the
  temptation also make a way to escape, that ye may
  be able to bear it.

14
Constructed Response Test

• Question
• Prove
• If f is defined on an interval and f(x)0, then
  f is constant on the interval
• Corrected
• Prove
• (10 points) If f is defined on an interval and
  f(x)0 for all x in the interval, then f is
  constant on the interval

15
Questions Sources

• Own class notes. Particular emphasis on examples
  and homework well covered.
• Exercises in the textbook or close related text.
• Old exams that you had administered in the past.
• Tests from other instructors.
• In all cases, revise the items carefully and try
  to adapt them to your overall teaching approach
  during the current semester.

16
Item Arrangement

• Organize the exam according to item types
  fill-in-the-blank, multiple-choice items,
  constructed response
• Order items from easiest to most difficult (Why?)
• Cluster items within item type by content area.

17
Test Directions

• How much time is available.
• Whether to show work on problems.
• Point totals on different items.
• Whether texts, class notes, or calculators can be
  used during the test.

18
Test Assembly

• Make an effort to use a mathematical typesetting
  software as LaTex.
• Avoid
• Mispelled words and misnumbered items or pages.
• An item split between two pages.
• Different page format.
• Not to include enough space for constructed
  response items.

19
Other Considerations

• Take the test yourself and record time.
• Students usually need to spend three times the
  time you spent solving the test.
• Return the graded exam quickly.
• Discuss the exam after graded. This is a very
  valuable learning activity.
• Show students score distribution.
• Do not answer specific grading questions during
  class time.