My first talk given at the Mathematics Instruction Colloquium on mathematics tutoring.

1. Mathematics Instruction Colloquium
Not Only About
Mathematics Tutoring
Department of Mathematics
University of Arizona
Ji Li @ September 25, 2007

2. Once upon a time…
I considered myself a
“math tutor”, since I
tutored so much. I
spent averagely 10
hours each week
tutoring.

3. The questions I asked
myself..
? How can I help students better
? How should I help them
? What do they get from me
? What do I get from tutoring
? What do others think about math tutoring

4. Categorizing tutees
• Types of Tutoring
 Student Level • Private Tutoring
 Pre-College Students • University Program
 Non-math majors • Calculus Common
 Math Majors Tutoring
• TYP Special Tutoring

5. Outline of this talk
• My experience as a private tutor and a
TYP tutor. My thoughts.
• My experience as a calculus tutor for
the common room tutoring. Tutoring
notes. Samples.
• On-line resources about math tutoring.
The traditional approach and the
technological approach.

6. Private tutoring
 Homework assignments: to do? or not to do?
 Questions that tutors might want to ask before helping
tutees with solving homework problems:
 What did you cover in class? Do you have any questions about the
course material?
 What techniques were you taught to solve this kind of problem?
How do you relate this example in class to this homework problem?
 Homework assignments revisited.
 A normal practice is, after hinting twice failed, you might just give
the answer to the tutee. You may want to reinforce their learning
by letting them try some similar problems right afterwards.
 Tutoring rates: a direct proportionality.
 The more you make them pay, the more helpful they are convinced
you are. Though this might not always be the case.

7. TYP : Transitional Year Program
• I was assigned to tutor three TYP
students in a year. Two of them passed
pre-calc in the first half year and went
into calculus one and failed.
• These are extremely responsible students,
working very hard on math. However, coming
with a weak background on math learning, they
are convinced that math is not to be mastered.
• I failed to convince them that understanding is
important, and I feel guilty.

8. No matter what type of tutees they are..
• Students come for help since they need help.
• This is indicating that tutees tend to be “weaker”
students, though sometimes it is not true.
• The “weaknesses” can be lacking prior knowledge, or
failing to master basic arithmetic and algebra, or others.
• What kind of help do they need?
• Most students expect tutors to solve math problems for
them.
• More advanced students expect to extract manipulative
rules from tutors in order to deal with the problems by
themselves later. Typically, they do not expect to
understand math, since that is too remote a goal. They
only expect to “deal” with math without further struggling.

9. Examples are easy, but homework is too hard!
• This is a complain that an experienced teacher or tutor
expect to hear.
• An observed phenomena is that a student who feels very
confident watching the tutor go over the problem solving
procedure will go back and continue to perform badly in
quizzes and exams.
• I consider it part of my responsibility to draw connections
for the tutee between understanding math and working on
math. In particular, I spent a lot of time make them work
under my presence. If they got a wrong answer, I asked
them “on which step you think you made the mistake?”

10. What has tutoring brought me?
One-to-one communication with students makes it
possible for me to
• correct mistakes right on the spot;
• give insights whenever possible;
• listen to students and understand them:
“Empathy” --- You might need to go back to
correcting mistakes: “I understand what you
are talking about, but this problem cannot be
solved this way because ……”

11. Tutoring is a different form of teaching
Looking back, I appreciate
having the chance to
communicate with
students and understand
them, especially because I
come from a different
culture in teaching and
mathematics teaching. In
a way, tutoring helped me
greatly with my
understanding of math
teaching.

12. What makes a good tutor?
 Define “good”
 Effective
 Patient
 Helpful
 Open to challenges
 Resourceful: know what-is-
needed-to-know

13. Part II
Calculus Tutoring
at the Common Room
in Brandeis

14. Tutoring room
 From Monday to Thursday 7 to 9pm, 3 tutors stay in
the tutoring room waiting for students of pre-calc,
calculus one and calculus two to drop by.
 Averagely 4 to 8 students show up each evening.
Each stays for 15 minutes to 1 hour.
 Experienced tutors include senior math majors and
senior graduate students.
 Inexperienced tutors include first year graduate
students and exchange students.

15. Tutoring notes come into being…
 Tutoring notes were prepared especially for the new tutors
who haven’t taught or studied in Brandeis, in order for them
to help students in a more efficient way.
 Tutoring notes were initiated by a former graduate student,
Ophir Feldman, and carried over by me after he left
Brandeis.
 Tutoring notes were based on teaching notes made by
Professor Susan Parker. They are actively updated from
semester to semester in order to cover new material.
 My job includes collecting, organizing, and distributing
tutoring notes to the tutors. I also help solving problems
when they arise during tutoring sessions.

16. Tutoring notes
 The tutoring notes are listed section by section,
chapter by chapter, giving a full picture of what is
being covered in classes while focusing on
important materials.
 In the tutoring notes, typical problems students
have with each section are described.
 Particular techniques and study aides used in
teaching certain topics are elaborated, since the
tutors are supposed to be familiar with them.

17. On-line resources
Traditional Approach
• Math Peer Tutoring
• Top Ten Tutoring Tips
Technological Approach
• CAI: Computer Aided Instruction
• ITS: Intelligent Tutoring System

18. The End.
Sample Tutoring Notes.