Mathematics Instruction Colloquium Not Only AboutMathematics Tutoring Department of Mathematics University of Arizona Ji Li @ September 25, 2007
Once upon a time… I considered myself a “math tutor”, since I tutored so much. I spent averagely 10 hours each week tutoring.
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
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
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.
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.
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.
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.
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?”
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 ……”
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.
What makes a good tutor? Define “good” Effective Patient Helpful Open to challenges Resourceful: know what-is- needed-to-know
Part II Calculus Tutoring at the Common Room in Brandeis
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.
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.
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.
On-line resourcesTraditional Approach • Math Peer Tutoring • Top Ten Tutoring Tips Technological Approach • CAI: Computer Aided Instruction • ITS: Intelligent Tutoring System