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Learning to Teach and Teaching to Learn Mathematics

Learning to Teach and Teaching to Learn Mathematics

Matt DeLong
Dale Winter
Series: MAA Notes
Volume: 57
Copyright Date: 2002
Edition: 1
Pages: 285
  • Cite this Item
  • Book Info
    Learning to Teach and Teaching to Learn Mathematics
    Book Description:

    Every year thousands of new mathematics instructors and teaching assistants begin their teaching careers, and, scores of experienced faculty seek ways to explore the new teaching possibilities offered by technological and pedagogical innovations. There is a great need for tools to train college mathematics instructors in both basic teaching skills and innovative methodologies. Learning to Teach and Teaching to Learn is a self-contained and extensive resource that addresses this need. It describes training and mentoring activities that have been successfully used in a variety of settings. with a wide range of new instructors, including graduate student teaching assistants, undergraduate tutors, graders and lab assistants, as well as postdoctoral, adjunct, part-time and new regular-rank faculty. It addresses a variety of teaching issues including cooperative learning, technology, and assessment.

    eISBN: 978-1-61444-313-1
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Preface
    (pp. vii-x)
  3. Table of Contents
    (pp. xi-xiv)
  4. Chapter 1 The Professional Development Program
    (pp. 1-6)

    We believe that it is important for a mathematics department to be actively involved in the professional development of its faculty and graduate students. Byprofessional developmentwe mean the training, assessment, and improvement of teaching skills and practices. Professional development that comes from within the mathematics department, rather than through non-disciplinary channels, is more likely to be meaningful and credible to the instructors who are involved. For example, sensibilities about teaching mathematics are sometimes quite different from those in other disciplines. Compare what is meant by “read the textbook” in a mathematics class to what is meant by the...

  5. Chapter 2 How to Use this Book
    (pp. 7-14)

    This book is intended to be a handbook for implementing three of the components of an integrated professional development program described in the previous chapter. Chapter 3 details a short pre-semester training course, although those departments that are able to commit to a longer pre-semester training program may use the model provided by Shure, Black, and Shaw [103]. Chapters 4 through 16 are devoted to the weekly in-semester training meetings. Chapter 17 is devoted to class visits and feedback. This chapter explains how to use the rest of the handbook to implement these three components. More detailed advice on running...

  6. Chapter 3 An Orientation Session for the Beginning of the Semester
    (pp. 15-42)

    The purpose of this chapter is to describe a session suitable for introducing new instructors to your mathematics program. As mentioned in Chapter 1 of this book, we envision a training program that includes intensive pre-semester training as an integral and important component. Throughout this book we have made reference to the pre-semester training materials developed by Shure, Black and Shaw [103] at the University of Michigan. Our experience suggests that such a pre-semester training program provides new instructors with a set of foundational experiences that the meetings described in Chapters 4–15 build upon.

    Unfortunately, circumstances such as budget,...

  7. Chapter 4 Making In-class Groups Work
    (pp. 43-54)

    Since the Tulane conference [42], substantial amounts of time and resources have been put towards developing materials for non-lecturing, student-centered classroom techniques. Some techniques that are used by many instructors are cooperative learning activities, student presentations, laboratory activities, discovery learning, and the Moore method. In our classrooms we extensively use the technique of having students work in cooperative groups on mathematical problems. In this chapter we focus on developing the instructors’ facility with implementing and managing in-class cooperative activities. If your program includes student-centered teaching methodologies not addressed by one of the meetings in this book, Chapter 16 provides support...

  8. Chapter 5 Getting Students to Read the Textbook
    (pp. 55-64)

    Observing textbooks on introductory collegiate mathematics, and instructors who use these textbooks, one notices that there is little consensus on the role or function of a mathematics textbook. Some textbooks attempt to provide a narrative that tries to access concepts through intuition, application, and explanation. Others attempt to provide an exhaustive resource and reference. Yet others function primarily as a repository of worked examples. In addition, there are the ubiquitous tensions between rigor and accessibility, and between conceptual understanding and skill acquisition.

    In our experience, many students use mathematics textbooks as little more than large collections of homework problems, templates...

  9. Chapter 6 Assessing and Evaluating Students’ Work
    (pp. 65-88)

    The mathematics course that we envision utilizes a variety of assessment techniques, including team homework, projects, student presentations and writing assignments. A common element of these assessment practices is the clear and precise communication of mathematical ideas.

    In many cases, students are expected to work cooperatively – to produce a single piece of work representing the collective efforts of three or four students. In order to provide sufficient challenge for a group of students and sufficient incentive for the students to work cooperatively (instead of simply dividing the work among themselves, and later compiling their individual contributions for submission) the problems...

  10. Chapter 7 Managing Homework Teams
    (pp. 89-104)

    As we mentioned in Chapter 4, cooperative learning is gaining popularity as a pedagogical device in introductory collegiate mathematics courses. Instructors are encouraging students to learn in teams in or out of the classroom, and many instructors, ourselves included, have their students work cooperatively inandout of the classroom. Chapter 4 was primarily concerned with issues of the implementation of cooperative learning in the classroom, whereas in this chapter we explore issues of implementation for cooperative learning outside of the classroom.

    In this chapter we discuss the management of “homework teams,” because we require our students to meet regularly...

  11. Chapter 8 Teaching During Office Hours
    (pp. 105-114)

    As all instructors are aware, teaching opportunities are not confined to the classroom. Office encounters provide one outlet for additional, and in this case more focused and personalized, instruction. Unfortunately, some instructors see office hours as an annoying burden and a waste of time that, in their eyes, could be more fruitfully spent on research or other duties. In addition, many students are reluctant to utilize office hours, because of various beliefs and perceptions that they hold.

    Most instructors readily recognize that a primary function of one-on-one teaching in office hours is to provide students with individualized instruction and help....

  12. Chapter 9 Establishing and Maintaining Control in Your Classroom
    (pp. 115-126)

    The introduction to this chapter is slightly longer than is typical. The idea of this introduction is to provide instructor trainers with a basic idea of what issues may be described under the title of “Control in the Classroom.”

    Instructor trainers are usually naturally talented and effective instructors who have a clear vision for what they want to make happen for the students in their class. Likewise, instructor trainers will often have a natural talent for clear communication, and will instinctively take steps to ensure that their classroom is an ideal environment for this communication to take place. As such,...

  13. Chapter 10 Proctoring Tests and Examinations
    (pp. 127-132)

    One of the “nuts and bolts” issues that all teachers must get to grips with is proctoring students during tests and exams, and taking appropriate action if they observe students cheating. Much of the advice and many of the precepts set out in this meeting will be obvious to experienced and capable instructors. In our experience, many beginning instructors are aware of the possibility of cheating and want to prevent it. However, most do not have clear ideas of exactly how to go about this. We have worked with instructors who sit at the front of the exam room, obviously...

  14. Chapter 11 Improving Teaching with Graphing Calculators and Computer Algebra Systems
    (pp. 133-148)

    The widespread availability of affordable graphing calculators and computers running powerful computer algebra systems (CAS) is changing the way elementary mathematics is taught. Research in mathematics education (see the suggested readings at the end of this chapter for examples) indicates that the careful use of appropriate technology can help students to achieve learning outcomes that are rare in more traditional mathematics courses. Graphing calculators and CAS have been likened to the microscopes of a biology lab. Just as students can use microscopes to directly observe the working of organisms and other biological systems, calculators and computers can be used by...

  15. Chapter 12 Making Lesson Plans
    (pp. 149-158)

    An obvious skill that needs to be acquired by new instructors is the ability to plan an effective lesson. In a course consisting primarily of lectures, this translates into writing clear and engaging lectures that include ways of assessing the lectures’ effectiveness. There has been much written on the art of preparing such lectures. On the other hand, in an interactive student-centered ¹course, planning an effective lesson translates into a very different activity. The instructor must decide how to balance the various teaching methodologies at his or her disposal so as to achieve the different learning goals set forth for...

  16. Chapter 13 Strategies for Motivating Students
    (pp. 159-168)

    A training program for new instructors will naturally begin with attention to day-to-day concerns. It is only after some familiarity and facility is achieved in these areas that a novice instructor has the opportunity for reflection on what is working in the classroom and why. One area for consideration at that point is the subject of student motivation.

    An instructor’s approach to student motivation will likely depend upon where he or she is situated on the pragmatist-idealist continuum. A total idealist would believe that the inherent beauty and power of mathematics should lead to intrinsic student motivation to learn the...

  17. Chapter 14 Dealing With Difficult Instructor-Student Situations
    (pp. 169-182)

    “The Torch or the Firehose?” is the Math and Physics recitation guide published by MIT and reproduced in [23], on page 185. It notes that,

    The classroom and section meeting are the business end of education. Here students and staff deal together with the stuff of the intellect. Here also idiosyncrasies in both become apparent.

    In our experience, and as reported in a survey of graduate student instructors’ experiences, [121], most instructors who teach a significant number of students will eventually find themselves in an “idiosyncratic” situation.

    We distinguish this meeting from the meeting titled, “Establishing and Maintaining Control in...

  18. Chapter 15 End-of-Semester Administration
    (pp. 183-196)

    By the end of their first semester of teaching, new instructors should have become somewhat comfortable with the day-to-day issues of planning their lessons, meeting students in office hours, grading homework, etc. Unfortunately, the end of the semester brings new and different stresses and struggles. The traditional pressure of grades places added importance to the students on mastering new and old material. In addition it provides temptation for students to cheat during the final exam or to bargain (or beg!) for grade changes after the exam. New instructors may be caught unaware by some of these issues. This meeting is...

  19. Chapter 16 Adapting Materials and Designing Your Own Meetings
    (pp. 197-204)

    In developing this book, we have tried to identify a collection of experiences for training college mathematics instructors that is comprehensive and well integrated. This is appropriate, as teaching is a highly complex activity, especially in the setting of a student-centered interactive classroom, and it is somewhat artificial to treat teaching issues as isolated from each other.

    The range of experiences that we have described in this book is consistent with our experience of the needs of graduate students and new faculty instructors at the University of Michigan. Naturally, other programs with different goals and methods may find that there...

  20. Chapter 17 Classroom Visits
    (pp. 205-236)

    An important component of a professional development program is a system of visits to new instructors’ classes. These visits take a substantial amount of time and effort, but they afford many benefits that cannot be gained from other aspects of a professional development program. Through class visits, instructors can get concrete, focused, and personal feedback. Through the sharing of sensible and helpful advice, the course coordinators can gain the respect and trust of their instructors. Visits keep the coordinators connected with the classrooms: the nature of the students, the classroom layout, and developing problems course—wide or with individual instructors....

  21. Appendix A Tips for Running Meetings
    (pp. 237-254)
  22. Appendix B The Michigan Introductory Program
    (pp. 255-264)
  23. Bibliography
    (pp. 265-270)