Two graduate students at a large state university, Otto and Felicia, teach parallel sections of calculus. On the first day of classes, Otto administers a test of basic skills. He advises students who do poorly on this test to drop back to pre-calculus. Most of them transfer to Felicia's section instead, since they have heard that she is a good teacher and her section is offered at the same time. The last student to transfer, Gil, did poorly on the test but has other technical abilities. Felicia, in consultation with the course's faculty supervisor, must decide whether to make an exception to the rules and allow Gil into her already crowded section, or to follow Otto's suggestion and advise him to repeat pre-calculus.
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A first year graduate student, Emily, is proctoring her first test. To her surprise, she observes possible evidence of a student cheating during the exam. She hesitates, unsure how best to proceed. As she is considering what her next action should be, she realizes that another student, who has subtly challenged her authority in the past, saw the whole episode, and is now watching closely to see what Emily will do next.
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(This case comes in two parts: the second part should be distributed only after discussion of the first part.)
A first semester calculus course is about to have a midterm on the Fundamental Theorem of Calculus. In part I of the case, the TA for the recitation section, Keng, holds a review session. In it, he finds himself confronted by students with little understanding of the meaning of the Fundamental Theorem.
In part II one of these students, who did well on the midterm, comes to see him. Though she can do the problems, she is concerned that she still does not entirely understand the material.
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(This case comes in three different versions: College Algebra, Calculus I, and Multivariable Calculus. The content of the problems in the versions differs, but the overall instructions are the same.)
In this case, participants are asked to grade sample student work from a class. They are asked to mark several problems from a given course as if they were questions on an exam, and then as if they were homework problems. During the discussion, participants will see each other's grades and discuss how they arrived at them.
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(This case has an optional second part, which may be distributed after discussion of the first part.)
Two graduate students, Kara and Louis, are teaching parallel sections of the same calculus course. When Louis bemoans the inclusion of Fourier series in the course syllabus, Kara points out that there are important applications of that material to waves, which she plans to show her class. Louis, unfamiliar with the applications, attends her class and is impressed. He decides to describe these applications to his own section. Unfortunately, Kara's class performs poorly on the quiz about the applications; Kara is further disheartened by a student asking her if ``the physics stuff'' will be on the final. Though Louis is enthusiastic, Kara questions the wisdom of her approach.
In part II, Louis is asked to take his office mate's calculus class for 2 lectures, and to cover the natural logarithm and exponential functions.
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Terry is alarmed to see her pre-Calculus section led astray by various calculator errors which distract the students from translation of functions, the topic of their exercises. She spends what seems like a long time trying to determine how the students generated various incorrect graphs. Her whole section appears mystified until, at last, a few students with good ideas speak up.
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A TA running a discussion section for a course in integral calculus decides to foster her students' independent thinking skills by having them work together in pairs. She is worried that the students too often rely on her to provide them with the answers. However, the pairing exercise does not go as smoothly as she had hoped, for a variety of reasons. She is left wondering how to organize the future discussion hours.
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Bill Baker is the TA for a recitation section of Calculus I. According to the syllabus, the class is learning about average and instantaneous velocity. Bill plans to spend a few minutes of his section on the homework and then present some supplementary material related to instantaneous velocity. However, he discovers that most of the students in his section do not understand average velocity. Many do not seem to have put in much effort on the homework prior to section.
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Evan is a well intentioned first year undergraduate who is close to failing his calculus class. He is stretched too thin among many activities. He seeks relief mid-way through the semester in the form of an extension on a project, is rebuffed by his TA, and continues to do poorly. After seeking help from the TA again late in the semester in a bumbling way, Evan realizes that he must choose between withdrawing from the class, with possible financial aid consequences, or trying to squeak by with a low grade.
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Daniel, an advanced graduate student, is teaching a section of Calculus I. After the first examination is handed back a surly student, Sam, comes to Daniel's office. Sam believes that he is unfairly penalized when he does not receive full credit for using the power rule, which has not yet been taught in the class, to answer an examination question which requires a derivative, rather than computing the limit of the difference quotient.
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Angelica, a graduate student from another country, is teaching a section of second semester Calculus. She has high expectations for the students in her class and is concerned over their poor performance to date. Angelica tries to boost her students' sagging study habits by introducing a draconian regime of quizzes, mid-semester. She is met with bemused indifference from the supervising professor, and outright indignation from her students.
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(This case comes in three versions: College Algebra, Calculus II, and Multivariable Calculus. The content of the problems in the versions differs, but the overall instructions are the same.)
This case asks participants to create a 50 minute exam based on a list of sample questions. Some of the questions exhibit various pitfalls a test writer might fall into, such as stating a problem unclearly, stating a problem so that poor understanding will produce a better partial answer than a slightly mistaken understanding, writing a problem which is very difficult to grade, and not considering the approaches which are possible if a calculator is allowed on the exam.
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(This case comes in two parts: the second should be handed out only after a discussion of the first part.)
A recent Ph.D. from an elite university confronts difficulties adapting to teaching at a large state school; he is confused that the lecture techniques which brought him success as a graduate student instructor are not working. In Part I, he struggles to respond to complaints from his students, getting pressure but no help from his department chair. In Part II, he hands out a survey; most of his class responds with complaints and some with hostility.
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Hugh Brightman, a second year graduate student, is teaching his own Calculus II class under faculty supervision after a successful year as a TA for a recitation section in a large class taught by a professor. Although not many students have been coming to his office hours, Hugh is confident that they are well prepared for his first hour exam. He is shocked when he discovers that they don't seem to have learned even the most basic techniques and concepts.
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