In Exercises 714, simplify each rational expression. Find all numbers that must be excluded from the domain
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In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
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y² - 4y - 5 y² + 5y + 4
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Sean McCreery
Two convictions guide my teaching. The first is that the classroom must be a space of interest, excitement, and discovery for students and teacher alike. Echoing the pedagogical creed of John Dewey, I believe each individual student learns best when every member of the class, instructor included, assumes the responsibility of learning, teaching, and generating ideas as a group. The second conviction that guides my teaching is that literary works are not merely objects to be consumed but occasions to be realized. I resist “the good-humoured feeling,” as Henry James wrote sardonically, “that a novel is a novel, as a pudding is a pudding, and that our only business with it could be to swallow it.” I believe that literature is the precipitate for a personal adventure, whose final outcome cannot be predicted in advance. All this is really to say that, no matter the activity, my goal is to offer students a point of access to the deeply rewarding challenges of close reading, rhetorical argumentative strength, and imaginative speculation that will empower college and high school students in all aspects of life.
Achieving this goal is not easy for any teacher, but there are particular obstacles confronting those of us who teach in the Humanities today. While every student could be by and large, bright, motivated, and enthusiastic learners, they face so many demands (friends, extracurricular activities, leadership positions, college applications, internships, jobs, general inertia) that it can be difficult for them to focus on academic work. Within this climate, I find that students welcome the round table feel of a seminar discussion as an intellectual oasis, where they can attend, closely and collectively, to an experience that is difficult to replicate outside of an English classroom. Students need to know, in a way that is applicable to them, that cultivating this oasis, making it as alive as possible, is our shared communal responsibility; in my mind the success of a class, in other words, depends on informed, sustained, and diligent participation from everyone. Be it a class of 25 or 2 this still stands. To encourage such participation to grow, I employ many different tactics. I often use technology, music, videos, websites, and other media as a springboard to discussion. Specific examples include creating wikipedia pages, using reddit to practice rhetorical skills, utilizing interactive websites such as Versal, and employing hands on activities such as the Adbusters media literacy kit.
In a more practical sense I have taken direction from John Dewey, and organize my classes as a group activity in which we are all fully engaged and are all personally responsible. For instance, I have designated pairs of students as “conveners” for each class, whose task is to facilitate our thinking and push us toward the fullest understanding of the text by their asking sophisticated questions at the outset and resisting facile consensus. The conveners can be advised to work from the premise that exploring questions is more valuable than arriving at answers. Simply put, rather than my asking “what did you think about,” I create a demand that students ask “what is up with” questions. With those questions, open dialogue indeed happens. The ideal classroom, as I see it, strikes a balance between delivery of content and interactive, participatory exchange. There are many ways to achieve this balance; in my experience, the most effective approach is to explicate the examined text in a way that points out paradoxes, inconsistencies, and other oddities that demand further consideration. This can be done either during class itself or in writing assignments. Lecturing itself, meanwhile, necessitates the ability to excite students with a diverse array of intellectual commitments and creative aspirations. Simply put, I believe an informative class is a fun class, and that a fun class is informative.
I would say that while it is possible for any student to struggle, when they get the help they need, usually via one to one tutoring, they tend to work through obstacles. We all know how learning curves can vary. Thus, as a teacher, academic adviser, athletic coach, or mentor, I have tried to be sensitive to each individual student’s needs, and it should be noted that I do firmly believe in differentiated instruction.
In short, learning should be both useful and fun for both student and teacher.
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