By Daniel Chazan
Explores the most important dynamics of educating - setting up who one's scholars are, what to coach and the way to engage with dynamic personalities. The booklet examines intimately a teacher's evolving understandings in their scholars, algebra and teachers-student school room roles.
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This quantity comprises the court cases of the 7th Workshop in Lie conception and Its functions, which used to be held November 27-December 1, 2009 on the Universidad Nacional de Cordoba, in Cordoba, Argentina. The workshop used to be preceded through a unique occasion, oEncuentro de teoria de Lieo, held November 23-26, 2009, in honour of the 60th birthday of Jorge A.
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Extra info for Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom (The Series on School Reform)
In the central three chapters of the book, I will illustrate how in the course of this pursuit, both mathematics itself and the history and philosophy of mathematics become important and practical resources. Thus, this book is a nonstandard mix of analysis of classroom episodes, curricular reasoning, and mathematics itself. However, for the most part, the book does not tackle the structure of schools or of the larger educational system; it assumes the difficulties of current organizational arrangements.
Here are some illustrations. Teachers often suggest to students that mathematical knowledge is special, different. Mathematical statements do not need to be qualified in the ways in which other statements must be. ). Mathematics seems to have a unique way of knowing that is different from the one utilized in other fields of knowledge. In the words of mathematician Philip Davis (1986), mathematics alone is not overthrown by experience; it can "establish beyond the question of doubt": History does not prove, sociology does not prove, physics does not prove, philosophy does not prove, religion (if we can forget the church's unrequited seven hundred year love affair with Aristotelianism) does not prove.
Since, in my teaching at the time, all of this work to compute the slope was being done without a graph, students did not use visual strategies, like counting over, for determining rise, run, and slope. The third step, finding the y-intercept, which regularly confused my dayschool students, was not justified in the text and is difficult to explain succinctly. At this point in the method, the slope has been determined, but the y-intercept has not been. 2. Finding the equation of a line. Reprinted with permission from Dolciani & Wooton (1970/73) determining where it crosses the y-axis (where the x-coordinate is 0).