By Dr. Heike Renate Biermann, Prof. Dr. Hans Niels Jahnke (auth.), Sebastian Rezat, Mathias Hattermann, Andrea Peter-Koop (eds.)
ISBN-10: 1461434882
ISBN-13: 9781461434887
ISBN-10: 1461434890
ISBN-13: 9781461434894
The variety of analysis domain names and theories within the box of arithmetic schooling has been an enduring topic of discussions from the origins of the self-discipline as much as the current. at the one hand the variety is considered a source for wealthy medical improvement nonetheless it provides upward thrust to the usually repeated feedback of the discipline’s loss of concentration and id. As a technique of targeting middle problems with the self-discipline the publication seeks to open up a dialogue approximately basic principles within the box of arithmetic schooling that permeate assorted study domain names and views. The publication addresses transformation as one basic concept in arithmetic schooling and examines it from diverse views. modifications are with regards to wisdom, with regards to symptoms and representations of arithmetic, on the topic of suggestions and ideas, and regarding tools for the educational of arithmetic. The e-book seeks to respond to the next questions: What will we learn about variations within the diverse domain names? What types of adjustments are the most important? How is transformation in every one case conceptualized?
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Additional info for Transformation - A Fundamental Idea of Mathematics Education
Example text
For example, in 1853 Carl Friedrich Collmann, teacher of mathematics at the Ratsgymnasium Bielefeld, published a textbook with a lengthy philosophically oriented introduction on the nature of mathematics. When contemplating things we are able to ignore and negate special properties of them, and by this we can so to speak pull off or abstract one or several features from things… The science which is concerned with considering relations of form and position and abstract quantities is called mathematics.
4). Thus, the whole solid has volume V ( y) = π r ( 2ry − y 2 ) − 2 y 3 + r 3 ; 3 For this function the equation of its secant line through the points II and I is formed. V2 − V1 f ( y2 ) − f ( y1 ) = y2 − y1 y2 − y1 Or V2 − V1 π r (2ry2 − y2 2 − 2ry1 + y12 ) + r 3 − r 3 − 2 y23 + 2 y13 = y2 − y1 3 y2 − y1 V2 − V1 π r (2r ( y2 − y1 ) − ( y2 2 − y12 ) − 2( y23 − y13 ) = ; y2 − y1 3 y2 − y1 V2 − V1 π 2 2 = r (2r − ( y2 + y1 ) − 2( y2 + y2 y1 + y1 ) y2 − y1 3 This is the equation of the secant; if point II approaches point I, then the secant changes to the tangent.
The elaboration of a theory-based framework for analyzing and comparing mathematics textbooks at the upper secondary level and the first semester at universities. The presentation of results of feasibility studies to show that this framework allows a reliable data collection for textbook comparisons. The feasibility studies were conducted with a small number of textbooks. This means particularly that we cannot yet report clear results concerning differences between textbooks at school and at university.