scholarly journals Conceptual Analysis of Derivative as a Rate of Change and Analysis of the Mathematics Textbooks

2021 ◽  
pp. 545-568
Author(s):  
Mahmut KERTİL
2010 ◽  
Vol 103 (7) ◽  
pp. 519-524
Author(s):  
Dawn Teuscher ◽  
Robert E. Reys

How do we mathematics teachers introduce the concepts of slope, rate of change, and steepness in our classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? Here we report the results of a study of high school Advanced Placement (AP) Calculus students who displayed misunderstandings about the meaning of these three concepts. We then share an example of a typical rate-of-change problem commonly found in mathematics textbooks that may contribute to the development of these misconceptions. Finally, we provide a classroom task that supports the discussion of the differences among these three concepts, and we ask readers to reflect on ways to help students differentiate among them.


2020 ◽  
Vol 653 ◽  
pp. 121-129
Author(s):  
RB Taylor ◽  
S Patke

Small mobile crustaceans are abundant on seaweeds. Many of these crustaceans rapidly abandon their host if it is detached from the seafloor and floats towards the surface, but the trigger for this ‘bailout’ behaviour is unknown. We tested 2 potential cues, i.e. rapid change in light and rapid change in water pressure, using >1 mm epifauna on the brown seaweed Carpophyllum plumosum as a model system. Bailout occurred in response to reduced water pressure, but not to changing light, as (1) bailout occurred at similar rates in light and dark, (2) bailout occurred on the seafloor when water pressure was reduced within a transparent chamber by the equivalent of ~0.5 m depth or more, and (3) little bailout occurred when water pressure was held constant within the chamber while seaweeds were raised to the surface. Increase in pressure (simulating sinking) did not induce bailout. The rate of bailout increased with increasing magnitude of pressure reduction but was not influenced greatly by the rate of change of pressure within the range tested (up to an equivalent of 0.4 m depth s-1). The use of pressure rather than light as a cue for bailout is consistent with the need for seaweed-associated crustaceans to rapidly abandon a detached host and relocate to suitable habitat during both day and night.


Author(s):  
Augustin Fragnière

It is now widely acknowledged that global environmental problems raise pressing social and political issues, but relatively little philosophical attention has been paid to their bearing on the concept of liberty. This must surprise us, because the question of whether environmental policies are at odds with individual liberty is bound to be controversial in the political arena. First, this article explains why a thorough philosophical debate about the relation between liberty and environmental constraints is needed. Second, based on Philip Pettit’s typology of liberty, it assesses how different conceptions of liberty fare in a context of stringent ecological limits. Indeed, a simple conceptual analysis shows that some conceptions of liberty are more compatible than others with such limits, and with the policies necessary to avoid overshooting them. The article concludes that Pettit’s conception of liberty as non-domination is more compatible with the existence of stringent ecological limits than the two alternatives considered.


1960 ◽  
Vol 8 (3) ◽  
pp. 241-253 ◽  
Author(s):  
Edward A. Suchman
Keyword(s):  

Author(s):  
Dubravka Glasnović Gracin

AbstractA mathematics textbook can be described as an officially authorized and pedagogically designed mathematics book written to provide mathematical knowledge to students. This description suggests the authority of the textbook - because it has been authorized by an administrative source and because it deals with authorized knowledge. This paper provides an overview of research on mathematics textbooks. The emphasis is on questions concerning the extent to which and how textbooks are used in mathematics education in Croatia and in the world.Research results show that mathematics textbooks are widely used in mathematics education worldwide. This finding points to the need for research on the content and structure of textbooks. Such studies are combined with the associated results on how textbooks are used in the classroom and which methods teachers apply in using textbooks in mathematics education. The results of the empirical studies show that teachers use textbooks for lesson preparation and pupils use mathematics textbooks for exercises to a great extent. These results imply that such an important role of textbooks in mathematics education deserves additional attention, with the goal of understanding and improving mathematics education.Key words: mathematics education; overview; research on textbook---SažetakMatematički udžbenik može se opisati kao službeno autorizirana i pedagoki osmiljena matematička knjiga napisana s ciljem da učenicima ponudi matematičke sadržaje. Taj opis sugerira autoritet udžbenika jer ga je autorizirao administrativni izvor i jer sadrži autorizirano znanje. Ovaj članak daje pregled istraživanja matematičkih udžbenika, a naglasak je na pitanjima u kojoj mjeri i kako se udžbenici koriste u nastavi matematike u Hrvatskoj i u svijetu.Rezultati raznih istraživanja pokazuju da se udžbenici u velikoj mjeri koriste u nastavi matematike irom svijeta. Taj nalaz ukazuje na potrebu za istraživanjem sadržaja i strukture matematičkih udžbenika. Uz to, prikazani su rezultati istraživanja o tome na koji se način udžbenici koriste u razredu i koje metode nastavnici prakticiraju prilikom upotrebe udžbenika na nastavi. Rezultati empirijskih studija pokazuju da nastavnici udžbenike većinom koriste za pripremu nastavnog sata, a učenici udžbenike koriste u najvećoj mjeri za vježbanje. Ti rezultati ukazuju na to da tako važna uloga udžbenika u matematičkom obrazovanju zaslužuje dodatnu pažnju s ciljem razumijevanja i poboljanja nastave matematike.Ključne riječi: istraživanje udžbenika; nastava matematike; pregled.


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