Learning and Teaching of Calculus

The Teaching and Learning of Calculus offers a fresh perspective on the challenges and difficulties of effectively engaging students. The authors argue convincingly that many of the difficulties in learning calculus result from ways students understand, or fail to understand, fundamental mathematical concepts in primary and early secondary school and offer alternative ways of understanding and thinking about early mathematics concepts that have natural extensions to learning calculus.



Areas covered include: -





What is calculus?



Foundational mathematical understandings



Concepts of calculus, including limits and approximations, rate of change and accumulation



Integration and implicit differentiation



Teaching, learning and curriculum



Throughout the text the authors show that teaching often fails because many calculus concepts are taught in a way that makes it difficult for students to connect ideas that they study in calculus with ideas that they already have--thus leading students to lean on memorization as a way to cope with instruction that makes little sense to them.

This important book proposes new ways of thinking about the ideas of calculus that will guide maths researchers, teachers and teacher educators in rethinking maths instruction.



The authors conclude by describing the ways in which many current practices in calculus curriculum and instruction are anathemas to high quality learning. They argue for a particular style of integrated active intellectual engagement that students must experience and important conceptual ideas with which students must engage if they are to build coherent, long lasting understandings of calculus that will support using it in other disciplines and supply a base for future mathematical learning.

　

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of advanced textbooks for teacher education which aims to advance the teaching of maths by integrating mathematics content teaching with the broader research and theoretical base of mathematics education.

Predarea si invatarea calculului ofera o perspectiva noua asupra provocarilor si dificultatilor implicarii eficiente a elevilor. Autorii sustin convingator ca multe dintre dificultatile in invatarea calculului rezulta din modurile in care elevii inteleg sau nu reusesc sa inteleaga conceptele matematice fundamentale din scoala primara si gimnaziala timpurie si ofera modalitati alternative de intelegere si gandire a conceptelor matematice timpurii care au extensii naturale invatarii Domeniile acoperite includ: -Ce este calculul? Intelegeri matematice fundamentale Concepte de calcul, inclusiv limite si aproximari, rata de schimbare si acumulare Integrare si diferentiere implicita Invatare, invatare si curriculum In tot textul, autorii arata ca predarea esueaza adesea, deoarece multe concepte de calcul sunt predate in o modalitate care face dificila pentru studenti sa conecteze ideile pe care le studiaza in calcul cu ideile pe care le au deja - ducandu-i astfel pe studenti sa se sprijine pe memorare ca o modalitate de a face fata instructiunilor care nu prea au sens pentru ei. Aceasta carte importanta propune noi moduri de gandire despre th Idei de calcul care ii vor ghida pe cercetatorii, profesorii si profesorii de matematica in regandirea instructiunilor matematice. Autorii concluzioneaza prin descrierea modurilor in care multe practici actuale in curriculum si instructiuni de calcul sunt anatemele invatarii de inalta calitate.