History of Teaching Calculus

Zuccheri, Luciana; Zudini, Verena

doi:10.1007/978-1-4614-9155-2_24

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…17 Further, in the period from 1918 to 1923, these teachers contributed to a process of adapting the mathematics teaching in the secondary schools of Trieste and of the surrounding region (called ''Venezia Giulia'') to that of the Kingdom of Italy. 18 16 The period of the beginning of the twentieth century, before the First World War, was crucial for the innovation of the teaching methods in mathematics instruction as well as for the introduction of new subjects in the secondary school programmes, first of all differential and integral calculus (see Zuccheri and Zudini 2014). In Jacob's opinion, the introduction of infinitesimal calculus in the new Austrian school curricula (with the Marchet Reform, which came into effect in the 1909/1910 school year) left various questions unanswered about aims, timing and depth of the treatment of the subject (Jacob 1913, p. 64).…”

Section: A Historical Example Of Application Of Mach's Ideas In Mathementioning

confidence: 99%

The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education

Zudini

Zuccheri

2016

Sci & Educ

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A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the ‘‘Jacob method’’ after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to ‘‘muscular activity’’ in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings,\ud equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the ‘‘theory of embodied mathematics’’, the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the ‘‘Jacob method’’ may be considered a historical example of didactical application of analogous ideas

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Section: A Historical Example Of Application Of Mach's Ideas In Mathementioning

confidence: 99%

The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education

Zudini

Zuccheri

2016

Sci & Educ

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“…Finally, students who are successful in these earlier mathematics courses may begin the study of calculus, which is typically restricted to advanced high school and college students. Calculus can be thought of the study of change in mathematical quantities, typically encompassing knowledge of derivatives, integrals, and limits (Zuccheri & Zudini, 2014).…”

Section: The Nature Of Secondary Mathematical Learningmentioning

confidence: 99%

Spatial Skills, Reasoning, and Mathematics

Newcombe¹,

Booth²,

Gunderson³

2019

The Cambridge Handbook of Cognition and Education

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Chapter for the Cambridge Handbook on Cognition and EducationModern technological societies are built on a foundation of mathematics. We could not have extensive trade without book-keeping-we would be stuck with a barter system. We could not build our long bridges without calculation --we would still be relying on ferries to cross bodies of water. We have made impressive improvements in agricultural science in the past century based in part on experiments using the statistics of "split plots". The examples could be multiplied but the lesson is clear. Given the importance of numeracy, there is good reason for educational systems to strive to teach mathematics effectively. Even though many children in contemporary schools succeed in learning to calculate, many others struggle or progress slowly, and even more never achieve the levels required for full participation in our technological society. There are many reasons for this situation, and many proposed remedies. One potential way to improve mathematics education involves harvesting our growing understanding of how human minds and brains process quantitative information, and how these processes develop.

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“…Enhancing calculus teaching has been the focus of many mathematics education reforms worldwide (Zuccheri & Zudini, 2014). In the United States, concerns regarding low passing rates, students not working on 'higher-level' problems (Ferrini-Mundy & Graham, 1991), and 'widespread weaknesses in numerical and symbolic manipulations' (Ruane, 2001, p. 1) were raised for the first time at the Tulane University Conference in 1986 (Douglas, 1986).…”

Section: Introductionmentioning

confidence: 99%