Using dynamic tools to develop an understanding of the fundamental ideas of calculus

Calculus limits involving infinity: the role of students’ informal dynamic reasoning

“…[18,38]). The results of this study further recommend that many students in first-semester calculus, who are largely bound for science and engineering, [22] do not necessarily need to encounter the formal definitions of the limit at all, but rather may be better served by developing a strong, robust dynamic reasoning component to their limit understanding.…”

“…The results of this study further recommend that many students in first-semester calculus, who are largely bound for science and engineering, [22] do not necessarily need to encounter the formal definitions of the limit at all, but rather may be better served by developing a strong, robust dynamic reasoning component to their limit understanding. That is, as opposed to being something that needs to be eventually replaced with the superior formal concept of a limit, the dynamic conception may be cognitively useful enough that it could be considered the end goal of student understanding in first-semester calculus, not simply the entry point to more 'formal' understandings (as in [15,16,18,19]). …”

“…Some recent studies which consider informal and formal reasoning appear to take informal, dynamic thinking as a starting point for leading students to the 'gold standard' of the formal definition of the limit (see [14][15][16][17][18]). This study, by contrast, explicitly moves away from the assumption that the formal definition of the limit must be an end-goal objective for first-year calculus students at all, since many are intending on majors outside of pure mathematics.…”

“…Another side to the research literature has focused more explicitly on students' understanding of the formal definition of the limit and how to help students advance to this understanding. [14][15][16][17][18][19] In reviewing the literature, most of the research is dedicated to student understanding of the specific limit structures lim x→a f (x) = L or lim n→∞ a n = L. In other words, when discussing real-valued functions, f(x), the studies tend to focus on f(x) approaching a finite limit L as x approaches a finite number a (e.g. [4,9,13,17,19]).…”

Ensino e Aprendizagem do Teorema Fundamental do Cálculo: algumas reflexões a partir de uma revisão sistemática de literatura<br>Teaching and Learning of the Fundamental Theorem of Calculus: some reflections from a systematic literature review

“…Por mais que alguns pesquisadores (ANACLETO, 2007;BRESSOUD, 2011;CAMPOS, 2007;GRANDE, 2013;PONCE-CAMPUZANO, 2013;PONCE-CAMPUZANO;MALDONADO-AGUILAR, 2014;VAJIAC;VAJIAC, 2008) Entretanto, as pesquisas analisadas (GRANDE, 2013;KOUROPATOV;DREYFUS, 2014;PONCE-CAMPUZANO, 2013;VERZOSA et al, 2014) mostram que as tecnologias digitais aliadas à prática docente podem contribuir para a compreensão dos conceitos envolvidos no TFC. Esses pesquisadores trabalharam com os softwares Maple e Geogebra, além de applets e vídeos, enfatizando que as tecnologias digitais promovem uma representação gráfica e numérica dinâmica, permitindo que os estudantes explorem o TFC sob múltiplas perspectivas (VERZOSA et al, 2014).…”