Calculus in European classrooms: curriculum and teaching in different educational and cultural contexts

Törner, Günter; Potari, Despina; Zachariades, Theodossios

doi:10.1007/s11858-014-0612-0

Cited by 26 publications

(20 citation statements)

References 30 publications

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“…In school, mathematical concepts are typically presented by examples, which are often based on visual representations or informal situations. These examples allow students to create a mental image and try to avoid reinforcing misconceptions typically held by students (Tall 1992;Törner et al 2014). Based on such examples, a formal description of properties (sometimes even a formal definition) might be introduced or developed.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Deeken

Neumann

Heinze

2019

Int. J. Res. Undergrad. Math. Ed.

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In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question whether there is a consensus among university instructors. The main goal of this study is therefore to describe the expected mathematical prerequisites for new STEM undergraduates. We conducted a Delphi study with German university instructors for first semester mathematics courses in STEM programs. The participants identified 179 prerequisites addressing: (1) mathematical content, (2) mathematical processes, (3) views about the nature of mathematics, and (4) personal characteristics. For 140 of these prerequisites there was a consensus regarding their necessity among the university instructors. The expected mathematical prerequisites are mainly on a basic level and do not require formalistic or abstract mathematical knowledge or abilities.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Deeken

Neumann

Heinze

2019

Int. J. Res. Undergrad. Math. Ed.

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“…The relational-visual category fulfils three components of the type of visual reasoning, namely the visual display through sketches of graphs or diagrams, the presence of visual actions by looking at problem situations can be represented graphically or diagrams, and the visual purpose that visualization results can reach a solution (Natsheh & Karsenty, 2014). Also, graphical representations and diagrams play an important role in developing mental visualization which is the basis for building formal understanding in depth (Delice & Kertil, 2013;Hoffkamp, 2011;Törner, Potari, & Zachariades, 2014).…”

Section: Category Of Reversible Reasoningmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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“…He showed the dominance of an algebraic approach to teaching differential equations in the upper secondary school in France and the lack of numeric and qualitative study of ODEs. Törner et al (2014) provides a first overview of the landscape with respect to Calculus teaching in European classrooms, an area where research is very limited. Czocher et al (2013) investigated topics in introductory differential equations in the US, and their relation with the knowledge that students are expected to retain from their Calculus courses.…”

Section: Textbooks and Calculus Materialsmentioning

confidence: 99%

Teaching and Learning of Calculus

Bressoud

Ghedamsi²,

Martínez-Luaces

et al. 2016

ICME-13 Topical Surveys

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Calculus in European classrooms: curriculum and teaching in different educational and cultural contexts

Cited by 26 publications

References 30 publications

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Teaching and Learning of Calculus

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