The many facets of a definition: The case of periodicity

Dormolen, Joop Van; Zaslavsky, Orit

doi:10.1016/s0732-3123(03)00006-3

Cited by 52 publications

(31 citation statements)

References 5 publications

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“…Van Dormolen & Zaslavsky, 2003), students' beliefs about them (Zaslavsky & Shir, 2005), and students' guided collaborative development of definitions in contexts new to them (Larsen & Zandieh, 2008;Zandieh & Rasmussen, 2010). Studies have suggested that students who spontaneously generate examples in response to new definitions later perform better on tasks involving the defined concepts (Dahlberg & Housman, 1997), and there has been much recent discussion of the way in which example generation tasks might help students to modify their example spaces so that these more closely coincide with the extensions of the defined concepts (Mason, 2002;Watson & Mason, 2005;Zazkis, Liljedahl & Chernoff, 2008;Zazkis & Leikin, 2008).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Classification and Concept Consistency

Alcock

Simpson

2011

Canadian Journal of Science, Mathematics and Technology Educati

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This paper investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accepted definition, but does not necessarily capture the more basic notion that there should be a fixed basis for classification. We examine students' classification of real sequences before and after exposure to definitions of 'increasing' and 'decreasing'; we develop an abductive 'plausible explanations' method to estimate the consistency within the participants' responses and suggest that this provides evidence that many students may lack what we call 'concept consistency'.Running head: Classification and Concept Consistency

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Section: Theoretical Backgroundmentioning

confidence: 99%

Classification and Concept Consistency

Alcock

Simpson

2011

Canadian Journal of Science, Mathematics and Technology Educati

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“…Basically, it was similar to the "copying" approach of Van Dormolen and Zaslavsky (2003) presented earlier. …”

Section: Le-23mentioning

confidence: 94%

“…For example, with respect to an irrational number, we hoped to expand beyond the common view that an irrational number is either a root of a prime number (e.g., 5 ) or a transcendental number (e.g., π). For a periodic function, we hoped to expand beyond the common view that periodic functions are solely or mostly trigonometric functions (Van Dormolen and Zaslavsky 2003). We were aware that this kind of task may provoke additional mathematical subtleties and unforeseen claims and ideas raised by the learners.…”

Section: Design Considerations For Eliciting Learners' Example-generamentioning

confidence: 99%

“…Van Dormolen and Zaslavsky (2003) discuss the meta-concept of a mathematical definition and illustrate it with the notion of a periodic function. They suggest the following pseudo-definition (p. 92, ibid.…”

Section: Case 2: Generating Examples Of a Periodic Functionmentioning

confidence: 99%

“…Some verified this based on the symbolic representation of the function and some used its graphical representation. These different approaches evoked a comparison between these representations and set the grounds for the originally intended approach described in Van Dormolen and Zaslavsky (2003), as cited earlier. Interestingly, while periodicity lends itself naturally to visual representations, this idea did not occur spontaneously.…”

Section: Le-23 8 Andmentioning

confidence: 99%

See 2 more Smart Citations

Example-Generation as Indicator and Catalyst of Mathematical and Pedagogical Understandings

Zaslavsky

Zodik

2014

Advances in Mathematics Education

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This chapter examines the activities of example-generation and exampleverification from both the teaching and learning perspectives. We closely examine how engaging learners in generating and verifying examples of a particular mathematical concept as a group activity serves both as an indicator of learners' understandings and a catalyst for enhancing their understanding and expanding their example space that is associated with the particular concept. We present two cases that illustrate how the mathematics instruction may look when classroom activities and discussions build on example-generation and example-verification -the first case focuses on the concept of an irrational number and the second on the notion of a periodic function. The learners in these cases are in-service secondary mathematics teachers (MTLs), and the teacher is a mathematics teacher educator (MTE). We show how this kind of learning environment lends itself naturally to genuine opportunities for learners to engage in meaningful mathematics, to share and challenge their thinking, and to sense the need for unpacking mathematical subtleties regarding definitions and ideas. For practicing and prospective mathe matics teachers, engaging in such activity and experiencing the potential learning opportunity that it offers is also likely to convince them to implement this approach in their classrooms.

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An instructional definition and assessment rubric for bioinformatics instruction

Tapprich

Reichart

Simon

et al. 2020

Biochem Molecular Bio Educ

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The lack of an instructional definition of bioinformatics delays its effective integration into biology coursework. Using an iterative process, our team of biologists, a mathematician/computer scientist, and a bioinformatician together with an educational evaluation and assessment specialist, developed an instructional definition of the discipline: Bioinformatics is “an interdisciplinary field that is concerned with the development and application of algorithms that analyze biological data to investigate the structure and function of biological polymers and their relationships to living systems.” The field is defined in terms of its two primary foundational disciplines, biology and computer science, and its interdisciplinary nature. At the same time, we also created a rubric for assessing open‐ended responses to a prompt about what bioinformatics is and how it is used. The rubric has been shown to be reliable in successive rounds of testing using both common percent agreement (89.7%) and intraclass correlation coefficient (0.620) calculations. We offer the definition and rubric to life sciences instructors to help further integrate bioinformatics into biology instruction, as well as for fostering further educational research projects.

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The many facets of a definition: The case of periodicity

Cited by 52 publications

References 5 publications

Classification and Concept Consistency

Classification and Concept Consistency

Example-Generation as Indicator and Catalyst of Mathematical and Pedagogical Understandings

An instructional definition and assessment rubric for bioinformatics instruction

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