Measuring Mathematical Competences of Engineering Students at the Beginning of Their Studies

Neumann, Irene; Rösken-Winter, Bettina; Lehmann, Malte; Duchhardt, Christoph; Heinze, Aiso; Nickolaus, Reinhold

doi:10.1080/0161956x.2015.1068054

Cited by 17 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…13 Within that period findings from five other projects on test development conducted in Germany (funded by other entities) were published and have therefore been included in the sample. 9 The reason for this simplification is that, as a rule, reports on test development do not explore this issue in depth or even touch upon it. More specific differentiations are discussed below (Section 5).…”

Section: Procedures For Ensuring Content Validitymentioning

confidence: 99%

Ensuring content validity of psychological and educational tests – the role of experts

Beck

2020

FLR

View full text Add to dashboard Cite

Many test developers try to ensure the content validity of their tests by having external experts review the items, e.g. in terms of relevance, difficulty, or clarity. Although this approach is widely accepted, a closer look reveals several pitfalls need to be avoided if experts' advice is to be truly helpful. The purpose of this paper is to exemplarily describe and critically analyse widespread practices of involving experts to ensure the content validity of tests. First, I offer a classification of tasks that experts are given by test developers, as reported on in the respective literature. Second, taking an exploratory approach by means of a qualitative meta-analysis, I review a sample of reports on test development (N = 72) to identify the common current procedures for selecting and consulting experts. Results indicate that often the choice of experts seems to be somewhat arbitrary, the questions posed to experts lack precision, and the methods used to evaluate experts' feedback are questionable. Third, given these findings I explore in more depth what prerequisites are necessary for their contributions to be useful in ensuring the content validity of tests. Main results are (i) that test developers, contrary to some practice, should not ask for information that they can reliably ascertain themselves ("truth-apt statements"). (ii) Average values from the answers of the experts which are often calculated rarely provide reliable information about the quality of test items or a test. (iii) Making judgements about some aspects of the quality of test items (e.g. comprehensibility, plausibility of distractors) could lead experts to unreliable speculations. (iv)When several experts respond by giving incompatible or even contradictory answers, there is almost always no criterion enabling a decision between them. In conclusion, explicit guidelines on this matter need to be elaborated and standardised (above all, by the AERA, APA, and NCME "Standards").

show abstract

Section: Procedures For Ensuring Content Validitymentioning

confidence: 99%

Ensuring content validity of psychological and educational tests – the role of experts

Beck

2020

FLR

View full text Add to dashboard Cite

show abstract

“…Proofs in mathematics and derivations in physics are methods that use axioms or basic definitions, which are taken to be valid, to arrive at logical conclusions and inferences. In mathematics education, general deductive paths of problem-solving (Neumann et al 2015;Polya 1957;Schoenfeld 1985); more specifically, proofs have been investigated for a long time (for geometry, see Beckmann 1989;Reiss and Heinze 2004). Proofing is a complex endeavour; therefore, to inform teaching and learning processes, Boero (1999) developed a simplified process model for proofing, which is comprised of six steps: production of a conjecture; formulation of the statement according to shared textual conventions; exploration of the content of the conjecture; selection and enchaining of coherent, theoretical arguments into a deductive chain; organization of the enchained arguments into a proof; and approaching a formal proof.…”

Section: Solely Theory-orientated Paths Of Knowledge Acquisitionmentioning

confidence: 99%

A framework to foster problem-solving in STEM and computing education

Priemer

Eilerts

Filler

et al. 2019

Research in Science & Technological Education

Self Cite

View full text Add to dashboard Cite

Background: Recent developments in STEM and computer science education put a strong emphasis on twenty-first-century skills, such as solving authentic problems. These skills typically transcend single disciplines. Thus, problem-solving must be seen as a multidisciplinary challenge, and the corresponding practices and processes need to be described using an integrated framework. Purpose: We present a fine-grained, integrated, and interdisciplinary framework of problem-solving for education in STEM and computer science by cumulatively including ways of problem-solving from all of these domains. Thus, the framework serves as a tool box with a variety of options that are described by steps and processes for students to choose from. The framework can be used to develop competences in problem-solving. Sources of evidence: The framework was developed on the basis of a literature review. We included all prominent ways of domain-specific problem-solving in STEM and computer science, consisting mainly of empirically orientated approaches, such as inquiry in science, and solely theory-orientated approaches, such as proofs in mathematics. Main argument: Since there is an increasing demand for integrated STEM and computer science education when working on natural phenomena and authentic problems, a problem-solving framework exclusively covering the natural sciences or other single domains falls short. Conclusions: Our framework can support both practice and research by providing a common background that relates the ways, steps, processes, and activities of problem-solving in the different domains to one single common reference. In doing so, it can support teachers in explaining the multiple ways in which science problems can be solved and in constructing problems that reflect these numerous ways. STEM and computer science educational research can use the framework to develop competences of problem-solving at a finegrained level, to construct corresponding assessment tools, and to investigate under what conditions learning progressions can be achieved.

show abstract

“…This requires active participation of the learner, guided and challenged by a teacher or lecturer (Tall, 1991b). In keeping with this, engineering curricula contain much more than just technical and procedural requirements (albeit no formal proofs), as the examples from Neumann et al (2015) and Alpers et al (2013) show. The question remains if university mathematics courses focus on the entirety of competences, or on what is sometimes perceived as the foundation of mathematics, namely basic skills and techniques.…”

Section: ) In His Mathematicsmentioning

confidence: 96%

“…The SEFI framework finds reasons why a student should only pass if he or she has mastered every task from the first part, neglecting "minor 'numerical' errors" (Alpers et al, 2013, p. 70). Other research is dedicated to "Conceptions of Understanding in Engineering Mathematics" (Khiat, 2010), to exploring theoretical frameworks for mathematical competencies for engineering students (Hochmuth, Roesken-Winter, & Jaworski, 2013;Noss & Kent, 2002), or to developing measurement instruments for them (Neumann et al, 2015). In more or less complex applications, future engineers are expected to use mathematical models and techniques to solve open practical problems which can be described not only by the number of competencies 29 http://www.teaching-learning.eu/fileadmin/documents/News/Theses_AdvBoard _2011_news.pdf 30 Alpers et al (2013) are well aware of the problem of resources, however.…”

Section: ) In His Mathematicsmentioning

confidence: 99%

Learning Strategies in Engineering Mathematics

Griese

2017

Studien Zur Hochschuldidaktik Und Zum Lehren Und Lernen Mit Digitalen Medien in Der Mathematik Und in Der Statistik

View full text Add to dashboard Cite

Measuring Mathematical Competences of Engineering Students at the Beginning of Their Studies

Cited by 17 publications

References 11 publications

Ensuring content validity of psychological and educational tests – the role of experts

Ensuring content validity of psychological and educational tests – the role of experts

A framework to foster problem-solving in STEM and computing education

Learning Strategies in Engineering Mathematics

Contact Info

Product

Resources

About