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The integral as accumulation function approach: A proposal of a learning sequence for collaborative reasoning

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11th grade students’ mathematical thinking and reasoning. The results show that the integral-as-accumulation-function has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.

Reasoning like a doctor or like a nurse? A systematic integrative review

When physicians and nurses are looking at the same patient, they may not see the same picture. If assuming that the clinical reasoning of both professions is alike and ignoring possible differences, aspects essential for care can be overlooked. Understanding the multifaceted concept of clinical reasoning of both professions may provide insight into the nature and purpose of their practices and benefit patient care, education and research. We aimed to identify, compare and contrast the documented features of clinical reasoning of physicians and nurses through the lens of layered analysis and to conduct a simultaneous concept analysis. The protocol of this systematic integrative review was published doi: 10.1136/bmjopen-2021-049862. A comprehensive search was performed in four databases (PubMed, CINAHL, Psychinfo, and Web of Science) from 30th March 2020 to 27th May 2020. A total of 69 Empirical and theoretical journal articles about clinical reasoning of practitioners were included: 27 nursing, 37 medical, and five combining both perspectives. Two reviewers screened the identified papers for eligibility and assessed the quality of the methodologically diverse articles. We used an onion model, based on three layers: Philosophy, Principles, and Techniques to extract and organize the data. Commonalities and differences were identified on professional paradigms, theories, intentions, content, antecedents, attributes, outcomes, and contextual factors. The detected philosophical differences were located on a care-cure and subjective-objective continuum. We observed four principle contrasts: a broad or narrow focus, consideration of the patient as such or of the patient and his relatives, hypotheses to explain or to understand, and argumentation based on causality or association. In the technical layer a difference in the professional concepts of diagnosis and the degree of patient involvement in the reasoning process were perceived. Clinical reasoning can be analysed by breaking it down into layers, and the onion model resulted in detailed features. Subsequently insight was obtained in the differences between nursing and medical reasoning. The origin of these differences is in the philosophical layer (professional paradigms, intentions). This review can be used as a first step toward gaining a better understanding and collaboration in patient care, education and research across the nursing and medical professions.

Developing self evaluation of critical thinking and clinical reasoning skills

Games to support teaching clinical reasoning in health professions education: a scoping review

Introduction: Given the complexity of teaching clinical reasoning to (future) healthcare professionals, the utilization of serious games has become popular for supporting clinical reasoning education. This scoping review outlines games designed to support teaching clinical reasoning in health professions education, with a specific emphasis on their alignment with the 8-step clinical reasoning cycle and the reflective practice framework, fundamental for effective learning. Methods: A scoping review using systematic searches across seven databases (PubMed, CINAHL, ERIC, PsycINFO, Scopus, Web of Science, and Embase) was conducted. Game characteristics, technical requirements, and incorporation of clinical reasoning cycle steps were analyzed. Additional game information was obtained from the authors. Results: Nineteen unique games emerged, primarily simulation and escape room genres. Most games incorporated the following clinical reasoning steps: patient consideration (step 1), cue collection (step 2), intervention (step 6), and outcome evaluation (step 7). Processing information (step 3) and understanding the patient’s problem (step 4) were less prevalent, while goal setting (step 5) and reflection (step 8) were least integrated. Conclusion: All serious games reviewed show potential for improving clinical reasoning skills, but thoughtful alignment with learning objectives and contextual factors is vital. While this study aids health professions educators in understanding how games may support teaching of clinical reasoning, further research is needed to optimize their effective use in education. Notably, most games lack explicit incorporation of all clinical reasoning cycle steps, especially reflection, limiting its role in reflective practice. Hence, we recommend prioritizing a systematic clinical reasoning model with explicit reflective steps when using serious games for teaching clinical reasoning.

When students tackle grammatical problems

When teaching grammar, one of the biggest challenges teachers face is how to make their students achieve conceptual understanding. Some scholars have argued that metaconcepts from theoretical linguistics should be used to pedagogically and conceptually enrich traditional L1 grammar teaching, generating more opportunities for conceptual understanding. However, no empirical evidence exists to support this theoretical position. The current study is the first to explore the role of linguistic metaconcepts in the grammatical reasoning of university students of Dutch Language and Literature. Its goal was to gain a better understanding of the characteristics of students’ grammatical conceptual knowledge and reasoning and to investigate whether students’ reasoning benefits from an intervention that related linguistic metaconcepts to concepts from traditional grammar. Results indicate, among other things, that using explicit linguistic metaconcepts and explicit concepts from traditional grammar is a powerful contributor to the quality of students’ grammatical reasoning. Moreover, the intervention significantly improved students’ use of linguistic metaconcepts.

Analogical Reasoning in Biomimicry Design Education

“Teaching is both an art and a science” (Harrison & Coll, 2008 p.1). Good teaching excites students and cultivates their curiosity to learn more than they are asked. But what if students’ blank faces tell you that the teaching did not land, what can you do? Using an analogy or metaphor to explain the principle helps students visualize and comprehend the knowledge of difficult, abstract concepts by making it familiar. The National Academy of Engineers issued a report in 2008 emphasizing the need for design engineers to develop 21st century skills, such as ingenuity and creativity, and to create innovative products and markets. However, designers have a hard time ignoring evident constraints on their concepts during their design process. This is especially difficult for novice designers when attempting to use analogical reasoning (Osborn, 1963; Hey et al. 2008). Hey et al. explains how the multitude of design considerations is even more difficult for novice as compared to expert designers who are more able to focus on the important features of a problem. Kolodner (1997) iterates how novice designers have difficulty sifting through the mass of information they encounter. They need help with the transfer of knowledge that analogical reasoning requires. When students can clearly extract and articulate what they have learned, this helps them to internalize this. Biomimicry education teaches the clear extraction and articulation while learning to decipher and transfer function analogies from biology to design. This transfer can also improve reasoning when solving problems (Wu and Weng, 2013), reacting to the challenge in a more ‘out-of-the-box’ manner (Yang et al. 2015). However, not being able to fully understand this “conceptual leap between biology and design” in an accurate manner, is sited as a key obstacle of this field (Rowland, 2017; Rovalo and McCardle 2019, p. 1). Therefore, didactics on how to teach this analogical leap to overcome the hurdles is essential. There is insufficient research on the effectivity of biomimicry education in design to help establish ‘best practices’. This thesis offers advice to fill this pedagogical gap to find out how to overcome the obstacle of analogical reasoning for novice designers, while practicing biomimicry. The contribution to science is a not earlier tested methodology that leads to a clearer understanding of the translation of biological strategies and mechanisms found in scientific research. This translation from biology to design in visual and textual manner, is called the Abstracted Design Principle (ADP) and is introduced and explained in detail in chapters 4, 5 and 6 of this thesis. Together with the proposed instructions, we sketch the net-gain of positive mind-set for novice designers on their path to design for a sustainable future.