How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling

Park, JinHyeong; Lee, Kyeong-Hwa

doi:10.29333/ejmste/92557

Cited by 4 publications

(6 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this article, we argue that abductive and deductive reasoning are related parts within scientific reasoning regarding model construction and model application. The theoretical considerations of abductive reasoning in modeling are supported by empirical work in mathematics [20] and geography [12,21,22]. Additionally, we give some insight into learners' performance in modeling processes which support abductive reasoning being a part of modeling competence within scientific reasoning.…”

Section: Introductionmentioning

confidence: 87%

“…For geoscience, Oh established a close connection between abduction and modeling (modeling-based abductive reasoning) [21,22] relating to research by Clement (addressing the solution of physical problems through abductive reasoning in modeling) [12]. Furthermore, Park and Lee point to the central role of abductive reasoning in mathematical modeling [20]. These studies rather focus on the role of abductive reasoning for constructing technically appropriate models in terms of content knowledge than on methodological (procedural and epistemic) knowledge as part of scientific reasoning competencies.…”

Section: State Of Researchmentioning

confidence: 99%

See 1 more Smart Citation

Modeling as Scientific Reasoning—The Role of Abductive Reasoning for Modeling Competence

2021

View full text Add to dashboard Cite

While the hypothetico-deductive approach, which includes inductive and deductive reasoning, is largely recognized in scientific reasoning, there is not much focus on abductive reasoning. Abductive reasoning describes the theory-based attempt of explaining a phenomenon by a cause. By integrating abductive reasoning into a framework for modeling competence, we strengthen the idea of modeling being a key practice of science. The framework for modeling competence theoretically describes competence levels structuring the modeling process into model construction and model application. The aim of this theoretical paper is to extend the framework for modeling competence by including abductive reasoning, with impact on the whole modeling process. Abductive reasoning can be understood as knowledge expanding in the process of model construction. In combination with deductive reasoning in model application, such inferences might enrich modeling processes. Abductive reasoning to explain a phenomenon from the best fitting guess is important for model construction and may foster the deduction of hypotheses from the model and further testing them empirically. Recent studies and examples of learners’ performance in modeling processes support abductive reasoning being a part of modeling competence within scientific reasoning. The extended framework can be used for teaching and learning to foster scientific reasoning competences within modeling processes.

show abstract

Section: Introductionmentioning

confidence: 87%

Section: State Of Researchmentioning

confidence: 99%

Modeling as Scientific Reasoning—The Role of Abductive Reasoning for Modeling Competence

2021

View full text Add to dashboard Cite

show abstract

“…Meanwhile, someone who uses overcoded abductive reasoning often makes guesses that are automatic or semi-automatic. It makes this reasoning less likely to support productive mathematical inquiry (Bellucci, 2018;Eco, 1983;Park & Lee, 2018). Therefore, someone who experiences overcoded abductive reasoning will tend to do the process of assimilation that does not produce a new scheme.…”

Section: S2's Answer In Episodementioning

confidence: 99%

“…In this case, it means that S2 has revised its abductive reasoning. Park and Kim (2017) and Park and Lee (2018) told that the revision of abductive reasoning also occurs in sample generalisation and modelling. The result may be a modification to the recognition template and is called generalising assimilation, even though it is also an accommodation (Norton, 2008;Steffe, 2002).…”

Section: S2's Answer In Episodementioning

confidence: 99%

“…Many researchers assume that abductive reasoning takes many roles in the development of science. These roles include building hypotheses (Kwon et al, 2006), generalizing models (Park & Lee, 2016), supporting the induction process (Rivera & Becker, 2007), increasing reasoning ability (Shodikin, 2017), generating new ideas (O'Reilly, 2016), building new schemes (Norton, 2008), solving mathematical problems (Cifarelli, 2016), being the main trigger for mathematical inquiry (Park & Lee, 2018), making claims about the validity of questions (Wu et al, 2016), and diagnosing medical errors (Velázquez-Quesada et al, 2013). Meanwhile, abductive reasoning itself is conjectural reasoning, whose opinions or conclusions are obtained based on incomplete information, where the conjecture itself is characterised as explicit statements that may be "right or wrong" (Norton, 2008).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Students’ Thinking Process When Using Abductive Reasoning in Problem Solving

et al. 2021

View full text Add to dashboard Cite

Background: Abductive reasoning is the process of making conjectures to explain surprising observations. Although this conjecture is not certain to be true, in solving a problem, this reasoning is very helpful to determine the best solution strategy. Objectives: The study aims to investigate whether all types of abductive reasoning lead to the formation of new schemes. Design: This research used a qualitative approach with a descriptive exploratory design. Setting and Participants: A total of 41 students of the research degree in mathematics education programme were involved in solving a task. Then, eight of them were chosen for an in-depth interview, representing the undercoded and overcoded abductive reasoning types. Data collection and analysis: The data collected were the results of the students' works and task-based interviews. Piaget's schema theory was used to analyse students' thinking processes using abductive reasoning. The analysis was carried out at all steps of problem solving, namely understanding the problem, devising a plan, carrying out the plan, and looking back. Results: Those who carried out overcoded abductive reasoning used this reasoning to determine problem solving strategies. Meanwhile, those who carried out undercoded abductive reasoning used it to determine problem solving strategies as well as to form new schemes. Conclusions: The results showed that students who did abductive reasoning did not always produce new schemes. This study also notes that the truth value of answers from the application of abductive reasoning in problem solving was open and the importance of the look back step to perform accommodation.

show abstract

Kompetenzmodell der Modellierkompetenz – Die Rolle abduktiven Schließens beim Modellieren

Krüger

Belzen

2021

ZfDN

View full text Add to dashboard Cite

ZusammenfassungIn diesem theoretischen Beitrag wird das Kompetenzmodell der Modellkompetenz durch Integration der Theorie des abduktiven Schließens ausdifferenziert und als Kompetenzmodell der Modellierkompetenz präsentiert. Abduktives Schließen in der Biologie heißt, ein biologisches Phänomen durch einen kausalen Rückschluss theoriebasiert oder kreativ bestmöglich zu erklären. Kreativität innoviert im Sinne der Erkenntnisgewinnung durch neues theoretisches Wissen den Prozess des Modellierens. Im ausdifferenzierten Kompetenzmodell wird abduktiv schließendes Erklären als neues Niveau hinzugefügt. Beim abduktiv schließenden Erklären bildet die Herstellung eines Modells die Basis für einen sich möglicherweise anschließenden deduktiven Überprüfungsprozess. Dieser umfasst bei der Anwendung des Modells das Ableiten von Hypothesen aus dem Modell und deren Testung. Bei dieser Anwendung eines Modells als Forschungswerkzeug stehen, im Gegensatz zur Anwendung als verständniserzeugendes Medium, prozedurale sowie epistemische Aspekte des Modellierens im Vordergrund. Fachdidaktische Arbeiten aus verschiedenen Disziplinen weisen auf die Bedeutung des abduktiven Schließens beim Modellieren hin. Ausgehend davon stellt sich die Frage, ob und wie abduktives Schließen beim Modellieren auf der Basis von theoretischem Fachwissen oder kreativer Innovation die Bedeutung eines Modells als Forschungswerkzeug hervorhebt.Die Berücksichtigung des abduktiven Schließens beim Modellieren stößt Vorhaben in drei Forschungsbereichen an: (1) Bezogen auf Grundlagenforschung gilt es zu klären, inwieweit die erfolgreiche Modellierung eines Phänomens von theoretischen Vorkenntnissen abhängt. (2) Bezogen auf die Erfassung von Modellierkompetenz ist zu prüfen, inwieweit unterschiedliche biologische Kontexte abduktives Schließen anregen. (3) Mit Blick auf eine Förderung von Modellierkompetenz ist zu untersuchen, inwieweit beim Modellieren biologisches Fachwissen für abduktives Schließen bei der Herstellung eines Modells dabei hilft, in eine deduktive Modellanwendung überzuleiten.

show abstract

How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling

Cited by 4 publications

References 12 publications

Modeling as Scientific Reasoning—The Role of Abductive Reasoning for Modeling Competence

Modeling as Scientific Reasoning—The Role of Abductive Reasoning for Modeling Competence

Students’ Thinking Process When Using Abductive Reasoning in Problem Solving

Kompetenzmodell der Modellierkompetenz – Die Rolle abduktiven Schließens beim Modellieren

Contact Info

Product

Resources

About