The Teaching of Mathematics Using APOS Theory

Arnon, Ilana; Cottrill, Jim; Dubinsky, Ed; Oktaç, Asuman; Fuentes, Solange Roa; Trigueros, María; Weller, Kirk

doi:10.1007/978-1-4614-7966-6_5

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…However, this is in direct contradiction to the central statement of Newtonian mechanics and represents an intuitive concept that is retained by students even after successfully passing exams [ 14 ]. Therefore, the systematic exploration of intuitive concepts has already led to didactic adaptation of university teaching in some fields [ 15 ], [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

Intuitive concepts in internal medicine and their occurrence in undergraduate medical students in different semesters

Harendza

Herzog

2022

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Background: Dealing with errors in medical practice is of great importance for patient safety. In the natural sciences, intuitive concepts, so-called misconceptions, are increasingly coming into focus of teaching because they lead to a faulty understanding of contexts and thus to faulty scientific reasoning. In medicine, intuitive concepts still play a subordinate role. However, once intuitive concepts have been memorized, they can become firmly established and, under certain circumstances, lead to diagnostic and treatment errors in medical practice. The aim of this study was to identify potential intuitive concepts in internal medicine and to analyze their occurrence in medical students from different semesters. Methods: Eight internists from different subspecialties were asked about intuitive concepts by means of a structured interview. A total of 17 intuitive concepts were identified. Using these concepts, a multiple-choice test was created with 17 patient cases. For each case, there were four possible answers: the correct answer, an incorrect answer that included the intuitive concept, the answer “both are incorrect”, and the answer “I am not sure”, which is to be understood in the sense of “I do not know whether one of the three answers is correct”. As an online multiple-choice test, these 17 cases were made available to all 2 nd , 6 th , and 12 th semester students ( N =1170, n =418 from the 2nd semester, n =425 from the 6 th semester, and n =327 from the 12 th semester, i.e., the final year) for four weeks in June 2015. The test had to be answered within nine minutes. A mixed logistic regression model was used for evaluation. Results: Of the N =317 participating students ( n =97 from the 2 nd semester, n =124 from the 6 th semester, and n =96 from the internship year, overall response rate 27.1%), on average, students from all three groups chose the intuitive concept most often, approximately 40%, although the correct answer increased toward the final year with simultaneously decreasing uncertainty and decreasing feeling of not knowing, respectively. In the final year, compared to the 2 nd semester, the intuitive concept was selected significantly more often for two questions ( p <0.01). For four questions, the intuitive concept was selected significantly less frequently in the final year ( p <0.01). Conclusion: Intuitive concepts can be identified in internal medicine and do not appear to be significantly reduced in students during the course of their studies. This suggests that this could also be the case for...

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Section: Introductionmentioning

confidence: 99%

Intuitive concepts in internal medicine and their occurrence in undergraduate medical students in different semesters

Harendza

Herzog

2022

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Analysis of difficulties for pre-service mathematics teacher in problem solving of division and divisibility based on theory of action, process, object, and schemes

Fitrianti

Suryadi

Kusnandi

2020

J. Phys.: Conf. Ser.

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Action, process, object, and schemes is an acronym of APOS. The difficulty in the perspective of APOS theory is the inability of students to access specific schemes in all situations, thereby inhibit the construction of other concept. Knowing student’s difficulties in using the concept of division and divisibility is necessary to design genetic decomposition of that concept. This article is a report from qualitative research that discusses conceptual issues about the idea of division and divisibility given by prospective mathematics teacher students who use the APOS theory. The data for the study were collected from an interview. The researcher took three interview subjects from 30 pre-service mathematics teachers who have attended and completed a test on the division and divisibility in an elementary number theory course. These participants were selected based on their performance in the test. However, the interview conducted showed that there are five difficulties involved and they include solving the divisibility problem on integers, algebraic manipulation and recognize structures in algebraic expressions that correspond to the division algorithm or the definition of divisibility., distinguishing between variables and parameters on division problem presented in algebraic expression, associating between division algorithm and definition, and application of divisibility properties and theorems.

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The Teaching of Mathematics Using APOS Theory

Cited by 2 publications

References 14 publications

Intuitive concepts in internal medicine and their occurrence in undergraduate medical students in different semesters

Intuitive concepts in internal medicine and their occurrence in undergraduate medical students in different semesters

Analysis of difficulties for pre-service mathematics teacher in problem solving of division and divisibility based on theory of action, process, object, and schemes

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