Basic mental models of integrals: theoretical conception, development of a test instrument, and first results

Greefrath, Gilbert; Oldenburg, Reinhard; Siller, Hans-Stefan; Ulm, Volker; Weigand, Hans-Georg

doi:10.1007/s11858-020-01207-0

Cited by 6 publications

(2 citation statements)

References 22 publications

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“…The schema in this study refers to the knowledge structure containing information about the core concepts and the relationships between the concepts. Furthermore, neither Bofferding (2014), Chinnapan (1998), as well as Greefrath et al (2020Greefrath et al ( , 2022 does not disclose and describe the process of accommodation of mental models during problem-solving. Whereas Oleson et al (2010), Piaget (1954), andvan Ments &Treur (2022) state that mental models experience an adaptation process through two forms, namely assimilation and accommodation, but according to Ifenthaler et al (2008) and van Ments and Treur (2022) mental models only experience accommodation processes.…”

Section: Introductionmentioning

confidence: 97%

Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

Rumite

Purwanto

Parta

et al. 2023

EURASIA J Math Sci Tech Ed

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A mental model is an essential element that influences the quality of problem-solving. This study explores mental models, strategies, and schemes that are active in solving the maximum rectangular area problem. The approach used in this study is a descriptive qualitative approach. A total of four pre-service mathematics teachers as subjects were selected from 108 prospective subjects involved in the study. Data collection was carried out by providing task sheets for solving the most significant rectangular area problem and semi-structured interviews. Data reduction, data presentation, and conclusion are three stages in analyzing the research data. This study indicates three mental models for pre-service mathematics teachers in solving maximum rectangular area problems: initial, adaptive, and formal. Each has different strategies and schemes that are active while solving problems. The results of this study imply that mental models influence the quality of the problem solving process until results are obtained.

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Section: Introductionmentioning

confidence: 97%

Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

Rumite

Purwanto

Parta

et al. 2023

EURASIA J Math Sci Tech Ed

View full text Add to dashboard Cite

show abstract

“…Therefore, a beginner in building his mental model is different from someone already an expert in his field in content, structure, and semiotics. Therefore, modifying learning depends on a mental model that is called conceptual change (Greefrath et al, 2021). According to cognitive psychologists, the mental model represents an internal scale model of external reality or a person's mental representation of an idea or concept (Haglund et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Mental Models and Creative Thinking Skills in Students’ Physics Learning

Batlolona

Diantoro

2023

Creativity Studies

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The study of mental models and creative thinking skills in students’ physics learning with the problem-based learning model has been scarce. This study aimed to analyze the relationship between mental models and creative thinking skills in high school students. Many previous research findings explain a relationship between mental models and creative thinking skills among students at the university level and workers. This mixed-methods study was conducted on high school students in Malang, East Java, Indonesia, aged between 14 and 15 years. The instrument used is in the form of mental models and creative thinking skills test questions. This finding explains no relationship between mental models and creative thinking skills because learning has not fully empowered mental models and creative thinking skills. On the other hand, learning at the previous level, students’ knowledge is still fragmented, so that is incomplete. Therefore, at the high school level, they need help to improve their mental models and creative thinking skills. This finding implies that teachers in developing learning materials, tools, and instruments must pay attention to the level of student knowledge so that learning can be more optimal.

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Mathematics teaching, learning, and assessment in the digital age

Weigand,

Trgalova,

Tabach

2024

ZDM Mathematics Education

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The role of teaching, learning, and assessment with digital technology has become increasingly prominent in mathematics education. This survey paper provides an overview of how technology has been transforming teaching, learning, and assessment in mathematics education in the digital age and suggests how the field will evolve in the coming years. Based on several decades of research and educational practices, we discuss and anticipate the multifaceted impact of technology on mathematics education, thus laying the groundwork for the other papers in this issue. After a brief introduction discussing the motivations for this issue, we focus our attention on three lines of research: teaching mathematics with technology, learning mathematics with technology, and assessment with technology. We point to new research orientations that address the issue of teaching with technology, specifically describing attempts to conceptualise teachers’ mathematical and digital competencies, perspectives that view teachers as designers of digital resources, and the design and evaluation of long-term initiatives to support teachers as they develop innovative teaching practices enhanced by digital technologies. Our examination shows that learning with technology is still marked by new conceptualizations raised by researchers that can further our understanding of this complex issue. These conceptualizations support the recognition that multiple resources, ranging from paper and pencil to augmented reality, participate in the learning process. Finally, assessment with technology, especially in the formative sense, offers new possibilities for offering individualised support for learners that can benefit from adaptive systems, though more tasks for conceptual understanding need to be developed.

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Basic mental models of integrals: theoretical conception, development of a test instrument, and first results

Cited by 6 publications

References 22 publications

Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

Mental Models and Creative Thinking Skills in Students’ Physics Learning

Mathematics teaching, learning, and assessment in the digital age

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