A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics

By Raymond Duval. 2006

1,427 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e38ac5b98197284537fca03d8592adaae48841d4

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Citations in the corpus

Scaffolding Based on Cognitive Conflict in Correcting the Students’ Algebra Errors (2018, background): “Duval (2006) explain that mathematical representtaion is the most basic and old idea that represents an object, but at the same time this idea can be elusive or too formal.”
Exploring mathematical connections of pre-university students through tasks involving rates of change (2018, background): “It is natural to resort to the use of representations while working with concepts that are not directly accessible [46], like the mathematical objects.”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, background): “On the other hand, conceptualizing decimals and fractions as interchangeable representations of the same numbers requires moving beyond their differences in form and behavior and focusing on their common reference (Duval, 2006; Markovits & Sowder, 1991), that is, realizing that they refer to the sam”
Purposefully Relating Multilingual Registers: Building Theory and Teaching Strategies for Bilingual Learners Based on an Integration of Three Traditions (2016, background): “7 Figure 3: Transitions between different representations (Bruner, 1967; Lesh, 1979; Duval, 2006)”
Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions (2010, neutral): “The use of these different representations (Duval, 1995, 2006), along with representations of non-ostensive objects that do not exist (Font et al. 2010), fosters the belief that mathematical representations are different from the mathematical objects they represent.”
Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom (2015, background): “Doing mathematics relies on using representations, since mathematical objects are not accessible without them (Duval, 2006; Janvier, 1987; Mason, 1987).”
Representation in Teaching and Learning Mathematics (2020, background): “Duval (2006) states that representation is something that stands for something else.”
ENACTED TYPES OF ALGEBRAIC ACTIVITY IN DIFFERENT CLASSES TAUGHT BY THE SAME TEACHER (2011, background): “Duval, 2006 ). Finally, the framework does not attend to intuitive and discovery-based aspects of algebraic reasoning (e.g.”
Getting the point: Tracing worked examples enhances learning (2015, background): “(semiotic representations) (Duval, 2006). However, although mathematics can be conceived as an abstract semiotic system, it does not mean that mathematical cognition is beyond the realm of sensation and body motion. As Núñez (2008) has argued, mathematics, perhaps the most abstract conceptual system”
Emergent mathematical thinking in the context of play (2010, background): “As schematic representations are representations of (spatial or conceptual) transformations and relationships between different objects, we assumed that this might be a meaningful basis for further formalised mathematical operations that are also based on transformations (see Duval, 2006).”
Towards a methodology for the characterization of teachers´ Didactic-Mathematical knowledge (2015, methodology): “Compare to solutions by Teachers A and B, this solution includes more representation systems, what is desirable, according to Duval (2006).”
Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers (2019, background): “In line with this, Duval (2006) stated that what concerns mathematical activity is pushed back into the background or explained either by conceptual understanding (or misunderstanding) or by a common pedagogical framework about the importance of student’ activity and the role of their mental…”