Schemas in Problem Solving

Marshall, Sandra P.

doi:10.1017/cbo9780511527890

Cited by 439 publications

(355 citation statements)

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“…Schema-based instruction may help students to learn stable information patterns and categorization schemes that would allow them to effectively use appropriate knowledge for dealing with different types of situation without extraneous cognitive load. For example, a schema-based instructional approach in the area of arithmetic word problems was investigated by Marshall (1995). The approach may need to be further explored and extended to different domains.…”

Section: Optimizing Executive Guidance In Knowledge Elaborationmentioning

confidence: 99%

Knowledge elaboration: A cognitive load perspective

Kalyuga

2009

Learning and Instruction

157

119

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The process of knowledge elaboration is considered from the perspective of cognitive load theory. This theory assumes that the available knowledge structures in long-term memory (LTM) are used to organize and guide cognitive processing in complex learning. Accordingly, the role of external instructional guidance in the process of knowledge elaboration could be described as providing a substitute for knowledge structures missing from LTM. Thus, the executive guidance in complex learning environments is shared between the person (based on his/her LTM knowledge structures) and another expert or instructional means. This article analyzes instructional implications of this assumption. Adaptive learning environments are suggested for tailoring knowledge elaboration processes to changing characteristics of individual learners. Means for identifying and predicting the learner's LTM-based executive guidance are proposed so that they can be utilized in the building of adaptive learning environments.

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Section: Optimizing Executive Guidance In Knowledge Elaborationmentioning

confidence: 99%

Knowledge elaboration: A cognitive load perspective

Kalyuga

2009

Learning and Instruction

157

119

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“…In this context, the advantage of using drawing, and the analogical and higher order thinking that comes from visualisation, is its 'By sidestepping our cognitive, verbal processing routes, we tend to produce clearer, more holistic images than we do with words'. contribution to our ability to problem solving (Marshall, 1995).…”

Section: Freehand Drawing In the Classroommentioning

confidence: 99%

Engaging Students in the Classroom: ‘How Can I Know What I Think Until I See What I Draw?’

Donnelly

Hogan

2013

Eur Polit Sci

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Recognising that the world into which students emerge upon graduation is characterised by constant change, we embrace a critical pedagogy that can be implemented in the classroom through the use of freehand drawing. Freehand drawing is a technique that can stimulate a critical stance, as visual representations allow us to comprehend the world differently, while permitting us see how others understand the world. First year students, in their first lecture, were asked to draw their interpretations of Irish politics and to explain in writing what they had drawn. The students were then placed in groups and asked to note what they saw in each other's drawings, allowing for the identification of general patterns and themes. In this context, freehand drawing facilitates our ability to: 'see' how we understand a topic and that there are multiple ways of understanding; test theories, orthodoxies and accepted truths; scrutinise tacit assumptions; and ponder other possibilities. In employing freehand drawing in this manner, our aim is to create a learning environment where students develop their capacity for critical self-reflection.

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“…Importantly, when solving such problems pupils are required to use certain schema/diagrams (Charalambous, Philippou, and Kyriakides 2004), which are based on Marshall's (1995) schema theory (ST). ST concerns arithmetic word problems and aims to provide solvers with a number of cognitive schemas that can be used as guides during the problem solution process.…”

Section: On Mathematical Problemsmentioning

confidence: 99%

“…To sum up, the prospective teachers talked here about the real-world verbal tasks labelled as problems that appear in the upper-primary National Textbooks of Cyprus (Charalambous et al 2004) and are based on Marshall's (1995) Schema Theory. In particular, four types of tasks are included in the textbooks: problems of change (something happens to a given quantityaddition or subtraction), problems of comparison (comparing quantities with addition, subtraction, multiplication or division), problems of grouping (putting quantities togetheraddition or subtraction), and problems of analogy (if… then… multiplication or division).…”

Section: Problems Related To Schema Theory -The Four Arithmetic Operamentioning

confidence: 99%

Defining mathematical problems and problem solving: prospective primary teachers’ beliefs in Cyprus and England

Xenofontos

Andrews

2013

Math Ed Res J

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A number of recent studies have investigated pre-and in-service teachers' beliefs concerning mathematical problem solving. However, researchers have typically examined participants' beliefs in relation to predetermined understandings of problem solving, assuming a definitional convergence among fellow scholars and teachers. Drawing on data from a small-scale comparative project, this paper discusses the similarities and differences of prospective elementary teachers' beliefs in Cyprus and England, about the nature of mathematical problems and problem solving. Twenty-four participants, each group of twelve from a well-regarded university in each country, were interviewed qualitatively at the exit point of their studies. Data analysis has revealed a variety of ways by which prospective teachers in both counties perceive the two notions. The results indicate that prospective teachers' beliefs are culturally located and that the concepts of "mathematical problem" and "problem solving" have different meanings across countries. Some implications for policy making are discussed at the end of the paper.

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Schemas in Problem Solving

Cited by 439 publications

References 0 publications

Knowledge elaboration: A cognitive load perspective

Knowledge elaboration: A cognitive load perspective

Engaging Students in the Classroom: ‘How Can I Know What I Think Until I See What I Draw?’

Defining mathematical problems and problem solving: prospective primary teachers’ beliefs in Cyprus and England

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