Relational Understanding and Instrumental Understanding.

By R. Skemp. 2006

1,982 citations recorded by the source corpus.

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Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers (2021, background): “Adopting this definition, without taking regard of the qualities of procedural knowledge (Table 2), could lead to what Skemp (1978) referred to as learning “rules without reason” (p. 9).”
The Development of Students' Helping Behavior and Learning in Peer-Directed Small Groups (2003, methodology): “Skemp (1978) called this type of knowledge instrumental understanding.”
Introducing Three Worlds of Mathematics (2004, background): “For several years I have been working with Eddie Gray and others on the ways in which we conceptualize different kinds of mathematical concept (Tall, 1995; Gray, Pitta, Pinto & Tall, 1999; Tall et al, 2000; Tall, Thomas, Davis, Gray, Simpson, 2000). Eddie and I were particularly interested in the di”
Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development (2014, background): “In a sense, one can also link this level to Skemp’s (1976) ‘‘instrumental understanding’’, though Skemp’s theory is”
A research framework for creative and imitative reasoning (2008, background): “Skemp (1978) distinguishes between instrumental and relational understanding, Sfard (1991), Asiala et al. (1996) and Tall (2004) analyse how development of understanding of objects and processes interact, and Pirie and Kieren (1994) describe levels of understanding.”
Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts (2007, background): “…gravitation towards certain types of mathematical thinking – and identify issues that their preparation for the classroom needs to address (for example, in terms of distinctions such as relational and instrumental understanding (Skemp 1976), conceptual and procedural knowledge (Hiebert 1986) etc.).”
Effects of classroom instruction on students’ understanding of quadratic equations (2006, methodology): “That dissertation was by Sproule (2000), who investigated the performance on different types of quadratic equations of high- and lowability upper-secondary students (in Grades 11 through 14) attending a Northern Ireland grammar school. She concluded that only very high ability students operated at a”
Understanding Students' Mathematical Errors and Misconceptions: The Case of Year 11 Repeating Students (2014, background): “Students follow methods and rules taught to them without knowing or being concerned about why those methods work, which Skemp (1976) [18] referred to as an instrumental understanding.”
Teachers' beliefs and practices related to mathematics instruction (2001, background): “The National Council of Teachers of Mathematics (NCTM, 1991) `Standardsa stress that This conceptualization of mathematics is similar to what Skemp (1978) refers to as an instrumental concept of mathematics*a set of "xed plans for performing mathematical tasks involving step-by step procedures.”