Preamble: From Models to Modeling

By K.P.E. Gravemeijer. 2002

66 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/53801cbea4e89a372594677234e9612c3db2c17b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Education

Citations in the corpus

Five different perspectives on mathematical modeling in mathematics education (2020, background): “…tend to investigate the teaching and learning of mathematical topics, such as calculus (Gravemeijer & Doorman, 1999; Doorman & Gravemeijer, 2009), data analysis (Gravemeijer, 2002), and functions (Doorman, Drijvers, Gravemeijer, Boon, & Reed, 2012), through the design of teaching experiments.”
A Thirty-Year Reflection on Constructivism in Mathematics Education in Pme (2006, methodology): “We would point to examples in the work at the Freudenthal Institute on Realistic Mathematic Education (RME) (De Lange, 1987, 2001; Gravemeijer, 1994, 2002), the work on additive and multiplicative conceptual fields (Harel & Confrey, 1994; Steffe, 1994; Vergnaud, 1996), theories of advanced…”
Concrete-Pictorial-Abstract: Surveying its origins and charting its future (2015, background): “Many proponents of concrete manipulatives have also made mention of this fading process; for instance, Goldstone & Son, 2005; Gravemeijer, 2002; Lehrer & Schauble, 2002; Lesh, 1979. More recently, McNeil & Fyfe (2012) reported on the positive effects of fading on the transfer performance for a sampl”
Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education (2004, background): “In relation to this, we discern four different types or levels of activity (Gravemeijer, 1999, 2002): 1. activity in the task setting, 2. referential activity, 3. general activity, and 4. more formal mathematical reasoning.”
Concreteness Fading in Mathematics and Science Instruction: a Systematic Review (2014, background): “…time, several researchers have adopted similar approaches to the concrete versus abstract debate, advocating the use of concrete materials that are eventually decontextualized or faded to more abstract materials (Goldstone and Son 2005; Gravemeijer 2002; Lehrer and Schauble 2002; Lesh 1979).”
Should you show me the money? Concrete objects both hurt and help performance on mathematics problems (2009, background): “Even when the perceptual details of an object seem to tap applicable real-world knowledge (e.g., knowledge of US currency), students may not automatically grasp the mathematical ideas when they look at the objects (cf. Ball, 1992; Gravemeijer, 2002; Meira, 1998).”