The Obstacle of Formalism in Linear Algebra

By J. Dorier, A. Robert, J. Robinet, Marc Rogalsiu. 2000

86 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/7a1175c6ecc3864e2c1ec28b222e298d319c2ff8

How researchers see this paper

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

In Artificial Intelligence

1. Michelle Zandieh
2. Megan Wawro

In Geometry and Topology

1. Hamide Dogan-Dunlap
2. Chris Rasmussen
3. Howard F. Blumenfeld
4. George Sweeney
5. Megan Wawro

In Theoretical Computer Science

1. Michelle Zandieh
2. Megan Wawro
3. Hamide Dogan-Dunlap
4. Chris Rasmussen
5. Howard F. Blumenfeld
6. George Sweeney

Citations in the corpus

• Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expressions (2007, background): “Although students can often solve the characteristic equation to find eigenvalues and eigenvectors, the meanings of these mathematical ideas tend not to be well understood by students ( Dorier, Robert, Robinet, & Rogalski, 2000; Rasmussen, 2001).”
• A hypothetical learning trajectory for conceptualizing matrices as linear transformations (2017, background): “the symbolic notation of linear algebra [24,25]; working with formal definitions in linear algebra [15]; and coordinating across the different modes or representations involved in linear algebra [17,18].”
• An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence (2012, background): “research has demonstrated that formal definitions are often a stumbling block for students [4, 5, 21].”
• Subspace in linear algebra: investigating students’ concept images and interactions with the formal definition (2011, background): “French universities, Dorier et al. (2000) reported many instances in which student difficulties seem to be due to a formalism obstacle, noting how “the lack of prior knowledge in logic and elementary set theory contribute to the production of errors in linear algebra itself” (p. 86).”
• Linear algebra students’ modes of reasoning: Geometric representations (2010, background): “Many also lack logic and set theory knowledge [3–10].”
• Linear algebra revisited: an attempt to understand students' conceptual difficulties (2009, background): “[5] call this the obstacle of formalism, and their studies confirm that students and teachers alike recognize formalism(1) as a massive obstacle to learning.”