Problem-solving before Instruction: Linear Algebra for Mechanical Engineers

Description

This lecture by the instructor presents the implementation of problem-solving before instruction (PS-I) designs in a linear algebra course for mechanical engineers at ETH Zürich. The session discusses the benefits of including preparatory exercises for core linear algebra concepts, based on productive failure principles, to enhance students' learning outcomes. The lecture covers the design and results of the PS-I approach, emphasizing the importance of challenging and activating students' prior knowledge to improve conceptual understanding and transfer in mathematics learning. The findings reveal positive impacts on exam performance and student engagement, highlighting the effectiveness of this innovative teaching method.

Official source

https://mediaspace.epfl.ch/media/0_7sprfsm7

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Related concepts (41)

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In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another. An example of this is the understanding of quantity in terms of directionality (e.g. "the price of peace is rising") or the understanding of time in terms of money (e.g. "I spent time at work today"). A conceptual domain can be any mental organization of human experience.

Conceptual blending

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.

Natural-language understanding

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Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .