Abstract
The transition to universitylevel mathematics is challenging for firstyear students,
particularly on the topic of mathematical reasoning and proving. This note describes
the design of the course ‘Linear Structures 1’ at the University of Twente, developed
with the goal to teach firstyear students the skill of writing mathematical proofs,
next to the topics of linear algebra. Unlike traditional courses, where this skill is
often only an implicit learning objective, our course aligns all activities to make
it tangible, explicit, and achievable for the students. The proposed course design
incorporates blended learning strategies, such as micro lectures, digital quizzes and
interactive inclass activities. We introduced the Proof of the week: an activity where
students write a short proof every week in a lowstakes and safe environment: the
only requirement is students show effort. We provide students with feedback on
their proofwriting through inclass discussions with peers and comments from the
teacher. Two notable outcomes are the improved quality of students’ proofs and the
75% reduction in grading time, which makes the course highly scalable.
particularly on the topic of mathematical reasoning and proving. This note describes
the design of the course ‘Linear Structures 1’ at the University of Twente, developed
with the goal to teach firstyear students the skill of writing mathematical proofs,
next to the topics of linear algebra. Unlike traditional courses, where this skill is
often only an implicit learning objective, our course aligns all activities to make
it tangible, explicit, and achievable for the students. The proposed course design
incorporates blended learning strategies, such as micro lectures, digital quizzes and
interactive inclass activities. We introduced the Proof of the week: an activity where
students write a short proof every week in a lowstakes and safe environment: the
only requirement is students show effort. We provide students with feedback on
their proofwriting through inclass discussions with peers and comments from the
teacher. Two notable outcomes are the improved quality of students’ proofs and the
75% reduction in grading time, which makes the course highly scalable.
Original language  English 

Number of pages  15 
Publication status  Submitted  19 Jul 2024 
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Course materials for Linear Structures 1
Litvak, N. (Creator), Lanting, L. S. (Data Collector) & Weedage, L. (Creator), Zenodo, 19 Jul 2024
DOI: 10.5281/zenodo.12779749, https://zenodo.org/records/12779750
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