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Mathematics on Need Basis –�Challenge for Students during Project�Work: A Case Study

Olga Timcenko,

Associate Professor,

Aalborg University, Denmark

ot@create.aau.dk

Symposium ITEM 2022

Innovation on Teaching Mathematics at HEI: Experiences on Classroom

Tenerife, March 15th – 18th, 2022

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Problem Statement: How to teach mathematics under the following conditions:

  • Engineering educational programs that transcend the division between technical, scientific and artistic disciplines;
  • A transposition from an industrial/engineering use of mathematics towards mathematics as building blocks in new digital products and creative expressions;
  • Students who lack basic skills, do not perceive mathematics as engineering students (should) do, do not relate to standard applications of mathematics.

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Problem-Based Learning (PBL), �Aalborg model: A solution?

Learning results from what the student does and thinks �and only from what the student does and thinks. �The teacher can advance learning only by influencing what the student does to learn.

Herbert Simon (2000), in:

Anderson, J. R., Reder, L.M., & Simon, H.A. (2000, Summer). Applications and Misapplications of Cognitive Psychology to Mathematics Education. Texas Educational Review.

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Time for reflection

  • PBL has proven successful throughout decades.

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  • However, how does it support the more “creative” modes of application of mathematics?

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  • How does technology influence students’ knowledge, conception and attitude towards mathematics?

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Methodology

  • This is not a systematic research, but a case study.
  • The case was chosen as the most representative among many collected during years of experience with supervising groups od students for their project work.
  • Criteria for choosing the case:
    • Average group of students
    • Project that required some mathematics knowledge
    • Quite a successful project, graded above-average (7 on -3 to 12 scale)

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Some other brief confusing examples

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Semester theme: Mediating Reality

  • 5th semester of Media Technology (Medialogy) studies
  • Classical engineering Calculus + Linear Algebra courses on the first semseter (with an excellent teacher!)
  • Mathematics for Computer Graphics & Games on the 5th semster
  • Students choose freely the problema to solve within the semester theme

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The Project: �Transferring optical illusions from 2D to 3D

M.C. Escher – Ascending and Descending (1960). The official M.C. Escher website, http://www.mcescher.com/Gallery/recogn-bmp/LW435.jpg

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The Project: �Transferring optical illusions from 2D to 3D

"Perth Impossible Triangle" by Bjørn Christian Tørrissen, http://bjornfree.com/galleries.html.

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The Project: �Transferring optical illusions from 2D to 3D

Rob Gonsalves – Tree House in Autumn

Students’ Problem Statement:

“How can we reproduce a perspective dependent illusion from a 2D picture into a 3D scene, and can we develop a method to repair the breaks in the illusion, which occur when moving the viewpoint in 3D space, by using a combination of visual perception techniques?”

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Depth Cues and Perspective Illusion

A possible solution for Tree House in Autumn

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Depth, Size and Emmert’s Law

3D Transformations

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Modelling the scene in Maya

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The final test setup

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Conclusions

  • The students are reluctant to use even slightly more mathematics than absolutely necessary to develop their product with minimal acceptable functionality
  • This can be attributed to lack of confidence and fear of added complexity

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Are Medialogy students:

  1. just an exceptional example of low achievers in math; or
  2. a pretty good representative of typical contemporary students?

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