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CAS Supporting Teaching and Learning of Linear Algebra

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Goal: To show some possibilities for using GeoGebra to help upper secondary school students learn to use CAS in preparation for university mathematics.

Goal: To show some possibilities for using GeoGebra to help upper secondary school students learn to use CAS in preparation for university mathematics.

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    CAS Supporting Teaching and Learning of Linear Algebra CAS Supporting Teaching and Learning of Linear Algebra Presentation Transcript

    • International GeoGebra Conference for Southeast Europe January 2011, Novi Sad, Serbia
      Computer Algebra Systems Supporting Teaching/ Learning Linear Algebra
      Ana Donevska Todorova
    • Overview
      Introduction
      Comparison
      Computer Algebra Systems
      Dynamic Software for Mathematics
      Teaching/ Learning Experiences
      University Education
      CAS Maxima and the online system moodle at the MIT University
      Secondary Education
      Some examples
      GCSE 2011
    • Introduction
      Faculties of engineering and informatics at the universities implement CAS:
      Mathematica
      Matlab
      during the contemporary lab classes in mathematics.
      First year students at universities are usually not familiar with any of the CAS or DGS and show lack of computer supported mathematics.
      Some possibilities to help the upper secondary school students in overcoming this problem and prepare them for university mathematics into lab.
      GCSE 2011
    • Comparison
      • Comparison of Computer Algebra Systems (CAS)
      • General Information
      http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
      GCSE 2011
    • Comparison
      • Comparison of Computer Algebra Systems (CAS)
      • Functionality
      http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
      GCSE 2011
    • Comparison
      • Comparison of Computer Algebra Systems (CAS)
      • Operating System Support
      http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
      GCSE 2011
    • Comparison
      Comparison of Dynamic Software for Mathematics (DSM)
      Operating System Support
      http://en.wikipedia.org/wiki/List_of_interactive_geometry_software#Comparison
      GCSE 2011
    • Comparison
      Comparison of Dynamic Software for Mathematics (DSM)
      Functionality
      GeoGebra Extras: Algebraic manipulations
      GCSE 2011
    • Online system moodle at MIT University Skopje
      GCSE 2011
    • Teaching/ Learning Experiences
      • University Education (MIT University Skopje)
      • Scores in Mathematics of the engineering students at the Faculty of Computer Sciences and Technologies
      *Resource http://moodle.mit.edu.mk/course/Matematika
      GCSE 2011
    • Implementation of the mathematics upgraded knowledge in other engineering subjects
      Quantitive linear models for optimization
      Example 1: A company produces three types of products in three different facilities (machines). For each product in each in each facility the required processing time is given in the following table:
      How many peaces of each of the products can be produced if the first facility has a capacity of 3200 working hours per month, the second facility 1700 and the third one 1300 working hours per month?
      • Solution (using wxMaxima)
      GCSE 2011
    • Implementation of the mathematics upgraded knowledge in other engineering subjects
      Laplace Transformation
      GCSE 2011
    • Teaching/ Learning Experiences
      Secondary Education
      Properties of Determinants
      Calculate the values of the following determinants:
      Using CAS Maxima calculate the values of the determinants given in the previous assignment.
      Compare the obtained results and the given determinants; and explain what you noticed.
      Write the conclusion in your own words.
      Write the property using mathematical symbols.
      GCSE 2011
    • Teaching/ Learning Experiences
      Secondary Education
      Properties of Determinants
      Using CAS Maxima calculate the values of the following determinants:
      Compare the obtained results and the given determinants; and explain what you noticed.
      Write the conclusion in your own words.
      Write the property using mathematical symbols.
      Generalize the property for n-dimension determinant.
      GCSE 2011
    • Teaching/ Learning Experiences
      Linear programming in GeoGebra
      Example:
      Two different types of products A and B can be produced on the machines M1 and M2.
      The capacity of M1 is 12000 working hours and the capacity of M2 is 6000 w. h.
      Required time for producing one product of type A on the machine is M1 is 3w. h. and on the machine M2 is 2 w. h.
      Required time for producing one product of type B on the machine is M1 is 3w. h. and on the machine M2 is 1 w. h.
      The needs of the market are 2500 products of type A and 3000 products of type B.
      The profit of the company is 4000 euros per one product A and 2000 euros per one product B.
      The management of the company has to create the optimal plan for producing the products A and B in order to achieve the best profit.
      GCSE 2011
    • Graphical Solution
      Systems of inequalities
      GCSE 2011
    • References
      Literature
      D. Todorova A.: The transition from secondary to teriary level mathematics emphasized in the course of linear algebra, International conference dedicated to prof. d-r. Gorgi Cupona, Ohrid, 2010.
      Donevska-Todorova, A. (2010): Difficulties in Mathematics for the Students in the First Year at Higher Education; Zbornik na MIT Universitet, Skopje, Macedonia, p. 177-184.
      Trencevski K.; Krsteska B.; Trencevski G.; Zdraveska S.; Linear algebra and analytic geometry for third year reformed gymnasium educatiom, Prosvetno delo, Skopje 2004.
      Roegner K. (2008) Linear Algebra as a Bridge Course for First-year Engineering students, Department of Mathematics, Technische Universität Berlin, Berlin Germany.
      Internet Recourses
      http://wxmaxima.sourceforge.net/wiki/index.php/Main_Page
      http://www.geogebra.org/cms/
      http://moodle.mit.edu.mk/course/Matematika
      http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
      http://en.wikipedia.org/wiki/List_of_interactive_geometry_software#Comparison
      GCSE 2011