Student thinking modes expressed while determining linear independence/dependence of sets of vectors

Roberto Carlos Trejo, University of Texas at El Paso

Abstract

On daily basis, mathematics educators across all levels (K-16) collaborate and create innovative ways to educate students and allow them to overcome the barriers they face in mathematics. A main concern with regards to learning is ensuring that students are making connections to mathematical concepts. A "linking mechanism" to address this particular concern, for linearly dependent and linearly independent sets of vectors in linear algebra, is computer systems. My research deals with using two computer systems, one numerical one graphical, to represent the linear dependence and independence of vectors. ^ Through two structured class assignments one for the numerical computer system and the other for the graphical computer system; first year linear algebra, students attempted to conjecture how linearly independent and dependent sets of vectors are represented graphically and numerically. The responses provided from the assignments were qualitatively analyzed and categorized as student thinking modes. ^ I will present results to student thinking modes used while solving problems relating to linearly independent and dependent sets of vectors. Results suggest that computer systems might be beneficial to the introduction of the concepts relating to linear independence and dependence of vectors.^

Subject Area

Education, Mathematics|Education, Curriculum and Instruction

Recommended Citation

Trejo, Roberto Carlos, "Student thinking modes expressed while determining linear independence/dependence of sets of vectors" (2007). ETD Collection for University of Texas, El Paso. AAI1444083.
http://digitalcommons.utep.edu/dissertations/AAI1444083

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