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Learning Linear Algebra Using Models and Conceptual Activities

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Challenges and Strategies in Teaching Linear Algebra

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

In this chapter, an innovative approach, including challenging modeling situations and tasks sequences to introduce linear algebra concepts is presented. The teaching approach is based on Action, Process, Object, Schema (APOS) Theory . The experience includes the use of several modeling situations designed to introduce some of the main linear algebra concepts. Results obtained in several experiences involving different concepts are presented focusing on crucial moments where students develop new strategies, and on success in terms of student’s understanding of linear algebra concepts. Conclusions related to the success of the use of the approach in promoting student’s understanding are discussed.

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Acknowledgements

Work funded by Asociación Mexicana de Cultura A.C. and ITAM.

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Authors and Affiliations

  1. Instituto Tecnológico Autónomo de México, ITAM, México City, Mexico

    María Trigueros

Authors
  1. María Trigueros
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Correspondence to María Trigueros .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oklahoma, Norman, Oklahoma, USA

    Sepideh Stewart

  2. College of Education, Florida State University, Tallahassee, Florida, USA

    Christine Andrews-Larson

  3. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, Israel

    Avi Berman

  4. Arizona State University, Mesa, Arizona, USA

    Michelle Zandieh

Appendix

Appendix

1.1 A Possible Solution to the Traffic (SLE) Problem

The following diagram shows a map of a sector of streets in the downtown area of a city. The traffic control center has installed sensors to detect the number of vehicles that transit by the sector. In the figure the arrows represent the direction of each street. In each intersection, we can consider that there is a roundabout that enables a continuous flux of traffic around the sector. Parking is not permitted. Can a street be closed without causing a traffic jam? What is the minimum number of cars that can be allowed to circulate through a street, to avoid traffic jams? (Table 2).

Table 2 Solution traffic problem
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1.2 A Possible Solution to Production Problem (li, ld)

A group of three industries produce goods to satisfy their own demand (to satisfy the demands of the industries in the group) and to satisfy external consumers demand. Supposing that the quantity of good produced by each industry satisfies the needs of all the other industries, its own demand and the consumers’ needs and that you know the production of the industries for nine periods of internal and external demand, how would you find the fractions of the production of each industry to satisfy those demands? How many data would you need to respond the former question and how would you chose them? Can you use what you found to predict the production needed for the 6th (Tables 3, 4 and 5).

Table 3 External demand for 9 months is millions of pesos
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Table 4 Production for 9 months in millions of pesos
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Table 5 Solution production problem
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1.3 A Possible Solution to Employment Problem (Eigen)

In an economy, there is a certain number of employed persons and a certain number of unemployed persons at a certain time. The number of employed and unemployed persons is considered as the labor force for the economy and can be considered constant. If the probability that an unemployed person finds a job at any time and the probability that an employed person continues in a job at the same period is known. Find a mathematical model that describes the dynamics of employment. According to your model, what would be expected to happen with the number of employed and unemployed persons in the long term? (Table 6).

Table 6 Solution employment problem
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Trigueros, M. (2018). Learning Linear Algebra Using Models and Conceptual Activities. In: Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (eds) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-66811-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-66811-6_2

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  • Print ISBN: 978-3-319-66810-9

  • Online ISBN: 978-3-319-66811-6

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