caa a22 4500 445881739 CHVBK 20180317145545.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10649-011-9325-2 doi (NATIONALLICENCE)springer-10.1007/s10649-011-9325-2 Teaching absolute value inequalities to mature students [Elektronische Daten] [Anna Sierpinska, Georgeana Bobos, Andreea Pruncut] This paper gives an account of a teaching experiment on absolute value inequalities, whose aim was to identify characteristics of an approach that would realize the potential of the topic to develop theoretical thinking in students enrolled in prerequisite mathematics courses at a large, urban North American university. The potential is demonstrated in an epistemological analysis of the topic. It is also shown that this potential is not realized in the way the topic is presently taught in prerequisite mathematics courses. Three groups of students enrolled in such courses were each exposed to one of three approaches we conceived for teaching the topic, labeled the procedural (PA), the theoretical (TA), and the visual (VA) approaches. The design of the three lectures was constrained by institutional characteristics of college-level courses, and informed by epistemological and didactical analyses of the topic. It was found that following the VA lecture, which proposed two equally valid mathematical techniques (graphical and analytic), one of which could be used to test the validity of results obtained by the other, students were more likely to engage in some aspects of theoretical thinking. They displayed more reflective and systemic thinking than other groups, and dealt more effectively with the logical intricacies of absolute value inequalities. VA students appeared to have a synthetic grasp of the inequalities, and a flexibility of thought not displayed by PA and TA students. However, without sufficient attention to tasks not easily solved by graphical means, VA approach provided students with a way to avoid the challenges of systemic and analytic thinking, some of which were more apparent in TA students. PA students expectedly behaved more as procedural knowers, but we saw interesting examples of engagement with theoretical thinking while dealing with the procedures proposed in the PA lecture. Springer Science+Business Media B.V., 2011 Absolute value inequalities nationallicence Mature students nationallicence Prerequisite mathematics courses nationallicence Learning by example nationallicence Theoretical thinking nationallicence Teaching experiment nationallicence Sierpinska Anna Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve blvd. West, H3G 1M8, Montreal, QC, Canada aut Bobos Georgeana Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve blvd. West, H3G 1M8, Montreal, QC, Canada aut Pruncut Andreea Université de Montréal, Montreal, Canada aut Educational Studies in Mathematics Springer Netherlands 78/3(2011-12-01), 275-305 0013-1954 78:3<275 2011 78 10649 https://doi.org/10.1007/s10649-011-9325-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-011-9325-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sierpinska Anna Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve blvd. West, H3G 1M8, Montreal, QC, Canada aut NATIONALLICENCE 700 1- Bobos Georgeana Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve blvd. West, H3G 1M8, Montreal, QC, Canada aut NATIONALLICENCE 700 1- Pruncut Andreea Université de Montréal, Montreal, Canada aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 78/3(2011-12-01), 275-305 0013-1954 78:3<275 2011 78 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer