Students’ Solution of Arrangement Problems and their Connection to Cartesian Product Problems

dc.contributor.authorTillema, Erik S.
dc.contributor.departmentSchool of Educationen_US
dc.date.accessioned2019-11-15T18:37:32Z
dc.date.available2019-11-15T18:37:32Z
dc.date.issued2019
dc.description.abstractTwo-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11–12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented a balanced mix of students operating with each of three different multiplicative concepts that have been identified in prior research. This paper reports on the 11 students who were using the first or second multiplicative concept. Students operating with different multiplicative concepts all experienced similar perturbing elements in their solution of APs relative to their solution of CPPs, but they operated differently to resolve these perturbing elements. These differences are identified and their significance discussed in relation to other research findings on students’ combinatorial and multiplicative reasoning.en_US
dc.eprint.versionAuthor's manuscripten_US
dc.identifier.citationTillema, E. S. (2019). Students’ solution of arrangement problems and their connection to Cartesian product problems. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2019.1608618en_US
dc.identifier.urihttps://hdl.handle.net/1805/21349
dc.language.isoenen_US
dc.publisherTaylor & Francisen_US
dc.relation.isversionof10.1080/10986065.2019.1608618en_US
dc.relation.journalMathematical Thinking and Learningen_US
dc.rightsPublisher Policyen_US
dc.sourceAuthoren_US
dc.subjectcombinatorial reasoningen_US
dc.subjectlearningen_US
dc.subjectsecond order modelsen_US
dc.titleStudents’ Solution of Arrangement Problems and their Connection to Cartesian Product Problemsen_US
dc.typeArticleen_US
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