Justifications for choices made in procedures
Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-re...
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Gespeichert in:
| Autor*in: |
Maciejewski, Wes [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Nature B.V. 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Educational studies in mathematics - Springer Netherlands, 1968, 101(2019), 3 vom: 21. März, Seite 325-340 |
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| Übergeordnetes Werk: |
volume:101 ; year:2019 ; number:3 ; day:21 ; month:03 ; pages:325-340 |
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10.1007/s10649-019-09886-7 |
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| 520 | |a Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. | ||
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10.1007/s10649-019-09886-7 doi (DE-627)OLC2027745513 (DE-He213)s10649-019-09886-7-p DE-627 ger DE-627 rakwb eng 370 510 VZ 17,1 ssgn Maciejewski, Wes verfasserin (orcid)0000-0002-4472-900X aut Justifications for choices made in procedures 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. Procedural flexibility Student justifications Mathematical flexibility Use of flexible cognition Star, Jon R. aut Enthalten in Educational studies in mathematics Springer Netherlands, 1968 101(2019), 3 vom: 21. März, Seite 325-340 (DE-627)129882585 (DE-600)300213-5 (DE-576)015178595 0013-1954 nnns volume:101 year:2019 number:3 day:21 month:03 pages:325-340 https://doi.org/10.1007/s10649-019-09886-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_110 AR 101 2019 3 21 03 325-340 |
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10.1007/s10649-019-09886-7 doi (DE-627)OLC2027745513 (DE-He213)s10649-019-09886-7-p DE-627 ger DE-627 rakwb eng 370 510 VZ 17,1 ssgn Maciejewski, Wes verfasserin (orcid)0000-0002-4472-900X aut Justifications for choices made in procedures 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. Procedural flexibility Student justifications Mathematical flexibility Use of flexible cognition Star, Jon R. aut Enthalten in Educational studies in mathematics Springer Netherlands, 1968 101(2019), 3 vom: 21. März, Seite 325-340 (DE-627)129882585 (DE-600)300213-5 (DE-576)015178595 0013-1954 nnns volume:101 year:2019 number:3 day:21 month:03 pages:325-340 https://doi.org/10.1007/s10649-019-09886-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_110 AR 101 2019 3 21 03 325-340 |
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10.1007/s10649-019-09886-7 doi (DE-627)OLC2027745513 (DE-He213)s10649-019-09886-7-p DE-627 ger DE-627 rakwb eng 370 510 VZ 17,1 ssgn Maciejewski, Wes verfasserin (orcid)0000-0002-4472-900X aut Justifications for choices made in procedures 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. Procedural flexibility Student justifications Mathematical flexibility Use of flexible cognition Star, Jon R. aut Enthalten in Educational studies in mathematics Springer Netherlands, 1968 101(2019), 3 vom: 21. März, Seite 325-340 (DE-627)129882585 (DE-600)300213-5 (DE-576)015178595 0013-1954 nnns volume:101 year:2019 number:3 day:21 month:03 pages:325-340 https://doi.org/10.1007/s10649-019-09886-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_110 AR 101 2019 3 21 03 325-340 |
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Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. © Springer Nature B.V. 2019 |
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Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. © Springer Nature B.V. 2019 |
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Abstract In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, Instructional Science, 10, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, algorithmic and anticipatory. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (Educational Studies in Mathematics, 67, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall. © Springer Nature B.V. 2019 |
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10.1007/s10649-019-09886-7 |
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