Incorrect Ways of Thinking About the Size of Fractions
Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, thes...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
González-Forte, Juan Manuel [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2022 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Author(s) 2022 |
|---|
| Übergeordnetes Werk: |
Enthalten in: International journal of science and mathematics education - Dordrecht : Springer Science + Business Media B.V., 2003, 21(2022), 7 vom: 03. Dez., Seite 2005-2025 |
|---|---|
| Übergeordnetes Werk: |
volume:21 ; year:2022 ; number:7 ; day:03 ; month:12 ; pages:2005-2025 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10763-022-10338-7 |
|---|
| Katalog-ID: |
SPR052937690 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR052937690 | ||
| 003 | DE-627 | ||
| 005 | 20230901064711.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 230901s2022 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10763-022-10338-7 |2 doi | |
| 035 | |a (DE-627)SPR052937690 | ||
| 035 | |a (SPR)s10763-022-10338-7-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a González-Forte, Juan Manuel |e verfasserin |0 (orcid)0000-0003-4020-7869 |4 aut | |
| 245 | 1 | 0 | |a Incorrect Ways of Thinking About the Size of Fractions |
| 264 | 1 | |c 2022 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © The Author(s) 2022 | ||
| 520 | |a Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. | ||
| 650 | 4 | |a Gap thinking |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Natural number bias |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Interviews |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Rational number |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Reverse bias |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Fernández, Ceneida |0 (orcid)0000-0002-4791-9247 |4 aut | |
| 700 | 1 | |a Van Hoof, Jo |0 (orcid)0000-0003-4752-6221 |4 aut | |
| 700 | 1 | |a Van Dooren, Wim |0 (orcid)0000-0001-5002-4340 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t International journal of science and mathematics education |d Dordrecht : Springer Science + Business Media B.V., 2003 |g 21(2022), 7 vom: 03. Dez., Seite 2005-2025 |w (DE-627)359787150 |w (DE-600)2098363-3 |x 1573-1774 |7 nnns |
| 773 | 1 | 8 | |g volume:21 |g year:2022 |g number:7 |g day:03 |g month:12 |g pages:2005-2025 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10763-022-10338-7 |z kostenfrei |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_SPRINGER | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_23 | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_31 | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_39 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_60 | ||
| 912 | |a GBV_ILN_62 | ||
| 912 | |a GBV_ILN_63 | ||
| 912 | |a GBV_ILN_65 | ||
| 912 | |a GBV_ILN_69 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_73 | ||
| 912 | |a GBV_ILN_74 | ||
| 912 | |a GBV_ILN_90 | ||
| 912 | |a GBV_ILN_95 | ||
| 912 | |a GBV_ILN_100 | ||
| 912 | |a GBV_ILN_105 | ||
| 912 | |a GBV_ILN_110 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_138 | ||
| 912 | |a GBV_ILN_150 | ||
| 912 | |a GBV_ILN_151 | ||
| 912 | |a GBV_ILN_152 | ||
| 912 | |a GBV_ILN_161 | ||
| 912 | |a GBV_ILN_170 | ||
| 912 | |a GBV_ILN_171 | ||
| 912 | |a GBV_ILN_187 | ||
| 912 | |a GBV_ILN_213 | ||
| 912 | |a GBV_ILN_224 | ||
| 912 | |a GBV_ILN_230 | ||
| 912 | |a GBV_ILN_250 | ||
| 912 | |a GBV_ILN_281 | ||
| 912 | |a GBV_ILN_285 | ||
| 912 | |a GBV_ILN_293 | ||
| 912 | |a GBV_ILN_370 | ||
| 912 | |a GBV_ILN_602 | ||
| 912 | |a GBV_ILN_636 | ||
| 912 | |a GBV_ILN_647 | ||
| 912 | |a GBV_ILN_702 | ||
| 912 | |a GBV_ILN_2001 | ||
| 912 | |a GBV_ILN_2003 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2005 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2007 | ||
| 912 | |a GBV_ILN_2008 | ||
| 912 | |a GBV_ILN_2009 | ||
| 912 | |a GBV_ILN_2010 | ||
| 912 | |a GBV_ILN_2011 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2020 | ||
| 912 | |a GBV_ILN_2021 | ||
| 912 | |a GBV_ILN_2025 | ||
| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
| 912 | |a GBV_ILN_2037 | ||
| 912 | |a GBV_ILN_2038 | ||
| 912 | |a GBV_ILN_2039 | ||
| 912 | |a GBV_ILN_2044 | ||
| 912 | |a GBV_ILN_2048 | ||
| 912 | |a GBV_ILN_2049 | ||
| 912 | |a GBV_ILN_2050 | ||
| 912 | |a GBV_ILN_2055 | ||
| 912 | |a GBV_ILN_2056 | ||
| 912 | |a GBV_ILN_2057 | ||
| 912 | |a GBV_ILN_2059 | ||
| 912 | |a GBV_ILN_2061 | ||
| 912 | |a GBV_ILN_2064 | ||
| 912 | |a GBV_ILN_2065 | ||
| 912 | |a GBV_ILN_2068 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_2093 | ||
| 912 | |a GBV_ILN_2106 | ||
| 912 | |a GBV_ILN_2107 | ||
| 912 | |a GBV_ILN_2108 | ||
| 912 | |a GBV_ILN_2110 | ||
| 912 | |a GBV_ILN_2111 | ||
| 912 | |a GBV_ILN_2112 | ||
| 912 | |a GBV_ILN_2113 | ||
| 912 | |a GBV_ILN_2118 | ||
| 912 | |a GBV_ILN_2122 | ||
| 912 | |a GBV_ILN_2129 | ||
| 912 | |a GBV_ILN_2143 | ||
| 912 | |a GBV_ILN_2144 | ||
| 912 | |a GBV_ILN_2147 | ||
| 912 | |a GBV_ILN_2148 | ||
| 912 | |a GBV_ILN_2152 | ||
| 912 | |a GBV_ILN_2153 | ||
| 912 | |a GBV_ILN_2188 | ||
| 912 | |a GBV_ILN_2190 | ||
| 912 | |a GBV_ILN_2232 | ||
| 912 | |a GBV_ILN_2336 | ||
| 912 | |a GBV_ILN_2446 | ||
| 912 | |a GBV_ILN_2470 | ||
| 912 | |a GBV_ILN_2472 | ||
| 912 | |a GBV_ILN_2507 | ||
| 912 | |a GBV_ILN_2522 | ||
| 912 | |a GBV_ILN_2548 | ||
| 912 | |a GBV_ILN_4035 | ||
| 912 | |a GBV_ILN_4037 | ||
| 912 | |a GBV_ILN_4046 | ||
| 912 | |a GBV_ILN_4112 | ||
| 912 | |a GBV_ILN_4125 | ||
| 912 | |a GBV_ILN_4126 | ||
| 912 | |a GBV_ILN_4242 | ||
| 912 | |a GBV_ILN_4246 | ||
| 912 | |a GBV_ILN_4249 | ||
| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
| 912 | |a GBV_ILN_4322 | ||
| 912 | |a GBV_ILN_4323 | ||
| 912 | |a GBV_ILN_4324 | ||
| 912 | |a GBV_ILN_4325 | ||
| 912 | |a GBV_ILN_4326 | ||
| 912 | |a GBV_ILN_4328 | ||
| 912 | |a GBV_ILN_4333 | ||
| 912 | |a GBV_ILN_4334 | ||
| 912 | |a GBV_ILN_4335 | ||
| 912 | |a GBV_ILN_4336 | ||
| 912 | |a GBV_ILN_4338 | ||
| 912 | |a GBV_ILN_4393 | ||
| 912 | |a GBV_ILN_4700 | ||
| 951 | |a AR | ||
| 952 | |d 21 |j 2022 |e 7 |b 03 |c 12 |h 2005-2025 | ||
| author_variant |
j m g f jmg jmgf c f cf h j v hj hjv d w v dw dwv |
|---|---|
| matchkey_str |
article:15731774:2022----::norcwyotiknaoths |
| hierarchy_sort_str |
2022 |
| publishDate |
2022 |
| allfields |
10.1007/s10763-022-10338-7 doi (DE-627)SPR052937690 (SPR)s10763-022-10338-7-e DE-627 ger DE-627 rakwb eng González-Forte, Juan Manuel verfasserin (orcid)0000-0003-4020-7869 aut Incorrect Ways of Thinking About the Size of Fractions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 Fernández, Ceneida (orcid)0000-0002-4791-9247 aut Van Hoof, Jo (orcid)0000-0003-4752-6221 aut Van Dooren, Wim (orcid)0000-0001-5002-4340 aut Enthalten in International journal of science and mathematics education Dordrecht : Springer Science + Business Media B.V., 2003 21(2022), 7 vom: 03. Dez., Seite 2005-2025 (DE-627)359787150 (DE-600)2098363-3 1573-1774 nnns volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 https://dx.doi.org/10.1007/s10763-022-10338-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2022 7 03 12 2005-2025 |
| spelling |
10.1007/s10763-022-10338-7 doi (DE-627)SPR052937690 (SPR)s10763-022-10338-7-e DE-627 ger DE-627 rakwb eng González-Forte, Juan Manuel verfasserin (orcid)0000-0003-4020-7869 aut Incorrect Ways of Thinking About the Size of Fractions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 Fernández, Ceneida (orcid)0000-0002-4791-9247 aut Van Hoof, Jo (orcid)0000-0003-4752-6221 aut Van Dooren, Wim (orcid)0000-0001-5002-4340 aut Enthalten in International journal of science and mathematics education Dordrecht : Springer Science + Business Media B.V., 2003 21(2022), 7 vom: 03. Dez., Seite 2005-2025 (DE-627)359787150 (DE-600)2098363-3 1573-1774 nnns volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 https://dx.doi.org/10.1007/s10763-022-10338-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2022 7 03 12 2005-2025 |
| allfields_unstemmed |
10.1007/s10763-022-10338-7 doi (DE-627)SPR052937690 (SPR)s10763-022-10338-7-e DE-627 ger DE-627 rakwb eng González-Forte, Juan Manuel verfasserin (orcid)0000-0003-4020-7869 aut Incorrect Ways of Thinking About the Size of Fractions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 Fernández, Ceneida (orcid)0000-0002-4791-9247 aut Van Hoof, Jo (orcid)0000-0003-4752-6221 aut Van Dooren, Wim (orcid)0000-0001-5002-4340 aut Enthalten in International journal of science and mathematics education Dordrecht : Springer Science + Business Media B.V., 2003 21(2022), 7 vom: 03. Dez., Seite 2005-2025 (DE-627)359787150 (DE-600)2098363-3 1573-1774 nnns volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 https://dx.doi.org/10.1007/s10763-022-10338-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2022 7 03 12 2005-2025 |
| allfieldsGer |
10.1007/s10763-022-10338-7 doi (DE-627)SPR052937690 (SPR)s10763-022-10338-7-e DE-627 ger DE-627 rakwb eng González-Forte, Juan Manuel verfasserin (orcid)0000-0003-4020-7869 aut Incorrect Ways of Thinking About the Size of Fractions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 Fernández, Ceneida (orcid)0000-0002-4791-9247 aut Van Hoof, Jo (orcid)0000-0003-4752-6221 aut Van Dooren, Wim (orcid)0000-0001-5002-4340 aut Enthalten in International journal of science and mathematics education Dordrecht : Springer Science + Business Media B.V., 2003 21(2022), 7 vom: 03. Dez., Seite 2005-2025 (DE-627)359787150 (DE-600)2098363-3 1573-1774 nnns volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 https://dx.doi.org/10.1007/s10763-022-10338-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2022 7 03 12 2005-2025 |
| allfieldsSound |
10.1007/s10763-022-10338-7 doi (DE-627)SPR052937690 (SPR)s10763-022-10338-7-e DE-627 ger DE-627 rakwb eng González-Forte, Juan Manuel verfasserin (orcid)0000-0003-4020-7869 aut Incorrect Ways of Thinking About the Size of Fractions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 Fernández, Ceneida (orcid)0000-0002-4791-9247 aut Van Hoof, Jo (orcid)0000-0003-4752-6221 aut Van Dooren, Wim (orcid)0000-0001-5002-4340 aut Enthalten in International journal of science and mathematics education Dordrecht : Springer Science + Business Media B.V., 2003 21(2022), 7 vom: 03. Dez., Seite 2005-2025 (DE-627)359787150 (DE-600)2098363-3 1573-1774 nnns volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 https://dx.doi.org/10.1007/s10763-022-10338-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2022 7 03 12 2005-2025 |
| language |
English |
| source |
Enthalten in International journal of science and mathematics education 21(2022), 7 vom: 03. Dez., Seite 2005-2025 volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 |
| sourceStr |
Enthalten in International journal of science and mathematics education 21(2022), 7 vom: 03. Dez., Seite 2005-2025 volume:21 year:2022 number:7 day:03 month:12 pages:2005-2025 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Gap thinking Natural number bias Interviews Rational number Reverse bias |
| isfreeaccess_bool |
true |
| container_title |
International journal of science and mathematics education |
| authorswithroles_txt_mv |
González-Forte, Juan Manuel @@aut@@ Fernández, Ceneida @@aut@@ Van Hoof, Jo @@aut@@ Van Dooren, Wim @@aut@@ |
| publishDateDaySort_date |
2022-12-03T00:00:00Z |
| hierarchy_top_id |
359787150 |
| id |
SPR052937690 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR052937690</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230901064711.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230901s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10763-022-10338-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR052937690</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10763-022-10338-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">González-Forte, Juan Manuel</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-4020-7869</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Incorrect Ways of Thinking About the Size of Fractions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gap thinking</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Natural number bias</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Interviews</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rational number</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reverse bias</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fernández, Ceneida</subfield><subfield code="0">(orcid)0000-0002-4791-9247</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Hoof, Jo</subfield><subfield code="0">(orcid)0000-0003-4752-6221</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Dooren, Wim</subfield><subfield code="0">(orcid)0000-0001-5002-4340</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">International journal of science and mathematics education</subfield><subfield code="d">Dordrecht : Springer Science + Business Media B.V., 2003</subfield><subfield code="g">21(2022), 7 vom: 03. Dez., Seite 2005-2025</subfield><subfield code="w">(DE-627)359787150</subfield><subfield code="w">(DE-600)2098363-3</subfield><subfield code="x">1573-1774</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:21</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:7</subfield><subfield code="g">day:03</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:2005-2025</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s10763-022-10338-7</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_647</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">21</subfield><subfield code="j">2022</subfield><subfield code="e">7</subfield><subfield code="b">03</subfield><subfield code="c">12</subfield><subfield code="h">2005-2025</subfield></datafield></record></collection>
|
| author |
González-Forte, Juan Manuel |
| spellingShingle |
González-Forte, Juan Manuel misc Gap thinking misc Natural number bias misc Interviews misc Rational number misc Reverse bias Incorrect Ways of Thinking About the Size of Fractions |
| authorStr |
González-Forte, Juan Manuel |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)359787150 |
| format |
electronic Article |
| delete_txt_mv |
keep |
| author_role |
aut aut aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
1573-1774 |
| topic_title |
Incorrect Ways of Thinking About the Size of Fractions Gap thinking (dpeaa)DE-He213 Natural number bias (dpeaa)DE-He213 Interviews (dpeaa)DE-He213 Rational number (dpeaa)DE-He213 Reverse bias (dpeaa)DE-He213 |
| topic |
misc Gap thinking misc Natural number bias misc Interviews misc Rational number misc Reverse bias |
| topic_unstemmed |
misc Gap thinking misc Natural number bias misc Interviews misc Rational number misc Reverse bias |
| topic_browse |
misc Gap thinking misc Natural number bias misc Interviews misc Rational number misc Reverse bias |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
International journal of science and mathematics education |
| hierarchy_parent_id |
359787150 |
| hierarchy_top_title |
International journal of science and mathematics education |
| isfreeaccess_txt |
true |
| familylinks_str_mv |
(DE-627)359787150 (DE-600)2098363-3 |
| title |
Incorrect Ways of Thinking About the Size of Fractions |
| ctrlnum |
(DE-627)SPR052937690 (SPR)s10763-022-10338-7-e |
| title_full |
Incorrect Ways of Thinking About the Size of Fractions |
| author_sort |
González-Forte, Juan Manuel |
| journal |
International journal of science and mathematics education |
| journalStr |
International journal of science and mathematics education |
| lang_code |
eng |
| isOA_bool |
true |
| recordtype |
marc |
| publishDateSort |
2022 |
| contenttype_str_mv |
txt |
| container_start_page |
2005 |
| author_browse |
González-Forte, Juan Manuel Fernández, Ceneida Van Hoof, Jo Van Dooren, Wim |
| container_volume |
21 |
| format_se |
Elektronische Aufsätze |
| author-letter |
González-Forte, Juan Manuel |
| doi_str_mv |
10.1007/s10763-022-10338-7 |
| normlink |
(ORCID)0000-0003-4020-7869 (ORCID)0000-0002-4791-9247 (ORCID)0000-0003-4752-6221 (ORCID)0000-0001-5002-4340 |
| normlink_prefix_str_mv |
(orcid)0000-0003-4020-7869 (orcid)0000-0002-4791-9247 (orcid)0000-0003-4752-6221 (orcid)0000-0001-5002-4340 |
| title_sort |
incorrect ways of thinking about the size of fractions |
| title_auth |
Incorrect Ways of Thinking About the Size of Fractions |
| abstract |
Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. © The Author(s) 2022 |
| abstractGer |
Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. © The Author(s) 2022 |
| abstract_unstemmed |
Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change. © The Author(s) 2022 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 |
| container_issue |
7 |
| title_short |
Incorrect Ways of Thinking About the Size of Fractions |
| url |
https://dx.doi.org/10.1007/s10763-022-10338-7 |
| remote_bool |
true |
| author2 |
Fernández, Ceneida Van Hoof, Jo Van Dooren, Wim |
| author2Str |
Fernández, Ceneida Van Hoof, Jo Van Dooren, Wim |
| ppnlink |
359787150 |
| mediatype_str_mv |
c |
| isOA_txt |
true |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s10763-022-10338-7 |
| up_date |
2024-07-03T15:53:07.274Z |
| _version_ |
1803573775329918976 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR052937690</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230901064711.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230901s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10763-022-10338-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR052937690</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10763-022-10338-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">González-Forte, Juan Manuel</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-4020-7869</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Incorrect Ways of Thinking About the Size of Fractions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gap thinking</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Natural number bias</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Interviews</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rational number</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reverse bias</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fernández, Ceneida</subfield><subfield code="0">(orcid)0000-0002-4791-9247</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Hoof, Jo</subfield><subfield code="0">(orcid)0000-0003-4752-6221</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Dooren, Wim</subfield><subfield code="0">(orcid)0000-0001-5002-4340</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">International journal of science and mathematics education</subfield><subfield code="d">Dordrecht : Springer Science + Business Media B.V., 2003</subfield><subfield code="g">21(2022), 7 vom: 03. Dez., Seite 2005-2025</subfield><subfield code="w">(DE-627)359787150</subfield><subfield code="w">(DE-600)2098363-3</subfield><subfield code="x">1573-1774</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:21</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:7</subfield><subfield code="g">day:03</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:2005-2025</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s10763-022-10338-7</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_647</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">21</subfield><subfield code="j">2022</subfield><subfield code="e">7</subfield><subfield code="b">03</subfield><subfield code="c">12</subfield><subfield code="h">2005-2025</subfield></datafield></record></collection>
|
| score |
7.398551 |