Transitions between conceptual and procedural knowledge profiles. Patterns in understanding fractions and indicators for individual differences
Knowledge profiles in conceptual and procedural fraction knowledge can vary among students. Given the cross-sectional design of previous studies, it is unclear whether these profiles can be altered or remain stable. Accordingly, we investigated (1) profiles of conceptual and procedural fraction know...
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| Veröffentlicht in: | Learning and individual differences Jg. 116; S. 102548 |
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| ISSN: | 1041-6080 |
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| Abstract | Knowledge profiles in conceptual and procedural fraction knowledge can vary among students. Given the cross-sectional design of previous studies, it is unclear whether these profiles can be altered or remain stable. Accordingly, we investigated (1) profiles of conceptual and procedural fraction knowledge, (2) their longitudinal transitions, and (3) the underlying factors. Data from N = 166 grade 7 students who participated in an intervention study with a pre-posttest design were analyzed. A latent transition analysis revealed six distinct profiles characterized by equal strength or weakness and varying conceptual and procedural knowledge levels, replicating individual differences in fraction knowledge. The longitudinal analysis showed that the knowledge profiles tended to be stable. Moreover, the profile transitions indicated gradual differences in the two types of knowledge rather than students catching up in one type of knowledge. Furthermore, the results suggest that basic arithmetic competence, and mathematics anxiety are related to profile membership.
Studying individual differences in conceptual and procedural fraction knowledge is highly important in education. It helps educators gain valuable insights into how students grasp this fundamental mathematical concept, as they can identify diverse knowledge profiles and underlying factors. By understanding these differences, teachers can develop tailored instruction to meet the specific needs of each learner, ultimately enhancing their understanding and mastery of fractions. This research deepens the understanding of fraction learning and offers valuable guidance for creating more effective and personalized teaching approaches.
•Varying individual profiles in conceptual and procedural fraction knowledge found.•Longitudinal analysis suggests stable profiles over time.•Transition paths show gradual improvement in knowledge types, not catching up in one.•Math anxiety and basic arithmetic competence linked to cluster membership |
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| AbstractList | Knowledge profiles in conceptual and procedural fraction knowledge can vary among students. Given the cross-sectional design of previous studies, it is unclear whether these profiles can be altered or remain stable. Accordingly, we investigated (1) profiles of conceptual and procedural fraction knowledge, (2) their longitudinal transitions, and (3) the underlying factors. Data from N = 166 grade 7 students who participated in an intervention study with a pre-posttest design were analyzed. A latent transition analysis revealed six distinct profiles characterized by equal strength or weakness and varying conceptual and procedural knowledge levels, replicating individual differences in fraction knowledge. The longitudinal analysis showed that the knowledge profiles tended to be stable. Moreover, the profile transitions indicated gradual differences in the two types of knowledge rather than students catching up in one type of knowledge. Furthermore, the results suggest that basic arithmetic competence, and mathematics anxiety are related to profile membership.
Studying individual differences in conceptual and procedural fraction knowledge is highly important in education. It helps educators gain valuable insights into how students grasp this fundamental mathematical concept, as they can identify diverse knowledge profiles and underlying factors. By understanding these differences, teachers can develop tailored instruction to meet the specific needs of each learner, ultimately enhancing their understanding and mastery of fractions. This research deepens the understanding of fraction learning and offers valuable guidance for creating more effective and personalized teaching approaches.
•Varying individual profiles in conceptual and procedural fraction knowledge found.•Longitudinal analysis suggests stable profiles over time.•Transition paths show gradual improvement in knowledge types, not catching up in one.•Math anxiety and basic arithmetic competence linked to cluster membership |
| ArticleNumber | 102548 |
| Author | Lenz, Katja Reinhold, Frank Wittmann, Gerald |
| Author_xml | – sequence: 1 givenname: Katja surname: Lenz fullname: Lenz, Katja email: katja-lenz@ph-gmuend.de – sequence: 2 givenname: Frank surname: Reinhold fullname: Reinhold, Frank – sequence: 3 givenname: Gerald orcidid: 0000-0003-2094-0908 surname: Wittmann fullname: Wittmann, Gerald |
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| Cites_doi | 10.1111/cdev.12218 10.1111/nyas.14715 10.1037/a0019824 10.1007/s10649-006-9036-2 10.1007/978-3-030-00491-0_7 10.1007/s11858-020-01213-2 10.1016/j.dr.2014.10.001 10.1037/0022-3514.86.1.148 10.1016/j.jecp.2011.08.012 10.1016/j.jmathb.2012.02.001 10.1016/j.lindif.2017.11.010 10.1016/j.learninstruc.2006.08.001 10.1037/edu0000025 10.1016/j.learninstruc.2014.03.002 10.1016/j.jecp.2012.07.009 10.1037/a0031200 10.1016/j.jecp.2014.08.006 10.1037/0022-0663.93.2.346 10.1037/a0017486 10.1207/s15327906mbr2804_2 10.1207/s15326985ep4001_3 10.3389/fpsyg.2013.00715 10.1037/xge0001382 10.1111/bjop.12244 10.1037/a0021276 10.1080/07370001003676603 10.1037/0033-2909.107.2.139 10.1037/0012-1649.27.5.777 10.1016/j.learninstruc.2004.06.015 10.1016/j.learninstruc.2013.12.004 10.29333/iejme/9282 10.1016/j.jecp.2013.02.001 10.1007/s10649-011-9338-x 10.1026/0049-8637/a000142 10.1016/j.learninstruc.2014.03.004 10.5964/jnc.v5i2.150 10.1007/s10649-018-9864-x 10.1080/14926156.2013.784828 10.1016/j.cedpsych.2012.07.001 10.3389/feduc.2020.00029 10.1037/a0016701 10.1177/0022219416662033 10.1016/j.cogpsych.2011.03.001 10.1007/s10649-006-9028-2 10.1111/bjep.12333 10.1037/dev0000275 10.18637/jss.v081.i04 |
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| Keywords | Latent transition analysis Conceptual knowledge Procedural knowledge Fractions Profiles |
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