Observing High-school Students' Mathematical Understanding and Mathematical Proficiency in the Context of Mathematical Modeling
Notice bibliographique
Résumé
The use of mathematical modeling in education has been investigated for the last five decades. The benefits of bringing modeling into mathematics classes are well known and well accepted, and modeling is becoming more common and more appealing to mathematics teachers. However, there are still unanswered questions and conjectures to be explored, so as to aid and encourage mathematics teaching through modeling. The present study uses classroom-based research to explore the use of modeling tasks within high-school mathematics classes, in order to provide insight into the teaching of mathematics for understanding. In this study, participants' were engaged in mathematical modeling tasks in which they were required to develop models for mathematical situations, instead of using an already known mathematical model or a given one. This investigation intended to comprehend what forms of mathematical understanding and mathematical proficiency are observed and how they are expressed when high-school students are engaged in this mathematical modeling setting. The research methodology is founded on design-based research, since it combines theoretical research knowledge with practical experiences, yielding practical knowledge (The Design-Based Research Collective, 2003). The classroom design framework is based on complexity science underpinnings. This is due to the fact that mathematics classes are acknowledged as complex systems, in which students collectively act and interact in order to develop, construct and enhance their mathematical ideas. These actions and interactions are believed to be non-linear, spontaneous and self-organized, characterizing a complex system that allows mathematical understanding to emerge (Davis & Simmt, 2003). In order to investigate students' mathematical understanding and proficiency while engaged in mathematical modeling tasks, four different tasks were proposed to a high-school class taking grade 11 mathematics. The class was composed of 27 students. Although all of them participated in the tasks, data was collected from the 12 students who provided consent. Tasks were applied during a four-month Alberta mathematics course. Audio and video recordings, students' mathematics journals and researcher field notes were collected. Post class sessions, students were invited to participate in recall interviews. Assuming that students' mathematical understanding is encompassed by students‘ mathematical proficiency, data analysis was conducted using Kilpatrick, Swafford and Findell's (2001) model of mathematical proficiency, where mathematical proficiency is composed by five strands, namely: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. The basis of the research data analysis framework consists of identifying indicators of each of Kilpatrick et al.'s strands in students' work, and then investigating how students undergo these strands along the modeling tasks. This research study offers insight into the use of mathematics modeling by: 1) portraying how mathematical modeling tasks foster high-school students‘ mathematical understanding and proficiency; and 2) showing the feasibility of implementing this kind of task in mathematics classes with time and curriculum constraints. The study revealed that students demonstrate mathematical understanding and proficiency during the course of the modeling tasks, even when they do not come to full resolutions of problems. Research outcomes indicate that mathematical modeling tasks promote students‘ mathematical understanding and proficiency and can be an important approach in the task of teaching for understanding.
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Comment cette classification a été obtenuedéplier
Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,001 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,001 | 0,001 |
| Communication savante | 0,000 | 0,001 |
| Science ouverte | 0,001 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,001 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».