Students' problem solving and understanding in learning mathematics through conceptually- and procedurally-focused instruction : a situated discourse approach
Notice bibliographique
Résumé
The nature and effect of two approaches to instruction in mathematics were studied from a situated cognition perspective, which emphasizes the pivotal role of discourse in knowledge comprehension. Typically, students must construct conceptual knowledge representations that integrate different types of information from diverse resources. Currently, little is known about how students' cognitive processes are influenced by distinct instructional approaches. The study focused on two problem-based methods: conceptually-focused instruction (CFI) and procedurally-focused instruction (PR). Both methods implemented common principles based on cognitive theories. Moreover, different characteristics were identified in the cognitive theories having different research traditions as their source. These differences provided insights for devising the two instructional approaches. A one-on-one tutoring setting was implemented for investigation. Of the two individual students in each matched pair, one was randomly assigned to CFI, and the other to PFI. There were a total of twelve one-on-one tutoring sessions, with six grade nine students in each condition. The researcher, an experienced high school mathematics teacher and counselor for the French Montreal School Board, was also the tutor in both conditions. The same two problems on linear functions, with gradual increase in difficulty, were solved in each method. Points of disjunction of approaches were achieved through variation in the type and degree of explanation (modeling strategy in Problem 1) and of scaffolding (coaching strategy in Problem 2). The results indicated that the different instructional conditions were implemented with consistency. Within the problem-based instruction framework and for the same problem-solving activity, it was possible for the tutor to maintain the focus on concepts vs. procedures. Although both approaches were equally beneficial to students, they affected the students' cognitive activity differently. Students' talk was more procedural in both approaches, but their speech was more balanced between concepts and procedures in CFI than in PH, indicating that students' cognitive processes were transferred differently from the modeling to the coaching discourse. These findings have implications for policymakers in education and for Quebec Ministry of Education standards. Future research is recommended to extend such findings to other populations of students and to additional types of teaching approaches.
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,002 | 0,009 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,001 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,001 |
| Communication savante | 0,002 | 0,001 |
| Science ouverte | 0,001 | 0,002 |
| Intégrité de la recherche | 0,001 | 0,001 |
| 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 source (Gemma direct ou Codex distillé), 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 ».