Quantitative Reasoning: Exploring Troublesome Thresholds
Notice bibliographique
Résumé
Conversations about teaching and student learning with faculty across many of the science disciplines will invariably lead to a number of shared concerns. One such concern typically revolves around quantitative reasoning (QR). This paper presents the results of a pilot study in which instructors and students were interviewed with a view to identifying key QR obstacles in earth, ocean, and environmental sciences courses at one Canadian university. The instructor point of view was obtained by interviewing faculty and graduate student teaching assistants, while the student perspective came from a focus group of undergraduate students from across these disciplines. In both cases, participants were asked about specific quantitative aspects of their courses where students struggle and strategies they were already using in these cases. We examine the possible role of threshold concepts in QR within the earth, ocean, and environmental sciences. Threshold concepts are transformative, often troublesome concepts that are key to developing true expertise in a discipline; once mastered, they are irreversible and can serve to bring together different aspects of the subject. As such, their possible role in QR holds potential for enhancing the learning. Meyer and Land (2005) suggest that in crossing these thresholds into new ways of viewing the discipline, or indeed, the world, the journey is somewhat akin to travelling through a portal, or liminal space, where uncertainty is common and developing understanding is not necessarily linear. We further explore a number of strategies that can be used to help students overcome the challenges that were identified.\nThe results revealed a range of themes considered troublesome that crossed all disciplines including applying math across changing contexts, a fear of math, the lack of student’s ability to reflect on their answers and therefore correct where necessary, and working with conversions and scale. Additionally, both faculty and students identified the difficulty many students have when working with data, in particular, plotting data, manipulating data and interpreting results, with and without the use of computer software packages. We note in particular that students’ difficulty in articulating or identifying threshold concepts may reflect their incomplete journey through the liminal stage. We need other strategies, such as looking at their work, in order to assess this more completely. Although no group specifically articulated concepts, they considered transformative amongst the troublesome concepts they identified. We suggest that there are learning thresholds within QR, and that these span all the sciences. Two such thresholds we propose based on our study are: (a) the ability to apply QR across a range of contexts and use it as a tool or a form of language for scientific problem solving, and (b) fluency in data literacy which enables a student to work through the scientific process. We conclude by presenting a set of strategies to help instructors guide students as they develop QR skills while working through these troublesome areas. These strategies include those suggested by faculty and students in this study, and others identified from evidence-based best practices in the literature.
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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 | 0,035 | 0,086 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,001 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,005 | 0,003 |
| Études des sciences et des technologies | 0,006 | 0,027 |
| Communication savante | 0,011 | 0,019 |
| Science ouverte | 0,004 | 0,012 |
| Intégrité de la recherche | 0,003 | 0,005 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,003 | 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 ».