Pedagogical Orientations towards the Integration of Language and Content: English Language Learnersâ Opportunities to Learn in Mathematics Classrooms
Bibliographic record
Abstract
Achieving equitable opportunities to learn has been recognized as an important issue in multilingual content classrooms. However, partially because mathematics is conceptualized as a language-free subject, there is limited research examining linguistic minority students’ opportunities to learn in mathematics classrooms. The purpose of this research is to identify linguistic minority students’ opportunities to learn in mathematics classrooms in a Canadian multilingual urban elementary school, where English was the main instructional language. \n Drawing on cultural historical activity theory, this study focuses on two aspects of learning: externalization, which emphasizes learners’ creation of new cultural artifacts and new contexts to apply the given artifacts, and internalization, which emphasizes learners’ acquisition of preexisting cultural artifacts. \n In this ethnographic study, I examined the activity systems of participatory action research (PAR) with the activity system of regular mathematics lessons. Within these activity systems, I focused on newly-arrived English language learners’ (ELLs) participation. Specifically, I examined the range of opportunities to learn afforded to students in the two activity systems and identified how focal ELLs accessed these opportunities to learn. \n In the activity system of PAR, which emphasized externalization, students conducted research and presented their conclusions in order to implement changes in their school environment. All students, however, did not participate equally. Specifically, the focal ELLs were not able to access these opportunities to learn as a result of group dynamics, marginalized social identities, and other students’ perceptions of their linguistic ability. \n In the activity system of regular mathematics lessons, which emphasized internalization, the teacher organized lessons in ways that allowed focal ELLs to receive extra support and resources to reach the curriculum expectations. These mathematics lessons allowed focal ELLs to increase their participation through mathematical reasoning, problem solving, and explanations with a variety of resources including visual representations.\n A critical examination of the interactions revealed that focal ELLs’ opportunities to learn were expanded or limited depending upon classroom configurations. Furthermore, this research suggests that students’ social identities serve as both a medium and a product of learning. These results have valuable implications for developing inclusive classroom practices and curriculum in multilingual content classrooms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.007 | 0.013 |
| Scholarly communication | 0.011 | 0.002 |
| Open science | 0.001 | 0.007 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".