<p>The choice of mathematical modelling tasks for research purposes is critical, and so is the presentation of tasks in research reports. The openness of modelling tasks positions modellers as decision makers. To assess opportunities for decision making in published modelling tasks, we develop a literature-based framework with 11 features of a modelling task that can hinder or entice decision making within different phases of the modelling process. We use the framework to code the statements of 109 modelling tasks from 67 journal articles published from 2011 through 2020. Subsequent coding addressed the settings in which the tasks were used for data collection. Results indicate that the tasks call for extensive decision making in mathematising and less decision making in structuring and simplifying and in interpreting and validating, suggesting that a notable number of the tasks might target applications of mathematics rather than holistic modelling activity. Our findings expand researchers’ understanding of assumption making by drawing attention to the objects of the assumptions (e.g., typical value, non-quantitative term). The study also offers different ways in which modellers’ identification of variables might be bounded by a task. We further reveal that variable identification might be linked to particular types of assumption making. Our results document minimal attention to implementation information in the published reports, and we thus call authors to provide task implementation details that pedagogically contextualize findings.</p>