Final answer:
Incidental learning is least likely with Mager-like objectives due to their specific and narrow focus on intentional instruction and measurable outcomes, which limit the potential for learning that is not directly targeted.
Step-by-step explanation:
Incidental or accidental learning refers to acquiring knowledge without a deliberate instructional aim, which occurs naturally as a byproduct of other activities. When considering the learning frameworks mentioned in the question, Mager-like objectives are explicit, performance-based objectives that state the expected outcome, conditions, and criteria for success, hence offering little room for incidental learning.
Alternatively, Gronlund-like objectives focus on general outcomes that allow some degree of incidental learning, especially when the objectives are broader or process-oriented. Bloom's Taxonomy is a classification system that organizes learning objectives but does not inherently prevent incidental learning. Lastly, Constructivist approaches encourage personal construction of knowledge through experience and reflection, often leading to a higher probability of incidental learning as students apply their experiences and engage with the content in personalized ways.
Therefore, incidental or accidental learning is "least" likely to take place when using Mager-like objectives due to their specific, narrow, and prescriptive nature that focuses on intentional instruction and concrete, measurable outcomes rather than open-ended exploration or experience-based learning.