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to understand better how expectations operate as a cultural force in learning groups, we have to make a distinction between two types of expectations: directives and beliefs.

very clear standards for students about points, grades, and keeping score, one sees a belief that school is about work and that students must be coerced or bribed into learning through the use of grades

one sees the belief that learning algebra is primarily about acquiring knowledge of procedures rather than developing understanding, and that memorization and practice are the most effective tools for that job. This theory of action, “One learns through memorization and practice,” made it hard for Karen to bring out and facilitate students’ thinking. Instead, thinking existed as an add-on to the regular rhythm of the class, something she did as an “extra” to the regular work of the class. Through her strong focus on grades and passing the course, even if one is “no good at mathematics,” Karen sent the message that our abilities are largely fixed and that “getting by” was all that some could hope to accomplish. One might not understand algebra, but with effort one could at least pass the course. Finally, in her efforts to promote order and control, certainly worthwhile and important goals in any classroom, Karen tilted the balance toward students’ becoming passive learners who were dependent on her.