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To better understand the resources available for teachers to make decisions, this study investigates the categories of appreciation that mathematics teachers express in relation to different ways of perceiving student work in problem-based lessons. Drawing on categories of perception and linguistic appraisal theory, we build up an analytic framework and analyze data from two groups of algebra teachers engaged in collaborative problem-based lesson design. Specifically, we report on the categories of appreciation that teachers articulated when evaluating student work through the lens of serviceability, that is, how the work supports or hinders the progression toward the lesson goals and how their appreciation is expressed across the interpersonal, textual, and ideational metafunctions.