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Mathematical solutions to textbook word problems are correlated with semantic relations between the objects described in the problem texts. In particular, division problems usually involve functionally related objects (e.g., tulips-vases) and rarely involve categorically related objects (e.g., tulips-daisies). We examined whether middle school, high school, and college students use object relations when they solve division word problems (WP) or perform the less familiar task of representing verbal statements with algebraic equations (EQ). Both tasks involved multiplicative comparison statements with either categorically or functionally related objects (e.g., "four times as many cupcakes [commuters] as brownies [automobiles]"). Object relations affected the frequency of correct solutions in the WP task but not in the EQ task. In the latter task, object relations did affect the structure of nonalgebraic equation errors. We argue that students use object relations as "semantic cues" when they engage in the sense-making activity of mathematical modeling.

Through examination of the career of the psychiatrist August Hoch (1868—1919), this essay challenges two assumptions implicit in histories of US progressive-era psychiatry: that the emergence of Freudian psychoanalysis signalled a devaluation of Kraepelin's contributions and that theoretical and therapeutic eclecticism inhibited psychiatric research. Locating Hoch's guiding principles within the context of Kraepelin's clinical psychiatry, I analyse how Hoch mediated the demands of classification and the dynamic understanding of persons in prosecuting a new kind of clinical research that would not have been possible within either the Kraepelinian or Freudian perspective alone.

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