Abstract
ABSTRACT We articulate two perspectives, termed co-occurrence and same extent, to capture our understanding of what six future U.S. mathematics teachers intended to express when generating drawings and equations for proportional relationships. We illustrate these perspectives through two case studies and make three contributions. First, the future teachers used co-occurrence and same extent across different forms of inscription. In other words, general orientations to expressing proportional relationships with inscriptions influenced how they generated equations. Second, the future teachers used the two perspectives to generate both normatively correct and normatively incorrect equations. Thus, whether or not they generated normatively correct equations was a matter of where and how they combined the two perspectives. Third, we conjecture that the two perspectives help explain why, at least for some, the x/a = y/b and 1/a • x = 1/b • y forms may provide more accessible entry points into linear equations than the traditional y = mx form..
Published Version
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