Comparing Elementary and Secondary Teachers’ Robust Understanding of Proportional Reasoning

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary pre-service teachers (PSTs) and 13 elementary PSTs drew upon when solving a comparison proportional reasoning problem. Data from written work and videos of PSTs’ explanations were analyzed using the robust understanding of proportional reasoning for teaching framework. Both elementary and secondary PSTs ubiquitously drew upon the same four knowledge resources (comparison of quantities, ratios, proportional situation, and ratio as measure). Elementary PSTs were more apt to counterproductively draw upon the knowledge resource ratios ≠ fractions, while secondary PSTs more often counterproductively drew upon equivalence. Mathematics educators can leverage the knowledge resources afforded by this task and strategically highlight productive and counterproductive resources to tailor instruction that develops PSTs’ robust understanding of proportional reasoning.