The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. We analyze dialogue to illustrate a process for determining whether a classroom instance offers such an opportunity and to demonstrate the usefulness of the construct in examining classroom discourse. This construct contributes to research and professional development related to teachers' mathematically productive use of student thinking by providing a lens and generating a common language for recognizing and agreeing on a critical core of student mathematical thinking that researchers can attend to as they study classroom practice and that teachers can aspire to notice and build upon when it occurs in their classrooms.

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Demand for total hip (THA) and knee arthroplasties (TKA) is expected to rise sharply by 2030. Increasing demand in conjunction with financial pressure requires the use of cost-effective total joint arthroplasty (TJA) strategies. This study examined the effects that day of week and surgery location [academic (AH) versus orthopaedic-specific (OsH) hospital] have on length of stay (LOS) and cost for primary TJA patients in one multihospital university-based medical center. An Institutional Review Board-approved database of adult patients undergoing primary THA or TKA from June 2013 to December 2014 was constructed. Surgery location, day of procedure, age, American Society of Anesthesiologists (ASA) classification, LOS, and cost were recorded for each patient. Data were compared for significant differences using analysis of variance, -Test or rank sum and for strength of correlations using Pearson's or Spearman's tests. A total of 1,291 patients met inclusion criteria. OsH showed significantly lower cost and shorter LOS than AH. Wednesday surgeries had significantly higher cost and longer LOS than all other days. Friday surgeries had significantly lower cost and shorter LOS than other days. ASA 3 and 4 were associated with the highest cost and longest LOS. LOS had a moderately strong direct correlation to cost. ASA did not have a strong correlation with LOS or cost. Data separated for THA and TKA showed similar results. At our institution, OsH provides more consistent and lower LOS and cost across all ASA classes. Wednesday and Thursday surgeries have increased LOS and cost than other days, which may be due to weekend discharge difficulties (average LOS is 3.0 days).

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