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Our purpose in this paper is to report on an observational study to show how students think about the links between the graph of a derived function and the original function from which it was formed. The participants were asked to perform the following task: they were presented with four graphs that represented derived functions and from these graphs they were asked to construct the original functions from which they were formed. The students then had to walk these graphs as if they were displacement–time graphs. Their discussions were recorded on audio tape and their walks were captured using data logging equipment and these were analysed together with their pencil and paper notes. From these three sources of data, we were able to construct a picture of the students’ graphical understanding of connections in calculus. The results confirm that at the start of the activity the students demonstrate an algebraic symbolic view of calculus and find it difficult to make connections between the graphs of a derived function and the function itself. By being able to ‘walk’ an associated displacement time graph, we propose that the students are extending their understanding of calculus concepts from symbolic representation to a graphical representation and to what we term a ‘physical feel’. [Copyright &y& Elsevier]

Introduction Tumor vaccines use various strategies to generate immune responses, commonly targeting generic tumor-associated antigens. The tumor lysate, particle-loaded, dendritic cell (TLPLDC) vaccine is produced from DC loaded with autologous tumor antigens, creating a patient-specific vaccine. Here, we describe initial phase I/IIa trial results. Methods This trial includes patients with any stage solid tumors, ECOG ≤1, and >4 months life-expectancy. A personalized vaccine is created using 1 mg of tumor and 120 ml blood (to isolate DC). Primary vaccination series (PVS) is four monthly inoculations. Patients are followed per standard of care (SOC). Endpoints include safety and tumor response (RECIST v1.1). Results 44 patients were enrolled and vaccinated consisting of 31 late stage patients with residual/measurable disease, and 13 disease-free patients after SOC therapies. While 4 patients progressed before completing the PVS, 12/31 (39%) demonstrated clinical benefit (2 complete responses, 4 partial responses, 6 stable disease). In the adjuvant setting, 46% of late stage patients remain disease free at a median of 22.5 months. Conclusions The TLPLDC vaccine is scalable, generates a personalized DC vaccine, and requires little autologous tumor tissue and few DC. The vaccine is safe, with primarily grade 0–2 toxicities, and nearly 40% clinical benefit rate in varied tumors, warranting further study. Trial Registration: ISRCTN81339386, Registered 2/17/2016. [ABSTRACT FROM AUTHOR]