@article{paul_grundmeier_moore-russo_2024, title={3D Manipulatives in Integral Calculus: Student Achievement and Confidence in Solids-Of-Revolution Tasks}, volume={2}, DOI={10.1080/19477503.2024.2312097}, abstractNote={In this university study, sections of an integral calculus course were randomly assigned to either a control or treatment group for a lesson on volumes of revolution. Both groups were given similar collaborative tasks, but only the students in the treatment group were given access to a set of 3D manipulatives. Pre- and post-assessments were administered to measure student achievement and confidence on the tasks comparing results for the control and treatment groups as well as for the male and female students. No statistically significant differences in student achievement were detected for the control or treatment group or by reported gender on either an immediate posttest or a delayed posttest. There was statistical significance in confidence after engaging in the 3D manipulative tasks favoring the treatment group. However, further inspection by gender revealed that while males in the treatment group were more likely to report higher confidence ratings than males in the control group, the reverse was true for females.}, journal={Investigations in Mathematics Learning}, publisher={Informa UK Limited}, author={Paul, Stepan and Grundmeier, Dusty and Moore-Russo, Deborah}, year={2024}, month={Feb}, pages={1–20} }
@article{moore-russo_martínez-planell_stanhope_seeburger_paul_vandieren_2024, title={Multivariable Calculus Instructors’ Reports of Resource use}, url={https://doi.org/10.1007/s40753-024-00243-5}, DOI={10.1007/s40753-024-00243-5}, journal={International Journal of Research in Undergraduate Mathematics Education}, author={Moore-Russo, Deborah and Martínez-Planell, Rafael and Stanhope, Shelby and Seeburger, Paul and Paul, Stepan and VanDieren, Monica M.}, year={2024}, month={Dec} }
@inproceedings{martinez-planell_moore-russo_seeburger_stanhope_paul_2024, title={Resource Use and Student Engagement in Multivariable Calculus}, url={http://sigmaa.maa.org/rume/Site/Proceedings.html}, booktitle={SIGMAA on RUME Annual Conference}, author={Martinez-Planell, Rafael and Moore-Russo, Deborah and Seeburger, Paul and Stanhope, Shelby and Paul, Stepan}, year={2024}, month={Feb} }
@article{chen_delp_paul_2023, title={Manipulative calculus: active learning with 3D models}, DOI={10.1090/psapm/079/00714}, abstractNote={Manipulative Calculus is a curriculum development project focused on creating active learning\index{active learning} lessons in calculus courses centered around digitally fabricated 3D models that we put into students’ hands. In these lessons, students are asked to make geometric sense of the concepts learned in the course through problems requiring them to handle, discuss, and sketch on the models. As of this writing, the lessons and models have been in use for several semesters by dozens of instructors and thousands of students. This paper reports on the development of the 3D models and lessons for multivariable calculus, experiences and assessments of their use in the classroom, and efforts to make the curricular materials accessible to other instructors.}, journal={Proceedings of Symposia in Applied Mathematics}, publisher={American Mathematical Society}, author={Chen, Janet and Delp, Kelly and Paul, Stepan}, year={2023}, pages={141–168} }
@inproceedings{paul_2023, place={Phoenix, Arizona}, title={What Can We Learn from Non-Euclidean Paper?}, url={http://archive.bridgesmathart.org/2023/bridges2023-219.html}, booktitle={Bridges 2023}, publisher={Tessellations Publishing}, author={Paul, Stepan}, editor={Holdener, Judy and Torrence, Eve and Fong, Chamberlain and Seaton, KatherineEditors}, year={2023}, pages={219–226} }
@inproceedings{paul_2021, place={Phoenix, Arizona}, title={The Flat Klein Bottle Rendered in Curved-Crease Origami}, url={http://archive.bridgesmathart.org/2021/bridges2021-47.html}, booktitle={Bridges 2021}, publisher={Tessellations Publishing}, author={Paul, Stepan}, editor={Swart, David and Farris, Frank and Torrence, EveEditors}, year={2021}, pages={47–54} }
@article{paul_2018, title={3D Printed Manipulatives in a Multivariable Calculus Classroom}, volume={28}, ISSN={1051-1970 1935-4053}, url={http://dx.doi.org/10.1080/10511970.2018.1445675}, DOI={10.1080/10511970.2018.1445675}, abstractNote={As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R3. This article describes three lessons for a multivariable calculus class in which students interact with 3D models to learn concepts relating to surfaces, solids, and multivariable functions. With each lesson are discussions and examples of student work based on the author's experience. Finally, the article includes a brief section on practical considerations for mathematics instructors thinking of using 3D printing technology in their classrooms.}, number={9}, journal={PRIMUS}, publisher={Informa UK Limited}, author={Paul, Stepan}, year={2018}, month={Jul}, pages={821–834} }
@misc{paul_chen_2018, title={Manipulative Calculus}, url={https://www.manipulativecalculus.com/}, author={Paul, Stepan and Chen, Janet}, year={2018} }
@article{paul_gu_2017, title={Tensor-splitting properties of $n$-inverse pairs of operators}, DOI={10.4064/sm8518-2-2017}, abstractNote={We study $n$-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an $n$-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from $l$- and $m$-inverse pa}, journal={Studia Mathematica}, author={Paul, Stepan and Gu, Caixing}, year={2017} }
@article{paul_2013, title={New methods for determining speciality of linear systems based at fat points in Pn}, url={http://dx.doi.org/10.1016/j.jpaa.2012.09.019}, DOI={10.1016/j.jpaa.2012.09.019}, journal={Journal of Pure and Applied Algebra}, publisher={Elsevier BV}, author={Paul, Stepan}, year={2013}, month={May} }
@article{moore-russo_martínez-planell_stanhope_seeburger_paul_vandieren, title={Multivariable calculus instructors' reports of resource use}, journal={International Journal of Research in Undergraduate Mathematics Education}, author={Moore-Russo, D. and Martínez-Planell, R. and Stanhope, S. and Seeburger, P. and Paul, S. and VanDieren, M.} }