The purpose of this qualitative study was to provide empirical evidence of the extent to which the types of tasks recommended by Sheffield for eliciting characteristics of mathematical promise allowed for the manifestation of these characteristics in primary-grade students within a problem-based learning (PBL) context. Data included student work collected from two mathematics PBL units, teacher interviews, surveys used by teachers to identify mathematically promising students and video-recorded classroom observations. Data analysis followed Miles and Huberman's data reduction method with findings reported as themes. Results indicate that students, including those from underserved populations, exhibit characteristics aligned with attributes signifying mathematical promise as proposed by Sheffield within a PBL context.

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is a fourth-yeard PhD candidate at the University of Notre Dame working with Dr. Chaoli Wang on High Performance Computing and Scientific Visualization. His main research focus is summarization and reconstruction of big data using GPU-acceleration and deep learning techniques. He has applied his research in isosurface selection for volume visualization and analysis, graph visualization, and is currently using deep learning techniques for analysis of unsteady flow simulations. He has completed a research internship at Argonne National Laboratory in summer 2018. He received his BSc (2014) and MSc (2016) in Software Engineering at the Vienna University of Technology. During his Master's program, he conducted research at the VRVis Research Center in Vienna and continued acquiring experience during a research internship at the University of California, Irvine. Miss Wenqing Chang, Xi'an Jiaotong UniversityWenqing Chang is currently a senior student in Information Engineering from Xi'an Jiaotong University. In 2018, she joined NUS Summer Workshop, developing a 2D webpage game using WebGL and rendering 3D animation using OpenGL. From the fall of 2018 to present, she is a lab researcher in wireless communication, built ambient backscatter enabled secondary communication model and right now is involved in deep learning for joint source-channel coding.

In this article, we present 2 technology-involved tasks that we use in our mathematics pedagogy courses to ostensibly give preservice secondary mathematics teachers (PSMTs) sample activities they can use in their teaching or use to assess their own future students' ability to apply trigonometric functions in contextual situations using technology. However, we have two other purposes for posing these tasks. One purpose is to provide occasions for PSMTs to self-assess their mathematical and technology knowledge, and subsequently take action to learn mathematics and technology features. The other purpose is to use such tasks as springboards for substantive discussions about teaching, learning, technology, and assessment. Such simulation tasks have engaged PSMTs and helped them develop their knowledge base for teaching mathematics.

Students think resiliently about using the quadratic formula, analyzing factors graphically, finding the shortest distance between two points, and finding margin of error.