MATH: EAGER:Mathematical Problem Solving Item Development Project

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Access to STEM careers relies heavily on student success in their foundational mathematics courses. Little is understood about the mathematical problem solving capacity students must develop in order to leverage mathematical knowledge from prior courses in learning mathematics central to their field of study. The Mathematical Problem Solving Item (MPSI) Development Project will create a pool of validated problems and associated assessment items that indicate a student's mathematical problem solving (MPS) in five key areas identified in the research literature: (a) sense-making/ orienting, (b) representing/ connecting, (c) challenge/ difficulty, (d) reviewing, and (e) defending/ justifying. To this end, the project will: (1) develop and refine items that indicate levels of MPS in the five areas stated above with students in college algebra and calculus. To this end, the project will pilot and refine items with approximately 1600 college algebra students and 1400 calculus student; (2) validate items by convening a panel of experts in MPS; and (3) use a pre- and post-assessment design to examine the extent to which the MPSI items capture the elements of MPS.In contrast to labor- and time-intensive measures of students' MPS capacity that involve task-based interviews and review of student work using detailed scoring rubrics, the MPSI item design will provide items that use a Likert-type scale and can be machine scored. The project will investigate the extent to which the items capture the impact of curricula in college algebra and calculus on MPS as well as the extent to which success in these mathematics courses can be inferred from student MPS profiles derived from performance on MPSI project items. The MPSI project will provide an important and efficient tool that separates skills, procedural knowledge, and conceptual knowledge gained in a course from the MPS levels needed to leverage this mathematical knowledge in future courses and to persist in STEM fields.