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Ethics education has been recognized as increasingly important to engineering over the past two decades, although disagreement exists concerning how ethics can and should be taught in the classroom. With active learning strategies becoming a preferred method of instruction, a collaboration of authors from four universities (University of Pittsburgh, University of Connecticut, Rowan University and New Jersey Institute of Technology) are investigating how game-based or playful learning with strongly situated components can influence first-year engineering students’ ethical knowledge, awareness, and decision making. This paper offers an overview and results of the progress to date of this three year, NSF Improving Undergraduate STEM Education (IUSE) grant that aims to (1) characterize the ethical awareness and decision making of first-year engineering students, (2) develop game-based learning interventions focused on ethical decision making, and (3) determine how (and why) game-based approaches affect students’ ethical awareness in engineering and the advantages of such approaches over non game-based approaches. Now in its second year, the authors have conducted a preliminary analysis of first-year students' ethical knowledge and organization via a concept mapping approach and have measured students' ethical reasoning using the Defining Issues Test 2 (DIT2) and Engineering Ethics Reasoning Instrument (EERI). Further, the authors have developed a suite of ethics-driven games that have been implemented across three of the universities, engaging over 400 first-year engineering students. Evaluation data has also been gathered for further game development and to assess initial student engagement and learning. Year 1 has provided insight into where first-year engineering students “are at” in terms of ethical knowledge and reasoning when they come to college, and how game-based instruction can be effective in the development of these students into moral agents who understand the consequences of their decisions. Further results from this investigation will provide the engineering education community with a set of impactful and research-based playful learning pedagogy and assessment that will help students confront social and ethical dilemmas in their professional lives. 

We propose a novel policy gradient method for multi-agent reinforcement learning, which leverages two different variance-reduction techniques and does not require large batches over iterations. Specifically, we propose a momentum-based decentralized policy gradient tracking (MDPGT) where a new momentum-based variance reduction technique is used to approximate the local policy gradient surrogate with importance sampling, and an intermediate parameter is adopted to track two consecutive policy gradient surrogates. MDPGT provably achieves the best available sample complexity of O(N -1 e -3) for converging to an e-stationary point of the global average of N local performance functions (possibly nonconcave). This outperforms the state-of-the-art sample complexity in decentralized model-free reinforcement learning and when initialized with a single trajectory, the sample complexity matches those obtained by the existing decentralized policy gradient methods. We further validate the theoretical claim for the Gaussian policy function. When the required error tolerance e is small enough, MDPGT leads to a linear speed up, which has been previously established in decentralized stochastic optimization, but not for reinforcement learning. Lastly, we provide empirical results on a multi-agent reinforcement learning benchmark environment to support our theoretical findings. 

For primitive nontrivial Dirichlet characters [Formula: see text] and [Formula: see text], we study the weight zero newform Eisenstein series [Formula: see text] at [Formula: see text]. The holomorphic part of this function has a transformation rule that we express in finite terms as a generalized Dedekind sum. This gives rise to the explicit construction (in finite terms) of elements of [Formula: see text]. We also give a short proof of the reciprocity formula for this Dedekind sum. 

Programmatic collaborations involving mathematicians and educators in the U.S. have been valuable but complex (e.g., Heaton & Lewis, 2011; Bass, 2005; Bass & Ball, 2014). Sultan & Artzt (2005) offer necessary conditions (p.53) including trust and helpfulness. Articles in Fried & Dreyfus (2014) and Bay-Williams (2012) describe outcomes from similarly collaborative efforts; however, there is a gap in the literature in attending to how race and gender intersect with issues of professional status, culture, and standards of practice. Arbaugh, McGraw and Peterson (2020) contend that “the fields of mathematics education and mathematics need to learn how to learn from each other - to come together to build a whole that is greater than the sum of its parts” (p. 155). Further, they posit that the two must “learn to honor and draw upon expertise related to both similarities and differences” across disciplines, or cultures. We argue that in order to do this, we must also take into account race, gender, language. For example, words like trust or helpfulness can read very differently when viewed from personal and professional culture, gender, or racial lenses. This poster shares personal vignettes from the perspective of three collaborators – one black male mathematician, one white female mathematics educator, and one white woman who was trained as a mathematician but works as a mathematics educator - illustrating some of the complexity of collaboration.