Workshop - Understanding Mathematical Explanation: Uniting Philosophical and Educational Perspectives; Spring 2020; New Brunswick, NJ

该奖项支持一个研讨会，通过将数学哲学家、认识论、心理学家和数学教育家聚集在一起，讨论各自领域的发展如何有意义地促进对数学解释的描述的发展，从而对数学解释的性质产生新的见解，从而将这些多个视角结合在一起。在研讨会期间，被邀请的发言者和与会者将有几次机会(在小组、工作组和非正式环境中)参与有关横向专题的重要工作。工作坊主办方亦计划在本地教育学院及学区刊登有针对性的广告，以吸引职前及在职教师参加是次会议。作为一个更广泛的影响，研讨会组织者预计这些结果将对数学解释的教育工作产生重大影响，这将反过来导致新的理解和教学方法，最终将影响所有教育水平的数学教师和学生。解释的概念是哲学和教育的核心。这些学科在解释在科学探究和课堂中的作用和性质方面取得了重大进展。然而，数学领域的解释概念已被证明是特别具有挑战性的；哲学家和教育家都不清楚数学解释需要什么，以至于它不仅仅是证明某些数学现象是这样的，而是解释为什么会这样。由于数学解释的哲学解释在教育研究中的影响很小，反之亦然，研讨会组织者希望将这些领域和一些相关领域的专家聚集在研讨会环境中，有可能促进我们对这两个领域的数学解释概念的了解和理解。他们计划通过邀请演讲者来增强这种潜力，这些演讲者不仅是从自己学科角度研究解释和理解的专家，而且对跨越传统学科边界和在自己的工作中使用不同的理论和方法传统持开放态度。这一奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports a workshop to develop new insights about the nature of mathematical explanation by bringing together philosophers of mathematics, epistemologists, psychologists, and mathematics educators to discuss how developments in their own fields could meaningfully contribute to the development of an account of mathematical explanation that unites these multiple perspectives. Invited speakers and attendees will be given several opportunities during the workshop (in panels, working groups, and informal settings) to engage in significant work on cross-cutting themes. The workshop organizers also plan to use targeted advertisement in local schools of education and school districts to attract interest among pre- and in-service teachers to attend the conference. As a broader impact, workshop organizers expect that these results will have a significant impact on educational work on mathematical explanation, and that this will in turn lead to new understandings and teaching methods that will ultimately impact teachers and students of mathematics at all educational levels.The notion of explanation is central to both philosophy and education. These disciplines have made significant developments concerning the role and character of explanations in scientific inquiry and in the classroom. However, the notion of explanation in the field of mathematics has proved to be particularly challenging; both philosophers and educators are unclear about what is needed in a mathematical explanation so that it goes beyond merely demonstrating that some mathematical phenomenon is so to explaining why it is so. Since here has been little influence of philosophical accounts of mathematical explanation in educational research, and vice versa, the workshop organizers expect that bringing together experts in these fields and some related fields in a workshop setting has potential to advance our knowledge and understanding of the notion of mathematical explanation in the both fields. They plan to enhance that potential by inviting speakers who are not only experts in the study of explanation and understanding from their own disciplinary perspective, but also open to crossing traditional disciplinary boundaries and to using different theoretical and methodological traditions in their own work.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.