The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on Ò symbols is an Ò¢Ò matrix (Ò is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting research questions posed by Euler with respect to Latin squares, namely regarding orthogonality properties, were only solved in 1959 [3]. Many other questions concerning Latin squares constructions still remain open today.From the perspective of the Constraint Programing (CP), Artificial Intelligence (AI), and Operations Research (OR) communities, combinatorial design problems are interesting since they possess rich structural properties that are also observed in real-world applications such as scheduling, timetabling, and error correcting codes. Thus, the area of combinatorial designs has been a good source of challenge problems for these research communities. In fact, the study of combinatorial design problem instances has pushed the development of new search methods both in terms of systematic and stochastic procedures. For example, the question of the existence and non-existence of certain quasigroups (Latin squares) with intricate mathematical properties gives rise to some of the most challenging search problems in the context of automated theorem proving [16]. So-called general purpose model generation programs, used to prove theorems in finite domains, or to produce counterexamples to false conjectures, have been used to solve numerous previously open problems about the existence of Latin squares with specific mathematical properties. Considerable progress has also been made in the understanding of symmetry breaking procedures using benchmark problems based on combinatorial designs [5,6,9,13]. More recently, the study of search procedures on benchmarks based on Latin squares has led to the discovery of the non-standard probability distributions that characterize complete (randomized) backtrack search methods, so-called heavy-tailed distributions [8].

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The Survey of Attitudes Toward Statistics or SATS was administered for three consecutive years to students in an Introductory Statistics course at Cornell University. Questions requesting demographic information and expected final course grade were added. Responses were analyzed to investigate possible differences between sexes and racial/ethnic groups. The findings showed that female students had significantly lower average scores than their male counterparts in affect, cognitive competency, and subject difficulty. In addition, they expected lower average final course grades. When expected and achieved grades were compared, both male and female students overestimated their final scores, but female students did so to a lesser extent. No differences in attitudinal scores or grade expectations were found between racial/ ethnic groups. However, significant differences between racial groups were found when comparing student's expected and actual grades. Asian students outperformed the other groups in both meeting their personal expectations and achieving significantly higher final grades. Latino and Black students had outcomes well below their expectations. These results suggest that educators should focus on differences between sexes when planning ways to improve students' confidence in their quantitative ability. They should also consider implementing strategies for minority students to achieve their expected final course grade.

Addressing common student questions in introductory STEM courses early in the term is one way that instructors can ensure that their students have all been presented with information about how to succeed in their courses. However, categorizing student questions and identifying evidence-based resources to address student questions takes time, and instructors may not be able to easily collect and respond to student questions at the beginning of every course. To help faculty effectively anticipate and respond to student questions, we 1) administered surveys in multiple STEM courses to identify common student questions, 2) conducted a qualitative analysis to determine categories of student questions (e.g., what are best practices for studying, how can in- and out-of- course time be effectively used), and 3) collaboratively identified advice on how course instructors can answer these questions. Here, we share tips, evidence-based strategies, and resources from faculty that instructors can use to develop their own responses for students. We hope that educators can use these common student questions as a starting point to proactively address questions throughout the course and that the compiled resources will allow instructors to easily find materials that can be considered for their own courses.