Houssein El Turkey

• University of New Haven

Fostering students’ mathematical creativity is important for their understanding and success in mathematics courses as well as their persistence in STEM, but it necessitates intentional instructional actions, such as designing and implementing tasks that have the potential to foster creativity. As teaching innovation requires support for instructor...

While there are numerous studies at the primary and secondary levels, research on mathematical creativity in the tertiary level is sparse, albeit growing. This book chapter is a scoping literature review, aiming to give a broad view of the research done at the tertiary level. Our group found that much of the literature (59%) was published in the la...

In this chapter, the Creativity Research Group shares results from a study in which progressions of undergraduate students’ perspectives of mathematical creativity in an introduction-to-proofs course were explored. The course was intentionally designed to value students’ creativity throughout in-class activities and out-of-class assignments. The Cr...

Numerous conceptions of creativity exist in the literature; yet these are commonly based on the perspectives of professional mathematicians. Including students’ perspectives in creativity is crucial not only for a more robust picture of what it means to be creative but also to combat damaging dominant narratives about who can be creative. We examin...

Creativity is crucial for doing mathematics, yet many United States students may not have opportunities to experience it in their courses. Moreover, the literature base on views of mathematical creativity lacks the student perspective. To explore the connections between views of and feeling creative, we examine differences in views of creativity be...

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned fro...

An exact $r$-coloring of a set $S$ is a surjective function $c:S\to [r]$. The rainbow number of set $S$ for equation $eq$ is the smallest integer $r$ such that every exact $r$-coloring of $S$ contains a rainbow solution to $eq$. In this paper, the rainbow numbers of $\mathbb{Z}_p$, for $p$ prime and the equation $a_1x_1 + a_2x_2 + a_3x_3 = b$ are d...

Challenging mathematics problems were posed as a substantial part of homework in an elective combinatorics course. The intent was to encourage undergraduate students' exploration as well as develop their technical writing skills. The bulk of students' grades on these problems rested on a three-page reflective write-up using a rubric on mathematical...

Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity....

A growing body of mathematics education research points the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative assessment...

In this article, we investigate the implementation of task performance tests in an undergraduate physics laboratory. Two performance tests were carried out over two semesters using the task of building a DC circuit. The first implementation in Spring 2014 had certain concerns such as the privacy of students' testing and their 'trial and error' atte...

Creativity is one of the most important aspects of mathematicians’ work (Sriraman 2004), whether it is an enlightenment that is somewhat unexpected or a product that is aesthetically pleasing (Borwein, Liljedahl & Zhai 2014). There are studies in the primary and secondary levels on mathematical creativity of students (e.g., Leikin 2009; Silver 1997...

The complexity of a module is the rate of growth of the minimal projective resolution of the module while the $z$-complexity is the rate of growth of the number of indecomposable summands at each step in the resolution. Let $\mathfrak{g}=\mathfrak{osp}(k|2)$ ($k>2$) be the type II orthosymplectic Lie superalgebra of types $B$ or $D$. In this paper,...

The complexity of a module is the rate of growth of the minimal projective resolution of the module while the $z$-complexity is the rate of growth of the number of indecomposable summands at each step in the resolution. Let $\mathfrak{g}=\mathfrak{osp}(k|2)$ ($k>2$) be the type II orthosymplectic Lie superalgebra of types $B$ or $D$. In this paper,...

The complexity of the simple and the Kac modules over the general linear Lie superalgebra $\mathfrak{gl}(m|n)$ of type $A$ was computed by Boe, Kujawa, and Nakano in 2012. A natural continuation to their work is computing the complexity of the same family of modules over the ortho-symplectic Lie superalgebra $\mathfrak{osp}(2|2n)$ of type $C$. The...

We provide a presentation of the Schur superalgebra and its quantum analogue which generalizes the work of Doty and Giaquinto for Schur algebras. Our results include a basis for these algebras and a presentation using weight idempotents in the spirit of Lusztig's modified quantum groups.