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Previous research on adaptive educational systems has shown that allowing the student to view their student model is useful in the learning process. Open student models help support meta-cognitive processes, such as self-assessment and reflection, and at the same time increase the student's trust in the system. Negotiable student models take this a step… (More)

We present a method for computing pth roots using a polynomial basis over finite fields Fq of odd characteristic p, p ≥ 5, by taking advantage of a binomial reduction polynomial. For a finite field extension F q m of Fq our method requires p − 1 scalar multiplication of elements in F q m by elements in Fq. In addition, our method requires at most (p − 1)m/p… (More)

Let F q be a finite field and consider an extension F q n where an optimal normal element exists. Using the trace of an optimal normal element in F q n , we provide low complexity normal elements in F q m , with m = n/k. We give theorems for Type I and Type II optimal normal elements. When Type I normal elements are used with m = n/2, m odd and q even, our… (More)

Swan (1962) gives conditions under which the trinomial x n + x k + 1 over F 2 is reducible. Vishne (1997) extends this result to trinomials over extensions of F 2. In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the finite field F q , where q is a power of an odd prime.

Optimal normal bases are special cases of the so-called Gauss periods (Disquisi-tiones Arithmeticae, Articles 343-366); in particular, optimal normal bases are Gauss periods of type (n, 1) for any characteristic and type (n, 2) for characteristic 2. We present the multiplication tables and complexities of Gauss periods of type (n,t) for all n and t = 3, 4,… (More)

Tutorial dialogues are considered as one of the critical factors contributing to the effectiveness of human one-on-one tutoring. We discuss how we evaluated the effectiveness of a general model of adaptive tutorial dialogues in both an ill-defined and a well-defined task. The first study involved dialogues in database design, an ill-defined task. The… (More)

In this paper, we look at initial results of data mining stu-dents' help-seeking behaviour in two ITSs: SQL-Tutor and EER-Tutor. We categorised help given by these tutors into high-level (HLH) and low-level help (LLH), depending on the amount of help given. Each student was grouped into one of ten groups based on the frequency with which they used HLH.… (More)