Algebraic Thinking in Middle School Students at Different Grades Conceptions about Generalization of Patterns

Girit, Dilek
Akyüz, Didem
Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (elektronik)


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In this thesis, our main objects of interest are piecewise polynomial functions (splines). For a polyhedral complex $\Delta$ in $\mathbb{\R}^n$, $C^{r}(\Delta)$ denotes the set of piecewise polynomial functions defined on $\Delta$. Determining the dimension of the space of splines with polynomials having degree at most $k$, denoted by $C^r_k(\Delta)$, is an important problem, which has many applications. In this thesis, we first give an exposition on splines and introduce different algebraic geometric metho...
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In this thesis we obtain several interesting algebraic properties of the operations used in the block cipher IDEA which are important for cryptographic analyzes. We view each of these operations as a function from $\mathbb Z_{2}^n \times \mathbb Z_{2}^n \to \mathbb Z_{2}^n$. By fixing one of variables $v(z)=\mathbf Z$ in $\mathbb Z_{2}^n \times \mathbb Z_{2}^n$, we define functions $\mathbf {f}_z$ and $\mathbf {g}_z$ from $\mathbb Z_{2}^n$ to $\mathbb Z_{2}^n$ for the addition $\BIGboxplus$ and the multipli...
Algebraic approaches to eigenvalue equations: The Wronskian method
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A recently proposed method for the solution of eigenvalue equations is applied to two different model potentials. Considerable improvements are observed if the algebraic requirements of the Wronskian method are enforced over a region instead of at a single point.
Algebraic spectral moments based moving clutter parameter estimation and clutter suppression
Oktar, Onur; Tanık, Yalçın; Department of Electrical and Electronics Engineering (2014)
In many modern radar systems, it is desired to detect the presence of targets in the interference which includes clutter and noise. Various signal processing techniques are proposed to effectively suppress the clutter and increase the signal to interference ratio. To achieve optimum suppression, radar system must know clutter characteristics and process the radar echoes based on these characteristics. For ground radars, the clutter environment characteristics are relatively stable and predictable. These cha...
Mathematical practices of teachers in technology-enhanced classrooms: A case of teaching slope concept
Yemen Karpuzcu, Seçil; Işıksal Bostan, Mine (2019-12-18)
While it is obvious that teachers need to have mathematical knowledge under different domains, few studies put forward teaching practices associating them with teacher moves in the background of the mathematical knowledge used in teaching in a technology enhanced classroom environment. Moreover, characterizing those practices can show a practical understanding of the knowledge for its usefulness in teaching in which tools and dynamic technologies are deemed necessary. In this study, we examined the characte...
Citation Formats
D. Girit and D. Akyüz, “Algebraic Thinking in Middle School Students at Different Grades Conceptions about Generalization of Patterns,” Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (elektronik), pp. 242–271, 2016, Accessed: 00, 2021. [Online]. Available: