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Full-Text Articles in Physical Sciences and Mathematics
Technology Integration In Secondary Mathematics Classrooms: Effect On Students’ Understanding, Megan Sheehan, Leah A. Nillas
Technology Integration In Secondary Mathematics Classrooms: Effect On Students’ Understanding, Megan Sheehan, Leah A. Nillas
Leah A. Nillas
Technology use in secondary mathematics courses has the potential to bring about broad changes in learning environment and teaching pedagogy, allowing students to communicate and collaborate in new ways and to conjecture, justify, and generalize findings. However, this potential is only realized when teachers use technology in ways encouraging these outcomes (Galbraith, 2006). The purpose of this study is to examine the integration of technology in secondary mathematics classrooms and to evaluate the effectiveness of its use in relation to students’ learning outcomes. This self study research was conducted in honors geometry and AP calculus classes. Data sources included transcripts …
Technology Integration In Secondary Mathematics Classrooms: Effect On Students’ Understanding, Megan Sheehan, Leah Nillas
Technology Integration In Secondary Mathematics Classrooms: Effect On Students’ Understanding, Megan Sheehan, Leah Nillas
Scholarly Publications
Technology use in secondary mathematics courses has the potential to bring about broad changes in learning environment and teaching pedagogy, allowing students to communicate and collaborate in new ways and to conjecture, justify, and generalize findings. However, this potential is only realized when teachers use technology in ways encouraging these outcomes (Galbraith, 2006). The purpose of this study is to examine the integration of technology in secondary mathematics classrooms and to evaluate the effectiveness of its use in relation to students’ learning outcomes. This self study research was conducted in honors geometry and AP calculus classes. Data sources included transcripts …
Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He
Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He
Scholarship
A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …
M-Refinable Extensions Of Real Valued Functions, John Meuser, Tian-Xiao He, Faculty Advisor
M-Refinable Extensions Of Real Valued Functions, John Meuser, Tian-Xiao He, Faculty Advisor
John Wesley Powell Student Research Conference
No abstract provided.
A Categorical Semantics For Fuzzy Predicate Logic, Lawrence Stout
A Categorical Semantics For Fuzzy Predicate Logic, Lawrence Stout
Scholarship
The object of this study is to look at categorical approaches to many valued logic, both propositional and predicate, to see how different logical properties result from different parts of the situation. In particular, the relationship between the categorical fabric I introduced at Linz in 2004 and the Fuzzy Logics studied by Hajek (2003) [5], Esteva et al. (2003) [1], and Hajek (1998) [4], comes from restricting the kind of structures used for truth values. We see how the structure of the various kinds of algebras shows up in the categorical logic, giving a variant on natural deduction for these …
When Does A Category Built On A Lattice With A Monoidal Structure Have A Monoidal Structure?, Lawrence Stout
When Does A Category Built On A Lattice With A Monoidal Structure Have A Monoidal Structure?, Lawrence Stout
Scholarship
In a word, sometimes. And it gets harder if the structure on L is not commutative. In this paper we consider the question of what properties are needed on the lattice L equipped with an operation * for several different kinds of categories built using Sets and L to have monoidal and monoidal closed structures. This works best for the Goguen category Set(L) in which membership, but not equality, is made fuzzy and maps respect membership. Commutativity becomes critical if we make the equality fuzzy as well. This can be done several ways, so a progression of categories is considered. …
Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout
Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout
Scholarship
In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a non-commutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of truth values. We then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type A with functors giving change of type and adjoints giving quantifiers. In the case …