Digital Commons Network^™

Issues In Primary Mathematics Education Computers: Classroom Practice And Curriculum Reform, Lorraine Kershaw, Kevin Jones, Len Sparrow

Research outputs pre 2011

The advent of an interactive multimedia approach in teaching and learning has opened up yet another horizon to be explored in search of the perceived potential of the computer in primary mathematics education. Benefits promoted have included its use as a motivational aid, the developing of content knowledge and problem solving skills of children of varying abilities, its capacity to support an integrated curriculum, and to assist children in controlling their own learning. Many have doubts about the veracity of these assertions and disagree about the types of appropriate uses of the computer. For classroom teachers, software and hardware availability, …

Issues In Primary Mathematics Education: Calculators: Research And Curriculum Implications, Len Sparrow, Lorraine Kershaw, Kevin Jones

Research outputs pre 2011

Calculators: Research and curriculum implications is one of a series of monographs on issues in primary mathematics education. It has been written to support initiatives in the development of student-centred learning programs at Edith Cowan University - programs designed to accommodate current views on effective adult learning strategies, as wells as the development of professional and generic (key) competencies. Irrespective of the nature of individual learning programs, students and teachers working at undergraduate and postgraduate levels will find the series useful- either as a synthesis of currently available research findings and reference material, to identify potentially significant initiatives and developments …

Number Sense And Computation In The Classroom, Kevin Jones, Lorraine Kershaw, Len Sparrow

Research outputs pre 2011

Number sense and computation in the classroom is one of a series of monographs on issues in primary mathematics education. It has been written to support initiatives in the development of student-centred learning programs at Edith Cowan University - programs designed to accommodate current views on effective adult learning strategies, as wells as the development of professional and generic (key) competencies. Irrespective of the nature of individual learning programs, students and teachers working at undergraduate and postgraduate levels will find the series useful- either as a synthesis of currently available research findings and reference material, to identify potentially significant initiatives …

Fibonacci Networks, Rama K. Govindaraju, M. S. Krishnamoorthy, Narsingh Deo

Faculty Bibliography 1990s

No abstract provided.

An Examination Of The Relationship Between Parental Attitudes And Student Achievement On Standardized Test Scores In Mathematics, Susan S. Lapp

Theses and Dissertations

The purpose of this study was to examine the relationship between parents' attitudes toward mathematics and students' standardized test scores in mathematics. Eighty-four parents of fourth-grade students in a southeastern military dependent school system were surveyed to determine their attitudes to mathematics when they were in elementary school and their attitudes about mathematics today. Parents also responded to questions about their children's abilities and attitudes toward mathematics.

Total scores for the survey were matched with the students' mathematics scores on the Iowa Test of Basic Skills (ITBS). The Pearson Product-Moment Correlation was used to compute the correlation coefficients. A positive …

Determining The Validity And Reliability Of An Instrument Designed To Measure Metacognitive Behaviours, Anne L. Martin

Theses : Honours

This project was designed to study the role of metacognition in mathematical problem solving. More specifically, it was designed to determine the validity and reliability of an instrument proposed to identify metacognitive behaviours in Year 7 children solving problems. The instrument was used to analyse audio tapes of pairs of students working on a non-routine problem (i.e., a problem that cannot be solved solely by the direct application of the basic operations). Analysis of the audio tapes involved categorizing metacognitive decisions as: orientation, organization, execution, and verification behaviours. A "cognitive-metacognitive" framework (Garofalo & Lester, 1985) was used as a basis …

Digital Morphometry : A Taxonomy Of Morphological Filters And Feature Parameters With Application To Alzheimer's Disease Research, Andrew Mehnert

Theses: Doctorates and Masters

In this thesis the expression digital morphometry collectively describes all those procedures used to obtain quantitative measurements of objects within a two-dimensional digital image. Quantitative measurement is a two-step process: the application of geometrical transformations to extract the features of interest, and then the actual measurement of these features. With regard to the first step the morphological filters of mathematical morphology provide a wealth of suitable geometric transfomations. Traditional radiometric and spatial enhancement techniques provide an additional source of transformations. The second step is more classical (e.g. Underwood, 1970; Bookstein, 1978; and Weibull, 1980); yet here again mathematical morphology is …

Nous As The Ground Of Aristotle's Metaphysics?, John J. Cleary

The Society for Ancient Greek Philosophy Newsletter

This paper explores the implications of Aristotle's puzzling suggestions that the possibility of first philosophy somehow depends on whether part of the soul is separable from material body. My Conjecture1 is that for Aristotle the science of metaphysics depends on a special activity of nous that grasps die self-identical essences which are objects of first philosophy, as distinct from physics and mathematics. From Aristotle's perspective, of course, it is the existence of such essences that makes metaphysics possible, but it is arguable that without a corresponding mode of cognition this would not be a human science. It is a moot …

Student Held Misconceptions Regarding Area And Perimeter Of Rectangles, Susan M. Carle

Critical and Creative Thinking Capstones Collection

Students enter the classroom with individual schemas, based on their experiences and ideas, which influence the reception, interpretation, and recollection of new information. Effective teachers must understand the implications of these existing schemas. As an experienced classroom teacher, the author finds students often manipulate and apply new information well in class, only to forget or alter the material a few weeks later;. When misconceptions are woven into schemas, they interfere with reception of information. This thesis examines specific student-held misconceptions about the area and perimeter of rectangles and the process of their identification and eradication. Identification of the misconception is …

On Image Segmentation Using Neural Networks And Fuzzy Sets., Ashish Ghosh Dr.

Doctoral Theses

During the last five decades or even more a large number of researchers are trying to design intelligent systems to perform tasks at which human beings are more efficient at present. One of the most important behavioral tasks in which human beings show their expertise is image analysis or recognition; where a large amount of pictorial data is processed in a very small amount of time (called real time). Widespread attempts have been made to develop intelligent systems (under different names, like pattern recognition system, image under- standing system, computer vision system etc.) for pictorial pattern analysis and recognition. The …

Stacking Ellipses -- Revisited, Calvin Jongsma

Faculty Work Comprehensive List

Response to the article “Stacking Ellipses” by Richard E. Pfiefer in The College Mathematics Journal, Vol. 22, No. 4 (Sep., 1991), pp. 312-313.

On Markov Processes Charecterised Via Martingale Problem., Abhay G. Bhatt Dr.

Doctoral Theses

Martingale approach to the study of finite dimensional diffusions was initiated by Stroock-Varadhan, who coined the term martingale problem. Their success led to a similar approach being used to study Markov processes occuring in other areas such as infinite particle systems, branching processes, genetic models, density dependent population processes, random evolutions etc.Suppose X is a Markov process corresponding to a semigroup (T)e20 with generator L. Then all the information about X is contained in L. We also have thatMf(t) := f(X(t)) – ∫t0 Lf(X(s))dsis a martingale for every f ∈ D(L). i.e. X is a solution to the martingale problem …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

The Wooster Voice (Wooster, Oh), 1993-09-10, Wooster Voice Editors

The Voice: 1991-2000

In this edition of the Voice, Lynne V. Cheney, former head of the National Endowment for the Humanities (NEH) under the Reagan and Bush administrations, kicks off Wooster’s annual forum. Taylor Hall and the mathematics department receive a donation of several new computers to be used for computer science classes. In a section called “Speak Your Mind” students are asked, and give opinions on, the College’s new smoking policy. Additionally, a cartoon critiques “Party on the Green” an annual outdoor concert hosted by the College. Athletic updates for the past week are highlighted on pages ten to twelve.

Classification Of The Tor-Algebras Of Codimension Four Almost Complete Intersections, Andrew R. Kustin

Faculty Publications

Let (R, m, k) be a local ring in which 2 is a unit. Assume that every element of k has a square root in k . We classify the algebras Tor'(R/J, k) as J varies over all grade four almost complete intersection ideals in R. The analogous classification has already been found when J varies over all grade four Gorenstein ideals [21], and when J varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebraso f codimension four Gorenstein rings, as well as the (usually …

Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.

Doctoral Theses

In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Another Cautionary Note On Interpreting Regression Results In Family Research: A Comment On Peterson And Gerson (1992), Alan J. Hawkins, Joseph A. Olsen, Richard R. Peterson, Kathleen Gerson

Faculty Publications

Occasionally in the family literature we receive reminders to be cautious about our interpretations of regressions results (e.g., Glenn & Kramer, 1985; Glenn & Shelton, 1983). After all, regression results are stated in the language of mathematics. We must be careful when we translate from the language of mathematics, which is blind to the human situation being represented by the numbers, into language that is meaningful in the human context. This brief not critiques the interpretation of regression results in an article by Peterson and Gerson (1992) that appeared in a recent issue of the Journal of Marriage and the …

Transfer And Steenrod Squares, Peter Ivo Litvanyi

Mathematics and Statistics

Commutators between the transfer and Steenrod squares have been investigated by several authors. Let X be a finite simplicial complex and $\tau$ be a regular involution on X. If $\tau$ has no fixed point, then the commutator is trivial by certain results in generalized cohomology theory. For involutions with possible fixed points, the commutator was first expressed by Bott as $\Delta\sp*$Sq$\sp{\rm i}$ + Sq$\sp{\rm i}\Delta\sp* = \mu$Sq$\sp{\rm i-1}\Delta\sp*.$ Here $\Delta\sp*$ is the transfer map and $\mu$ denotes the connecting morphism of the Smith sequence. Another formula, closely related to the one above, was given by Kubelka and gives the commutator …

On The Distribution Of Sums Of Residues, Jerrold R. Griggs

Faculty Publications

No abstract provided.

Survival Function Estimation Under Random Censoring., Debajyoti Dhar Dr.

Doctoral Theses

Statistical methods for life data analysis are used to measure, compare and predict characteristics of the distribution of the time to some particular event of interest, often called failure after a length of time, called life time. Failure can occur at most once for an individual. Examples of failure time include the lifetimes of machine components in industrial reliability, the duration of strikes or periods of unemployment in economic studies, the time taken by subjects to complete specified tasks in psychological experiments, the lengths of tracks photographic plates in particle physics and the on survival time of patients in clinical …

Generalised Inverses Of Matrices Over Rings., K. Manjunatha Prasad Dr.

Doctoral Theses

For a complex or a real matrix A, a matrix G is called a generalized inverse ( or g-inverse) of A if(1) AGA = AThe theory of generalized inverses over the field of complex numbers is well- studied in the literature (see (2), (11), (33), and (62) for an extensive bibliography). Even for matrices over a general field the above equation carries over. In fact, even for matrices over a general ring, equation (1) makes sense. Hence one can talk of g-inverses of matrices over general rings. Some work on g-inverses of matrices over fields also can be found in …

On Some Measurement Problem In Economics., Nachiketa Chattopadhyay Dr.

Doctoral Theses

In many branches of economie theory, quantitative relationships play a major role. Translating actions of individuals or groups of individuals, in the various soci- etal processes of production, distribution or consumption, into measurable or quan- tifiable notions has been one of the most important problems. When we take the society as a whole, diverse economic activities of ita memhers need to be collectively presented and it has given rise to interesting aggregation problems. Economists have tried to solve these problems by constructing social index numbers. Simi- larly, quantifying actions of individual units (for example, a firm /a consumer) has brought …

Besov-Spaces On Domains In Rd, Ronald A. Devore, Robert C. Sharpley

Faculty Publications

No abstract provided.

Hydrodynamic And Electrohydrodynamic Instability Of Shear Flows And The Numerical Simulation Of Viscous Droplets, Kenzu Abdella

Digitized Theses

In this thesis, we investigate three fluid dynamic problems involving various physical mechanisms which exhibit interfacial instability. These problems have wide ranging industrial, scientific and engineering applications.;In the first problem, we investigate the linear stability of the unbounded Couette flow of two fluids separated by a plane interface. The exact dispersion relation is solved asymptotically and numerically to analyze the effects of the four stability parameters of the flow; the ratio of the viscosities, the ratio of the density, the surface tension and gravity. While our results confirm most of the earlier reported theories involving shear flows of fluids of …

Models For Steady State Flow Past A Cylinder, Sergio J. D'Alessio

Digitized Theses

Three steady state models for determining the flow of a viscous incompressible Newtonian isothermal fluid past a two-dimensional cylindrical object are proposed. These models offer numerical methods of solving the governing Navier-Stokes equations as well as a mathematical understanding of the nature of the flow.;In the first model, the behaviour of the vorticity is patterned for both large and small distances by expressing the vorticity as {dollar}\zeta\ =\ \Phi\rm e\sp{lcub}\rm F{rcub}{dollar} with F chosen to accommodate both boundary-layer and wake theory. The resulting equations are then solved by finite differences and by the method of Dennis and Chang (1970).;The second …

On The Characterization Of Finite Dimensional Hida Distributions., Kyoung Sim Lee

LSU Historical Dissertations and Theses

The mathematical framework of white noise analysis is based on an infinite dimensional analogue of the Schwartz distribution theory. The Lebesgue measure on $\IR\sp{k}$ is replaced with standard Gaussian measures $\mu$ on infinite dimensional spaces. There is an infinite dimensional analogue $({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*$ of a Gel'fand triple ${\cal E}\subset E\subset{\cal E}\sp*$ which is obtained from ${\cal S}(\IR\sp{k})\subset L\sp2(\IR\sp{k})\subset{\cal S}\sp*(\IR\sp{k})$ in a general setup. There are spaces $({\cal E}\sp\beta),({\cal E}\sp\beta)\sp*, \beta\in\lbrack 0,1)$ with $({\cal E}\sp\beta)\subset({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*\subset({\cal E}\sp\beta)\sp*.$. The compositions of Schwartz distributions and Gaussian random variables have been discussed. A new Gel'fand triple ${\cal H}(\IR\sp{k})\subset{\cal …

Hankel Operators On Hilbert Spaces, Pachara Wanpen

Doctoral Dissertations

In this paper we consider the Hankel operators from two points of view. On one hand the Hankel operator is induced by the coefficient sequence $a\sb0,a\sb1,a\sb2,\...$ and operates on a Hilbert space $H\sp2(\beta)$ with $\Sigma\sbsp{n=0}{\infty}\ \beta(n)\sp2 < \infty.$ In this situation we can find necessary conditions and sufficient conditions for the Hankel operator to be bounded. However, with compactness and Hilbert-Schmidt we can get only sufficient conditions. On the other hand we look at the Hankel operator $H\sb{f,\alpha}$ and little Hankel operator $h\sb{f,\alpha},$ with symbol function f, that operates on a weighted Bergman space. In this case we can determine bounded, compact, Hilbert Schmidt, or trace class operators of the Hankel operator $H\sb{f}$ and $h\sb{f,\alpha}.$ We also give a good estimate of bounded norm of little Hankel operators with a particular symbol function $f = z\bar g$ where g is in the Bloch space.

Approximate Equivalence Invon Neumann Algebras, Hui-Ru Ding

Doctoral Dissertations

In this paper we investigate approximate equivalence in von Neumann algebras. We find a necessary and sufficient condition for two normal operators to be approximately equivalent in any von Neumann algebra ${\cal R}$ acting on a separable Hilbert space H with unitaries in ${\cal R}.$ For the approximate equivalence of two unital representations from a given C$\*$-algebra to any von Neumann algebra acting on a separable Hilbert space, we find the necessary condition for the general case. Finally we investigate an interesting class of C$\*$-algebras, closed under direct sum, direct limit and quotient map, which contains C(X) and $M\sb{n}(A),$ where …

Peirce And Logicism: Notes Towards An Exposition, Susan Haack

Articles

No abstract provided.