Mathematics Commons^™

Existence Of Three Solutions To A Non-Homogeneous Multi-Point Bvp Of Second Order Differential Equations, Yuji Liu

Turkish Journal of Mathematics

This paper is concerned with a non-homogeneous multi-point boundary value problem of second order differential equation with one-dimensional p-Laplacian. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of BVP are established. Two examples are presented to illustrate the main results.

On Graded Prime And Primary Submodules, Kürşat Hakan Oral, Ünsal Teki̇r, Ahmet Göksel Ağargün

Turkish Journal of Mathematics

Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.

A Note On Weighted A_P(G)-Modules, Serap Öztop

Turkish Journal of Mathematics

Let G be a locally compact abelian group and w be a weight function on G. In this paper, we show that the space A_{p,w}(G) is a Banach module over the Figà-Talamanca Herz algebra A_p(G) and study the multiplier space from A_p(G) to A_{p,w}(G).

On Almost Complex Structures In The Cotangent Bundle, Ari̇f Sali̇mov, Aydin Gezer, Seher Aslanci

Turkish Journal of Mathematics

E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold M_n to its cotangent bundle T^{\ast} (M_n). Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold M_n to T^{\ast} (M_n) and proved that when \varphi defines an integrable almost complex structure on M_n, its complete lift ^C \varphi is a complex structure. The main result of the present paper is the following theorem: Let \varphi be an almost complex structure on a Riemannian manifold M_n. Then the complete lift ^C …

Rotational Embeddings In E^4 With Pointwise 1-Type Gauss Map, Kadri̇ Arslan, Bengü Kiliç Bayram, Betül Bulca, Young Ho Ki̇m, Cengi̇zhan Murathan, Günay Öztürk

Turkish Journal of Mathematics

In the present article we study the rotational embedded surfaces in E^4. The rotational embedded surface was first studied by G. Ganchev and V. Milousheva as a surface in E^4. The Otsuki (non-round) sphere in E^4 is one of the special examples of this surface. Finally, we give necessary and sufficient conditions for the flat Ganchev-Milousheva rotational surface to have pointwise 1-type Gauss map.

The Wright Message, 2011-2012, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Around Wright Hall
-- New College
-- Programs Revision
-- Math ≠ 800
-- Baumler Mathematics Education Scholarship
-- Two Retire
-- Putnam Exam
-- Math Ed Lab - Then and now
-- 2011 - 2012 Tenure-Stream Faculty
-- Making an Impact
-- The Question
-- Spotlight on Undergraduates
-- Projects and Grants
-- P.S.M. Program in Industrial Mathematics
-- Actuarial Science Alumni
-- Department of Mathematics Contribution Form
-- Department of Mathematics Funds

Prospective Teachers’ Conceptions About Teaching Mathematically Talented Students: Comparative Examples From Canada And Israel, Mark Applebaum, Viktor Freiman, Roza Leikin

The Mathematics Enthusiast

In this paper we analyze prospective mathematics teachers' conceptions about teaching mathematically talented students. Forty-two Israeli participants learning at mathematics education courses for getting their teaching certificates, and fifty-four Canadian pre-service (K-8) teachers participating in mathematics didactics course were asked to solve a challenging mathematical task. We performed comparative analysis of problem-solving strategies, solution results and participants' success. Based on the discussion with 25 Israeli participants we composed an attitude questionnaire, in which prospective teachers were asked to express their degree of agreement with statements expressing different beliefs about education of mathematically talented students. The questionnaire was presented to 56 …

Mathematical And Didactical Enrichment For Pre-Service Teachers: Mentoring Online Problem Solving In The Casmi Project, Manon Leblanc, Viktor Freiman

The Mathematics Enthusiast

In order to teach successfully, future teachers should not only be educated about students’ conceptions, but also about different forms of knowledge and classroom culture. In our research, we examined whether the participation in the Internet-based challenging problem solving community CASMI contributes to the development of the aforementioned awareness and understanding in order to meet the needs of all students including the gifted ones. The results obtained enabled us to note that the pre-service teachers’ perceptions of the project as a source of enrichment are mainly positive. However, analyzing schoolchildren’s strategies, the participants preferred to use pre-determined criteria instead of …

Disrupting Gifted Teenager’S Mathematical Identity With Epistemological Messiness, Paul Betts, Laura Mcmaster

The Mathematics Enthusiast

Mathematics is widely perceived as a universal and uncontested discipline, contrary to the philosophy of mathematics literature. Other researchers have considered the potential role of philosophy in school, but there is little work with gifted students engaged with issues concerning the nature of mathematics. We developed a philosophy of mathematics unit intended to enlarge gifted students’ perceptions of the nature of mathematics by exposing the uncritical and tidy rendering of mathematics within school math. Using a narrative methodology, we attended to gifted student’s students’ stories of relationship with mathematics, based on the premise that a person’s relationship with mathematics is …

Gifted Students And Advanced Mathematics, Edward J. Barbeau

The Mathematics Enthusiast

The extension to a wide population of secondary education in many countries seems to have led to a weakening of the mathematics curriculum. In response, many students have been classified as “gifted” so that they can access a stronger program. Apart from the difficulties that might arise in actually determining which students are gifted (is it always clear what the term means?), there are dangers inherent in programs that might be devised even for those that are truly talented.

Sometimes students are moved ahead to more advanced mathematics. Elementary students might be taught algebra or even subjects like trigonometry and …

The Promise Of Interconnecting Problems For Enriching Students’ Experiences In Mathematics, Margo Kondratieva

The Mathematics Enthusiast

The interconnecting problem approach suggests that often one and the same mathematical problem can be used to teach various mathematical topics at different grade levels. How is this approach useful for the development of mathematical ability and the enrichment of mathematical experiences of all students including the gifted ones? What are the benefits for teachers’ and what would teachers need to implement this approach? What directions would further research on these issues take? The paper discusses these and closely related questions.

I propose that a long-term study of a progression of mathematical ideas revolved around one interconnecting problem is useful …

Creativity Assessment In School Settings Through Problem Posing Tasks, Ildikó Pelczer, Fernando Gamboa Rodríguez

The Mathematics Enthusiast

Research in math education on mathematical creativity relies on the idea that creativity is potentially within all students and it can be fostered by properly structured activities. The tasks most commonly used for its assessment are problem solving and problem posing. In our approach we use problem posing tasks to get insight into students’ creativity. Based on a qualitative analysis of the participants’ answers to the questionnaire that followed the task, we define algorithmic, combined and innovative creativity as constructs that can be put in correspondence with the types and level of knowledge involved in the problem posing task. We …

Forthcoming Tmme Vol8,No3 [August 2011: Special Section On The North Calotte Conference In Mathematics Education : Tromsø-2010], Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Tme Volume 8, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

Editorial: Opening 2011’S Journal Treasure Chest, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Vignette Of Doing Mathematics: A Meta-Cognitive Tour Of The Production Of Some Elementary Mathematics, Hyman Bass

The Mathematics Enthusiast

Mathematics educators, including some mathematicians, have, in various ways, urged that the school curriculum provide opportunities for learners to have some authentic experience of doing mathematics, opportunities to experience and develop the practices, dispositions, sensibilities, habits of mind characteristic of the generation of new mathematical knowledge and understanding – questioning, exploring, representing, conjecturing, consulting the literature, making connections, seeking proofs, proving, making aesthetic judgments, etc. (Polya 1954, Cuoco et al 2005, NCTM 2000 - Standard on Reasoning and Proof). While this inclination in curricular design has a certain appeal and merit, its curricular and instructional expressions are often contrived, or …

Transcriptions, Mathematical Cognition, And Epistemology, Wolff-Michael Roth, Alfredo Bautista

The Mathematics Enthusiast

The epistemologies researchers bring to their studies mediate not only their theories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce mathematical knowing to linguistic/mathematical structures, which, in the case of embodiment/enactivist theories, undermines the very argument about the special nature of mathematical knowing. The purpose of this study is to illustrate how different transcriptions of mathematics lessons are generally used to support different epistemologies of mathematical knowing/competence. As part of our third illustration, we provide embodiment/enactivist researchers with an innovative means of representing classroom …

Revisiting Tatjana Ehrenfest-Afanassjewa’S (1931) “Uebungensammlung Zu Einer Geometrischen Propädeuse”: A Translation And Interpretation, Klaus Hoechsmann

The Mathematics Enthusiast

No abstract provided.

New Perspectives On Identification And Fostering Mathematically Gifted Students: Matching Research And Practice, Viktor Freiman, Ali Rejali

The Mathematics Enthusiast

This special section of vol8,nos1&2 of The Montana Mathematics Enthusiast is a result of tremendous enthusiastic team work of many outstanding mathematics educators worldwide who are concerned with the issues related to mathematical giftedness and devoted to share with the international community their ideas, research results and best practices. The idea of the special issue on mathematical giftedness arose during the Topic Study Group 6 (TSG6) meeting at the 11th International Congress on Mathematics Education (ICME-11) in Monterrey, Mexico, in 2009 led by Viktor Freiman and Ali Rejali in collaboration with Mark Applebaum, Pablo Dartnell, and Arne Mogensen. More than …

Problem-Based Learning In Mathematics, Thomas C. O'Brien, Chris Wallach, Carla Mash-Duncan

The Mathematics Enthusiast

A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations, he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge and helps them to solve their problems with stimulating questions, he may give them a taste for, and some independent means of, independent thinking.