Disrupting Gifted Teenager’S Mathematical Identity With Epistemological Messiness,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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],
2011
University of Montana
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,
2011
University of Montana
Editorial: Opening 2011’S Journal Treasure Chest,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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,
2011
University of Montana
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.
The Proficiency Challenge: An Action Research Program On Teaching Of Gifted Math Students In Grades 1-9,
2011
University of Montana
The Proficiency Challenge: An Action Research Program On Teaching Of Gifted Math Students In Grades 1-9, Arne Mogensen
The Mathematics Enthusiast
The paper describes design and outcome of a 3-year action research program on the teaching mathematics to gifted students in grades 1-9 in mixed ability classes in Denmark 2003- 2006. The intention was to combine ideas and experience of many teachers with theories and suggestions of researchers to test and develop useful recommendations for future teaching.
Modular And Graceful Edge Colorings Of Graphs,
2011
Western Michigan University
Modular And Graceful Edge Colorings Of Graphs, Ryan Jones
Dissertations
Abstract attached as separate file.
Hamiltonicity And Connectivity In Distance-Colored Graphs,
2011
Western Michigan University
Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski
Dissertations
Abstract attached as separate file.
Relation Liftings On Preorders And Posets,
2011
Academy of Sciences of the Czech Republic
Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil
Engineering Faculty Articles and Research
The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.
Normal And Δ-Normal Configurations In Toric Algebra,
2011
Oberlin College
Normal And Δ-Normal Configurations In Toric Algebra, Liam Solus
Honors Papers
Toric algebra is a field of study that lies at the intersection of algebra, geometry, and combinatorics. Thus, the algebraic properties of the toric ideal IA defined by the vector configuration A are often characterizable via the geometric and combinatorial properties of its corresponding toric variety and A, respectively. Here, we focus on the property of normality of A. A normal vector configuration defines the toric ideal of a normal toric variety. However, the definition of normality of A is based entirely on the algebraic structures associated with A without regard to any of its combinatorial properties. In this paper, …
Optimal Summer Camp Layout,
2011
Oberlin College
Optimal Summer Camp Layout, Anthony Bonifonte
Honors Papers
Convex optimization is an important branch of operations research. It generalizes linear programming and offers powerful tools for modelling problems and discovering optimal solutions to real world problems. Mathematically it is an interesting topic because it ties together many branches: linear algebra, multivariable calculus, and numerical analysis, to name a few. Modelling a problem as a convex optimization problem can be challenging but offers many benefits. Algorithm design is critically important to ensure precision of solutions that solve with minimal computation power. From an engineering perspective it is also incredibly useful, since many more situations can be modeled than with …
Equality Of P-Partition Generating Functions,
2011
Bucknell University
Equality Of P-Partition Generating Functions, Ryan Ward
Honors Theses
To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.
Springer Representations On The Khovanov Springer Varieties,
2011
University of Richmond
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …
