Digital Commons Network^™

For The Rest Of Your Life, Mike Fletcher

The Mathematics Enthusiast

‘For the Rest of Your Life’ is a new TV game show. Contestants play to win money every month. This can be for as little as one month or, if every one of their guesses is correct, for the rest of their lives.

Learning, Participation And Local School Mathematics Practice, Cristina Frade, Konstantinos Tatsis

The Mathematics Enthusiast

This paper reports on a study whose aim was to examine students’ learning in terms of participation in collective mathematical discussions. Our basic theoretical assumptions are based on a combination of situated learning perspectives and a framework that links social and psychological approaches of mathematical activity and learning. The research was carried out in a Year-8 classroom (students were aged 12 to 13), and the mathematical subject under investigation was area measurement. Data are presented to illustrate possible correspondences between ‘signs’ of learning and ‘local’ changes of participation. We conclude by discussing some pedagogical implications resulting from the study.

If A.B = 0 Then A = 0 Or B = 0?, Cristina Ochoviet, Asuman Oktaç

The Mathematics Enthusiast

We present a study carried out in Uruguay, with secondary school students and tertiary level mathematics students, concerning the zero-product property. In our research we observed that when early secondary and late secondary school students have to solve equations of the form (ax + b)(cx + d) = 0, they do not always apply the property, even when it is the only available tool and have received specific instruction on its application to the resolution of equations of this type. We also detected an error that students make when they have to verify the solutions of this type of equations. …

The Origins Of The Genus Concept In Quadratic Forms, Mark Beintema, Azar Khosravani

The Mathematics Enthusiast

We present an elementary exposition of genus theory for integral binary quadratic forms, placed in a historical context.

The Impact Of Undergraduate Mathematics Courses On College Student’S Geometric Reasoning Stages, Nuh Aydin, Erdogan Halat

The Mathematics Enthusiast

The purpose of this study is to investigate possible effects of different college level mathematics courses on college students’ van Hiele levels of geometric understanding. Particularly, since logical reasoning is an important aspect of geometric understanding, it would be interesting to see whether there are differences in van Hiele levels of students who have taken non-geometry courses that emphasize or focus on logic and proofs (Category I) and those that don’t (Category II). We compared geometric reasoning stages of students from the two categories. One hundred and forty nine college students taking various courses from the two categories have been …

Elementary School Pre-Service Teachers’ Understandings Of Algebraic Generalizations, Jean E. Hallagan, Audrey C. Rule, Lynn F. Carlson

The Mathematics Enthusiast

It is critical for all students to learn algebra, including the ability to generalize, to function in our increasingly complex world. This pretest/intervention/posttest study of preservice elementary teachers (N = 63) in their math methods course assessed their knowledge of writing and applying algebraic generalizations using instructor-made rubrics along with analysis of work samples and reported insights. Initially, although most subjects could solve a specific case, they had considerable difficulty determining an algebraic rule. After a problemsolving- based teaching intervention, students improved in their ability to generalize, however, they encountered more difficulty with determining the algebraic generalization for items arranged …

A Longitudinal Study Of Student’S Representations For Division Of Fractions, Sylvia Bulgar

The Mathematics Enthusiast

The representations that students use as part of their mathematical problem solving can provide us with a window into their grasp of the concepts they are exploring and developing. In this paper, the author indicates how these representations can evolve over time and enrich the understanding of division of fractions, often thought to be the most difficult of elementary school mathematical topics. The results of this research suggest that when appropriate problems are provided for students, in a meaningful context, they can demonstrate understanding of division of fractions that is durable over time, and that they are able to flexibly …

Catch Me If You Can!, Steve Humble

The Mathematics Enthusiast

Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individuals understanding of the subject.

The three activities described in this article can all be used outside the classroom in a maths lesson. Teaching mathematical concepts in this way engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can occur in the classroom. By taking maths beyond the classroom, we can more clearly illustrate the connections between the real world and what they are studying …

Fostering Connections Between The Verbal, Algebraic, And Geometric Representations Of Basic Planar Curves For Student’S Success In The Study Of Mathematics, Margo F. Kondratieva, Oana G. Radu

The Mathematics Enthusiast

We discuss the significance of making connections between the verbal, algebraic, and geometric representations of basic mathematical objects for students’ understanding of mathematical instructions. Our survey of 499 students enrolled in a precalculus university course reveals that such connections are not always present, even if the objects themselves are familiar to the students. We stress that the ability of making these connections needs to be specifically addressed in teaching mathematics at various levels. A proper attention to the matter contributes to the formation of students’ mathematical background, which makes a difference for their success in study of calculus, in particular.

How To Increase Mathematical Creativity- An Experiment, Kai Brunkalla

The Mathematics Enthusiast

Creativity is an integral part of mathematics. In this article I examine the increase in awareness of creativity in mathematics using Fröbel’s blocks in a college classroom. A majority of students found the introduction of the “gifts” of the founder of Kindergarten to a college geometry classroom enhancing their interest in mathematics. They judged the wooden blocks helpful in their understanding of geometry. The students showed increased awareness of creativity in mathematics.

Korean Teachers’ Perceptions Of Student Success In Mathematics: Concept Versus Procedure, Insook Chung

The Mathematics Enthusiast

This article examines the Korean classroom teachers’ beliefs about mathematics education in elementary schools. Their perceptions about contributing factors to Korean students’ high achievement scores in international comparative studies in the area of mathematics are explored. Elementary classroom teachers were surveyed using the researchermade questionnaire (Teacher Perception about Mathematics Curriculum) and 141 teachers completed the questionnaire. The data collected was analyzed by a descriptive analysis. The results reveal that the majority of classroom teachers agreed that real life applications, processing skills, using concrete instructional manipulatives, and conceptual knowledge are very important in teaching children mathematics. Most of teachers participating in …

Book X Of The Elements: Ordering Irrationals, Jade Roskam

The Mathematics Enthusiast

Book X from The Elements contains more than three times the number of propositions in any of the other Books of Euclid. With length as a factor, anyone attempting to understand Euclidean geometry may be hoping for a manageable subject matter, something comparable to Book VII’s investigation of number theory. They are instead faced with a dizzying array of new terminology aimed at the understanding of irrational magnitudes without a numerical analogue to aid understanding. The true beauty of Book X is seen in its systematic examination and labeling of irrational lines. This paper investigates the early theory of irrationals, …

Tme Volume 6, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

2009-2010 Course Catalog, University Of Montana--Missoula. Office Of The Registrar

University of Montana Course Catalogs, 1895-2024

An annual catalog of courses and course descriptions offered at the University of Montana.

Fatigue Risk Management: Modeling The Sleep/Wake-Based Dynamics Of Performance, Peter J. Mccauley

Graduate Student Theses, Dissertations, & Professional Papers

Several biomathematical models have been developed to predict cognitive performance impairment due to sleep loss and/or circadian misalignment. In essence, these models are all based on the Two-Process Model (TPM) which contains a homeostatic process for the build-up and decline of sleep pressure across days, and a circadian process to keep track of time of day. The TPM has been used successfully to predict performance under conditions of total sleep deprivation. However, for conditions of chronic sleep restriction, the TPM predicts a rapid stabilization of performance impairment (within a day or two)---which is not in agreement with experimental observations. This …

A Methodology For Planning Road Best Management Practices Combining Wepp: Road Erosion Modeling And Simulated Annealing Optimization, James Anderson Efta

Graduate Student Theses, Dissertations, & Professional Papers

Erosion from forest roads is a known problem in mountainous terrain. To abate these negative consequences, physical Best Management Practices (BMPs) are implemented, sometimes with no knowledge of erosion hot spots. With the need to minimize water quality impacts while at the same time accounting for multiple considerations and constraints, road BMP planning at the watershed scale is a difficult task. To assist in this planning process, a methodology is presented here that combines WEPP: Road erosion predictions with simulated annealing optimization. Under this methodology, erosion predictions associated with BMP options for a segment comprise the objective function of an …

Curriculum Improvement: The Teacher Perspective On Change In The Classroom, Heather C. Davis

Graduate Student Theses, Dissertations, & Professional Papers

This study explored the curriculum change experiences of five social studies teachers, from three high schools within one school district located in a western Montana city, integrating an economics curriculum in their eleventh grade U.S. history classrooms for the first time. A review of the related literature on this topic revealed several areas of consideration regarding teachers' curriculum change experiences which guided the data collection and analysis process: commitment, workload, capacity, collaboration, and perception of the teaching profession. This qualitative, within case study was designed to add to the body of quantitative research on curriculum change. Data collection sources include: …

Norm-Preserving Criteria For Uniform Algebra Isomorphisms, Rebekah Yates

Graduate Student Theses, Dissertations, & Professional Papers

Let A ⊂ C(X) and B ⊂ C(Y ) be uniform algebras with Choquet boundaries δA and δB. We establish sufficient conditions for a surjective map T: A → B to be an algebra isomorphism. In particular, we show that if T: A → B is a surjection that preserves the norm of the sums of the moduli of algebra elements, then T induces a homoemorphism between the Choquet boundaries of A and B such that |Tf| = |f| on the Choquet boundary of B. If, in addition, T preserves the norms of all linear combinations of algebra elements and …

Operational Report 2008, University Of Montana--Missoula

University of Montana Annual Financial Reports, 1918-2012

University of Montana annual financial report for fiscal year ending June 30, 2008.

Montana Kaimin, November 19, 2008, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Montana Kaimin, November 18, 2008, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Air Compression As A Mechanism For The Underdamped Slug Test Response In Fractured Glacier Ice, Toby W. Meierbachtol, Joel T. Harper, Neil Humphrey, Jeremy Shaha, John Bradford

Geosciences Faculty Publications

Artificial perturbations of borehole water levels, known as slug tests, are a useful means of characterizing the glacier hydrologic system. Slug tests were performed on Bench Glacier, Alaska, in 21 boreholes over three field seasons during the transition from a winter to a summer drainage mode. Fifty-four slug tests were conducted, with water level monitoring in up to five boreholes adjacent to the slugged borehole. Seven of the slug tests were performed in conjunction with dye dispersion tests to identify water pathways within the slugged borehole following perturbation. Nearly 60% of monitored adjacent boreholes showed a hydraulic connection to the …

Montana Kaimin, October 29, 2008, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Current Unrestricted Operating Budgets, Fiscal Year 2009, University Of Montana--Missoula. Office Of Administration And Finance

University of Montana Current Unrestricted Operating Budgets, 1993-2017

The unrestricted operating budget of the University of Montana, issued by the Office of University Planning, Budgeting and Analysis under the Office of Administration and Finance.

Um Deadline To Apply For Goldwater Scholarships Nov. 6, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

Department Of Mathematical Sciences Newsletter, Fall 2008, University Of Montana--Missoula. Department Of Mathematical Sciences

Newsletters from the Department of Mathematical Sciences at UM

Symmetry, Student Talks and The Simpsons: a Report from an MAA Conference / Rebekah Yates -- Meet the Mac Johnson Family Scholarship Winners -- Math Preparation of Elementary Teachers at UM is Among the Best / Jim Hirstein -- Notes from the Chair / David Patterson -- New Faculty: Ke Norman / Rick Billstein -- MathThematicsCurriculum Revision Completed / Jim Hirstein -- Honors Calculus in two Acts / Bharath Sriraman -- Alumni News -- Summer 2009 Graduate Courses for Secondary and Middle School Math Teachers -- Online Giving -- Wintersession Course January 2009 -- Professor Jon Graham earns …

Molecular-Orientation-Dependent Ac Stark Effect And Its Impact On Multiphoton Processes, Xi Chu

Chemistry and Biochemistry Faculty Publications

We study the dependence of the ac Stark shifts of electronic energies on the molecular orientation relative to the polarization direction of an incident intense laser field, using a three-dimensional non-Hermitian Floquet method and H(2)+ as a model system. Simultaneously, we also study the orientation-dependent high-order harmonic generation (HHG) and multiphoton ionization (MPI). We find that with the presence of near-one-photon resonance, the Stark effect strongly mixes electronic states of different symmetries to create quasienergy states (QESs). The orientation dependence of multiphoton processes, in which these QESs play an important role, becomes complex. Population transfer is better achieved with aligned …

Graduate, Professional School Fair At Um Oct. 1, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

Montana Kaimin, September 18, 2008, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Grizzly Football Game Day Program, September 13, 2008, University Of Montana--Missoula. Athletics Department

Grizzly Football Game Day Programs, 1914-2012

Program created for a Grizzly football game.