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Styer, Robert – PRIMUS, 2014

The "Unsolved Problems in Number Theory" book by Richard Guy provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain.

Descriptors: College Mathematics, Mathematics Instruction, Numbers, Seminars

Miele, Anthony M. – ProQuest LLC, 2014

The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian,…

Descriptors: High School Students, Student Attitudes, Mathematics, Questionnaires

Debnath, Lokenath – International Journal of Mathematical Education in Science and Technology, 2016

This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and "k"-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's…

Descriptors: Mathematics, Mathematics Instruction, Mathematical Applications, Numbers

Feldman, Ziv – ProQuest LLC, 2012

Although elementary number theory topics are closely linked to foundational topics in number and operations and are prevalent in elementary and middle grades mathematics curricula, little is currently known about how students and teachers make sense of them. This study investigated pre-service elementary teachers' developing understanding of…

Descriptors: College Mathematics, Number Concepts, Preservice Teachers, Elementary School Teachers

Gabel, Mika; Dreyfus, Tommy – Educational Studies in Mathematics, 2017

The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer's choices regarding its presentation. Adopting Perelman's New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We…

Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Theories

Zetriuslita; Wahyudin; Jarnawi – International Education Studies, 2017

This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…

Descriptors: Mathematical Logic, Critical Thinking, Personality Traits, Problem Based Learning

Srinivasan, V. K. – International Journal of Mathematical Education in Science and Technology, 2010

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.

Descriptors: High Schools, Academically Gifted, Number Concepts, Birth

Gkioulekas, Eleftherios – International Journal of Mathematical Education in Science and Technology, 2017

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is…

Descriptors: Numbers, Mathematical Logic, Validity, Mathematics Instruction

AsKew, A.; Kennedy, K.; Klima, V. – PRIMUS, 2018

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Descriptors: Arithmetic, Music Theory, Correlation, Numbers

Camenga, Kristin A. – PRIMUS, 2017

Inquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry…

Descriptors: Mathematics Instruction, Inquiry, Student Attitudes, Teaching Methods

Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max – Mathematics Teaching in the Middle School, 2016

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

Descriptors: Mathematics Instruction, Problem Solving, Fractions, Mathematics Activities

Pathak, H. K. – International Journal of Mathematical Education in Science and Technology, 2008

In this article, we shall discuss some interesting, viable, meaningful, applicable and productive conjectures and methods to deal with some fundamental results in the theory of numbers.

Descriptors: Number Concepts, Theories, Mathematical Logic, Validity

Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him – International Journal of Mathematical Education in Science and Technology, 2014

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

Descriptors: Problem Solving, Number Concepts, Numbers, Teaching Methods

Papadopoulos, Ioannis; Iatridou, Maria – Mathematics Education Research Journal, 2010

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

Descriptors: Number Concepts, Grade 10, Problem Solving, Geometric Concepts

Kimani, Patrick M.; Olanoff, Dana; Masingila, Joanna O. – Mathematics Teaching in the Middle School, 2016

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

Descriptors: Problem Solving, Mathematics Instruction, Mathematics Activities, Task Analysis