The purpose of this study was to examine the ways advanced mathematics students define "number" and the degree to which their definitions extend to different number domains. Of particular interest for this study are learners' fundamental conceptions of number and the implications for learners' interpretations of complex numbers (a + bi).…

The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher's knowledge effects the students' knowledge. A teacher should use appropriate mathematical explanation to be understood well by…

In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…

Solving problems involving absolute value is one of the hardest topics for students learning in elementary algebra course. This is an important topic in student's mathematics life since absolute value functions are important example of a function which is continuous on the real line but not differentiable at the origin. A deep understanding of…

Children's intuitive understanding of numbers begins early in life, and their numbers-related knowledge influences instructors' teaching practices. The number zero is more difficult to teach and learn than other numbers. The purpose of this study was to investigate how preschool teachers perceive the number zero and design their teaching practices…

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the…

This paper explores the dimensions of knowledge and the ways of thinking (procedural or proceptual thinking) adopted by 157 Lebanese students in different grades when defining and identifying irrational numbers when locating them on the number line. It searches for a relation between the performance of the participants and their different grades.…

The method of proof by mathematical induction follows from Peano axiom 5. We give three properties which are often used in the proofs by mathematical induction. We show that these are equivalent. Supposing the well-ordering property we prove the validity of this method without using Peano axiom 5. Finally, we introduce the simplest form of…

Six possible ways of defining prime numbers are given, and additional activities on the topic are suggested. (MK)

Number sense is easy to recognize but difficult to define and hence, to teach. In this article, number sense is defined in terms of the knowledge known to underline it, as identified in cognitive developmental theory and research. A preK-2 mathematics program, called Number Worlds, that was specifically developed to teach this knowledge is…

Certain definitions introduce appropriate concepts, among which are the definitions of the counting functions of the primes and twin primes, along with definitions of the correlation coefficient in a bivariate sample space. It is argued conjecturally that the characteristic functions of the prime "p" and of the quantity "p"+2 are highly…

This learning module provides students with practice in applying mathematical operations to vocational agriculture. The module consists of unit objectives, definitions, information, problems to solve, worksheets suitable for various levels of vocational agriculture instruction, and answer keys for the problems and worksheets. This module provides…