This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

The purpose of this study is to develop design principles for crafting tasks that will encourage conjecturing and proving in the context of elementary number theory at the undergraduate level. From the analyses of the written work of 46 prospective mathematics teachers on a task designed according to these principles, we think that there is…

Current research and policy statements regarding mathematics teacher preparation support shifting the focus of content courses for prospective elementary teachers (PTs) towards the mathematics that elementary teachers are expected to teach, or "content knowledge for teaching mathematics" (CKTM). This paper describes a research-based…

In this paper we report our findings from a study, in which 177 undergraduate pre-service teachers had to verify a statement of elementary number theory at the onset of a lecture serving as a bridging course. The answers were categorized to investigate the qualities of the given argumentations. We also separated the results of three different…

To implement current reforms regarding proof and reasoning in secondary school mathematics successfully, pre-service secondary mathematics teachers must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that pre-service secondary mathematics teachers had for…

One of the most intriguing objectives when teaching computer science in mid-adolescence high school students is attracting and mainly maintaining their concentration within the limits of the class. A number of theories have been proposed and numerous methodologies have been applied, aiming to assist in the implementation of a personalized learning…

Society's relationship to knowledge and what is considered to be factual is changing. Effective teaching models focused on leveraging strategic control of the knowledge from teachers to learners in virtual learning environments are critical to insuring a positive path is charted. The Knowledge Development Model serves as the guide for determining…

The purpose of this study was to determine the relationship between mathematics and reading/language arts Comprehensive Assessment Program (TCAP) scores at a selected elementary school. The sample consisted of 12 randomly selected males in a third grade classroom. Data were collected for this study using the overall reading/language arts subtest…

How do parents contribute toward their child's academic productivity? This article analyzes studies conducted over the last 30 years on this topic. During these three decades a number of theories and theoretical frameworks have been developed to answer this fundamental question. There have been nine national studies published and six reviews of…

Elementary number theory is a standard topic in the mathematical preparation of preservice elementary teachers. To understand elementary number theory, a student must be comfortable with the representation of natural numbers as the product of primes. This paper discusses methods for accomplishing this goal in a mathematics course. It also…

Not all of mathematics can be taught in formal textbooks. Just as an English course can be enlivened by selections from literature, a mathematics course can gain depth and interest from special readings. This volume can be read in conjunction with the SMSG First Course in Algebra or Intermediate Mathematics. It introduces the subject of number…

The domain of number theory lends itself particularly well to generic argument, presented with the intention of conveying the force and structure of a conventional generalized argument through the medium of a particular case. The potential of generic examples as a didactic tool is virtually unrecognized. Although the use of such examples has good…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This discussion focuses upon potential implications of research conducted on preservice teachers' understanding of introductory topics from elementary number theory. Comments interlace three levels of consideration and recapitulate what is striking as some of the most interesting and important findings raised in the presentations, and flesh out…

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Bridge to…