Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

There are three hypotheses for this research: 1. High school mathematics students in urban public schools, who are provided interactive technology resources during normal course work, will experience a multiplier effect of enhanced learning in mathematics. They will have an increase in positive dispositions indicative of their identity development…

The No Child Left Behind Act of 2001 put a focus on each child in a school being proficient. Since 1957 when Sputnik was launched, the United States has been attempting to improve its schools. The existing literature has a gap as to how to turn around an underperforming school in a fairly short period of time. A qualitative case study methodology…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

This paper outlines an innovative game-based approach to learning introductory programming that is grounded in the development of computational thinking at an abstract conceptual level, but also provides a direct contextual relationship between game-play and learning traditional introductory programming. The paper proposes a possible model for,…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

Current methods for detecting growth of students' problem-solving skills in math focus mainly on analyzing changes in test scores. Score-level analysis, however, may fail to reflect subtle changes that might be evident at the item level. This article demonstrates a method for studying item-level changes using data from a multiwave experiment with…

The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

A method of solving the Schrodinger equation using a basis set expansion is described and used to calculate energy levels and wavefunctions of the hindered rotation of ethane and the ring puckering of cyclopentene. The calculations were performed using a computer algebra package and the calculations are straightforward enough for undergraduates to…

Despite the rigorous debate around the purposes of higher education and the associated concept of graduate attributes, science education at the tertiary level has remained largely impervious to engaging with these ideas. This may be due to the emphasis on the knowledge base of the hard science as opposed to the emphasis on the knower in the…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

This study explored how the process of Response to Intervention (RTI) has changed the roles of three veteran special educators. The background knowledge of these teachers that helped make the initiative successful, as well as the "building blocks" that were present in the initial implementation of RTI models in their settings, were…

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

We have applied the "practical paradigm" in teaching problem solving to secondary school students. The key feature of the practical paradigm is the use of a practical worksheet to guide the students' processes in problem solving. In this paper, we report the diffusion of the practical paradigm to university level courses for prospective…

In this paper, we consider collective problem-solving challenges and a particular structuring objective: lead groups of learners to make their shared problem-solving organization explicit. Such an objective may be considered as a way to lead learners to consider building and maintaining a shared organization, and/or as a way to provide a basis for…