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…

Many students encounter difficulties in science and mathematics. Earlier research suggested that although intuitions are often needed to gain new ideas and concepts and to solve problems in science and mathematics, some of students' difficulties could stem from the interference of intuitive reasoning. The literature suggests that overcoming…

This study used an ethnographic research design to explore the perceptions of 27 families with preschool children whose parents or guardians designated themselves as culturally diverse. Multiple data sources were collected over 9 months in the field, including transcripts of focus group meetings and individual parental interviews, preschool…

In this research we present the use of some technologies in problem solving activities (at different secondary school grades), aimed at finding a model for a geometric configuration, and representing this model in various ways: through a construction, through a Cartesian graph, etc. The task is part of a teaching experiment, in which students used…

Today, more than ever, teachers must work effectively and efficiently to meet seemingly contradictory demands placed on them by society. On the one hand, school personnel are tasked with attaining and publicly reporting high levels of student achievement in response to No Child Left Behind. On the other, school personnel must ensure that students…

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and…

Eight trigrams (BaGua) is a philosophy that has played an essential role in Chinese life. The purpose of the present study is to extend the theory to organizational problem-solving, so that individuals can engage in creative problem solving and justification to discover the most effective approaches. Questionnaires were returned by 259 research…

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…