This research contributes to meeting a need for a teaching methodology which allows students to construct their own knowledge, and which can replace or enhance a traditional pedagogy involving the exposition of ideas, techniques and worked examples by the teacher, leading to illustrative exercises by students. While many students successfully learn within the traditional classroom environment, many students are mystified by the mathematical concepts which teachers attempt to impart to them. This study aimed to demonstrate that a pedagogy based on the process of mathematical modelling substantially assists the acquisition and understanding of mathematical ideas, concepts, methods and theories, as well as improving students' attitudes to mathematics and their competency in communicating their mathematical solutions. Over a two year period, a year 8 program in a Queensland Catholic College was re-designed, appropriate resources were constructed, and a mathematical modelling course was implemented and evaluated with one class of students. Students completed surveys at the start and end of the trial teaching year to investigate changes in attitude to mathematics. Quantitative data were collected in the form of test results in common with another class in the school. Qualitative data were collected in the form of student journal statements, and teacher classroom observations in diary form. Excerpts of work from five students were chosen for detailed case studies. The study was expanded in the following year, in which the trial program was implemented by all year 8 teachers in the school who then provided evaluations of the course and the methodology. The five case- study students were also included in follow-up evaluations nine months after completing the course. The results of the study indicate that students improved, in varying degrees with respect to their mathematical knowledge; their competency in solving problems; and their competency in communicating solutions. Some students also demonstrated an improved attitude to mathematics, but this was not conclusive for all students in the study. The study provides insights and implications for teachers of mathematics.