Requirements
The portfolio must consist of two pieces of work assigned by the teacher and completed by the student during the course. Each piece of student work contained in the portfolio must be based on:
- an area of the syllabus
- one of the two types of tasks
- type I—mathematical investigation
- type II—mathematical modelling.
The level of sophistication of the students’ mathematical work should be similar to that contained in the syllabus. Each portfolio must contain two pieces of student work, each of the two types of task: the portfolio must contain one type I and one type II piece of work. These tasks should be completed at intervals throughout the course and should not be left until towards the end.
Portfolio work will be integrated into the course of study so that it enhances student learning by introducing a topic, reinforcing mathematical meaning or taking the place of a revision exercise. Therefore, each task will correspond to the course of study devised by the teacher in terms of the knowledge and skills that the students have been taught.
Technology
The need for proper mathematical notation and terminology, as opposed to calculator or computer notation is stressed and reinforced, as well as adequate documentation of technology usage. Students will be required to reflect on the mathematical processes and algorithms the technology is performing, and communicate them clearly and succinctly.
Type I — Mathematical Investigation
While many teachers incorporate a problem-solving approach into their classroom practice, students also should be given the opportunity formally to carry out investigative work. The mathematical investigation is intended to highlight that:
- the idea of investigation is fundamental to the study of mathematics
- investigation work often leads to an appreciation of how mathematics can be applied to solve problems in a broad range of fields
- the discovery aspect of investigation work deepens understanding and provides intrinsic motivation
- during the process of investigation, students acquire mathematical knowledge, problem-solving techniques, a knowledge of fundamental concepts and an increase in self-confidence.
All investigations develop from an initial problem, the starting point. The problem must be clearly stated and contain no ambiguity. In addition, the problem should:
- provide a challenge and the opportunity for creativity
- contain multi-solution paths, that is, contain the potential for students to choose different courses of action from a range of options.
Essential skills to be assessed
- Producing a strategy
- Generating data
- Recognizing patterns or structures
- Searching for further cases
- Forming a general statement
- Testing a general statement
- Justifying a general statement
- Appropriate use of technology
Type II — Mathematical Modelling
Problem solving usually elicits a process-oriented approach, whereas mathematical modelling requires an experimental approach. By considering different alternatives, students can use modelling to arrive at a specific conclusion, from which the problem can be solved. To focus on the actual process of modelling, the assessment should concentrate on the appropriateness of the model selected in relation to the given situation, and on a critical interpretation of the results of the model in the real-world situation chosen.
Mathematical modelling involves the following skills.
- Translating the real-world problem into mathematics
- Constructing a model
- Solving the problem
- Interpreting the solution in the real-world situation (that is, by the modification or amplification of the problem)
- Recognizing that different models may be used to solve the same problem
- Comparing different models
- Identifying ranges of validity of the models
- Identifying the possible limits of technology
- Manipulating data
Essential skills to be assessed
- Identifying the problem variables
- Constructing relationships between these variables
- Manipulating data relevant to the problem
- Estimating the values of parameters within the model that cannot be measured or calculated from the data
- Evaluating the usefulness of the model
- Communicating the entire process
- Appropriate use of technology
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