2 The Purpose of the Portfolio Task To provide students with opportunities to be rewarded for mathematics carried out under ordinary conditions, that is, without the time limitations and pressure associated with written examinations. Consequently, the emphasis should be on good mathematical writing and thoughtful reflection.The portfolio is also intended to provide students with opportunities to increase their understanding of mathematical concepts and processes. It is hoped that, by doing portfolio work, students benefit from these mathematical activities and find them both stimulating and rewarding.
3 The specific purposes of portfolio work are to: Develop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematicsProvide opportunities for students to complete extended pieces of mathematical work without the time constraints of an examinationEnable students to develop individual skills and techniques and to allow them to experience the satisfaction of applying mathematical processes on their ownProvide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematicsProvide students with the opportunity to discover, use and appreciate the power of a calculator or computer as a tool for doing mathematicsEnable students to develop the qualities of patience and persistence, and to reflect on the significance of the results they obtainProvide opportunities for students to show, with confidence, what they know and what they can do
4 The portfolio is internally assessed by the teacher and externally moderated by the IBO. Assessment criteria have been developed to relate to the objectives of the mathematical courses.
5 Students are expected to: Know and use appropriate notation and terminologyOrganize and present information and data in tabular, graphical and/or diagrammatic formsRecognize patterns and structures in a variety of situations, and make generalizationsDemonstrate an understanding of and the appropriate use of mathematical modellingRecognize and demonstrate an understanding of the practical applications of mathematicsUse appropriate technological devices as mathematical tools
6 Tasks Type l – Mathematical Investigation Essential skills to be assessedProducing a strategyGenerating dataRecognising patterns or structuresSearching for further casesForming a general statementTesting a general statementJustifying a general statementAppropriate use of technology
7 Type ll – Mathematical Modelling Mathematical modelling involves the following skills:Translating the real-world problem into mathematicsConstructing a modelSolving the problemInterpreting the solution in the real-world situationRecognizing that different models may be used to solve the same problemComparing different modelsIdentifying ranges of validity of the modelsIdentifying the possible limits of technologyManipulating data
8 Essential skills to be assessed for Type ll Identifying the problem variablesConstructing relationships between these variablesManipulating data relevant to the problemEstimating the values of parameters within the model that cannot be measured or calculated from the dataEvaluating the usefulness of the modelCommunicating the entire processAppropriate use of technology
9 Internal Assessment Criteria Type l – Mathematical Investigation:A: Use of notation and terminologyB: CommunicationC: Mathematical process – searching for patternsD: Results – generalizationE: Use of technologyF: Quality of workType ll – Mathematical ModellingA: Use of notation and terminologyB: CommunicationC: Mathematical process – developing a modelD: Results – interpretationE: Use of technologyF: Quality of work
10 Criterion A: Use of notation and terminology Correct mathematical notation is required (correct vector notation), but it can be accompanied by calculator notation, particularly when students are substantiating their use of technology.Appropriate use of mathematical symbols is also required. (Example: π should be used rather than the word “pi”).Word processing the portfolio does not increase the level of achievement for the Criterion A and B. Using x^2 instead of x2, would be considered a lack of proper usage and a student would not achieve level 2.
11 Criterion B: Communication If in reading a pupils work, I have to pause to clarify where a result came from or how it was achieved this generally indicates flawed communication. Level 2 cannot be achieved if the student only writes down mathematical computations without explanation.Graphs, tables and diagrams should accompany the work in the appropriate place and not be attached to the end of the document. Graphs must be correctly labelled.
12 Criterion C: Mathematical Process Type lStudents can only achieve a level 3 if the amount of data generated is sufficient to warrant an analysis. A level 4 can be achieved if everything is ready to produce the statement. Testing further cases and commenting on the results is sufficient to award level 5. If a student gives a proof or justification of the correct statement, no further cases need be investigated in order to award level 5.Type llAt achievement level 5, applying the model to other situations could include, for example, a change of parameter or more data.
13 Criterion D: ResultsType lA student who gives a correct formal proof of the general proof of the general statement that does not take into account scope or limitations would achieve level 4.Type ll“Appropriate degree of accuracy” means appropriate in the context of the task. A minor error in accuracy (eg. Using 10sf instead of 2 or 3) might not prevent a student progressing from level 3 to level 4, but could stop them progressing from level 4 to level 5.
14 Criterion E: Use of Technology A statement confirming appropriate use of technology is necessary to achieve level 3.Using a computer and/or graphics calculator to generate only graphs or tables may not significantly contribute to the development of the task.
15 Criterion F: Quality of Work Students who satisfy all the requirements correctly achieve level 1. For a student to achieve level 2, work must show precision, insight and a sophisticated level of mathematical understanding. (It must be presented beyond ordinary expectations).
16 One of the main purposes of portfolio work is to help students to learn the importance of writing “good” mathematics.Remember that the work you produce is for other people to read. It needs to be clear and logical, and contain appropriate links and explanations.
17 AuthenticityAny portfolio work submitted for assessment must be entirely your own work.The content can be checked against other students and any text that has been produced on the topic.
18 Assessment Deadline You have 10 days to complete your portfolio. As per the Assessment policy, extensions can only be granted in extreme circumstances and you must discuss this prior to the due date with Mrs Anderson.