IB Portfolio IB Portfolio TasksTasks

20% of final grade20% of final grade

The Purpose of the Portfolio The Purpose of the Portfolio TaskTask

To provide students with opportunities to be To provide students with opportunities to be rewarded for mathematics carried out under rewarded for mathematics carried out under ordinary conditions, that is, without the time ordinary conditions, that is, without the time limitations and pressure associated with written limitations and pressure associated with written examinations. Consequently, the emphasis should examinations. Consequently, the emphasis should be on good mathematical writing and thoughtful be on good mathematical writing and thoughtful reflection.reflection.

The portfolio is also intended to provide students The portfolio is also intended to provide students with opportunities to increase their understanding with opportunities to increase their understanding of mathematical concepts and processes. It is of mathematical concepts and processes. It is hoped that, by doing portfolio work, students hoped that, by doing portfolio work, students benefit from these mathematical activities and find benefit from these mathematical activities and find them both stimulating and rewarding.them both stimulating and rewarding.

The specific purposes of portfolio work are to:The specific purposes of portfolio work are to: Develop students’ personal insight into the nature of Develop students’ personal insight into the nature of

mathematics and to develop their ability to ask their own mathematics and to develop their ability to ask their own questions about mathematicsquestions about mathematics

Provide opportunities for students to complete extended Provide opportunities for students to complete extended pieces of mathematical work without the time constraints of pieces of mathematical work without the time constraints of an examinationan examination

Enable students to develop individual skills and techniques Enable students to develop individual skills and techniques and to allow them to experience the satisfaction of applying and to allow them to experience the satisfaction of applying mathematical processes on their ownmathematical processes on their own

Provide students with the opportunity to experience for Provide students with the opportunity to experience for themselves the beauty, power and usefulness of themselves the beauty, power and usefulness of mathematicsmathematics

Provide students with the opportunity to discover, use and Provide students with the opportunity to discover, use and appreciate the power of a calculator or computer as a tool appreciate the power of a calculator or computer as a tool for doing mathematicsfor doing mathematics

Enable students to develop the qualities of patience and Enable students to develop the qualities of patience and persistence, and to reflect on the significance of the results persistence, and to reflect on the significance of the results they obtainthey obtain

Provide opportunities for students to show, with confidence, Provide opportunities for students to show, with confidence, what they know and what they can dowhat they know and what they can do

The portfolio is internally The portfolio is internally assessed by the teacher assessed by the teacher and externally moderated and externally moderated by the IBO. Assessment by the IBO. Assessment criteria have been criteria have been developed to relate to the developed to relate to the objectives of the objectives of the mathematical courses.mathematical courses.

Know and use appropriate notation and Know and use appropriate notation and terminologyterminology

Organize and present information and data in Organize and present information and data in tabular, graphical and/or diagrammatic formstabular, graphical and/or diagrammatic forms

Recognize patterns and structures in a variety Recognize patterns and structures in a variety of situations, and make generalizationsof situations, and make generalizations

Demonstrate an understanding of and the Demonstrate an understanding of and the appropriate use of mathematical modellingappropriate use of mathematical modelling

Recognize and demonstrate an understanding Recognize and demonstrate an understanding of the practical applications of mathematicsof the practical applications of mathematics

Use appropriate technological devices as Use appropriate technological devices as mathematical toolsmathematical tools

Students are expected to:Students are expected to:

TasksTasks

Type l – Mathematical InvestigationType l – Mathematical InvestigationEssential skills to be assessedEssential skills to be assessed Producing a strategyProducing a strategy Generating dataGenerating data Recognising patterns or structuresRecognising patterns or structures Searching for further casesSearching for further cases Forming a general statementForming a general statement Testing a general statementTesting a general statement Justifying a general statementJustifying a general statement Appropriate use of technologyAppropriate use of technology

Type ll – Mathematical ModellingType ll – Mathematical ModellingMathematical modelling involves the following skills:Mathematical modelling involves the following skills: Translating the real-world problem into Translating the real-world problem into

mathematicsmathematics Constructing a modelConstructing a model Solving the problemSolving the problem Interpreting the solution in the real-world situationInterpreting the solution in the real-world situation Recognizing that different models may be used to Recognizing that different models may be used to

solve the same problemsolve the same problem Comparing different modelsComparing different models Identifying ranges of validity of the modelsIdentifying ranges of validity of the models Identifying the possible limits of technologyIdentifying the possible limits of technology Manipulating dataManipulating data

Essential skills to be assessed for Type llEssential skills to be assessed for Type ll Identifying the problem variablesIdentifying the problem variables Constructing relationships between these Constructing relationships between these

variablesvariables Manipulating data relevant to the problemManipulating data relevant to the problem Estimating the values of parameters within Estimating the values of parameters within

the model that cannot be measured or the model that cannot be measured or calculated from the datacalculated from the data

Evaluating the usefulness of the modelEvaluating the usefulness of the model Communicating the entire processCommunicating the entire process Appropriate use of technologyAppropriate use of technology

Internal Assessment CriteriaInternal Assessment Criteria

Type l – Mathematical Type l – Mathematical InvestigationInvestigation: :

A: Use of notation and A: Use of notation and terminology terminology

B: CommunicationB: Communication

C: Mathematical process C: Mathematical process – searching for patterns– searching for patterns

D: Results – D: Results – generalizationgeneralization

E: Use of technologyE: Use of technology

F: Quality of workF: Quality of work

Type ll – Mathematical Type ll – Mathematical ModellingModelling

A: Use of notation and A: Use of notation and terminologyterminology

B: CommunicationB: Communication

C: Mathematical process C: Mathematical process – developing a model– developing a model

D: Results – D: Results – interpretationinterpretation

E: Use of technologyE: Use of technology

F: Quality of workF: Quality of work

Criterion A: Use of notation and terminologyCriterion A: Use of notation and terminology Correct mathematical notation is required Correct mathematical notation is required

(correct vector notation), but it can be (correct vector notation), but it can be accompanied by calculator notation, accompanied by calculator notation, particularly when students are particularly when students are substantiating their use of technology.substantiating their use of technology.

Appropriate use of mathematical symbols Appropriate use of mathematical symbols is also required. (Example: is also required. (Example: ππ should be should be used rather than the word “pi”). used rather than the word “pi”).

Word processing the portfolio does not Word processing the portfolio does not increase the level of achievement for the increase the level of achievement for the Criterion A and B. Using x^2 instead of xCriterion A and B. Using x^2 instead of x22, , would be considered a lack of proper would be considered a lack of proper usage and a student would not achieve usage and a student would not achieve level 2.level 2.

Criterion B: CommunicationCriterion B: Communication If in reading a pupils work, I have to pause If in reading a pupils work, I have to pause

to clarify where a result came from or how to clarify where a result came from or how it was achieved this generally indicates it was achieved this generally indicates flawed communication. Level 2 cannot be flawed communication. Level 2 cannot be achieved if the student only writes down achieved if the student only writes down mathematical computations without mathematical computations without explanation. explanation.

Graphs, tables and diagrams should Graphs, tables and diagrams should accompany the work in the appropriate accompany the work in the appropriate place and not be attached to the end of the place and not be attached to the end of the document. Graphs must be correctly document. Graphs must be correctly labelled.labelled.

Criterion C: Mathematical ProcessCriterion C: Mathematical ProcessType lType l Students can only achieve a level 3 if the Students can only achieve a level 3 if the

amount of data generated is sufficient to amount of data generated is sufficient to warrant an analysis. A level 4 can be warrant an analysis. A level 4 can be achieved if everything is ready to produce achieved if everything is ready to produce the statement. Testing further cases and the statement. Testing further cases and commenting on the results is sufficient to commenting on the results is sufficient to award level 5. If a student gives a proof or award level 5. If a student gives a proof or justification of the correct statement, no justification of the correct statement, no further cases need be investigated in order to further cases need be investigated in order to award level 5.award level 5.

Type llType ll At achievement level 5, applying the model At achievement level 5, applying the model

to other situations could include, for example, to other situations could include, for example, a change of parameter or more data.a change of parameter or more data.

Criterion D: ResultsCriterion D: ResultsType lType l

A student who gives a correct formal proof A student who gives a correct formal proof of the general proof of the general of the general proof of the general statement that does not take into account statement that does not take into account scope or limitations would achieve level 4. scope or limitations would achieve level 4.

Type llType ll““Appropriate degree of accuracy” means Appropriate degree of accuracy” means appropriate in the context of the task. A appropriate in the context of the task. A minor error in accuracy (eg. Using 10sf minor error in accuracy (eg. Using 10sf instead of 2 or 3) might not prevent a instead of 2 or 3) might not prevent a student progressing from level 3 to level 4, student progressing from level 3 to level 4, but could stop them progressing from level but could stop them progressing from level 4 to level 5.4 to level 5.

Criterion E: Use of TechnologyCriterion E: Use of Technology A statement confirming appropriate A statement confirming appropriate

use of technology is necessary to use of technology is necessary to achieve level 3.achieve level 3.

Using a computer and/or graphics Using a computer and/or graphics calculator to generate only graphs or calculator to generate only graphs or tables may not significantly tables may not significantly contribute to the development of the contribute to the development of the task.task.

Criterion F: Quality of WorkCriterion F: Quality of Work

Students who satisfy all the Students who satisfy all the requirements correctly achieve level requirements correctly achieve level 1. For a student to achieve level 2, 1. For a student to achieve level 2, work must show precision, insight work must show precision, insight and a sophisticated level of and a sophisticated level of mathematical understanding. (It mathematical understanding. (It must be presented beyond ordinary must be presented beyond ordinary expectations).expectations).

One of the main purposes of portfolio One of the main purposes of portfolio work is to help students to learn the work is to help students to learn the importance of writing “good” importance of writing “good” mathematics.mathematics.

Remember that the work you Remember that the work you produce is for other people to read. produce is for other people to read. It needs to be clear and logical, and It needs to be clear and logical, and contain appropriate links and contain appropriate links and explanations.explanations.

AuthenticityAuthenticity

Any portfolio work submitted for Any portfolio work submitted for assessment must be entirely your assessment must be entirely your own work. own work.

The content can be checked against The content can be checked against other students and any text that has other students and any text that has been produced on the topic.been produced on the topic.

Assessment DeadlineAssessment Deadline

You have 10 days to complete your You have 10 days to complete your portfolio.portfolio.

As per the Assessment policy, As per the Assessment policy, extensions can only be granted in extensions can only be granted in extreme circumstances and you extreme circumstances and you must discuss this prior to the due must discuss this prior to the due date with Mrs Anderson.date with Mrs Anderson.