Mathematics internal assesment

The purpose of the portfolio is 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.
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 mathematics
• provide opportunities for students to complete extended pieces of mathematical work without
the time constraints of an examination
• enable students to develop individual skills and techniques, and to allow them to experience the
satisfaction of applying mathematical processes on their own
• provide students with the opportunity to experience for themselves the beauty, power and
usefulness of mathematics
• provide students with the opportunity to discover, use and appreciate the power of a calculator
or computer as a tool for doing mathematics
• enable students to develop the qualities of patience and persistence, and to reflect on the
significance of the results they obtain
• provide opportunities for students to show, with confidence, what they know and what they can
The portfolio is internally assessed by the teacher and externally moderated by the IBO. Assessment
criteria have been developed to relate to the mathematics objectives. In developing these criteria,
particular attention has been given to the objectives listed here, since these cannot be easily addressed
by means of timed, written examinations.
Where appropriate in the portfolio, students are expected to:
• know and use appropriate notation and terminology
• organize and present information and data in tabular, graphical and/or diagrammatic forms
• recognize patterns and structures in a variety of situations, and make generalizations
• demonstrate an understanding of and the appropriate use of mathematical modelling
• recognize and demonstrate an understanding of the practical applications of mathematics
• use appropriate technological devices as mathematical tools.
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
• type II—mathematical modelling.
The level of sophistication of the students’ mathematical work should be similar to that contained in
the syllabus. It is not intended that additional topics are taught to students to enable them to complete a
particular task.
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.

This is the required type of math.
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

The criteria will be attached after this submission. The Math should be high level Calculus/Statistics


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