Introduction

With the rapid pace of technological development, it is essential that students are equipped with a solid base of mathematical knowledge which is flexible enough to be used in a variety of work environments.

The Mathematics department is committed to enabling students to develop a positive attitude toward a lifelong learning of mathematics. We encourage students to develop patience and persistence when solving problems. We emphasize the need to develop and apply information and to communicate and use technology skills in the study of mathematics. As part of our commitment to a holistic education, we ensure that the math program emphasizes the many and varied relationships between mathematics and other disciplines. As a department within an international school we also highlight the international dimensions of mathematics and its varied cultural and historical perspectives. TISA operates a five year integrated math program (MYP mathematics) which is followed by the two year International Baccalaureate Program. At IB level TISA offers Math Studies, Math Standard and Math Higher levels. The framework for MYP mathematics is organized so that students can work at two different levels of ability: standard mathematics and extended mathematics from M3 – M5.


Staff

The Maths Department consists of the following personnel:
Aims

The aims of the teaching and study of MYP mathematics are to encourage and enable students to:

• enjoy mathematics and to develop curiosity as well as an appreciation of its elegance and power
• develop an understanding of the principles and nature of mathematics
• communicate clearly and confidently in a variety of contexts
• develop logical, critical and creative thinking, and patience and persistence in problem solving
• develop power of generalization and abstraction
• apply and transfer skills to a wide range of situations including real life, other areas of knowledge and future developments
• appreciate how developments in technology and mathematics have influenced each other
• appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics
• appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives
• appreciate the contribution of mathematics to other areas of knowledge
• develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
• develop the ability to reflect critically upon their own work and the work of others.

Placement Policy

At the beginning of M3 students complete a placement test which, along with their results from M2, helps determine whether they move into the Extended or Standard class.

Movement between Standard and Extended Classes

Math classes in years M3-M5 are divided into a Standard and an Extended program. Movement between the standard and extended programs is easiest during M3 and becomes progressively more problematic by the end of M5. This is due to differentiation between the two levels with respect to topics covered.

Students may move between levels as they continue to develop their mathematical skills. In order to move from Math Standard to Math Extended students need to achieve a high level on a minimum of 3 consecutive assessment items (greater than or equal to level 6 for Criterion A or a score of 14 or higher for criteria B, C and D for an Investigation). Students can be moved from a Math Extended class to a Math Standard Class if they have achieved less than a level 4 on Criteria A or a score of less than 10 for criteria B, C and D for an Investigation on 3 consecutive assessment items. Parents of course will be notified of any impending changes. M5 students do need to be aware that the deadline for registration for the MYP certificate is usually mid-October of each academic year. Any level changes after this date will involve payment of the MYP change of registration fee. Movement between courses is possible until the beginning of term 3.

Entry to IB Math Courses

The Math Dept encourages students to aim high and achieve the best they can at the highest possible level. Students also need to demonstrate that they are capable of studying at a particular level.

However there should be no assumptions that a student in M5 can automatically move into a Diploma Math course of their choice. The following levels of expertise and understanding have to be attained in the respective M5 Math course as a pre-requisite to entry to Diploma courses. Emphasis here is on the score for Criteria A in their M5 results, but consideration will also be given to the Criteria B, C and D scores as there are internally assessed ―investigative type assignments in the Diploma Math courses. Students should have a minimum combined score of 8 / 20 for these 3 Criteria (sustained score).

For (consideration for) entry to HL (Higher Level) Math, a student has to consistently achieve a minimum level of 6 out of 8 under Criterion A (Knowledge and Understanding) in the M5 extended Math class.

For (consideration for) entry into the Math Standard Level course, a student has to consistently achieve a minimum level of 4 out of 8 under Criterion A (Knowledge and Understanding) in the M5 extended Math class. If a student is in the M5 Standard class, they will have to be consistently scoring a level 7 or higher for Criteria A in order to be considered for Math Standard level in IB 1

For entry into Math Studies, a student has to consistently achieve a minimum level of 3 out of 8 under Criterion A (Knowledge and Understanding) in the M5 Standard class. Students who achieve lower than this level in M5 Standard may be required to repeat the year M5 Math course. Much will depend on their results in other subjects

A combination of aptitude and a willingness to work hard are important for success in the IB diploma. In addition to the grade pre-requisites as listed above, we also recommend that attitude towards the subject and the students‘ overall work ethic be taken into consideration, particularly when borderline cases apply.


Assessment Criteria MYP – taken from the 2011 new guide

Criterion A: Knowledge and understanding



Criterion B: Investigating patterns



Criterion C: Communication in mathematics



Criterion D: Reflection in mathematics



TISA Math Dept Assessment Policy MYP (M1 – M5) – including Homework

The Criteria

a) In MYP, the 4 Criteria used for assessment are:

Criteria		Desciption		Max’m marks allocated
A		Knowledge and Understanding		8
B		Investigating patterns		8
C		Communication		6
D		Reflection and Evaluation		6

All tests, exams and the vast majority of homework tasks are assessed according to Criteria A
The Investigations (1 or 2 for each term) assess the other 3 Criteria (B, C and D)
Whilst the rubrics for various assessed tasks may change, the maximum marks available are set as above.

b) Diploma Math

Math Studies Assessment Criteria

There are 2 examination papers (Paper 1 and Paper 2), on consecutive days and each take 90 minutes to complete. Each paper contributes 40% for the final grade.
The remaining 20 % comes from an internally graded and externally moderated Math Project - the criteria for this is listed in the table below.

Criteria		Desciption		Max’m marks allocated
A		Introduction		2
B		Information / Measurement		3
C		Mathematical Processes		5
D		Interpretation of Results		3
E		Validity		2
F		Structure and Communication		3
G		Commitment		2

Math Standard Level Assessment Criteria

There are 2 examination papers (Paper 1 and Paper 2), on consecutive days and each take 90 minutes to complete. Each paper contributes 40% for the final grade.

The remaining 20 % comes from two pieces of internally graded and externally moderated coursework tasks – Type I (mathematical investigation) and Type II (mathematical modeling). The assessment criteria for these are listed in the tables below.

Type I

Criteria		Desciption		Max’m marks allocated
A		Use of terminology and notation		2
B		Communication		3
C		Mathematical process – searching for patterns		5
D		Results - generalization		5
E		Use of technology		3
F		Quality of work		2

Type II

Criteria		Desciption		Max’m marks allocated
A		Use of terminology and notation		2
B		Communication		3
C		Mathematical process – developing a model		5
D		Results – interpretation		5
E		Use of technology		3
F		Quality of work		2

Maths High Level Assessment Criteria

There are 3 examination papers (Paper 1 and Paper 2), on consecutive days and each take 90 minutes to complete. Each paper contributes 30% for the final grade. Paper 3 is taken some days later. It is one hour long, based on the chosen HL Option topic, and constitutes 20% of the final assessment.

The remaining 20 % comes from two pieces of internally graded and externally moderated coursework tasks – Type I (mathematical investigation) and Type II (mathematical modelling). The assessment criteria for these are listed in the tables below.

Type I

Criteria		Desciption		Max’m marks allocated
A		Use of terminology and notation		2
B		Communication		3
C		Mathematical process – searching for patterns		5
D		Results - generalization		5
E		Use of technology		3
F		Quality of work		2

Type II

Criteria		Desciption		Max’m marks allocated
A		Use of terminology and notation		2
B		Communication		3
C		Mathematical process – developing a model		5
D		Results – interpretation		5
E		Use of technology		3
F		Quality of work		2

Homework

M1 and M2 will have a graded homework assignment approximately every 2 weeks. This will usually be a longer piece of work (approx 30 – 45 mins) than the normal homework set – we aim to set a minimum of 2 home-works per week. Work books will be collected and a comment made approximately each 2 weeks. The homework tasks may be written on separate sheets, in the back of the students general work book or as a continuation of the normal class room work – it is up to the teacher how this will be set out.

M3 – M5 will also have some homework graded. It will be assessed approximately every 2 – 3 weeks. The Extended classes will usually have tasks that are longer than those set for the Standard classes.

The information above applies to both the extended and Standard classes in M3 – M5, as well as the general classes in M1 and M2. It is different in the Diploma program.

When students do not complete homework, they must finish the set work the next night or during break times. If students are persistently not completing all their homework, a note will be sent home to parents in the diary. Follow up to this is at the discretion of the teacher.

IB Diploma Homework

All IB Math classes have homework set as it is imperative to do so in order to both complete the required work in the syllabus and especially to practice skills learnt in class relating to the syllabus content. The amount of work actually set depends to a fair degree on the actual level of Math course and the stage of the course work.

As a minimum requirement however, there will be homework set on at least 2 separate occasions during a normal school week, or if it is only set once, then it would be an extended amount of work requiring 2 – 4 days to complete (this happens quite a lot in Higher level Math classes). The homework set should take between 1-2 hours to complete for the Standard Math courses and 2-3 hours for the Extended Math course (average per week). Completed homework needs to be sighted by the teacher and checked to see that correct processes are followed. A record of missed or incomplete homework tasks will be kept to assist with report writing. Some homework tasks may be graded and used in the calculations for the end of term grade – this is up to the discretion of the teacher, but in all cases the end of term grade will be determined by tests that come from past exam questions. Some graded homework assignments (especially in HL courses) will also be taken into account when determining the end of term grade, but not in determining the predicted grade.

Frequency of Assessment

In each terms we aim to have at least 3 tests completed, 2 investigations (although this is often difficult to achieve in each of the 3 terms) and regular graded homework activities. The number of graded homework tasks will vary depending on the year level, but there is likely to be at least 3 per term in M3 – M5 and 3-4 for M1 – M2. M4 and M5 will also have an exam in both Term 2 and Term 3. At the end of the school year the M3 class have a longer test than normal to help prepare them for the idea of exams later in M4 onwards. Tests and Investigations are expected to be signed by the parent(s) after they have been graded.

Use of Criteria (see above for the actual list of the 4 Criteria A, B, C and D) in the MYP.

At the end of each term, the final grade (from 1 – 7) is obtained using all the assessed tasks from that term. A weighting is applied to the exams (they count for double a normal test), and all the homework grades are combined to become the equivalent of one test grade. The most sustained level within each Criteria is used, not the average level.

The boundaries for the actual grades are determined by the IB and is as follows (for each year level):

Grade Boundaries

Grade		Boundaries
1		0 - 4
2		5 - 8
3		9 – 12
4		13 - 17
5		18 - 21
6		22 - 25
7		26 - 28

If a student has an overall grade that is “right on the boundary” ie within one mark of the next boundary, there may be cause to give the student the grade from the accompanying boundary – depending on the teacher’s justification of this (eg as a consequence of general class work results).

Summative and Formative assessments

Exams for M4 and M5 at the end of the year and mid-term 2 along with end of unit tests are Summative assessments and the other set assessments are Formative.

Student Reflection and Self Assessment

All Investigations have Criteria D as part of the assessed component – these deal with reflections (eg why did you choose a particular method to solve a problem and what are the advantages / disadvantages of the methods you could have chosen). In some investigations students are asked to provide some self assessment, and at the end of each test students have the opportunity to comment on how they felt re the success or otherwise of the test.

Standardisation / Moderation

The teachers meet and discuss / standardise grading of assignments, particularly in the earlier part of the school year and where there are year levels being taught by more than one teacher. M5 coursework is sent away for moderation (Extended and Standard classes separately) in March. Samples of work from 4 students (one above average, 2 average and one below average) is sent. The materials sent consist of 2 samples for each of the 4 Criteria, and must include 1 exam.

ELS students

This is provided by the ELS Department if there is deemed to be a need for support within the classroom. The ELS teacher generally provides this support twice a week and works closely with the students in most need of the support.

Learning Support

This is provided by the Learning Support Department if there is deemed to be a need for support within the classroom. The ELS teacher generally provides this support twice a week and works closely with the students in most need of the support.

Student Portfolios

All Math students keep their assessed work in a portfolio which is kept by the teacher. This portfolio is then used to help the teacher and the student during 3 way conferences and the ongoing summary sheet of grades obtained helps determine the end of term / year grade.