Mathematics

Introduction to Department

Mathematics is important, both in school and beyond. The TIS secondary mathematics program aims to prepare students to use it in both contexts. The school follows the guidelines of the Middle Years Programme (MYP) for students in grades 6-10 and the Diploma Programme in grades 11 and 12.

The MYP sets a framework that focuses on four branches of mathematical study: Number, Algebra, Geometry and trigonometry, Statistics and probability. In addition to mathematics topics, the program is designed to foster problem-solving, communication, collaboration, and an understanding of real-life contexts and situations.

The three IB Diploma Mathematics courses are designed for different types of students: those who wish to study mathematics in depth, either as a subject in its own right or to pursue their interests in areas related to mathematics; those who wish to gain a degree of understanding and competence to understand better their approach to other subjects; and those who may not as yet be aware how mathematics may be relevant to their studies and in their daily lives.

Each course is designed to meet the needs of a particular group of students. Therefore, great care is taken to select the course that is most appropriate for an individual student. In making this selection, individual students should be advised to take account of the following factors:

  • their own abilities in mathematics and the type of mathematics in which they can be successful
  • their own interest in mathematics and those particular areas of the subject that may hold the most interest for them
  • their other choices of subjects within the framework of the Diploma Programme
  • their academic plans, in particular the subjects they wish to study in the future
  • their choice of career.

Teachers assist with the selection process and offer advice to students. The courses available are:

Mathematical Studies SL – This course has an emphasis on applications of mathematics, and the largest section is on statistical techniques. It is designed for students with varied mathematical backgrounds and abilities.

Mathematics Standard Level – This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background in their university studies.

Mathematics Higher Level – This course caters for students with a good background in mathematics who are competent in a range of analytical and technical skills. The majority of these students will be expecting to include mathematics as a major component of their university studies

MYP Aims

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

  • enjoy mathematics, develop curiosity and begin to appreciate 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
  • develop confidence, perseverance, and independence in mathematical thinking and problem-solving
  • develop powers of generalization and abstraction
  • apply and transfer skills to a wide range of real-life situations, 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.

IBO MYP Mathematics subject brief

MYP student assessment is done through four criteria. These criteria are meant to assess the full realm of mathematical understanding. They are: Knowing and understanding, Investigating patterns, Communicating, and Applying mathematics in real- life contexts.

Assessment
Assessment is done through many forms, including homework, participation, projects, investigations (with an emphasis on real-life contexts), and tests and examinations. Assessments are done using the IBMYP assessment guidelines, focusing on four specific assessment criteria:

Criterion A: Knowing and understanding. This criterion looks at how well a student can demonstrate an understanding of key concepts and skills. Assessment tasks for this criterion will generally be class tests and examinations but could also include real-life problems and investigations that may have a variety of solutions.

Criterion B: Investigating patterns. This criterion examines to what extent the student is able to investigate problems by choosing and selecting appropriate techniques and to reason from specific cases to generalizations. Assessment tasks for this criterion will generally be mathematical investigations of a complexity which is appropriate to the grade level. They are often set in real-life contexts.

Criterion C: Communication. In this criterion, a student’s ability to use appropriate language, vocabulary, and representation are assessed, as well as the student’s ability to clearly explain his or her reasoning. Students are encouraged to choose and use appropriate ICT tools such as graphic display calculators, screenshots, graphing, spreadsheets, drawing and word-processing software to enhance communication. Assessment tasks for this criterion are likely to be real-life problems and investigations.

Criterion D: Applying Mathematics in real-life contexts. Students are expected to identify the relevant elements of the authentic real-life situation, select appropriate mathematical strategies to model the authentic real-life situation, apply the selected mathematical strategies to reach a correct solution and to explain whether the solution makes sense in the context of the authentic real-life situation. Assessment tasks are usually investigations and real-life problems. These types of tasks will provide students with opportunities to use the mathematical concepts and skills they have learned in a meaningful context.

DP Subject Aims – The aims are same for all of three DP Mathematics classes

The aims of all mathematics courses in group 5 are to enable students to:

  • enjoy mathematics, and develop an appreciation of the elegance and power of mathematics
  • 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
  • employ and refine their powers of abstraction and generalization
  • apply and transfer skills to alternative situations, to other areas of knowledge and to 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 disciplines, and as a particular “area of knowledge” in the TOK course.

Subject specific information
At the sixth and seventh grade level, all classes are organized by homerooms. This allows for a heterogeneous mix as students solidify basic understandings of mathematics and are introduced to some of the more complex ideas of the subject. At TIS the aim is to maximize the potential of each student; therefore, from grade 8 upwards, we create mathematics classes based on a student’s skill level enabling us to group students for targeted instruction leading to more effective teaching and learning. Standard Level courses present the concepts and skills that are normally covered by students of that grade level. Extended Level courses are for those students who have strong math skills and understanding and who are able to work with a program that offers acceleration in either pacing or concept level. Students are placed in Extended Level courses based on teacher recommendation, MYP Criteria scores for the semester and standardized test scores.

This structure complements the structure of the Mathematics framework outlined in the IBMYP Mathematics guide which draws a distinction in terms of the development of skills and concepts in Mathematics over the course of the programme according to a standard/extended split. The standard/extended split also aligns well with the three-way split of the Mathematics courses within the IB Diploma: Mathematical Studies, Standard level and Higher level.

Required equipment

The items that we wish your child to have with them in their mathematics lessons are as follows:

  • Colored pens for writing and corrections
  • HB pencils
  • Eraser
  • Pencil sharpener
  • Highlighter
  • 30 cm ruler
  • Protractor
  • Compass
  • Scientific calculator for grade 6 and 7
  • Starting in grade 8 students are required to have a graphic display calculator. The TIS preferred model is the Texas Instruments TI-84+ calculator

MYP units of study

Grade 6
Geometry
Number System
Fractions
Statistics
Integers

Grade 7
Ratio and Proportion
Percentage
Probability
Algebra
Geometry

Grade 8
Linear Equations and Linear Functions
Simultaneous Equations
Pythagoras Theorem
Statistics
Trigonometry (right triangles)
Congruence and Similarities

Grade 9
Sets, Venn diagrams and Probability
Introduction to Polynomials
Quadratic Functions
Surface Area/Volume
Circle

Grade 10
Exponential and Logarithms
Statistics
Trigonometry (non-right triangles)
Vectors
Arithmetic and Geometric Sequences and Series

Diploma Programme Topics, Units and Options

Mathematical Studies
Topic 1 Number and algebra
Topic 2 Descriptive Statistics
Topic 3 Logic, sets and probability
Topic 4 Statistical applications
Topic 5 Geometry and trigonometry
Topic 6 Mathematical models
Topic 7 Differential calculus

Project
The project is an individual piece of work involving the collection of information or the generation of measurements, and the analysis and evaluation of the information or measurements.

Mathematics Standard Level
Topic 1 Algebra
Topic 2 Functions and equations
Topic 3 Circular functions and trigonometry
Topic 4 Vectors
Topic 5 Statistics and probability
Topic 6 Calculus

Mathematics exploration
Internal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics.

Mathematics Higher Level
Topic 1 Algebra
Topic 2 Functions and equations
Topic 3 Circular functions and trigonometry
Topic 4 Vectors
Topic 5 Statistics and probability
Topic 6 Calculus

Option Syllabus content
Students must study one of the following options as listed below
Topic 7 Statistics and probability
Topic 8 Sets, relations and groups
Topic 9 Calculus
Topic 10 Discrete mathematics

Mathematics exploration
Internal assessment in mathematics HL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics.