MATHEMATICS PHILOSOPHY STATEMENT
Mathematics aims to give students an appreciation of the usefulness, power and beauty of the subject. The language of mathematics enables people to model events and situations, and provides a key to understanding the world in which we live. A study of mathematics also provides the opportunity to study the language of mathematics for its own sake.
With the rapid pace of technological development, it is difficult to foresee the mathematical knowledge that students will need during their lifetime. Therefore, it is essential that students are equipped with a solid base of mathematical knowledge, related skills and attitudes to enable them to adapt as their needs arise.
Students will be required to use mathematics and mathematical skills in many aspects of their lives. Their knowledge and understanding of these concepts will be required for personal decision making, and participation in civic and cultural affairs. Many of the skills learned in mathematics are applied in other subject areas. Thus, teachers of mathematics at BIS will actively seek opportunities to link mathematical skills to teaching and learning in the other subject areas. For example, science teachers will teach mathematical concepts such as graphical representation and skills such as graph construction. In order to establish such links with other subjects, teachers are advised to share the aims and objectives of mathematics with their colleagues. The holistic approach to mathematics at BIS implies the need:
• For mathematics teachers to work closely with their colleagues both within the mathematics department and with other departments;
• to ensure coordination and integration of subject matter across other subjects; and
• to encourage a reflective approach to learning.
Mathematics promotes an understanding of how cultural, societal and historical influences from a variety of cultures have influenced mathematical thought, and brought about its evolution. Students should be able to understand and discuss the international nature of mathematics.
Mathematics and the Fundamental Concepts of the MYP
Mathematics is useful.
ϖ Mathematics is essential for living. Some aspects of mathematics are required by individuals in order to function adequately as members of society. These aspects include strategies, skills and techniques involved in number facts, computation, mathematical problemsolving and reasoning.
ϖ Mathematics is important and useful in many fields of endeavor. These fields include the sciences, medicine, economics, commerce, industry, engineering, business and the arts.
ϖ Mathematics provides a means of oral and written communication. Mathematics can be used to present and convey information in many ways. Some of these include explanations, figures, letters, tables, charts, diagrams, graphs and drawings.
ϖ Mathematics provides opportunities for development of reasoning abilities.
Mathematics is part of our culture.
ϖ Mathematics has been part of human activity since the earliest times. It has made, and continues to make, a significant contribution to human culture.
ϖ Mathematics allows children to appreciate their cultural heritage more fully by providing insights into many of the creative achievements of the human race.
Mathematics can be part of our leisure.
ϖ Mathematics is a source of interesting and appealing puzzles and problems. When mathematics is enjoyable it encourages curiosity, exploration, discovery and invention.
As such the Mathematics Program at Bali International School will reflect an emphasis on the development of a positive attitude towards Mathematics through the solving of real life problems.
Strands of Mathematics
This is not meant to be a sequence in which these branches should be taught. The framework simply outlines concepts and skills which exemplify mathematics at BIS.
Number
Numeracy is an essential skill. A numerate individual has an understanding of number concepts and the skills of estimation and calculation. Students should understand that numeracy is a form of communication which has developed since humankind’s earliest beginnings, and that the evolution of mathematics is multicultural.
Algebra
An understanding of pattern recognition is fundamental to further learning in mathematics. Teachers should, where appropriate, assist students’ understanding of algebra by applying skills and reviewing concepts in practical and everyday situations.
Geometry and Trigonometry
The study of geometry and trigonometry enhances spatial awareness and gives insights into the realms of construction and navigation.
Statistics and Probability
Statistical literacy is an awareness and understanding of the concepts and skills involved in collecting, collating and analyzing data. Students should use these skills in their investigations and use a variety of technologies. They should be aware of both the power and limitations of statistics used to support and counter opinions and propaganda, how statistics may serve to emancipate and oppress, and how statistics may be used to both inform and misinform.
Discrete Mathematics
An understanding of systems has become increasingly important for people to effectively participate in today’s post-industrial/technological age. Discrete mathematics is a relatively new branch of mathematics which has its roots in abstract algebra and has adopted the language and notations of graph theory. Students should be aware of the real-world applications of discrete mathematics which may include road or rail networks, computer networks, communication networks, optimal routes, time- and project-management techniques, and critical path analysis.
PRACTICAL APPLICATIONS
The purpose of mathematics is to help children understand and function in the real world. Therefore all mathematical concepts should be explicitly linked to practical applications through activities, discussions and projects. These would vary depending on the concept and the developmental age of the students. Here is an example of what you might see in BIS classrooms:
Grade Six: Calculate profit and loss - During a study of the stock market students will need to calculate the profit and loss they experience during the trading of stocks and shares. (Standard 3: Processes of Computation)
PROBLEM SOLVING
A problem is a situation for which
the individual sees no obvious path
to obtaining the solution. Problem
solving is finding that solution.
The main objective in Math is to apply skills to real problems. Often it is difficult to determine which mathematical skills to apply in real life, as problems are more complex and usually have more than one method or solution. Therefore, each year, the following problem solving strategies should be developed with the students, and be consciously referred to and evaluated in each situation. This provides students with the skills needed to start the process of solving the problem.
Problem solving skills should be a major goal of the mathematics program at every grade level. Students must be helped to develop a wide range of skills and strategies for solving a variety of problem types. Therefore, each year, the following problem solving strategies should be practiced with the students, and be consciously referred to and evaluated in each situation. This provides students with the skills needed to start the process of solving the problem.
Teaching and learning problem solving skills is an interactive process. The key is communication and one way to foster this is by structuring lessons so students work in small groups.
Student’s Role:
Think creatively
Take intellectual risks
Use logical reasoning
Be open to more than one answer
Persevere!
Teacher’s Role:
All of the above and…
Listen
Accept unusual solutions
Interact but don’t interfere
Guide, but don’t give answers
Emphasize the process not the solution
Problem Solving Strategies
The strategies presented to students remain constant, though the difficulty of the problems varies with age. The following examples are simplified. Of course the best problem solving opportunities arise out of real classroom activities.
Restate the problem and get rid of useless information: Yuki went to Matahari. He bought a new pair of shoes for Rp 75,000. Then he went to the food court. One krupuk cost Rp 500 and the lumpia cost Rp 1,500 each but if you bought 3 you got on free. He spent Rp 4,500 on lumpia. How many did he get?
Use a table, a picture, manipulative or act it out: A farmer must cross the river carrying only one item at a time. He has with him a dog, a goose and a bag of corn. Left alone, the dog will eat the goose and the goose will eat the corn. How can he get across safely?
Look for a pattern: Carina entered a pancake-eating contest. She knew Cosmo, the champion could eat 30. This was her training schedule. How many days until Carina could eat 30 pancakes?
Work backwards: Oliver bought a bag of peanuts. He put half of them on his desk. He gave half of what he had left to his friend Eugene. After that he had 16 peanuts. How many peanuts were in the bag when he bought it?
Simplify the numbers: The BIS PTA is throwing a party for all 560,743 residents of Sanur. They want to serve hotdogs. Last time they gave a party for 230 people and used 415 hotdogs. How many hotdogs will they need this time?
Eliminate possibilities and list remaining options: There is something in the Mystery Box. By asking questions, students figure out what it could and could not be.
Find and solve sub-problems: Rio’s mom agreed to pay him Rp 30,000 to wash all the windows in the house. Rio washed 30 windows in 2 hours and then Denna came over to help. Each of them washed 10 more windows. To be fair, how much money should Rio give Denna for his work?
THE MATHEMATICS STANDARDS
The standards are based on the McRel standards. They define different areas of math. We’ve sorted our learning outcomes by strands and then again by standards to make sure that our curriculum provides balanced coverage of all areas.
Standard 1: Uses a variety of strategies in the problem-solving process.
Standard 2: Understands and applies basic and advanced properties of the concepts of numbers.
Standard 3: Uses basic and advanced procedures while performing the processes of computation.
Standard 4: Understands and applies basic and advanced properties of the concepts of measurement.
Standard 5: Understands and applies basic and advanced properties of the concepts of geometry.
Standard 6: Understands and applies basic and advanced properties of the concepts of statistics, data analysis and probability
Standard 7: Understands and applies basic and advanced properties of the concepts of functions and algebra.