Mathematics

At Cardinal Carter Catholic High School, students in the International Baccalaureate Diploma Programme are enrolled in either the Standard Level (SL) or Higher Level (HL) IB Mathematics course. In both sections, students are engaged in mathematical inquiry, while making cross-curricular links to other subject areas. Students are required to utilize their critical thinking skills to investigate complex mathematical problems, while demonstrating resilience when encountering challenges. Technology is an integral part of the learning process and assessment.

The Higher Level course allows students to study topics beyond the high school curriculum including abstract and concrete topics such as mathematical proof, calculus and statistics.

Students in the programme also engage in a self-directed exploration, where students’ curiosity and creativity are celebrated. They are able to make connections between a variety of disciplines, linking mathematics to real-word problems.

The IB Mathematics courses are rigorous in nature, as they provide students with the opportunity to continuously expand their knowledge, take risks in learning new concepts and communicate their findings and discoveries.

subject-brief-dp-math-analysis-and-approaches-en.pdf

In the IB Mathematics programme, students make use of technology to engage in inquiry-based learning as they compare, examine and analyse various characteristics and features of functions. Not only do students become familiar with utilising graphing calculators, but they also learn how to leverage other computer software programs like Desmos.

Through this inquiry-based learning model, students utilize Google Sheets to calculate measures of central tendency of data sets while studying statistics. They work collaboratively to construct linear regression models, analyse trends in the data, and to identify correlations between variables.

Through cooperative learning, students become inquirers and reflective thinkers, as they work through challenges and collaborate with their peers to problem solve. Students develop the skills necessary to reflect on their findings and communicate their thought processes with others. Students engage in “Math Talk” sessions both in-person and remotely, where they have opportunities to engage in higher-order questioning and mathematical reasoning. Students develop the skills necessary to articulate their thinking, pose questions of their own and analyse the justifications and methodologies of others.

When engaging in exploration tasks, students are asked to find connections between mathematics and real world applications. Through their own curiosity and investigation, students discover the relevance of mathematics across other disciplines including economics, science and physics.

Higher Level (HL)

I. Course description and aims

The IB DP further mathematics higher level (HL) course caters for students with a very strong background in mathematics who have attained a high degree of competence in a range of analytical and technical skills, and who display considerable interest in the subject. Most of these students will expect to study mathematics at university, either as a subject in its own right or as a major component of a related subject. The course is designed specifically to allow students to learn about a variety of branches of mathematics in depth and also to appreciate practical applications. It is expected that students taking this course will also be taking mathematics HL.

The nature of the subject is such that it focuses on different branches of mathematics to encourage students to appreciate the diversity of the subject. Students should be equipped at this stage in their mathematical progress to begin to form an overview of the characteristics that are common to all mathematical thinking, independent of topic or branch.

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.

III. Assessment model

Having followed the further mathematics HL course, students will be expected to demonstrate the following.

• Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.

• Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.

• Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation.

• Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.

• Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.

• Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analysing information, making conjectures, drawing conclusions and testing their validity.

Standard Level (SL)

I. Course description and aims

The IB DP mathematical studies standard level (SL) course focuses on important interconnected mathematical topics. The syllabus focuses on: placing more emphasis on student understanding of fundamental concepts than on symbolic manipulation and complex manipulative skills; giving greater emphasis to developing students’ mathematical reasoning rather than performing routine operations; solving mathematical problems embedded in a wide range of contexts; using the calculator effectively. There is an emphasis on applications of mathematics and statistical techniques. It is designed to offer students with varied mathematical backgrounds and abilities the opportunity to learn important concepts and techniques and to gain an understanding of a wide variety of mathematical topics, preparing them to solve problems in a variety of settings, develop more sophisticated mathematical reasoning and enhance their critical thinking.

The aims of all DP mathematics courses are to enable students to:

• enjoy and develop an appreciation of the elegance and power of mathematics