Principles of Mathematics

Academic

This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite: MTH1W, Grade 9 De-streamed Mathematics

Type

Academic

Credit Value

1.0

Curriculum Policy

https://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf#page=47

 

OVERALL CURRICULUM EXPECTATIONS

 

The Mathematical Processes

Students learn and apply the mathematical processes as they work to achieve the expectations outlined in the curriculum. All students are actively engaged in applying these processes throughout the course.

The mathematical processes that support effective learning in mathematics are as follows:

• problem solving
• reasoning and proving
• reflecting
• connecting
• communicating
• representing
• selecting tools and strategies

The mathematical processes can be understood as the processes through which all students acquire and apply mathematical knowledge, concepts, and skills. These processes are interconnected. Problem solving and communicating have strong links to all of the other processes. A problem-solving approach encourages students to reason their way to a solution or a new understanding. As students engage in reasoning, teachers further encourage them to pose questions, make conjectures, and justify solutions, orally and in writing. The communication and reflection that occur before, during, and after the process of problem solving support students as they work to articulate and refine their thinking and to examine the problem they are solving from different perspectives. This opens the door to recognizing the range of strategies that can be used to arrive at a solution. By understanding how others solve a problem, students can begin to reflect on their own thinking (a process known as “metacognition”) and the thinking of others, as well as their own language use (a process known as “metalinguistic awareness”), and to consciously adjust their own strategies in order to make their solutions as efficient and accurate as possible.

The mathematical processes cannot be separated from the knowledge, concepts, and skills that students acquire throughout the course. All students problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of mathematical concepts, and the skills required in all strands.

 

TEACHING AND LEARNING STRATEGIES

Teachers have the most important role in the success of students in mathematics. Teachers are responsible for ensuring that all students receive the highest quality of mathematics education. This requires them to have high academic expectations of all students, provide appropriate supports for learning, and believe that all students are capable math learners. Teachers bring expertise and skills to providing varied and equitable instructional and assessment approaches to the classroom. Teachers plan a mathematics program using an asset-based approach that affirms students’ identities, reflects their lived experiences, leverages their strengths, and addresses their needs in order to ensure equitable, accessible, and engaging learning opportunities for every student. The attitude with which teachers themselves approach mathematics is critical, as teachers are important role models for students.

 

Teachers place students’ well-being and academic success at the centre of their mathematics planning, teaching, and assessment practices, and understand how the learning experiences they provide will develop an appreciation of mathematics and foster a healthy attitude and engagement in all students. Teachers have a thorough understanding of the mathematics content they teach, which enables them to provide relevant and responsive, high-quality mathematical opportunities through which all students can develop their understanding of mathematical knowledge, concepts, and skills. Teachers understand the learning continua along which students develop their mathematical thinking and, with effective use of direct instruction and high-quality mathematical tasks, can thus support all students’ movement along these continua. Teachers provide ongoing meaningful feedback to all students about their mathematics learning and achievement, which helps to build confidence and provide focused next steps. Teachers support students in developing their ability to solve problems, reason mathematically, and connect the mathematics they are learning to the real world around them. They recognize the importance of emphasizing and illustrating the usefulness of mathematics in students’ lives, and of integrating mathematics with other areas of the curriculum – such as making connections with science, engineering, art, and technology to answer scientific questions or solve problems, or engaging in political debate and community development. They recognize the importance of supporting students in learning about careers involving mathematics, and of supporting the development of students’ mathematical agency to grow their identity as capable mathematical thinkers.

ASSESSMENT AND EVALUATION

As summarized in Growing Success 2010, the primary purpose of assessment and evaluation is to improve student learning.

The seven fundamental principles given below lay the foundation for rich and challenging practice. When these principles are fully understood and observed by all teachers, they will guide the collection of meaningful information that will help inform instructional decisions, promote student engagement, and improve student learning.

To ensure that assessment, evaluation, and reporting are valid and reliable, and that they lead to the improvement of learning for all students, teachers use practices and procedures that:

• are fair, transparent, and equitable;
• support all students;
• are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
• are communicated clearly to students and parents at the beginning of the school year or course and at other appropriate points throughout the school year or course;
• are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
• provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
• develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.

 

Seventy per cent of the final grade (a percentage mark) in a course will be based on evaluation conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement, with special consideration given to more recent evidence. Thirty per cent will be based on a final evaluation administered at or towards the end of the course.

 

ACCOMMODATIONS FOR STUDENTS

All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning can be identified by the teacher, but recommendations from a School Board generated Individual Education Plan (IEP) if available can also be consulted. Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners.

Examples of accommodations (but not limited to) include:

• Adjustment and or extension of time required to complete assignments or summative tasks
• Providing alternative assignments or summative tasks
• Use of scribes and/or other assistive technologies
• Simplifying the language of instruction

 

THE FINAL GRADES

The final Grades

The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning. The final percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline. A credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade will be determined as follows:

• 70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will reflect the student’s most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement.
• 30% of the grade will be based on final evaluations administered at the end of the course. The final assessment may be a final exam, a final project, or a combination of both an exam and a project.

 

THE REPORT CARDS

Two official report cards are issued – midterm and final. Each report card will focus on two distinct but related aspects of student achievement. First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student’s strengths, areas for improvement and next steps. Second, the learning skills are reported as a letter grade, representing one of four levels of accomplishment. The report cards contain separate sections for the reporting of these two aspects. The report card also indicates whether an OSSD credit has been earned.