The Middle Level Mathematics objectives, for reasons of clarity and emphasis, are divided into six strands. These strands are: problem solving, numbers and operations, ratio and proportion, geometry/measurement, data management, and algebra. Many research studies indicate that instruction in mathematics should regularly demonstrate its applicability to real life. Therefore, even though the student learning objectives are detailed in separate strands, they are intended to be taught in an integrated fashion. Problem solving is an integral component of all strands and is to be incorporated throughout the program.
Any single resource will not cover all of the concepts and skills of this Curriculum Guide. Instead, a variety of resources/materials, including print, software, manipulatives, and videos should be employed. From these, select activities and content that coincide with student learning styles, individual teaching styles, and the philosophy of the curriculum.
The development and sequencing of the concepts should follow a logical progression using certain necessary principles to show the relationships between the concepts. Teachers should not restrict themselves to using just one instructional strategy when teaching a concept. When choosing among the teaching strategies available, teachers might consider the intellectual aptitude of their students, what they already know about the concept, the nature of the concept, its significance in the structure of the other mathematical concepts, and the level of performance expected.
Frequently, there are several appropriate ways to accomplish any particular learning objective. Students should be encouraged to use a variety of approaches and to explain their methods. Through discussions with the teachers and with other students, they gain a better insight into mathematical concepts and become better able to use mathematical terminology correctly.
Below is a brief description of each of the strands in the Middle Level Mathematics program.
Problem Solving
Mathematics should revolve around problems, questions, or concerns that students view as pertinent to their present world and that of the future. Problem solving is the avenue that generates excitement, challenge, and meaningfulness in mathematics. It is a vehicle for developing concepts. Many of the skills and strategies of problem solving should be individually explored and then applied to assist in solving a variety of problems. Problem solving allows students to develop a perspective on daily life that includes mathematics. It provides motivation for learning different techniques.
Numbers and Operations
In this strand the emphasis is on students developing "number sense". The curriculum advocates that this is best accomplished by students searching for and understanding the many patterns and relationships among numbers. Being able to use mental calculation and estimation strategies is paramount. Critical is the understanding of the concepts of whole and rational numbers, and when to apply basic operations. Integers and negative rational numbers are introduced in the Middle Level curriculum. Calculator skills are also included. The calculator is considered a tool for studying number patterns, solving realistic problems, and eliminating tedious computations.
Ratio and Proportion
Ratio and Proportion is a strand that is unique to the Middle Level curriculum. Its importance is due to the abundant applications in: daily use, measurement, scales and scaling, other mathematics areas, and other school subjects. Proportional reasoning develops slowly but is important for a variety of problem-solving activities. These concepts are important in understanding percent and probability. They are also used with similar figures in the Geometry/Measurement strand. Emphasis is on understanding the concepts of ratio, proportion, and percent rather than on computational facility.
Geometry/Measurement
The development of geometric concepts and the cultivation of spatial awareness is best accomplished through the continuous integration of geometry in the curriculum. Students learn these concepts by actively manipulating, drawing, constructing, and creating geometric shapes and objects and making connections to the real world. Geometry should be experiential and reflected in the student's environment as an exciting and applicable ingredient of mathematics.
Emphasis is on the development of "measurement sense" when students are actively engaged in the processes of comparing, estimating, and measuring. Regular integration with other Required Areas of Study such as Science, Physical Education, and Social Studies makes this strand one in which applicability can be demonstrated easily.
Data Management
Mathematics courses today place emphasis on statistics and probability because we are repeatedly encountering data and information in everyday life from which we must make intelligent economic and political decisions. The collection, display, and analysis of data is a process used to solve many problems. Graphs, charts, and lists relaying numbers and statistics are a part of our daily lives. At an early age, students have begun to learn the processes of data management. Many activities and instructional ideas to support this rationalization are suggested in this guide.
Also included in this strand is a section on probability. Probability is the area of mathematics that analyzes the chance of something occurring. In everyday life, we are exposed to statements of probability. Students should understand how to interpret them.
Algebra
Algebra extends the study of operations and relationships of numbers to the use of variables. It provides the ability to represent mathematical rules using symbols. Given suitable instruction, Middle Level students can learn some of the fundamental aspects of algebra. They should also understand the notion of function as a rule or mapping that assigns to each member of one set a member of another set. Whenever possible, the practical applications of functions should be studied. The emphasis is on developing an understanding of basic concepts rather than on the manipulation of symbols or the extensive use of terminology.
Graphing on the coordinate plane is included in this strand. Links with transformational geometry and measurement formulas are also encouraged.
The scope and sequence gives the reader an overview of the specific objectives as they occur in each of Grades 6-9. In addition, those objectives that were started in Grade 5 and continue into Grade 6 are listed, as are those in Grade 9 that extend to Grade 10. The scope and sequence is not intended to list objectives in an optimal teaching order. Each objective is coded according to its position in the document.
As was indicated earlier, no single resource matches the Mathematics curriculum. To facilitate a resource-based approach, the use of a variety of resources instead of a single textbook is highly recommended.
Teachers may find it necessary for each student to have a basal textbook that covers the majority of the content. If so, then other reference texts must be used. Some teachers may wish to have their students work in groups of two or three and to use multiple recommended texts. In any case, the approach should coincide with student learning styles and individual teaching styles. It is also recommended that non-print materials such as software and videos be used, in order to enhance the delivery of the course.
A resource-based learning approach requires long-term planning and coordination within a school or school division. In-school administrators, the teacher-librarian, and others need to take an active role to assist with this planning.
Instructional approaches that emphasize group work and develop independent learning abilities make it possible to utilize limited resources in a productive way.