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ae> I•w9 SENIOR HIGH MATHEMATICS MATHEMATICS 33 COURSE OF STUDIES IMPLEMENTATION SEPTEMBER - 1991 CURRICULUM BRANCH /dlberfci EDUCATION May 1991 UNIVERSITY LIBRARY UNIVERSITY OF ALBERT* MATHEMATICS 33 PROGRAM RATIONALE AND PHILOSOPHY A. To setgoalsand make informed choices, students concepts. Mostimportant, students must be able need an array of thinking and problem-solving to solve problems using the mathematical skills. Fundamental to this is an understanding processes developed, and be confident in their of mathematical techniques and processes that ability to apply known mathematical skills and will enable them to apply the basic skills concepts in the acquisition ofnew mathematical necessary to address everyday mathematical knowledge. In addition, the ability oftechnology situations, as well as acquire higher order skills to provide quick and accurate computation and in logical analysis and methods for makingvalid manipulation, to enhance conceptual inferences. understanding and to facilitate higher order thinking, should be recognized and used by A knowledge of mathematics is essential for a students. well-educated citizenry. However, the need for and use ofmathematics in the life ofthe average The majority of students who enter senior high citizen is changing. Emphasis has shifted school exhibit mainly concrete operational from the memorization of mathematical behaviours with regard to mathematics. formulas and algorithms toward a more Students are expected to acquire much abstract dynamic view of mathematics as a precise understanding in senior high school courses. language, used to reason, interpret and The course content of the Senior High School explore. There is still a need for the logical Mathematics Program is designed to be development ofconcepts and skills as a basis for cognitively appropriate for the students. It must the appropriate use ofmathematical information be presented in a way that is consistent with the to solve problems. The more traditional students' ability to understand. To this end, the problem-solving techniques, combined with Senior High School Mathematics Program techniques such as estimation and simulation, includes the course sequences Mathematics and incorporated with modern technology, are 16-26, 14-24, 13-23-33 and 10-20-30 plus the tools with which mathematical problems are Mathematics 31. Although transfer by students solved. among courses ofdifferent sequences is possible, each course sequence in itself is a complete Change inthe way in which mathematics is used program. The course sequences commensurate is necessitating a concurrent change in the with differing abilities, interests and emphases of mathematics education. Students aspirations, are designed to enable students to need to understand the ideas that make up have success in mathematics. As well, the fundamental concepts and how they are related. mathematics program reflects the changing They also require familiarity with the needs of society, and provides students with the applications of a variety of mathematical mathematical concepts, skills and attitudes Mathematics33 (SeniorHigh) A.l (May 1991) 2 necessary to cope with the challenges of the future. The Mathematics 13-23-33 sequence is the mainstream mathematics program designed for students who require mathematics to prepare them for many post-secondary programs at universities, colleges, trades and employment. This sequence emphasizes an inductive development of topics in algebra, geometry, trigonometry, statistics and consumer mathematics. Mathematics 13-23-33 satisfies the requirements for the GeneralHigh SchoolDiploma. Mathematics 33 (SeniorHigh) A. (May 1991) GENERAL LEARNER EXPECTATIONS B. Students are expected to be mathematically of a number of vehicles as the learning literate at the conclusion of their senior high focus. At the same time, the students involved school mathematics education. Mathematical inthe learningsituationare affected inwhatand literacy refers to students' ability and how they learn by forces that have impact on inclination to manage the demands of their them. world through the use ofmathematical concepts and procedures to communicate, reason and The Content of the Senior High School solve problems. More specifically, students will Mathematics Program is the body of knowledge beexpectedto: that is tobe acquiredbystudents. In the various senior high school mathematics courses, it is • have achieved understanding of the basic made upoftopicsthatcanbecategorized intoone mathematical concepts, and developed the ormore ofthe listed strands. skills and attitudes needed to become responsible and contributing members of In each course in the Senior High School society Mathematics Program, students will focus on • applybasic mathematical skills and concepts problem solving. The Problem-Solving inpractical situations Context refers to the instruction emphases • have developed the skills, concepts and within which the specific content attitudes that will ensure success in the expectations can be acquired. The various mathematical situations that occur in future entries indicated in the model suggest processes educational endeavours, employment and that belong to the problem-solving context and everyday life may be used by students as vehicles for learning • have developed the skills, concepts and the content. attitudes that will enable the acquisition of mathematical knowledge beyond the The Impacts on the problem-solving context are conclusionofsecondaryeducation those skills, attitudes and experiences that are • havedevelopedcriticalandcreativethinking possessed by the students and teachers involved, aswell astheresources they may use throughout skills • be able to communicate mathematical ideas the learningprocess. They include the influence exerted by the culture and beliefs of the effectively • understand how mathematics can be used to community as reflected by the school. The investigate, interpret and make decisions in effectiveness ofthecontext in enabling a student humanaffairs toacquire the content isdependent on the skilful • understand how mathematics can be used in management by the teacher ofthose items that theanalysisofnaturalphenomena haveanimpactona student'slearning. • understand the connections and interplay among various mathematical concepts and betweenmathematicsandotherdisciplines • understand and appreciate the positive contributions of mathematics, as a science andasanart,tocivilization andculture. A General Model for Mathematical Literacy for Senior High School Programs is presented on the following page, which outlines the factors that affect what and how students learn as they become mathematically literate. The model is fluid in that the content can be learned in a problem-solving context that engages any Mathematics 33(SeniorHigh) B.l (May 1991) A General Model for Mathematical Literacy for Senior High School Programs IMPACTS COMMUNITY STUDENT TEACHER p R CRITICAL R E QUANTITATIVE THINKING S FACILITY 1 N P T u R R C M E a S A L T L H E 1 M » E T M E 4 r A R £ T A s C * 1 C Y 1 r A v L LANGUAGE IN t MATHEMATICS N G APPLICATIONS CREATIVE THINKING LANGUAGE OF MATHEMATICS TECHNOLOGICAL HISTORYOF PROCESS MATHEMATICS TECHNOLOGY PEDAGOGY Mathematics 33 (SeniorHigh) B.2 (May 1991) . SPECIFIC LEARNER EXPECTATIONS C. PROGRAMORGANIZATION mathematics is to learn to solve problems, problem-solving expectations occur throughout The major part ofthe contentofeach senior high all areas of the specific learner expectations. school mathematics course consists of topics Students must have the background skills and requiredofall studentswhotake the course. The knowledge necessary to achieve these required content comprises 80 per cent of the expectations successfully, using problem-solving course and contains the concepts, skills and techniques. attitudes that all students are expected to acquire. As well, the required portion of all The units ofthe course are broken into a number courses includes specific expectations for ofconcepts. A concept is an abstract or general problemsolvingandthe useoftechnology. idea about specific instances that have common properties or an identifiable relationship to one Each course includes a compulsory component another. The concepts are presented as comprising 20 per cent ofthe course, made up of mathematical definitions or theorems or as elective material that is consistent with the statements of mathematical ideas or content and expectations of the required abstractions. In the course of studies, concepts component. The elective material provides are stated as "Students will be expected to for enrichment, remediation, or innovative demonstrateanunderstandingthat ." . . or experimental presentations or activities. It is not intended to provide acceleration or Supporting each concept are a number of skills. advanced placement. However, horizontal Skills are intellectual or physical capabilities enrichment and extension is appropriate and that will be developed in the context of the students should have access to elective material particularconcept. Inthe course ofstudies, skills thatservestheirindividual needs and interests. are stated as"Students willbeexpectedto ." . Evaluation of students in the Senior High Skills specifically related to the use of School Mathematics Program will involve technology identify areas in which scientific assessment ofthe level ofachievement of all of calculators and/or computer technology are the learner expectations, including applied by students as tools to be used for concepts, skills and attitudes, as well as calculations, manipulation or graphing, orto aid problem-solving and technological in the analysis of problems. Technological expectations. For more information regarding expectations are defined explicitly throughout evaluation, consult the Teacher Resource the learner expectations. In many cases, a ManualforSeniorHighMathematics. particular technology is indicated for investigation or analysis. It is in these situations that the use of technology enables PROGRAM STRUCTURE students to engage in critical and creative thinkingandproblemsolving. Each course begins with a list of attitude expectations. These attitudes embody a Studentswill be expected to learn how and when mathematical attitude or frame of mind for a to use technology and have a demonstrated student to view the world. The attitude proficiency in estimation and mental expectations should be woven into the fabric of mathematics. To use technology effectively, theentirecourse. students must be able to judge the reasonableness ofan answer and understand the The problem-solving expectations outline a importance of making a judgment about the variety of procedures, strategies, skills and resultofacalculationorsolution. checking techniques for solving problems. Because a major purpose for studying Mathematics 33 (SeniorHigh) C.l (May 1991) The words verify and prove appear throughout • Prove - to substantiate the validity of an the learner expectations. For the purposes of operation, solution, formula or the Senior High School Mathematics Program, theorem in general and to provide theyare interpretedas: logical arguments for each step in the process. • Verify - to substantiate the validity of an operation, solution, formula or theorem through the use of examples that may or may not be generalized; Mathematics 33 Program Structure ATTITUDES PROBLEMSOLVING Attitudes 1. Students will be expected to demonstrate an attitude associated with mathematical literacy. In particular, studentswillbeexpectedto: 1.1 be confident in their mathematical knowledge and in their ability to acquire new knowledge 1.2 demonstrate persistence, resolve, flexibility and ingenuity in finding the solution to problems 1.3 develop intellectual curiosityand opennessto new ideas, insights and change inthe pursuit ofmathematical knowledge 1.4 exhibitanattitudeofcuriosity and spontaneity, and appreciate creativityand innovationin representingsituationsmathematically 1.5 becriticalandconstructive inapproachingnewideasandnewprocesses 1.6 acceptthe importance ofcommunicationskills in mathematics Mathematics33 (SeniorHigh) C.2 (May 1991)