Grades 9 To 12 Mathematics - Province Of Manitoba

IntroductionPurpose of the DocumentThis document provides sets of learning outcomes to beused as a common base for defining mathematicscurriculum expectations that willbe mandated in Grades 9, 10, 11,The frameworkand 12. This common base shouldcommunicatesresult in consistent studenthigh expectationsoutcomes in mathematics acrossfor students’the WNCP jurisdictions and enablemathematicaleasier transfer for students movinglearnings.from one jurisdiction to another.This document is intended toclearly communicate high expectations for students’mathematical learnings in Grades 9, 10, 11, and 12 to alleducation partners across the jurisdictions, and to facilitatethe development of common learning resources.Beliefs about Students andMathematics LearningStudents are curious, activeMathematicallearners with individual interests,understandingabilities, needs, and career goals.is fostered whenThey come to school with varyingstudents build on theirknowledge, life experiences,own experiences andexpectations, and backgrounds. Aprior knowledge.key component in developingmathematical literacy in students ismaking connections to these backgrounds, experiences,goals, and aspirations.Students construct their understanding of mathematicsby developing meaning based on a variety of learningexperiences.This meaning is best developed when learners encountermathematical experiences that proceed from simple tocomplex and from the concrete to the abstract. The useof manipulatives, visuals, and a variety of pedagogicaland assessment approaches can address the diversity oflearning styles and developmental stages of students.At all levels of understanding, students benefit fromworking with a variety of materials, tools, and contextswhen constructing meaning about new mathematicalideas. Meaningful student discussions also provideessential links among concrete, pictorial, and symbolicrepresentations of mathematics.Students need frequentopportunities to developand reinforce theirconceptualunderstanding,procedural thinking, andproblem-solving abilities.By addressing these threeinterrelated components,students will strengthentheir ability to applymathematical learning totheir daily lives.“Conceptual understandingis defined as comprehendingmathematical concepts,relations, and operations to buildnew knowledge.” (Kilpatrick,Swafford, and Findell 5)Procedural thinking involves“carrying out procedures flexibly,accurately, efficiently, andappropriately.”Problem solving involves“engaging in understanding andresolving problem situationswhere a method or solution isnot immediately obvious.”(OECD 12)Introduction3

The learning environment should value, respect, andaddress all students’ experiences and ways of thinking,so that students are comfortable taking intellectual risks,asking questions and posing conjectures. Students need toexplore mathematics through solving problems in order tocontinue developing personal strategies and mathematicalliteracy. It is important to realize that it is acceptable tosolve problems in different ways and that solutions mayvary depending upon how the problem is understood.best when it is contextualized and not taught as discretecontent.Assessment for learning, assessment as learning, andassessment of learning are all critical to helping studentslearn mathematics. A variety of evidence and a variety ofassessment approaches should be used in the mathematicsclassroom.A variety of teaching and assessment strategies arerequired to build upon the diverse knowledge, cultures,communication styles, skills, attitudes, experiences, andlearning styles of students.First Nations, Métis, and Inuit PerspectivesFirst Nations, Métis, and Inuit students in Manitoba comefrom diverse geographic areas and have varied culturaland linguistic backgrounds. Students attend schools in avariety of settings, includingurban, rural, and isolatedTeachers needcommunities. Teachers need toto understand therecognize and understand thediversitydiversity of cultures within schoolsof students’ culturesand the diverse experiences ofand experiences.students.First Nations, Métis, andInuit students often have a whole-world view of theenvironment; as a result, many of these students live andlearn best in a holistic way. This means that studentslook for connections in learning and learn mathematics4Many First Nations, Métis, and Inuit students come fromcultural environments where learning takes place throughactive participation. Traditionally, little emphasis wasplaced upon the written word. Oral communication, alongwith practical applications and experiences, is important tostudent learning and understanding.The strategies used must go beyond the incidentalinclusion of topics and objects unique to a culture orregion and strive to achieve higher levels of multiculturaleducation (Banks and Banks, 1993).Affective DomainA positive attitude is an important aspect of the affectivedomain that has a profound effect on learning.Environments that create a sense of belonging, supportrisk taking, and provideopportunities for success helpTo experiencestudents to develop and maintainsuccess, studentspositive attitudes and selfmust be taught to setconfidence. Students with positiveachievable goals andattitudes toward learningassess themselvesmathematics are likely to beas they work towardmotivated and prepared to learn,these goals.to participate willingly inK inder gar ten to Gr ade 8 Mathematic s Manitoba Cur r ic ulum Fr amewor k of Outc ome s: (2013)

classroom activities, to persist in challenging situations,and to engage in reflective practices.Teachers, students, and parents need to recognize therelationship between the affective and cognitive domainsand to nurture those aspects of theaffective domain that contribute toCuriosity aboutpositive attitudes. To experiencemathematics issuccess, students must be taught tofostered when studentsset achievable goals and assessare actively engaged intheir environment.themselves as they work towardthese goals.Striving toward success and becoming autonomous andresponsible learners are ongoing, reflective processes thatinvolve revisiting the setting and assessing of personalgoals.QQcommit themselves to lifelong learningbecome mathematically literate citizens, usingmathematics to contribute to society and to thinkcritically about the worldStudents who have met these goalsQQgain an understanding and appreciation of the role ofmathematics in societyQQexhibit a positive attitude toward mathematicsQQengage and persevere in mathematical problem solvingQQcontribute to mathematical discussionsQQtake risks in performing mathematical tasksQQexhibit curiosity about mathematics and situationsinvolving mathematicsIn order to assist students in attaining these goals, teachersare encouraged to develop a classroom atmosphere thatfosters conceptual understanding throughGoals for StudentsThe main goals of mathematics education are to preparestudents toQQMathematics educationmust prepare studentsto use mathematics tothink critically aboutthe world.QQQQQQcommunicate and reasonmathematicallyuse mathematics confidently,accurately, and efficiently to solveproblemsappreciate and value mathematicsmake connections betweenmathematical knowledge and skills and theirapplicationsQQtaking risksQQthinking and reflecting independentlyQQsharing and communicating mathematicalunderstandingQQsolving problems in individual and group projectsQQpursuing greater understanding of mathematicsQQappreciating the value of mathematics throughouthistoryQQIntroduction5

Conceptual FrameworkforGrades 9to12 Mathemat icsThe chart below provides an overview of how mathematical processesand the nature of mathematics influence learning TANCYNUMBER SENSEPATTERNSRELATIONSHIPSSPATIAL SENSEUNCERTAINTY101112The topics of study vary in the courses forGrades 9 to 12 mathematics.Topics include:AlgebraFinancial MathematicsGeometryLogical ReasoningMeasurementNumberProbabilityRelations and FunctionsStatisticsTrigonometryMATHEMATICAL PROCESSES:GENERAL LEARNING OUTCOMES,SPECIFIC LEARNING OUTCOMES,AND ACHIEVEMENT INDICATORSCOMMUNICATION, CONNECTIONS, MENTALMATHEMATICS AND ESTIMATION, PROBLEM SOLVING,REASONING, TECHNOLOGY, VISUALIZATIONConceptual Framework for Grades 9 to 12 Mathematics7

Mathematical ProcessesThe seven mathematical processes are critical aspects oflearning, doing, and understanding mathematics. Studentsmust encounter these processes regularly in a mathematicsprogram in order to achieve the goals of mathematicseducation.The common curriculum framework incorporates thefollowing interrelated mathematical processes. It isintended that they permeate the teaching and learning ofmathematics.Students are expected toQQnnnnnnnCommunication [C]Connections [CN]Mental Mathematicsand Estimation [ME]Problem Solving [PS]Reasoning [R]Technology [T]Visualization [V]QQQQQQQQQQQQ8use communication in orderto learn and express theirunderstandingmake connections amongmathematical ideas, otherconcepts in mathematics,everyday experiences, and otherdisciplinesdemonstrate fluency with mentalmathematics and estimationdevelop and apply new mathematical knowledgethrough problem solvingdevelop mathematical reasoningselect and use technology as a tool for learning andsolving problemsdevelop visualization skills to assist in processinginformation, making connections, and solving problemsAll seven processes should be used in the teaching andlearning of mathematics. Each specific learning outcomeincludes a list of relevant mathematical processes. Allseven processes should be incorporated into learningexperiences but the identified processes are to be used as aprimary focus of instruction and assessment.Communication [C]Students need opportunities toread about, represent, view, writeabout, listen to, and discussmathematical ideas. Theseopportunities allow students tocreate links among their ownlanguage and ideas, the languageand ideas of others, and theformal language and symbols ofmathematics.Students mustbe able tocommunicatemathematical ideas ina variety of ways andcontexts.Communication is important in clarifying, reinforcing,and modifying ideas, attitudes, and beliefs aboutmathematics. Students should be encouraged to usea variety of forms of communicatio

Acknowledgementsv ac k n o w l e d G e M e n t s The Grades 9 to 12 Mathematics: Manitoba Curriculum Framework of Outcomes is a revision of the Western and Northern Canadian Protocol (WNCP) The Common Curriculum Framework for K–9 Mathematics and The Common Curriculum Framework for Grades 10–12 Mathematics, developed through the cooperative efforts of the four western provinces and three .