MATHEMATICS KINDERGARTEN TO GRADE 9 - Alberta.ca

MATHEMATICSKINDERGARTEN TOGRADE 9INTRODUCTIONThe Mathematics Kindergarten to Grade 9Program of Studies has been derived from TheCommonCurriculumFrameworkforK–9 Mathematics:Western and NorthernCanadian Protocol, May 2006 (the CommonCurriculum Framework). The program of studiesincorporates the conceptual framework forKindergarten to Grade 9 Mathematics and thegeneral outcomes and specific outcomes that wereestablished in the Common CurriculumFramework.BACKGROUNDThe Common Curriculum Framework wasdeveloped by the seven ministries of st Territories, Nunavut, Saskatchewanand Yukon Territory) in collaboration withteachers, administrators, parents, businessrepresentatives, post-secondary educators andothers. The framework identifies beliefs aboutmathematics, general and specific studentoutcomes, and achievement indicators agreedupon by the seven jurisdictions.BELIEFS ABOUT STUDENTS ANDMATHEMATICS LEARNINGStudents are curious, active learners withindividual interests, abilities and needs. They Alberta Education, Alberta, Canadacome to classrooms with varying knowledge, lifeexperiences and backgrounds. A key componentin successfully developing numeracy is Students learn by attaching meaning to what theydo, and they need to construct their own meaningof mathematics. This meaning is best ces that proceed from the simple to thecomplex and from the concrete to the abstract.Through the use of manipulatives and a variety ofpedagogical approaches, teachers can address thediverse learning styles, cultural backgrounds anddevelopmental stages of students, and enhancewithin them the formation of sound, transferablemathematical understandings.At all levels,students benefit from working with a variety ofmaterials, tools and contexts when constructingmeaning about new mathematical ideas.Meaningful student discussions provide essentiallinks among concrete, pictorial and symbolicrepresentations of mathematical concepts.The learning environment should value andrespect the diversity of students’ experiences andways of thinking, so that students are comfortabletaking intellectual risks, asking questions andposing conjectures. Students need to exploreproblem-solving situations in order to developpersonal strategies and become mathematicallyliterate. They must realize that it is acceptable tosolve problems in a variety of ways and that avariety of solutions may be acceptable.Mathematics (K–9) /12007 (Updated 2016)

FIRST NATIONS, MÉTIS AND INUITPERSPECTIVESFirst Nations, Métis and Inuit students in northernand western Canada come from diversegeographic areas with varied cultural andlinguistic backgrounds. Students attend schools ina variety of settings, including urban, rural andisolated communities. Teachers need tounderstand the diversity of students’ cultures andexperiences.First Nations, Métis and Inuit students often havea holistic view of the environment—they look forconnections in learning and learn best whenmathematics is contextualized. They may comefrom cultures where learning takes place throughactive participation. Traditionally, little emphasiswas placed upon the written word, so oralcommunication and practical applications andexperiences are important to student learning andunderstanding. By understanding and respondingto nonverbal cues, teachers can optimize studentlearning and mathematical understanding.A variety of teaching and assessment strategieshelp build upon the diverse knowledge, riences and learning styles of students.Research indicates that when strategies go beyondthe incidental inclusion of topics and objectsunique to a culture or region, greater levels ofunderstanding can be achieved (Banks and Banks,1993).AFFECTIVE DOMAINA positive attitude is an important aspect of theaffective domain and has a profound impact onlearning. Environments that create a sense ofbelonging, encourage risk taking and provideopportunities for success help develop andmaintain positive attitudes and self-confidencewithin students. Students with positive attitudestoward learning mathematics are likely to bemotivated and prepared to learn, participatewillingly in classroom activities, persist inchallenging situations and engage in reflectivepractices.2/ Mathematics (K–9)2007 (Updated 2016)Teachers, students and parents need to recognizethe relationship between the affective andcognitive domains, and attempt to nurture thoseaspects of the affective domain that contribute topositive attitudes.To experience success,students must be taught to set achievable goalsand assess themselves as they work toward thesegoals.Striving toward success and becomingautonomous and responsible learners are ongoing,reflective processes that involve revisiting thesetting and assessing of personal goals.EARLY CHILDHOODYoung children are naturally curious and developa variety of mathematical ideas before they enterKindergarten. Children make sense of theirenvironment through observations and interactionsat home, in daycares, in preschools and in thecommunity. Mathematics learning is embedded ineveryday activities, such as playing, reading,beading, baking, storytelling and helping aroundthe home.Activities can contribute to the development ofnumber and spatial sense in children. Curiosityabout mathematics is fostered when children areengaged in, and talking about, such activities ascomparing quantities, searching for patterns,sorting objects, ordering objects, creating designsand building with blocks.Positive early experiences in mathematics are ascritical to child development as are early literacyexperiences.GOALS FOR STUDENTSThe main goals of mathematics education are toprepare students to: use mathematics confidently to solve problemscommunicate and reason mathematicallyappreciate and value mathematicsmake connections between mathematics and itsapplications Alberta Education, Alberta, Canada

commit themselves to lifelong learning become mathematically literate adults, usingmathematics to contribute to society.Students who have met these goals will: gain understanding and appreciation of thecontributions of mathematics as a science,philosophy and art exhibit a positive attitude toward mathematics engage and persevere in mathematical tasksand projects contribute to mathematical discussions take risks in performing mathematical tasks exhibit curiosity. Alberta Education, Alberta, CanadaMathematics (K–9) /32007 (Updated 2016)

CONCEPTUAL FRAMEWORK FOR K–9 MATHEMATICSThe chart below provides an overview of how mathematical processes and the nature of mathematicsinfluence learning outcomes.GRADESTRANDK123456789NumberPatterns and Relations Patterns Variables and EquationsShape and Space Measurement 3-D Objects and 2-D Shapes TransformationsNATUREOFMATHEMATICSGENERAL OUTCOMESANDSPECIFIC OUTCOMES Change, Constancy,Number Sense,Patterns, Relationships,Spatial Sense,UncertaintyStatistics and Probability Data Analysis Chance and UncertaintyMATHEMATICAL PROCESSES – Communication, Connections, Mental Mathematicsand Estimation, Problem Solving, Reasoning,Technology, Visualization Achievement indicators for the prescribed program of studies outcomes are provided in the companiondocument Alberta K–9 Mathematics Achievement Indicators, 2016.MathematicalProcessesThere are critical components that students must encounter in a mathematicsprogram in order to achieve the goals of mathematics education and embracelifelong learning in mathematics.Students are expected to:Communication [C] communicate in order to learn and express their understandingConnections [CN] connect mathematical ideas to other concepts in mathematics, toeveryday experiences and to other disciplinesMental Mathematics andEstimation [ME] demonstrate fluency with mental mathematics and estimationProblem Solving [PS] develop and apply new mathematical knowledge through problemsolvingReasoning [R] develop mathematical reasoningTechnology [T] select and use technologies as tools for learning and for solving problemsVisualization [V] develop visualization skills to assist in processing information, makingconnections and solving problems.The program of studies incorporates these seven interrelated mathematicalprocesses that are intended to permeate teaching and learning.4/ Mathematics (K–9)2007 (Updated 2016) Alberta Education, Alberta, Canada

COMMUNICATION [C]Students need opportunities to read about,represent, view, write about, listen to and discussmathematical ideas. These opportunities allowstudents to create links between their ownlanguage and ideas, and the formal language andsymbols of mathematics.Communication is important in clarifying,reinforcing and modifying ideas, attitudes andbeliefs about mathematics. Students should beencouraged to use a variety of forms ofcommunication while learning mathematics.Students also need to communicate their learningusing mathematical terminology.Communication helps students make connectionsamong concrete, pictorial, symbolic, oral, writtenand mental representations of mathematical ideas.CONNECTIONS [CN]Contextualization and making connections to theexperiences of learners are powerful processes indeveloping mathematical understanding. This canbe particularly true for First Nations, Métis andInuit learners. When mathematical ideas areconnected to each other or to real-worldphenomena, students begin to view mathematicsas useful, relevant and integrated.Learning mathematics within contexts and makingconnections relevant to learners can validate pastexperiences and increase student willingness toparticipate and be actively engaged.The brain is constantly looking for and makingconnections. “Because the learner is constantlysearching for connections on many levels,educators need to orchestrate the experiencesfrom which learners extract understanding. Brain research establishes and confirms thatmultiple complex and concrete experiences areessential for meaningful learning and teaching”(Caine and Caine, 1991, p. 5). Alberta Education, Alberta, CanadaMENTAL MATHEMATICS AND ESTIMATION[ME]Mental mathematics is a combination of cognitivestrategies that enhance flexible thinking andnumber sense. It is calculating mentally withoutthe use of external memory aids.Mental mathematics enables students to determineanswers without paper and pencil. It improvescomputational fluency by developing efficiency,accuracy and flexibility.“Even more important than performingcomputational procedures or using calculators,students need greater facility with estimation andmental math than ever before” (National Councilof Teachers of Mathematics, May 2005).Students proficient with mental mathematics“become liberated from calculator dependence,build confidence in doing mathematics, becomemore flexible thinkers and are more able to usemultiple approaches to problem solving”(Rubenstein, 2001, p. 442).Mental mathematics “provides the cornerstone forall estimation processes, offering a variety ofalternative algorithms and nonstandard techniquesfor finding answers” (Hope, 1988, p. v).Estimation is used for determining approximatevalues or quantities or for determining thereasonableness of calculated values. It often usesbenchmarks or referents. Students need to knowwhen to estimate, how to estimate and whatstrategy to use.Estimation assists individuals in makingmathematical judgements and in developinguseful, efficient strategies for dealing withsituations in daily life.Mathematics (K–9) /52007 (Updated 2016)