IntroductionThe Alberta 10–12 Mathematics Program ofStudies with Achievement Indicators has beenderived from The Common CurriculumFramework for Grades 10–12 Mathematics:Western and Northern Canadian Protocol, January2008 (the Common Curriculum Framework). Theprogram of studies incorporates the conceptualframework for Grades 10–12 Mathematics andmost of the general outcomes and specificoutcomes that were established in the CommonCurriculum Framework.

1. Alberta Grade 4 Math
2. Alberta Program Of Studies Illustrative Examples

(Note: Some of theoutcomes for Mathematics 20-2 and 30-2 in thisprogram of studies are different from the outcomesfor Foundations of Mathematics in the CommonCurriculum Framework.). Beliefs About Students & Mathematics LearningStudents are curious, active learners withindividual interests, abilities, needs and careergoals.

They come to school with varyingknowledge, life experiences, expectations andbackgrounds. A key component in developingmathematical literacy in students is makingconnections to these backgrounds, experiences,goals and aspirations.Students construct their understanding ofmathematics by developing meaning based on avariety of learning experiences. This meaning isbest developed when learners encountermathematical experiences that proceed fromsimple to complex and from the concrete to theabstract. The use of manipulatives, visuals and avariety of pedagogical approaches can address thediversity of learning styles and developmentalstages of students.

At all levels of understanding,students benefit from working with a variety ofmaterials, tools and contexts when constructingmeaning about new mathematical ideas.Meaningful student discussions also provideessential links among concrete, pictorial andsymbolic representations of mathematics.The learning environment should value, respectand address all students’ experiences and ways ofthinking, so that students are comfortable takingintellectual risks, asking questions and posingconjectures. Students need to explore mathematicsthrough solving problems in order to continuedeveloping personal strategies and mathematicalliteracy. It is important to realize that it isacceptable to solve problems in different ways andthat solutions may vary depending upon how theproblem is understood. Affective DomainA positive attitude is an important aspect of theaffective domain and has a profound effect on learning.Environments that create a sense of belonging, supportrisk taking and provide opportunities for success helpstudents to develop and maintain positive attitudes andself-confidence. Students with positive attitudes towardlearning mathematics are likely to be motivated andprepared to learn, to participate willingly in classroomactivities, to persist in challenging situations and toengage in reflective practices.Teachers, students and parents need to recognize therelationship between the affective and cognitivedomains and to nurture those aspects of the affectivedomain that contribute to positive attitudes. Toexperience success, students must be taught to setachievable goals and to assess themselves as theywork toward these goals.Striving toward success and becoming autonomousand responsible learners are ongoing, reflectiveprocesses that involve revisiting the setting andassessing of personal goals. Mathematical ProcessesThe seven mathematical processes arecritical aspects of learning, doing andunderstanding mathematics.

Students mustencounter these processes regularly in amathematics program in order to achieve thegoals of mathematics education.This program of studies incorporates thefollowing interrelated mathematicalprocesses. CommunicationStudents need opportunities to read about,represent, view, write about, listen to and discussmathematical ideas. These opportunities allowstudents to create links among their own languageand ideas, the language and ideas of others, and theformal language and symbols 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 learningby using mathematical terminology.Communication can play a significant role inhelping students make connections amongconcrete, pictorial, symbolic, verbal, written andmental representations of mathematical ideas.Emerging technologies enable students to engagein communication beyond the traditional classroomto gather data and share mathematical ideas. ConnectionsContextualization and making connections to theexperiences of learners are powerful processes indeveloping mathematical understanding.

Whenmathematical ideas are connected to each other orto real-world phenomena, students begin to viewmathematics as 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 experiences fromwhich learners extract understanding. Brainresearch establishes and confirms that multiplecomplex and concrete experiences are essential formeaningful learning and teaching” (Caine andCaine, 1991, p. Mental Mathematics And EstimationMental mathematics is a combination of cognitivestrategies that enhance flexible thinking andnumber sense. It involves using strategies toperform mental calculations.Mental mathematics enables students to determineanswers without paper and pencil. It improvescomputational fluency by developing efficiency,accuracy and flexibility in reasoning andcalculating.“Even more important than performingcomputational procedures or using calculators isthe greater facility that students need—more thanever before—with estimation and mental math”(National Council of 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 a cornerstone for allestimation processes, offering a variety ofalternative algorithms and nonstandard techniquesfor finding answers” (Hope, 1988, p.

V).Estimation is used for determining approximatevalues or quantities, usually by referring tobenchmarks or referents, or for determining thereasonableness of calculated values. Estimation isalso used to make mathematical judgements and todevelop useful, efficient strategies for dealing withsituations in daily life. When estimating, studentsneed to learn which strategy to use and how to useit.

Problem SolvingProblem solving is one of the key processes andfoundations within the field of mathematics.Learning through problem solving should be thefocus of mathematics at all grade levels. Studentsdevelop a true understanding of mathematicalconcepts and procedures when they solve problemsin meaningful contexts. Problem solving is to beemployed throughout all of mathematics andshould be embedded throughout all the topics.When students encounter new situations andrespond to questions of the type, How wouldyou.? Or How could you.?, the problem-solvingapproach is being modelled.

Students develop theirown problem-solving strategies by listening to,discussing and trying different strategies.In order for an activity to be problem-solvingbased, it must ask students to determine a way toget from what is known to what is sought. Ifstudents have already been given ways to solve theproblem, it is not a problem, but practice. Studentsshould not know the answer immediately. A trueproblem requires students to use prior learnings innew ways and contexts.

Problem solving requiresand builds depth of conceptual understanding andstudent engagement. Students will be engaged ifthe problems relate to their lives, cultures,interests, families or current events.Both conceptual understanding and studentengagement are fundamental in moulding students’willingness to persevere in future problem-solvingtasks.Problems are not just simple computationsembedded in a story, nor are they contrived. Theyare tasks that are rich and open-ended, so theremay be more than one way of arriving at a solutionor there may be multiple answers. Good problemsshould allow for every student in the class todemonstrate his or her knowledge, skill orunderstanding. Problem solving can vary frombeing an individual activity to a class (or beyond)undertaking.In a mathematics class, there are two distinct typesof problem solving: solving contextual problemsoutside of mathematics and solving mathematicalproblems.

Finding the maximum profit givenmanufacturing constraints is an example of acontextual problem, while seeking and developinga general formula to solve a quadratic equation isan example of a mathematical problem.Problem solving can also be considered in terms ofengaging students in both inductive and deductivereasoning strategies. As students make sense of theproblem, they will be creating conjectures andlooking for patterns that they may be able togeneralize.

This part of the problem-solvingprocess often involves inductive reasoning. Asstudents use approaches to solving the problem,they often move into mathematical reasoning thatis deductive in nature.

It is crucial that students beencouraged to engage in both types of reasoningand be given the opportunity to consider theapproaches and strategies used by others in solvingsimilar problems.Problem solving is a powerful teaching tool thatfosters multiple, creative and innovative solutions.Creating an environment where students openlylook for, and engage in, finding a variety ofstrategies for solving problems empowers studentsto explore alternatives and develops confident,cognitive mathematical risk-takers. ReasoningMathematical reasoning helps students thinklogically and make sense of mathematics. Studentsneed to develop confidence in their abilities toreason and to justify their mathematical thinking.Questions that challenge students to think, analyzeand synthesize help them develop an understandingof mathematics. All students need to be challengedto answer questions such as, Why do you believethat’s true/correct? Or What would happen if.Mathematical experiences provide opportunitiesfor students to engage in inductive and deductivereasoning. Students use inductive reasoning whenthey explore and record results, analyzeobservations, make generalizations from patternsand test these generalizations.

Students usedeductive reasoning when they reach newconclusions based upon the application of what isalready known or assumed to be true. The thinkingskills developed by focusing on reasoning can beused in daily life in a wide variety of contexts anddisciplines. TechnologyTechnology can be used effectively to contribute toand support the learning of a wide range ofmathematical outcomes. VisualizationVisualization “involves thinking in pictures andimages, and the ability to perceive, transform andrecreate different aspects of the visual-spatial world”(Armstrong, 1993, p.

The use of visualization inthe study of mathematics provides students withopportunities to understand mathematical conceptsand make connections among them.Visual images and visual reasoning are importantcomponents of number, spatial and measurementsense. Number visualization occurs when studentscreate mental representations of numbers.Being able to create, interpret and describe a visualrepresentation is part of spatial sense and spatialreasoning. Spatial visualization and spatial reasoningenable students to describe the relationships amongand between 3-D objects and 2-D shapes.Measurement visualization goes beyond theacquisition of specific measurement skills.Measurement sense includes the ability to determinewhen to measure and when to estimate and involvesknowledge of several estimation strategies (Shaw andCliatt, 1989, p.

150).Visualization is fostered through the use of concretematerials, technology and a variety of visualrepresentations. It is through visualization thatabstract concepts can be understood concretely bythe student. Visualization is a foundation to thedevelopment of abstract understanding, confidenceand fluency. ChangeIt is important for students to understand thatmathematics is dynamic and not static. As aresult, recognizing change is a key component inunderstanding and developing mathematics.Within mathematics, students encounterconditions of change and are required to searchfor explanations of that change. To makepredictions, students need to describe andquantify their observations, look for patterns,and describe those quantities that remain fixedand those that change.

For example, thesequence 4, 6, 8, 10, 12, can be described as:. skip counting by 2s, starting from 4. an arithmetic sequence, with first term 4 and a common difference of 2. a linear function with a discrete domain(Steen, 1990, p. 184).Students need to learn that new concepts ofmathematics as well as changes to already learnedconcepts arise from a need to describe andunderstand something new. Integers, decimals,fractions, irrational numbers and complex numbersemerge as students engage in exploring newsituations that cannot be effectively described oranalyzed using whole numbers.Students best experience change to theirunderstanding of mathematical concepts as a result ofmathematical play.

ConstancyMany important properties in mathematics do notchange when conditions change. Examples ofconstancy include:. the conservation of equality in solving equations. the sum of the interior angles of any triangle. the theoretical probability of an event.Some problems in mathematics require students tofocus on properties that remain constant.

Alberta Grade 4 Math

Therecognition of constancy enables students to solveproblems such as those involving constant rates ofchange, lines with constant slope, or direct variationsituations. Number SenseNumber sense, which can be thought of as deepunderstanding and flexibility with numbers, isthe most important foundation of numeracy(British Columbia Ministry of Education, 2000,p. Continuing to foster number sense isfundamental to growth of mathematicalunderstanding.A true sense of number goes well beyond theskills of simply counting, memorizing facts andthe situational rote use of algorithms. Studentswith strong number sense are able to judge thereasonableness of a solution, describerelationships between different types ofnumbers, compare quantities and work withdifferent representations of the same number todevelop a deeper conceptual understanding ofmathematics.Number sense develops when students connectnumbers to real-life experiences and whenstudents use benchmarks and referents. Thisresults in students who are computationallyfluent and flexible with numbers and who haveintuition about numbers.

Evolving number sensetypically comes as a by-product of learningrather than through direct instruction. However,number sense can be developed by providingmathematically rich tasks that allow students tomake connections. PatternsMathematics is about recognizing, describing andworking with numerical and non-numerical patterns.Patterns exist in all of the mathematical topics, and itis through the study of patterns that students canmake strong connections between concepts in thesame and different topics. Working with patterns alsoenables students to make connections beyondmathematics. The ability to analyze patternscontributes to how students understand theirenvironment.Patterns may be represented in concrete, visual,auditory or symbolic form. Students should developfluency in moving from one representation toanother.Students need to learn to recognize, extend, createand apply mathematical patterns. This understandingof patterns allows students to make predictions andjustify their reasoning when solving problems.Learning to work with patterns helps developstudents’ algebraic thinking, which is foundationalfor working with more abstract mathematics.

Spatial SenseSpatial sense involves the representation andmanipulation of 3-D objects and 2-D shapes. Itenables students to reason and interpret among3-D and 2-D representations.Spatial sense is developed through a variety ofexperiences with visual and concrete models.It offers a way to interpret and reflect on thephysical environment and its 3-D or 2-Drepresentations.Some problems involve attaching numerals andappropriate units (measurement) to dimensionsof objects. Spatial sense allows students to makepredictions about the results of changing thesedimensions.Spatial sense is also critical in students’understanding of the relationship between theequations and graphs of functions and,ultimately, in understanding how both equationsand graphs can be used to represent physicalsituations. UncertaintyIn mathematics, interpretations of data and thepredictions made from data inherently lack certainty.Events and experiments generate statistical data thatcan be used to make predictions. It is important thatstudents recognize that these predictions(interpolations and extrapolations) are based uponpatterns that have a degree of uncertainty. Thequality of an interpretation or conclusion is directlyrelated to the quality of the data it is based upon.

Anawareness of uncertainty provides students with anunderstanding of why and how to assess thereliability of data and data interpretation.Chance addresses the predictability of the occurrenceof an outcome. As students develop theirunderstanding of probability, the language ofmathematics becomes more specific and describesthe degree of uncertainty more accurately.

Thislanguage must be used effectively and correctly toconvey valuable messages. Course Sequences & TopicsThe Alberta 10–12 Mathematics Program ofStudies with Achievement Indicators includescourse sequences and topics rather than strandsas in The Alberta K–9 Mathematics Program ofStudies with Achievement Indicators. Threecourse sequences are available: “-1,” “-2” and“-3.” A combined course (Mathematics 10C) isthe starting point for the “-1” course sequenceand the “-2” course sequence. Each topic arearequires that students develop a conceptualknowledge base and skill set that will be usefulto whatever course sequence they have chosen.The topics covered within a course sequence aremeant to build upon previous knowledge and toprogress from simple to more complexconceptual understandings. Goals of Course SequencesThe goals of all three course sequences are to provideprerequisite attitudes, knowledge, skills andunderstandings for specific post-secondary programsor direct entry into the work force.

All three coursesequences provide students with mathematicalunderstandings and critical-thinking skills. It is thechoice of topics through which those understandingsand skills are developed that varies among coursesequences. When choosing a course sequence,students should consider their interests, both currentand future. Students, parents and educators areencouraged to research the admission requirementsfor post-secondary programs of study as they vary byinstitution and by year. Outcomes and Achievement IndicatorsThe program of studies is stated in terms of generaloutcomes, specific outcomes and achievementindicators.General outcomes are overarching statementsabout what students are expected to learn in eachcourse.Specific outcomes are statements that identifythe specific knowledge, skills andunderstandings that students are required toattain by the end of a given course.Achievement indicators are samples of howstudents may demonstrate their achievement ofthe goals of a specific outcome. The range ofsamples provided is meant to reflect the scope ofthe specific outcome.In the specific outcomes, the word including indicates that any ensuing items must beaddressed to fully meet the learning outcome.The phrase such as indicates that the ensuingitems are provided for clarification and are notrequirements that must be addressed to fullymeet the learning outcome.The word and used in an outcome indicates thatboth ideas must be addressed to fully meet thelearning outcome, although not necessarily at thesame time or in the same question.

The word and used in an achievement indicator implies thatboth ideas should be addressed at the same timeor in the same question. Links to Information and Communication Technology (ICT) OutcomesSome curriculum outcomes from Alberta Education’sInformation and Communication Technology (ICT)Program of Studies can be linked to outcomes in themathematics program so that students will develop abroad perspective on the nature of technology, learnhow to use and apply a variety of technologies, andconsider the impact of ICT on individuals andsociety. The connection to ICT outcomes supportsand reinforces the understandings and abilities thatstudents are expected to develop through the generaland specific outcomes of the mathematics program.Effective, efficient and ethical application of ICToutcomes contributes to the mathematics programvision.Links to the ICT outcomes have been identified forsome specific outcomes. These links appear insquare brackets below the process codes for anoutcome, where appropriate. The complete wordingof the relevant outcomes for ICT is provided in theAppendix.

Instructional FocusEach course sequence in The Alberta 10–12Mathematics Program of Studies with AchievementIndicators is arranged by topics. 4.1 Explain the relationships between similar right triangles and the definitions of the primarytrigonometric ratios.

4.2 Identify the hypotenuse of a right triangle and the opposite and adjacent sides for a givenacute angle in the triangle. 4.3 Solve right triangles. 4.4 Solve a problem that involves one or more right triangles by applying the primarytrigonometric ratios or the Pythagorean theorem. 4.5 Solve a problem that involves indirect and direct measurement, using the trigonometric ratios,the Pythagorean theorem and measurement instruments such as a clinometer or metre stick. 6.1 Express a linear relation in different forms, and compare the graphs. 6.2 Rewrite a linear relation in either slope–intercept or general form.

6.3 Generalize and explain strategies for graphing a linear relation in slope–intercept, general orslope–point form. 6.4 Graph, with and without technology, a linear relation given in slope–intercept, general orslope–point form, and explain the strategy used to create the graph. 6.5 Identify equivalent linear relations from a set of linear relations.

6.6 Match a set of linear relations to their graphs. 8.1 Express the equation of a linear function in two variables, using function notation. 8.2 Express an equation given in function notation as a linear function in two variables.

8.3 Determine the related range value, given a domain value for a linear function;e.g., if f( x) = 3 x – 2, determine f(–1). 8.4 Determine the related domain value, given a range value for a linear function;e.g., if g( t) = 7 + t, determine t so that g( t)= 15. 8.5 Sketch the graph of a linear function expressed in function notation.

(It is intended that the equations will have no more than two radicals.). 3.1 Determine any restrictions on values for the variable in a radical equation. 3.2 Determine the roots of a radical equation algebraically, and explain the process used to solvethe equation. 3.3 Verify, by substitution, that the values determined in solving a radical equation algebraicallyare roots of the equation. 3.4 Explain why some roots determined in solving a radical equation algebraically areextraneous. 3.5 Solve problems by modelling a situation using a radical equation.

3.1 Explain, using examples, the difference between a permutation and a combination. 3.2 Determine the number of ways that a subset of k elements can be selected from a set of ndifferent elements. 3.3 Determine the number of combinations of n different elements taken r at a time to solve aproblem. 3.4 Explain why n must be greater than or equal to r in the notation n C r or. 3.5 Explain, using examples, why n C r = n C n−r or. 3.6 Solve an equation that involves n C r or notation, such as n C 2 = 15 or = 15.

4.1 Explain the patterns found in the expanded form of ( x + y) n, n ≤ 4 and n N, bymultiplying n factors of ( x + y). 4.2 Explain how to determine the subsequent row in Pascal’s triangle, given any row. 4.3 Relate the coefficients of the terms in the expansion of ( x + y) n to the ( n + 1) row in Pascal’striangle. 4.4 Explain, using examples, how the coefficients of the terms in the expansion of ( x + y) n aredetermined by combinations. 4.5 Expand, using the binomial theorem, ( x + y) n.

4.6 Determine a specific term in the expansion of ( x + y) n. 2.1 Explain, using examples, how scale diagrams are used to model a 2-D shape or a 3-D object.

2.2 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shapeor a 3-D object and its representation. 2.3 Determine, using proportional reasoning, an unknown dimension of a 2-D shape or a3-D object, given a scale diagram or a model.

2.4 Draw, with or without technology, a scale diagram of a given 2-D shape, according to aspecified scale factor (enlargement or reduction). 2.5 Solve a contextual problem that involves a scale diagram. 2.1 Determine the measures of angles in a diagram that includes parallel lines, angles andtriangles, and justify the reasoning. 2.2 Identify and correct errors in a given solution to a problem that involves the measures ofangles. 2.3 Solve a contextual problem that involves angles or triangles.

2.4 Construct parallel lines, given a compass or a protractor, and explain the strategy used. 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed bythe lines and a transversal. (It is intended that the equations have only one radical.). 4.1 Determine any restrictions on values for the variable in a radical equation. 4.2 Determine, algebraically, the roots of a radical equation, and explain the process used tosolve the equation. 4.3 Verify, by substitution, that the values determined in solving a radical equation are roots ofthe equation.

4.4 Explain why some roots determined in solving a radical equation are extraneous. 4.5 Solve problems by modelling a situation with a radical equation and solving the equation. 1.1 Provide examples of statements of probability and odds found in fields such as media,biology, sports, medicine, sociology and psychology.

1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). 1.3 Express odds as a probability and vice versa. 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. 1.5 Explain, using examples, how decisions may be based on probability or odds and onsubjective judgments. 1.6 Solve a contextual problem that involves odds or probability.

2.1 Compare the strategies for performing a given operation on rational expressions to thestrategies for performing the same operation on rational numbers. 2.2 Determine the non-permissible values when performing operations on rational expressions. 2.3 Determine, in simplified form, the sum or difference of rational expressions that have thesame denominator. 2.4 Determine, in simplified form, the sum or difference of two rational expressions that havedifferent denominators. 2.5 Determine, in simplified form, the product or quotient of two rational expressions.

3.1 Determine, using angle measurements, if two or more regular or irregular polygons are similar. 3.2 Determine, using ratios of side lengths, if two or more regular or irregular polygons aresimilar. 3.3 Explain why two given polygons are not similar. 3.4 Explain the relationships between the corresponding sides of two polygons that havecorresponding angles of equal measure.

3.5 Draw a polygon that is similar to a given polygon. 3.6 Explain why two or more right triangles with a shared acute angle are similar. 3.7 Solve a contextual problem that involves similarity of polygons. 1.1 Explain, using examples, the difference between volume and surface area. 1.2 Explain, using examples, including nets, the relationship between area and surface area. 1.3 Explain how a referent can be used to estimate surface area.

1.4 Estimate the surface area of a 3-D object. 1.5 Illustrate, using examples, the effect of dimensional changes on surface area. 1.6 Solve a contextual problem that involves the surface area of 3-D objects, including spheres,and that requires the manipulation of formulas. 3.1 Draw a 2-D representation of a given 3-D object.

3.2 Draw, using isometric dot paper, a given 3-D object. 3.3 Draw to scale top, front and side views of a given 3-D object. 3.4 Construct a model of a 3-D object, given the top, front and side views. 3.5 Draw a 3-D object, given the top, front and side views. 3.6 Determine if given views of a 3-D object represent a given object, and explain the reasoning.

3.7 Identify the point of perspective of a given one-point perspective drawing of a 3-D object. 3.8 Draw a one-point perspective view of a given 3-D object. 2.1 Identify income and expenses that should be included in a personal budget. 2.2 Explain considerations that must be made when developing a budget; e.g., prioritizing,recurring and unexpected expenses. 2.3 Create a personal budget based on given income and expense data. 2.4 Collect income and expense data, and create a budget.

2.5 Modify a budget to achieve a set of personal goals. 2.6 Investigate and analyze, with or without technology, “what if ” questions related topersonal budgets. 1.1 Solve a contextual problem involving the application of a formula that does not requiremanipulation. 1.2 Solve a contextual problem involving the application of a formula that requires manipulation. 1.3 Explain and verify why different forms of the same formula are equivalent. 1.4 Describe, using examples, how a given formula is used in a trade or an occupation. 1.5 Create and solve a contextual problem that involves a formula.

1.6 Identify and correct errors in a solution to a problem that involves a formula. 3.1 Explain the process of unit analysis used to solve a problem (e.g., given km/h and time inhours, determine how many km; given revolutions per minute, determine the number ofseconds per revolution). 3.2 Solve a problem, using unit analysis. 3.3 Explain, using an example, how unit analysis and proportional reasoning are related; e.g., tochange km/h to km/min, multiply by 1h/60min because hours and minutes are proportional(constant relationship).

3.4 Solve a problem within and between systems, using proportions or tables; e.g., km to m orkm/h to ft/sec. ReferencesAlberta Education.

Alberta Program Of Studies Illustrative Examples

The Alberta K–9 Mathematics Program of Studies with Achievement Indicators. Edmonton, AB: Alberta Education, 2007.Alberta Education, System Improvement Group. Western and Northern Canadian Protocol (WNCP) Consultation with Post-SecondaryInstitutions, Business and Industry Regarding Their Requirements for High School Mathematics: Final Report on Findings. Edmonton, AB: Alberta Education, 2006. Available at (Accessed February 6, 2008).Alberta Learning.

Information and Communication Technology (ICT) Program of Studies. Edmonton, AB: Alberta Learning, 2000–2003.(Accessed February 6, 2008).Armstrong, Thomas. 7 Kinds of Smart: Identifying and Developing Your Many Intelligences. New York, NY: Plume, 1993.Banks, J. Multicultural Education: Issues and Perspectives. Boston, MA: Allyn and Bacon, 1993.British Columbia Ministry of Education. The Primary Program: A Framework for Teaching.

Victoria, BC: British Columbia Ministry of Education, 2000.Caine, Renate Nummela and Geoffrey Caine. Making Connections: Teaching and the Human Brain. Alexandria, VA: Association for Supervision and Curriculum Development, 1991.Hope, Jack A.

Mental Math in the Primary Grades. Palo Alto, CA: Dale Seymour Publications, 1988.McAskill, B. WNCP Mathematics Research Project: Final Report. Victoria, BC: Holdfast Consultants Inc., 2004.

Available at(Accessed February 6, 2008).National Council of Teachers of Mathematics. Computation, Calculators, and Common Sense: A Position of the National Council of Teachers of Mathematics.

(Accessed February 6,2008).Rubenstein, Rheta N. 'Mental Mathematics beyond the Middle School: Why? Mathematics Teacher 94, 6 (September 2001), pp. 442 - 446.Shaw, J. 'Developing Measurement Sense.'

Trafton (ed.), New Directions for Elementary School Mathematics: 1989 Yearbook (Reston, VA: National Council of Teachers of Mathematics, 1989), pp. 149 - 155.Steen, L. On the Shoulders of Giants: New Approaches to Numeracy. Washington, DC: Mathematical Sciences Education Board, National Research Council, 1990.Western and Northern Canadian Protocol for Collaboration in Basic Education (Kindergarten to Grade 12).

The Common Curriculum Framework for K - 9 Mathematics: Western and Northern Canadian Protocol. January 2008.

February 6, 2008).