Knowledge and employability : mathematics 16-26

2005·1 MB·English

by  Alberta. Alberta Education

Int\tTsit\ofAlbertaI ilu.m
1620 2172 2788
KNOWLEDGE AND EMPLOYABILITY
MATHEMATICS 16-26
Policy: Knowledge and Employability courses provide students who meet the criteria with
opportunities to experience success and become well-prepared for employment, further studies,
citizenship and lifelong learning (Knowledge andEmployability CoursesPolicy 1.4.2).
VISION • when meaningful connections are made
between schooling and personal
Through Knowledge and Employability courses, experiences.
students become active, responsible citizens,
achieve their educational and career goals, Knowledge and Employability courses assist
improve the quality of life for themselves and students to make the transition from school to
their families, and positively impact their the workplace and community, prepare for
communities. responsible citizenship, and be recognized,
respected and valued by employers and further
PHILOSOPHY AND RATIONALE education providers. The skills, abilities and
work effort that Knowledge and Employability
The development of a distinctive sequence of courses promote include:
courses such as Knowledge and Employability
• academic and occupational skills of a
is based on input about the needs of learners standard determined by the workplace to be
gathered from consultations with education
necessary for success
stakeholders throughout the province.
• practical applications through on- and off-
campus experiences and/or community
To meet the educational needs of students,
partnerships
Knowledge and Employability courses are
designed forthe student who learns best: • career development skills to explore careers,
develop a career-focused portfolio and
when the focus is on the development and assess career skills
ation of reading, writing and • interpersonal skills to ensure respect,
matical literacy,1 and essential support and cooperation with others.
yability skills
gh experiential learning activities
QA
14
C22
A3 laticalliteracy: Selectingandapplyingappropriate mathematicaloperations, problem-solvingstrategies, tools and
ogy, andcommunicatingusingmathematicalvocabularyinhome, workplaceandcommunityexperiences.
A333
2005
ge and Employability Mathematics 16-26 /l
gr. 10-11
ducation,Alberta,Canada (2005 Draft)
CURR GD
HIST
Digitized by the Internet Archive
in 2012 with funding from
University of Alberta Libraries
http://archive.org/details/knowemplomath162605albe
KNOWLEDGE AND EMPLOYABILITY
MATHEMATICS 16-26
Policy: Knowledge and Employability courses provide students who meet the criteria with
opportunities to experience success and become well-prepared for employment, further studies,
citizenship and lifelong learning (K/wuledge andEmployability CoursesPolicy 1.4.2).
VISION • when meaningful connections are made
between schooling and personal
Through Knowledge and Employability courses, experiences.
students become active, responsible citizens,
achieve their educational and career goals, Knowledge and Employability courses assist
improve the quality of life for themselves and students to make the transition from school to
their families, and positively impact their the workplace and community, prepare for
communities. responsible citizenship, and be recognized,
respected and valued by employers and further
PHILOSOPHY AND RATIONALE education providers. The skills, abilities and
work effort that Knowledge and Employability
The development of a distinctive sequence of courses promote include:
courses such as Knowledge and Employability
• academic and occupational skills of a
is based on input about the needs of learners standard determined by the workplace to be
gathered from consultations with education
necessary for success
stakeholders throughout the province.
• practical applications through on- and off-
campus experiences and/or community
To meet the educational needs of students,
partnerships
Knowledge and Employability courses are
designed forthe student who learns best: • career development skills to explore careers,
develop a career-focused portfolio and
• when the focus is on the development and assess careerskills
application of reading, writing and • interpersonal skills to ensure respect,
mathematical literacy,1 and essential support and cooperation with others.
employability skills
• through experiential learning activities
1. Mathematicalliteracy: Selectingandapplyingappropriate mathematicaloperations, problem-solvingstrategies, tools and
technology, andcommunicatingusingmathematicalvocabularyinhome, workplaceandcommunityexperiences.
Knowledge and Employability Mathematics 16-26 /I
©Alberta Education, Alberta,Canada (2005 Draft)
Aboriginal Perspectives and Experiences instruction may include thematic units, subject
For historical, constitutional and social reasons, integration within units and/or projects in other
an understanding of First Nations, Metis and subjects.
Inuit (FNMI) experiences and perspectives, and
recognition that First Nations, Metis and Inuit Community and Workplace Connections
students have particular needs and requirements Knowledge and Employability courses provide
is necessary to enable all students to be students with practical and applied opportunities
respectful and responsible citizens. to develop basic reading, writing and
mathematical literacy. Community and
Knowledge and Employability courses serve to workplace connections ensure learning within
applied contexts and connect the school with
facilitate positive experiences that will help
environments beyond school, and may include
Aboriginal students better see themselves in the
tours to local business and industry,
curriculum and assist non-Aboriginal students to mentorships, job shadowing and work
develop a better understanding ofAlberta's First experience.
Nations, Metis and Inuit peoples.
Knowledge and Employability courses promote
GOALS OF KNOWLEDGE AND
the development of career portfolios. Career
EMPLOYABILITY COURSES portfolios help students connect their school
experience to the world beyond school. Each
Knowledge and Employability courses provide portfolio will include exemplars ofthe student's
on- and off-campus experiences and can be used
students with practical and applied opportunities
to develop competencies necessary to meet or when the student is seeking employment or
other post-secondary opportunities. Items
exceed the following goals:
appropriate for inclusion in career portfolios
• earn a senior high school credential are: resumes, samples of written work, awards
• enter the workplace upon leaving school and/or their representations, teacher and self-
with employability and occupational skills evaluation checklists, workplace assessment
that meet industry standards tools and employer letters ofrecommendation.
• make successful transitions to other courses SAFETY
or to further education and training
• become responsible and contributing
Safety is emphasized and incorporated
members ofsociety.
throughout Knowledge and Employability
courses. Courses include basic safety rules and
CROSS-CURRICULAR COMMUNITY
guidelines, and the safe use oftools, equipment
AND WORKPLACE CONNECTIONS and materials in school, home, community and
workplace settings.
Programs ofstudy and resources for Knowledge
TECHNOLOGY
and Employability courses are distinctive, in
part, because they promote cross-curricular,
community and workplace connections. Because technology is best learned within an
applied context, Information and
Communication Technology (ICT), and the use
Cross-curricular Connections
of computers and other technologies are
Knowledge and Employability courses promote
included in Knowledge and Employability
the integration of subjects to emphasize their courses to help students make the transition to
interrelationships and connections to other the world beyond school.
school subjects. The philosophy of Knowledge
and Employability courses is that students learn
best when they can clearly recognize
connections, applications and relevance to a
variety ofeveryday experiences. Organizing for
2/ Mathematics 16-26 Knowledge and Employability
(2005 Draft) ©AlbertaEducation,Alberta,Canada
ESSENTIAL UNIVERSAL SKILLS For information about identifying students for
AND STRATEGIES
enrollment in one or more courses, see
Knowledge and Employability Courses Policy
Knowledge and Employability courses and the Information Manualfor Knowledge and
emphasize universal skills and strategies that are Employability Courses.
essential to all students, includingthe following.
RATIONALE AND PHILOSOPHY OF
• Interpersonal skills to promote teamwork
KNOWLEDGE AND
and respect for, support of and cooperation
EMPLOYABILITY MATHEMATICS
with others.
• Critical thinking to promote the analysis and
appropriate applications ofinformation. Knowledge and Employability Mathematics
• Creative thinking to promote identification focuses on developing essential mathematics
of unique connections among ideas and knowledge, skills and attitudes in mathematics
insightful approaches to questions and needed for everyday living at home, in the
issues. workplace and in the community.
• Decision making to promote making timely
and appropriate decisions. Knowledge and Employability Mathematics
• Problem solving to promote the ability to courses are designed for students whose needs,
identify or pose problems, and apply interests and abilities are best served through
learning to consider the causes, dimensions basic mathematical literacy. Emphasis is on the
ofand solutions to problems. acquisition of practical life skills and
• Metacognition2 is thinking about thinking proficiency in using mathematics to solve
and enables students to become more aware everyday problems, accommodate change,
of their own thinking and learning interpret information and create new knowledge
processes, and gain greater control ofthese within the contexts ofthe home, the workplace
and the community.
processes.
RELATIONSHIP TO OTHER Mathematics competencies are developed
COURSES through a problem-solving, experiential
approach, using problems and activities that
directly relate to students' current and future
To enable students, as appropriate, to progress experiences. A variety of everyday activities
to other Knowledge and Employability course(s)
and problems, along with community
and/or other secondary courses, each
partnerships, help students understand and
Knowledge and Employability course is
appreciate the role of mathematics in our
consistent with the rationale, philosophy,
society. Knowledge and Employability
program foundations and organization of other
Mathematics courses begin at the student's level
secondary courses.
ofunderstanding. The use ofmanipulatives and
ENROLLMENT KNOWLEDGE other strategies/tools assists in addressing the
IN
AND EMPLOYABILITY COURSES diversity of learning styles and developmental
stages ofindividual students.
Students may take one or more courses in the Knowledge and Employability Mathematics
sequence at any time during grades 8 through courses emphasize career/life skills, teamwork,
12. Students may be enrolled in all courses, or a communication skills and thinking processes.
combination of Knowledge and Employability
Information and Communication Technology
and other courses.
(ICT) outcomes, the use of calculators.
2. Metacognition: Learning-to-learnstrategies;awarenessofprocessesandstrategiesoneuseswhenlearning.
Knowledge and Employability Mathematics 16-26 /3
©AlbertaEducation,Alberta,Canada (2005 Draft)
computers and other technologies are integrated • promote the integration of curriculum and
into the courses to help students solve problems, community partnerships to connect
and connect with the world beyond school. mathematics to other school subjects and to
otherenvironments.
Knowledge and Employability Mathematics
courses derived from The Common Curriculum Students will solve everyday problems to
Framework for K-12 Mathematics: Western achieve the outcomes in this program ofstudies.
Outcomes are organized into the four
Canadian Protocolfor Collaboration in Basic STRANDS ofMathematics:
Education (1995) and The Common Curriculum
FrameworkforK-12. Mathematics Grade 10 to 1. Number
Grade 12: Western Canadian Protocol for 2. Patterns and Relations
Collaboration in Basic Education (1996). 3. Shape and Space
Outcomes have been created and/or modified as 4. Statistics and Probability.
needed.
CONCEPTUAL FRAMEWORK FOR
These courses make reference to the standards K-12 MATHEMATICS
set out by the National Council of Teachers of
Mathematics (NCTM). Mathematics includes developing mathematical
processes in the context of the nature of
GOALS OF KNOWLEDGE AND mathematics to assist students in achieving the
EMPLOYABILITY MATHEMATICS goals of mathematics education and to
encourage lifelong learning in mathematics.
The goals for students include developing the
following mathematics competencies in the The conceptual framework outlined in this
context ofsolving everyday problems: section:
• identify the problem, and select and apply • summarizes the philosophical view toward
appropriate problem-solving strategies, mathematics and mathematics education
mathematical operations and tools • presents a multifaceted viewofmathematics
• estimate and calculate solutions accurately • presents the discipline as aset ofinterwoven
• evaluate the process, result and personal/ skills, procedures and concepts.
group performance
• develop teamwork skills and use appropriate The following graphic illustrates how student
vocabulary to reason and communicate outcomes in mathematics are organized by
strand and are influenced by mathematical
mathematically <
processes and the nature ofmathematics.
• apply mathematical literacy to everyday
life/work situations.
COMPONENTS OF KNOWLEDGE AND
EMPLOYABILITY MATHEMATICS
Mathematics has similarities with, and linkages
to, other mathematics courses. However,
Knowledge and Employability courses and
resources are distinctive in that they:
• provide students with practical and applied
opportunities to develop mathematical
competencies
4/ Mathematics 16-26 Knowledge and Employability
(2005 Draft) ©AlbertaEducation,Alberta,Canada
UNIVERSITY LIBRARY
UNIVERSITY OF ALBERTA
KNOWLEDGE AND EMPLOYABILITY MATHEMATICS
Students use a PROBLEM SOLVING APPROACHtocompletecalculationsand solveword
problems ineveryday home, workplaceand communitycontexts.
COMPONENTS OF MATHEMATICS Embedded throughout
NATURE OF
STRAND
MATHEMATICS:
Number Change, Constancy,
Number Concepts and Dimension (size and
scale),Number, Pattern,
Operations
Quantity, Relationship,
Patterns and Relations GENERAL
Shape, Uncertainty
Patterns and Relationships OUTCOMES
and
Variables and Equations
Statistics and Probability SPECIFIC MATHEMATICAL
OUTCOMES
DataCollection and PROCESSES:
Analysis Communication,
Shape and Space Connections, Estimation
and Mental Mathematics,
Measurement, 3-D Objects
Reasoning, Technology,
and 2-D Shapes and
Visualization,Pro blem
Transformations
Solving
NATURE OF MATHEMATICS
Stability, conservation, equilibrium, steady state
and symmetry are terms used to describe
Knowledge and Employability Mathematics
constancy.
courses focus on making connections between
components of the nature of mathematics and Students need to be aware ofthe properties that
everyday home, workplace and community
remain constant so that they can solve problems
applications. The nature of mathematics involving constants such as rates of change,
includes the following components: lines with constant slope, direct variation
situations, orthe angle sums oftriangles.
Change Quantity
Constancy Relationships
Dimension (size and scale)
Dimension Shape
Number Uncertainty The concept of dimension is generally
associated with 3-D objects, 2-D shapes or 1-D
Pattern
lines, and needs to be developed within an
environment ofphysical objects.
Change
To make predictions, students need to describe
Physical objects will be described using
and quantify their observations, attempt to build
measurement concepts and pattern recognition,
patterns, and identify those quantities that
ratherthan memorization offormulas.
remain fixed and those quantities that change.
Number
Constancy
Number, number systems and the operations on
The most important properties in mathematics numbers are vital to all mathematics learning.
and science relate to those properties that do not The use of number must go beyond procedure
change when outside conditions change.
Knowledge and Employability Mathematics 16-26 /5
©AlbertaEducation, Alberta,Canada (2005 Draft)
and accuracy to include what is called number Relationships
sense. Number sense includes: The study ofmathematics is the development of
relationships between and among things. For
• an intuitive feeling about numbers and their
students in Knowledge and Employability
multiple relationships
courses, mathematics should prepare the way for
• construction of the meaning of number
them to make relationships between
through a variety ofexperiences
mathematics in school and everyday
• development of an appreciation of the need
applications. Students should look for
for numbers beyond whole numbers relationships among physical things, as well as
• an appreciation and ability to make quickand
the data used to describe those things.
accurate estimations for computation and
Relationships will be described visually,
measurement
symbolically, orally and in written form.
• the ability to detect arithmetic errors
• knowledge of place value and the effects of Shape
arithmetic operations. Shape in mathematics is central to geometry but
also includes geometric representations of
Many numerical calculations can be performed algebraic relations, the geometry of maps and
with technologies such as calculators and the creation of networks of plane figures that
computers, and students must be able to can be used to construct 3-D objects. It is very
determine if the desired calculations have been important for students to look for and use
done correctly. similarities, congruences, patterns,
transformations, dilatations and tessellations in
Number sense includes recognition of number
the solution ofa range ofeveryday problems.
patterns that can be used to count, make
predictions, describe shapes and compare. The use of language to describe shapes is an
important aspect of mathematics. This
Pattern
description allows for the classification of
Patterns exist in number, geometry, algebra and objects according to various attributes, and the
data. By helping students recognize, extend, naming and analysis ofobjects. Technology can
create and use patterns as a routine aspect of be used to analyze and depict shape.
their lives, mathematics will become a useful
tool to assist them in their systematic and Uncertainty
intellectual understandingoftheirenvironment. Uncertainty involves data, chance,
measurements and errors. Problems dealing
Quantity * with data, together with numbers in context
In everyday situations, people classify, measure found in the mass media, can be solved within
and order things. To this end, some of the the school mathematics program so long as the
outcomes are about single numbers, numbers data provided and the problems posed have
attached to units ofmeasure, and ordered sets of some meaning and relevance to students.
numbers. Other outcomes are about the
interpretation of numbers and of number Chance deals with the predictable and the
systems. unpredictable outcomes of events. Students
from an early age are expected to deal with the
With the growing use of technology to process concept of chance. As they mature, the
numerical information, it is essential for language they use to describe chance becomes
students to have a wide range of estimation more sophisticated and involves the vocabulary
skills so that they can evaluate whether or not ofprobability theory.
the numerical output provided by a calculator or
a computer is a reasonable solution to a given
problem.
6/ Mathematics 16-26 Knowledge and Employability
(2005 Draft) ©AlbertaEducation, Alberta,Canada
MATHEMATICAL PROCESSES mathematics to other subjects, and from
mathematics to their daily experiences. When
Students encounter the critical components of mathematical ideas are connected to each other
mathematics process in order to achieve the through concrete, pictorial and symbolic
goals of mathematics education and to representations, students begin to view
encourage lifelong learning in mathematics. mathematics as an integrated whole.
Students in Knowledge and Employability
Mathematics courses will build on and apply
Reasoning
mathematical processes using everyday home,
workplace and community problems. Students need to develop confidence in their
ability to reason and to justify their thinking
This program of studies incorporates the within and outside of mathematics. The power
following seven interrelated mathematical of reasoning helps students to make sense of
processes that are intended to permeate teaching mathematics, to be logical in their thinking and
and learning. to convince others.
Communication [C] - communicate using Inductive reasoning helps students explore and
appropriate mathematical vocabulary make conjectures from activities that allow
Connections [CN] - connect mathematical ideas generalizations from apattern ofobservations.
to other concepts in mathematics, to everyday
experiences and to other subjects Deductive reasoning helps students test
Estimation and Mental Mathematics [E] - use conjectures and build arguments that serve to
validate thinking. Deductive reasoning builds a
estimation and mental mathematics, where
structured body ofknowledge.
appropriate
Problem Solving [PS] - relate and apply new Technology
mathematical knowledge through problem Technology, such as calculators and computers
solving can be used as tools for a variety of purposes
Reasoning [R] - reason andjustify thinking and including to organize and display data, perform
solutions calculations and reinforce the learning of
Technology [T] - select and use appropriate mathematical concepts.
technologies as tools to solve problems
Visualization
Visualization [V] - use visualization to assist in Analyzing and interpreting a visual summary
processing information, making connections and
aids in understanding and making predictions
solving problems.
from everyday information and data.
Communication
Students need to communicate mathematical The use of images in the study of mathematics
provides students with the opportunity to
ideas clearly and effectively, orally and in
understand mathematical concepts and to make
writing.
connections among them.
Communication will help students make
connections among different representations of Problem Solving
mathematical ideas including verbal, physical, Students develop a true understanding of
graphic, pictorial, symbolic and mental mathematical concepts and procedures when
representations. they solve problems in meaningful contexts.
Through problem solving the strands of
Connections Knowledge and Employability Mathematics are
Students need numerous and varied experiences developed.
in order to appreciate the usefulness of
mathematics. Students will explore Problem solving also provides opportunities for
connections within mathematics, from students to be active in constructing
Knowledge and Employability Mathematics 16-26 II
©AlbertaEducation, Alberta,Canada (2005 Draft)
mathematical meaning, learn problem-solving Students will apply mathematical vocabulary,
strategies, practise a variety of concepts and skills and strategies to work with others, as
skills, and communicate mathematical ideas. members of a team or independently, as
appropriate, to solve problems and complete
Problem-solving situations in Knowledge and tasks.
Employability Mathematics should come from
the everyday experiences of the student. Students will communicate mathematics
Students will attach mathematical meaning to processes, strategies and solutions in written and
familiar activities. verbal form.
Students will determine which mathematical Students will investigate the roles of
operation(s) can be used to solve everyday mathematics and technology in a variety of
problems, and will then solve problems, using career/workplace situations.
technology as appropriate.
PROBLEM-SOLVING FRAMEWORK FOR
KNOWLEDGE AND EMPLOYABILITY MATHEMATICS
Understand the Problem
askquestions
sort and classify information
look forpatterns
interpretpictures, charts, tablesandgraphs
identify key words
simplify questions
identify important and unimportant information
Teamwork
Thinkofa Plan
Look Back • work independently oras a developan action plan
memberofagroup
identify the appropriate
check solutions for • demonstrate teamworkskills
materialsand tools for
reasonablenessand accuracy such as listening, accepting
implementing the action plan
using strategies such asopposite the ideasofothers,
draw apicture, usesymbols
operations, estimation, pencil and evaluating personal
or manipulatives
paper, a calculator, acomputer performance and analyzing
predict/estimate solutionsto
evaluate choicesand the process group interactions
the problem
in problem solving, then redefine
theaction plan as appropriate
examine the applicationofa Carry Out the Plan
concept/strategy in othersubject
areas, the home orthe workplace use datagathered from avariety ofelectronic and othersources
evaluate the appropriatenessof to solvethe problem
technology and other tools usedto solve the problem usingpencil and paper, manipulatives,
investigate and solve the problem symbols, a calculator,acomputerorothertool/strategy
state solutions to the problem in aconclusion sentence
describe and/ordemonstrate solutions,e.g., in ajournal or
computerpresentation, using manipulatives orsymbols
apply communication strategiessuch as sharing ideasclearly,
using appropriate listening and representing skills
8/ Mathematics 16-26 Knowledge and Employability
(2005 Draft) ©AlbertaEducation.Alberta, Canada