MATHEMATICS
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A Curriculum Framework for
Seventh-day Adventist Secondary Schools
Mathematics
Curriculum Framework
Third Edition June 2000
ACKNOWLEDGEMENTS
The
South Pacific Division Curriculum Unit has enlisted the help of a number of
teachers in preparing this document. We
would like to thank all who have contributed time, ideas, materials and support
in many tangible and intangible ways.
In particular, the following people have helped most directly in the writing
and editing of this document:
First
Edition 1990
Lyn
Ashby Doonside
Adventist High School
Mike
Bartlett Carmel Adventist
College
Chris
Cowled Oakleigh Adventist
School
Rae
Doak Sydney Adventist
High School
Allan
Dalton Lilydale Adventist
Academy
Gordon
Howard Avondale
Adventist High School
Karen
Hughes Auckland Adventist
High School
John
Oxley Brisbane
Adventist High School
Graeme
Plane Murwillumbah Adventist
High School
Alastair
Stuart Longburn Adventist
College
Steve
Walker Carmel Adventist
College
Stan
Walshe Longburn Adventist
College
Robert
Wareham Nunawading Adventist
High School
Roddy
Wong Sydney Adventist High
School
Second
Edition 1999
Lyndon
Chester Tweed Valley Adventist
College
Malcolm
Coulson North NSW Conference
Education Director
Stephen
Littlewood Border Christian College
Ralph
Luchow Tweed Valley
Adventist College
Craig
Mattner Carmel Adventist
College
Ray
Minns Northpine
Christian College
Wilfred
Pinchin Avondale College
Robert
Wareham Nunawading Adventist
College
Third
Edition 2000
Ray
Minns Northpine
Christian College
It
is our wish that teachers will use this document to improve their teaching and
so better attain the key objectives of Seventh-day Adventist education.
Sincerely
Barry
Hill
Director,
Secondary Curriculum Unit
South
Pacific Division, Seventh-day Adventist Church
Department
of Education
148
Fox Valley Road June
2000
WAHROONGA
NSW 2076 Third
Edition
Table of Contents
table of
Contents . .. .. . . . . 4
section 1 introduction. . . .. . . . . 5
section 2
philosophy . . . . . .. 8
3.1 Steps in Planning Units and Lessons . . . . . 13
3.2 Sample Units of Work -
Probability . . . . . 15
- Statistics . . . . . . . 16
section 4
planning elements . ... . . . 17
4.1 Ideas for Teaching Mathematics in a Christian Context . . . 18
4.2 List of Mathematical Processes and Skills . .. . . 27
4.3 Detailed Objectives of Mathematics . . . . . 28
4.4 Values and Concepts in Mathematics Topics . . . . 30
4.5 Attitudes to Classwork . . . . . . . 37
4.6 Assessment . . . . . . . . 39
section 5
appendices . . . .. . . . 41
5.1 What are Values? . . . . . . . 42
5.2 A Christian Approach to Values . . . . . . 42
5.3 A Christian Approach to Teaching Mathematics .. . . . 43
SECTION 1
Introduction
INDEX
1.1 What is a Framework? . . . . . 6
1.2 Using the Framework . . . . . .7
1.1 what is a Framework?
In the Adventist secondary school context, a
“framework” is a statement of values and principles that guide curriculum
development. These principles are derived from Adventist educational philosophy
which states important ideas about what Seventh-day Adventists consider to be
real, true and good.
A framework is also a practical document intended to
help teachers sequence and integrate the various elements of the planning
process as they create a summary of a unit or topic.
The framework is not a syllabus.
The framework is not designed to do the job of a
textbook. Although it contains lists of
outcomes, values, and teaching ideas, the main emphasis is on relating values
and faith to teaching topics and units.
One objective of the framework is to show how
valuing, thinking and other learning skills can be taught from a Christian
viewpoint. The Adventist philosophy of Mathematics influences this process.
A second objective is to provide some examples of
how this can be done. The framework is
therefore organised as a resource bank of ideas for subject planning. It provides ideas, issues, values and
activities to teach these.
The framework has three target audiences:
1.
All
Mathematics teachers in Adventist secondary schools.
2.
Principals
and administrators in the Adventist educational system.
3.
Government
authorities who want to see that there is a distinctive Adventist curriculum
emphasis.
1.2
Using the Framework
Before attempting to use this document for the first
time, it is suggested that you read through this whole framework.
Notice that the framework is comprised of the
following:- explanation of a framework and its use, philosophy and objectives,
suggestions on how to plan units of work, key planning elements, examples of
topic plans, lists of important ideas, values, issues, teaching strategies, and
other elements which are useful in building a planning summary.
These components are grouped into five
sections. The nature and purpose of
each section are set out below.
Section 1 – introduction
Section one sets out the purpose of having a
framework. It explains what a framework
is and shows how to use it in a teacher’s program and on a regular basis to
enhance one’s teaching and make it more Christian oriented.
Section 2 – philosophy
This is the philosophical section. It contains a philosophy statement, a
rationale ( a statement of the value base for teaching mathematics), and a set
of objectives which have a Christian bias.
This section is meant to help teachers refresh their
memories of the Christian perspective they should teach from. They may consult this section when looking
at longer-term curriculum planning, and when thinking about unit
objectives. They may also consider the
adapting it or using it to form part of their program of work.
Section 3 – planning a unit of work
Section three is of the “how-to” section of the
framework. It explains procedures
teachers can follow when planning an overall course, topic, or unit of work
while thinking from a Christian perspective.
It ends with sample units of work compiled after working through the
steps. Because it suggests ideas for integrating knowledge, values and learning
processes in teaching, this section is the heart of the document.
Section 4 – planning elements
This section contains the various lists of ideas, values and teaching
strategies that teachers may consult when working their way through Section
three of the framework. It is a kind of
mini dictionary of ideas to resource that steps followed in Section three.
Section
5 – appendices
Section five
contains ideas for teaching that may lie outside the immediate context of the
classroom. It assists teachers in
explaining in more detail some of the more specific ideas and approaches
presented in this framework. It
examines the meaning of values and how a Christian should approach values in
mathematics, both of which are useful as reminders of good teaching and
learning practice.
SECTION 2
Philosophy
INDEX
2.1 A Philosophy of Mathematics . . . . 9
2.2 Rationale . . . . . . . . 10
2.3 Mathematics Objectives . . . . . 11
2.1 a philosophy of mathematics
Everywhere in nature there are evidences of mathematical
relationships. These are shown in ideas
of number, form, design and symmetry, and in the constant laws governing the
existence and harmonious working of all things. Through its study of these laws, ideas and processes, mathematics
can reveal some of God's creative attributes, particularly His constancy.
Whereas the student cannot comprehend the absolute
unchangeable nature of God, mathematical dependability demonstrates clearly the
consistency of God and His perfect creation.
This is a demonstration of total dependability.
Mathematics may also develop students' capacity to
use appropriate thought processes to more clearly identify aspects of truth
which relate to natural laws and design.
Such truth is predictable, in that given a set of axioms and the
appropriate mathematical processes, the result is always as expected. Therefore when students learn mathematical
processes, axioms and laws, they may be further enabled to more clearly
identify God's design and handiwork in nature.
While mathematics is a pure science, allowing many hypotheses and
conjectures to be conclusively demonstrated as being either correct or
incorrect, it also opens possibilities of knowledge that defies either proof or
disproof. Examples are infinite
smallness and infinite greatness. This
unusual balance between the unexplained and the clearly evident provides the
student with an accurate picture of an infinite and eternal God, whom we can
neither prove nor disprove, yet in whom we believe. However, God has created rules and functions that can be
demonstrated as an evidence of His presence.
As the language of the universe, mathematics helps
show us how God is made manifest there.
It expresses this part of God’s quality in its patterns of space and
number that are partly aesthetic and spiritual. The spiritual dimension of mathematics transcends logic and
reason. It asks ultimate questions,
reveals the marvels of human imagination, presents amazing ideas, and changes the
way we think about the world.
2.2 rationale
There are many reasons why students should learn
mathematics.
Firstly, they need to master basic mathematical
skills in order to cope with the demands of life. Such demands include being numerically literate, gaining the
tools for future employment, developing the prerequisites for further
education, and appreciating the relationship between mathematics and
technology.
Secondly, mathematics is the language of the
sciences, and many disciplines depend on this subject as a symbolic means of
communication.
Thirdly,
a particularly important life skill is decision-making. Mathematics education can play an important
part in developing students' general decision-making and problem solving
skills.
A fourth justification for learning mathematics is the need for students
to use the subject as an important means of discovering truth. The discipline clearly and precisely
presents aspects of knowledge which are helpful in finding out truth about the
structure and patterns of the environment, and of some of the ways in which God
has communicated with man.
The fifth reason for studying mathematics is closely
associated with the quest for truth. It
is that mathematics assists our search for beauty. Students develop their aesthetic aptitudes by looking at patterns
in nature and by appreciating the precision and symmetrical beauty in God's
creation.
The
sixth justification for mathematics is that it is an important aid in
developing the creativity of the individual.
Here the student has limitless opportunity to test his skills against
the immutability of God's law. In a
very real sense the student will develop confidence as he or she examines the
consistency of law.
2.3 mathematics objectives
The study of mathematics aims to enable students to:
1.
Develop
willingness to perceive the spiritual dimension in mathematics.
2.
Develop
an awareness that mathematical order and precision are characteristic of God
the Creator.
3.
Develop
a growing knowledge of God's faithfulness and dependability through studying
mathematics as a language of the universe.
4.
Develop
the ability to make links between mathematical concepts and other aspects of
experience, whether these aspects are largely intellectual, practical or
spiritual.
5.
Develop
the ability to identify values and make value judgments about mathematical
ideas and quality.
Attitude
to Mathematics
1.
Perceive
mathematics as a living art, one which is intellectually exciting,
aesthetically satisfying, and relevant to applications which help meet life
needs.
2.
Develop
a positive, adventurous attitude to learning mathematics, which includes
enjoyment of learning.
3.
Appreciate
the value of calculating devices in mathematics.
4.
Develop
a positive set of emotional competencies through learning mathematics. Examples
are self-discipline, self-confidence, patience, and courage.
Learning
of Mathematics
1.
Use
mathematics in coping with, controlling and determining factors which will
influence their present and future environments.
2.
maintain and increase their range of basic mathematical skills.
3.
develop the ability to communicate using the symbolism and procedures of
mathematics.
4.
Develop
competence in applying mathematics in a wide variety of life situations.
5.
Develop
the skills of logical thinking and presentation.
6.
develop the synthesis skills of using techniques from different areas of
mathematics to solve a problem.
7.
develop skills in talking, listening, reading and writing about
mathematics.
8.
support other fields of study which make use of mathematical techniques.
SECTION 3
Planning a unit
of work
3.1 Steps in Planning Units and Lessons . . . 13
3.2 Sample Units of Work - Probability . . . 15
- Statistics . . . 16
3.1 steps IN PLANNING units AND LESSONS
When planning courses, units and lessons, there are
some essential planning elements to keep in mind. Suggestions for going about the planning process are set out
below.
On the following pages there are examples of how
unit plans may appear in work programs.
A Overview
1.
Read
government requirements to find the syllabus requirements, content to cover,
objectives, scope and sequence. These
will be unique to each state, although there will be some degree of similarity
in junior school with the recent moves towards a national core outcomes-based
curriculum.
2.
Fit
the topics to the school calendar and weekly timetable to create units of
work. Take into account public
holidays, exam blocks, revision time for tests/exams, school camps, sporting
days, school photos, competitions, known excursions, and any other form of
known interruption. It is always best
to gain the yearly picture to determine what can and cannot be covered for the
teacher’s as well as the student’s sanity.
Ensure topics are not rushed by allowing some extra time every so
often. By doing this, unexpected events
such as excursions can be compensated for and one’s anxiety will be reduced.
B Composing a Topic
1.
Gather
information on the topic, including possible texts and resources. Contact your local Education Department,
especially the subject Curriculum Development Officer. Ring other schools in your district and talk
to teachers in your subject area. Most
teachers are more than willing to help.
2.
Refer
to Section 4 for outcomes in each of the four areas of knowledge, skills,
higher processes, and values that you could incorporate into your unit of
work. Section 3.2 has sample units of
work. Try to compose your unit of work
from a Christian framework.
3.
Start
to think about the main assessment tasks of the unit. Think beyond the standard test.
Try to cater for individual differences in assignment. In Section 4.5 you will find a range of
ideas.
4.
Break
the information into lessons with appropriate time for the elements to be
covered each lesson. Allow time for
activities (in or out of the classroom), for possible research or computer
time, and for revision.
5.
Sequence
the lessons with appropriate links between them.
C
Individual Lessons
1.
List
the most important outcomes. Knowledge
outcomes include content, and the concepts and worldview of mathematics. Skills outcomes describe abilities that
follow knowledge and practice. Higher
Processes include elements of processes such as inquiry, problem solving and
data processing. Values are of many
kinds. See .those in Section 4.1. Some
are teachable more directly and others are taught less directly by exposure and
experience. Some are assessable, and
some are not.
2. Determine how
these outcomes (knowledge, skills, higher processes, values) will be achieved.
3.
Devise
interesting teaching strategies and look for supporting resources.
4.
Create
and refine teaching notes.
D Post
Lesson Planning
1.
Evaluate
during and after teaching. Make notes
where you can improve for next time.
2.
Modify
future teaching.