The School of Mathematics
Level 1
Exploring the World of
Mathematics
By James Nickel, B.A., B.Th., B.Miss., M.A.
Dean of the School of Mathematics
Patria Academy International,
A division of Patria Institute, LLC
Week 1
Introduction to the Course
“Logic or reason can be justified
only in the equation that the fear
of the Lord is the beginning (i.e.,
the substructure) of all
knowledge.”
James Nickel
Week 1 Summary
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The Biblical basis for learning
mathematics.
Course materials.
The Learning Model.
Mathematics: The Language of
Science.
Why Learn Math?
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Biblical Christians have always believed
strongly in education.
Why? It is essential for redeemed man to
read, write, and count.
Why Learn Math?
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The Biblical Christian presupposes that on
the basis of the Bible we can truly know
God’s verbal and written revelation.
This knowledge is not exhaustive (e.g., the
Bible does not reveal knowledge about
quadratic equations), but it is knowledge
that brings a true perspective to all aspects
of the human endeavor, eternal and
temporal.
Why Learn Math?
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Psalm 36:9 states, “In Thy light, we see
light.”
Colossians 2:3 states, “… in Christ are
hidden all the treasures of wisdom and
knowledge.”
All aspects of wisdom and knowledge (not
just the “spiritual” parts and including
analytical knowledge like mathematical
equations) find integrative meaning,
purpose, and perspective in the full and
complete revelation of God in Christ.
Knowledge and the fear of God
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True knowledge can only be acquired by a
reverent submission to the Living God.
• Proverbs 1:7, “The fear of the LORD is the
beginning of knowledge: but fools despise
wisdom and instruction.”
• Proverbs 9:10, “The fear of the LORD is the
beginning of wisdom: and the knowledge of
the holy is understanding.”
• Psalm 111:10, “The fear of the LORD is the
beginning of wisdom: a good understanding
have all they that do his commandments: his
praise endureth for ever.”
Knowledge and the fear of God
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Man knows on the basis of fearing
God.
Man knows on the basis of the
revelation that God has given in
Scripture, in Christ, and in creation.
Man knows only surface truth if he
does not acknowledge God.
Man knows truly only when he fears
God.
Mathematics and God’s Creation
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The Biblical Christian must know how
to count in order to understand and
develop the created order.
Since all knowledge is based upon God
and since the ability to count, like
reading and writing, is God’s gift to
man, then it is imperative that we, as
parents and teachers, seek to develop
these gifts in our children and our
students.
Mathematics and God’s Creation
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There are many realms of
mathematics.
• The theory of number,
• the practice of arithmetic, and
• the description of the patterned order of
creation.
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Since mathematics reflects the
patterns of God’s created order, then
the language of that pattern is
mathematics.
Mathematics and the Dominion
Mandate
“God commands His children to subdue
and replenish the earth and take dominion
over it . mathematics is essential in
subduing and replenishing tasks .
Without a working knowledge of the
patterns of God’s speech used in the
creation, humans are powerless to
replenish the earth and are in danger of
being themselves subdued by it.”
Larry Zimmerman, Truth and the Transcendent (Florence,
Kentucky: Answers in Genesis, 2000), p. 65.
Why Learn Math?
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We learn math in order to catch a
glimpse of God’s creational speech.
We use our knowledge of that speech
to steward God’s creation (i.e., to
carry out the dominion mandate).
Why Learn Math?
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As we learn mathematics, we are
one step away from discerning the
patterned order of creation.
As we learn this patterned order, we
are one step away from encountering
the Living God.
Why Learn Math?
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The astronomer Johannes Kepler
(1572-1630) encountered the Living
God as he explored the mathematics
of God’s creation.
After he developed the law of the
elliptical motion of the planets
around the Sun, he fell to his knees
and exclaimed, “My God! I am
thinking Thy thoughts after Thee!”
Course Summary
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Mathematical Ways of Thinking
Number Sequences
Functions and Their Graphs
Large Numbers and Logarithms
Symmetry and Regular Figures
Mathematical Curves
Methods of Counting
The Mathematics of Uncertainty
An Introduction to Statistics
Topics in Topology
Basic Introduction to Algebra
Course Materials
Text
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Textbook: Mathematics: A Human
Endeavor (Third Edition), published
by W. H. Freeman (1994) - Author:
Harold R. Jacobs, a veteran high
school mathematics teacher, now
retired, who loves teaching the
subject.
Course Materials
(Ancillary)
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Student Workbook for Jacobs
Mathematics: A Human Endeavor
(Third Edition), by Susan Knueven
Wong.
Mathematics handbooks.
Course Materials
Calculators
TI Graphing Calculator and Casio fx-260
SOLAR Fraction are required.
Course Materials
Software
The Geometer’s Sketchpad (student edition)
is highly recommended.
Course Materials
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Paper (graph)
Course Materials
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Two three-ring binders.
• First binder: two tabs.
Lesson notes.
 Definitions (Glossary).
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• Second binder: two tabs.
Completed homework problems.
 Quizzes and Exams.
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Course Materials
Writing toolkit
1.Pencil (#2 lead or 0.5mm or 0.7mm
mechanical lead pencil).
2.Red ink pen or red pencil.
3.Straightedge (ruler – preferably in
both metric and British Imperial
units; i.e., inches).
4.Protractor (preferably circular).
5.Compass.
The Learning Model
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Learn to study independently.
DVD instruction: Biblical Christian
perspectives and meaning along with
an overview of what is being taught
in the text.
The Learning Model
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If you get stuck, re-read and study
the material again and again until
you understand it.
Complete solutions manual is
provided.
• Use this manual as a last resort.
• First, work hard at trying to understand
and do each problem.
Five-fold purpose
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Train in self-government.
Understand God’s providential
control of history and appreciate
the richness of the heritage of
Biblical Christianity.
Comprehend Biblical Christian
presuppositions as the true
foundation understanding and doing
mathematics.
Five-fold purpose
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Lay Biblical foundations and build
upon those foundations in
succeeding levels through the
principle of review and extension.
Show that God in Christ is the
source of all wisdom and knowledge
– that in any aspect of life,
mathematics included, true
meaning and purpose can be found
only in submission to Him.
Mathematics and the Nature of the
Biblical God
“… in exploring mathematics one is
exploring the nature of God’s rule over
the universe, i.e., one is exploring the
nature of God Himself.”
Vern Poythress, “A Biblical View of Mathematics,” in
Foundations of Christian Scholarship, p. 184.
Mathematics and Language
“In mathematics, we have a universal
language, valid, useful, intelligible
everywhere in place and time.”
Edward Kasner, Mathematics and the Imagination
“Mathematics is a linguistic activity;
its ultimate area is preciseness of
communication.”
William L. Schaaf
Mathematics and Language
“Without this language (mathematics) most of the
intimate analogies of things would have remained
forever unknown to us; and we should forever
have been ignorant of the internal harmony of the
world, which is the only true objective reality ....
This harmony ... is the sole objective reality, the
only truth we can attain; and when I add that the
universal harmony of the world is the source of all
beauty, it will be understood what price we should
attach to the slow and difficult progress which
little by little enables us to know it better.”
Henri Poincaré, The Value of Science Popular Science Monthly, 1906, pp.
195-196.
Mathematics and Language
“Mathematics, too, is a language, and as
concerns its structure and content it is the
most perfect language which exists, superior
to any vernacular; indeed, since it is
understood by every people, mathematics
may be called the language of languages.
Through it, as it were, nature herself speaks;
through it the Creator of the world has
spoken, and through it the Preserver of the
world continues to speak.”
C. Dillmann, Die Mathematik die Fackelträgerin einer neuen Zeit
(Stuttgart, 1889), p. 5.