The School of Mathematics Level 1 Exploring the World of Mathematics

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The School of MathematicsLevel 1Exploring 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

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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
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Week 1 Summary

• The Biblical basis for learning mathematics.
• Course materials.
• The Learning Model.
• Mathematics The Language of Science.

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Why Learn Math?

• Biblical Christians have always believed strongly
  in education.
• Why? It is essential for redeemed man to read,
  write, and count.

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Why Learn Math?

• The Biblical Christian presupposes that on the
  basis of the Bible we can truly know Gods 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.

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Why Learn Math?

• Psalm 369 states, In Thy light, we see light.
• Colossians 23 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.

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Knowledge and the fear of God

• True knowledge can only be acquired by a reverent
  submission to the Living God.
• Proverbs 17, The fear of the LORD is the
  beginning of knowledge but fools despise wisdom
  and instruction.
• Proverbs 910, The fear of the LORD is the
  beginning of wisdom and the knowledge of the
  holy is understanding.
• Psalm 11110, 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.

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Knowledge and the fear of God

• 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.

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Mathematics and Gods Creation

• 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 Gods gift to man, then it is imperative that
  we, as parents and teachers, seek to develop
  these gifts in our children and our students.

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Mathematics and Gods Creation

• There are many realms of mathematics.
• The theory of number,
• the practice of arithmetic, and
• the description of the patterned order of
  creation.
• Since mathematics reflects the patterns of Gods
  created order, then the language of that pattern
  is mathematics.

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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 Gods 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.
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Why Learn Math?

• We learn math in order to catch a glimpse of
  Gods creational speech.
• We use our knowledge of that speech to steward
  Gods creation (i.e., to carry out the dominion
  mandate).

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Why Learn Math?

• 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.

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Why Learn Math?

• The astronomer Johannes Kepler (1572-1630)
  encountered the Living God as he explored the
  mathematics of Gods 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!

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Course Summary

• 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

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Course MaterialsText

• 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.

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Course Materials(Ancillary)

• Student Workbook for Jacobs Mathematics A Human
  Endeavor (Third Edition), by Susan Knueven Wong.
• Mathematics handbooks.

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Course MaterialsCalculators

• TI Graphing Calculator and Casio fx-260 SOLAR
  Fraction are required.

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Course MaterialsSoftware

• The Geometers Sketchpad (student edition) is
  highly recommended.

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Course Materials

• Paper (graph)

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Course Materials

• Two three-ring binders.
• First binder two tabs.
• Lesson notes.
• Definitions (Glossary).
• Second binder two tabs.
• Completed homework problems.
• Quizzes and Exams.

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Course MaterialsWriting 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.

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The Learning Model

• Learn to study independently.
• DVD instruction Biblical Christian perspectives
  and meaning along with an overview of what is
  being taught in the text.

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The Learning Model

• 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.

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Five-fold purpose

1. Train in self-government.
2. Understand Gods providential control of history
   and appreciate the richness of the heritage of
   Biblical Christianity.
3. Comprehend Biblical Christian presuppositions as
   the true foundation understanding and doing
   mathematics.

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Five-fold purpose

1. Lay Biblical foundations and build upon those
   foundations in succeeding levels through the
   principle of review and extension.
2. 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.

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Mathematics and the Nature of the Biblical God
in exploring mathematics one is exploring the
nature of Gods 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.
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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
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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.
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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.