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The School of Mathematics Level 1 Exploring the World of Mathematics

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.

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The School of Mathematics Level 1 Exploring the World of Mathematics

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  1. 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

  2. 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

  3. Week 1 Summary • The Biblical basis for learning mathematics. • Course materials. • The Learning Model. • Mathematics: The Language of Science.

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

  5. Why Learn Math? • 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.

  6. Why Learn Math? • 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.

  7. Knowledge and the fear of God • 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.”

  8. 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.

  9. Mathematics and God’s 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 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.

  10. Mathematics and God’s 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 God’s created order, then the language of that pattern is mathematics.

  11. 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.

  12. Why Learn Math? • 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).

  13. 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.

  14. Why Learn Math? • 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!”

  15. 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

  16. 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.

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

  18. Course MaterialsCalculators TI Graphing Calculator and Casio fx-260 SOLAR Fraction are required.

  19. Course MaterialsSoftware The Geometer’s Sketchpad (student edition) is highly recommended.

  20. Course Materials • Paper (graph)

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

  22. Course MaterialsWriting toolkit • Pencil (#2 lead or 0.5mm or 0.7mm mechanical lead pencil). • Red ink pen or red pencil. • Straightedge (ruler – preferably in both metric and British Imperial units; i.e., inches). • Protractor (preferably circular). • Compass.

  23. 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.

  24. 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.

  25. Five-fold purpose • 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.

  26. Five-fold purpose • 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.

  27. 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.

  28. 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

  29. 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.

  30. 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.

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