Questions for Students

Much thanks must go to all those colleagues through the years that have contributed to this growing list of questions. Some of these questions are my own and others have been composed by those colleagues of mine that have proven themselves able to catalyze rich classroom discussions. 

Questions per Discipline

ARTS | Fine and Performing

  1. What does beauty look and sound like?

  2. Does art have any boundaries?

  3. How does art reflect, preserve, and/or change culture?

  4. What makes a performance compelling?

  5. Are all captivating and compelling performances good?

  6. Are the arts useful?

  7. How might God be glorified through the arts?


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HISTORY | General

  1. Who ought to rule?

  2. How does one evaluate the credibility of a historian?

  3. What makes any form of government necessary?

  4. How does human depravity compromise forms of governance?

  5. How are power and authority abused?

  6. How does history shape religion and how does religion shape history?

  7. Who determines historical truth?

  8. How does geography effect the development of a civilization?

  9. How does history inform our character?

  10. How do we interpret history?

  11. How do wars shape civilizations?

  12. What is a just war?

  13. What are the perils of a deconstructionist approach to / interpretation of history?


  1. Why are naming, defining, comparing, and categorizing necessary parts of mathematical thinking?

  2. What attributes are common to all shapes?

  3. At what point can a number of mathematical categories become excessive and unhelpful?

  4. Is mathematics created or discovered?

  5. Is mathematics a language?

  6. What has motivated the discovery and/or development of mathematics over time and across cultures?

  7. Can mathematics exist apart from observable phenomena?

  8. How do you choose the form (algebraic, visual, numerical, etc.) in which a mathematical relationship is best represented?

  9. How might the particular form in which a mathematical relationship is represented be misleading?

  10. How do we account for the remarkable ability of mathematics to accurately describe, model, and predict natural phenomena?

  11. How does mathematics help us understand the qualities of creation and the attributes of the Creator?

  12. Can a mathematical model ever perfectly described a natural phenomena?

  13. What are the qualities of those "real-world" situations that can best be modeled by mathematics?

  14. What is a proof?

  15. What makes a mathematical argument persuasive and convincing?

  16. What makes a mathematical argument eloquent and beautiful?

  17. What criteria can be used to determine whether or not a proof is worthy of imitation?

  18. What good can come from mathematics?

  19. How can mathematics improve our ability to steward our gifts and talents? To love our neighbor?

  20. Are certain applications of mathematics more worthy of pursuit than others? Why?

MATHEMATICS | Shapes and Numbers

  1. What characteristics of shapes and solids can be measured?

  2. Under what circumstances can you conclude that a pattern exists?

  3. How are multiplication and addition related? How are division and subtraction related?

  4. Are all numbers compositions of other numbers? Are their certain numbers that cannot be decomposed?

  5. How are positive and negative signs like adjectives? Are numbers nouns?

  6. When are common denominators necessary? Why?

  7. Are the irrational numbers any more or less real than rational numbers?

  8. Are positive and negative infinity numbers or ideas?

  9. Could the zero power of a negative number have been defined to be equal to anything other than one?


  1. What makes one form of an expression any more or less simple than another?

  2. In what ways can the form of two different expressions, known to be equivalent, be altered without destroying their equivalence?

  3. How can two statements of equality be combined to form a third statement of equality?

  4. Why is an understanding of inverse operations a prerequisite to equation solving?

  5. Do all quadratic equations have two distinct and real solutions? Why or why not?

  6. What makes certain exponential equations more difficult to solve than others?

  7. In what ways do exponents and logarithms behave similarly?


  1. What makes a mathematical argument convincing?

  2. What is a proof? What purposes do proofs serve in geometry?

  3. How are conjectures generated and supported?

  4. Does every pair of non-parallel lines have one point of intersection?

  5. What is the difference between an isometric transformation and a dilation of a plane figure?

  6. Are there certain right triangles that are more "special" than others? Why?

  7. Can all shapes be decomposed into a set of adjacent triangles? Why or why not?

  8. What kinds of figures are constructible?

  9. Why might mathematicians limit themselves to a consideration of constructible forms?

  10. Under what circumstances might a non-Euclidean geometry (ex. hyperbolic, spherical) be a better interpretive lens through which to interpret phenomena?

  11. What are the various ways in which a plane can intersect a cone or pair of cones? How can the shapes of the resulting cross-sections be described?


MATHEMATICS | Trigonometry

  1. Why are there 360 degrees or 2pi radians in one rotation?

  2. Why might one unit of degree measurement (degrees, radians) be preferred over another?

  3. Why does the value of a trigonometric ratio depend only on the value of the angle?

  4. Why are trigonometric functions sometimes referred to as "circular" functions?

  5. How do certain trigonometric functions behave similarly to rational functions?

  6. How can trigonometric identities be derived geometrically?


  1. What kinds of relationships can be represented by mathematical functions?

  2. How do you choose the form (algebraic, visual, numerical, etc.) in which a mathematical relation or function is best represented?

  3. Do all functions have inverse functions? Why or why not?

  4. Why might the domain and/or range of a function be restricted?

  5. What determines the shape of a polynomial function?

  6. What determines the "end-behavior" of a function?

  7. What types of natural phenomena can exponential functions effectively model?

  8. What happens when the denominator of a function approaches zero? Equals zero?

  9. What is an asymptote? How are horizontal, vertical, and oblique asymptotes similar/different from one another?

  10. What kinds of relationships can be described more accurately by introducing time as a parameter?

MATHEMATICS | Sequences, Series, Probability, and Statistics

  1. What are the advantages and disadvantages of describing a sequence recursively?

  2. Do all infinite series converge upon a particular sum? Why or why not?

  3. Are there unusual sets of data for which a particular statistics may be misleading?

  4. How must large and small samples of a population be interpreted differently?


  1. How can lines be used to approximate the behavior and/or characteristics of curves?

  2. How can you be certain that an object is in motion?

  3. When are average and instantaneous rates of change the same? Different?

  4. What is a derivative?

  5. What can we learn about a function through a consideration of its first derivative? Second derivative?

  6. What is a limit?

  7. What do we mean when we call a function continuous?

  8. What does it mean to say that a function behaves "asymptotically"?

  9. Why must the derivative of a periodic function also be periodic?

  10. How can we use calculus to determine optimal conditions?

  11. Can all algebraic relationships expressed in the form of a single equation be differentiated implicitly? Why or why not?

  12. What is a differential? How is a differential like or unlike zero?

  13. Why might the displacement of a particle not be equal to the total distance traveled by a particle?

  14. Why is the derivative of an exponential function also exponential?

  15. Why is it necessary to restrict the range of an inverse trigonometric function?

  16. How is a slope field similar to a putting green on a golf course?

  17. Can the area of any bound region or the volume of any bound solid be determined?

  18. How do you effectively approximate the length of a curve?


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  1. How does historical context inform our reading of literature?

  2. How does authorial motive/intent inform our reading of literature?

  3. Why do people write literature?

  4. Why do we study the pagan classics?

  5. What is myth? Why write myth?

  6. How does one read both critically and receptively?

  7. How does literature shape culture? 

  8. How does literature shape our interpretation of history?

  9. Does all literature contain a metanarrative (ex. creation, fall, redemption)?

SCIENCE | General

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