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Calculus Game Play: Limits

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Limits

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The criteria we use for designing probing questions are:

  • Ask students to explain or elaborate on their thinking.
  • Ask students to use prior knowledge and apply it to a current problem or idea.
  • Ask students to justify or prove their ideas.

The criteria we use for designing guiding questions are:

  • Ask for a specific answer or ask for the next step of a solution when students are confused or stuck.
  • Ask students to think about or recall a general heuristic or strategy (Polya, 1947).
  • Ask a sequence of factual questions that provides ideas or hints that scaffold or lead toward understanding a concept or completing a procedure.

The criteria we use for designing factual questions are:

  • Ask students for a specific fact or definition (Vacc, 1993).
  • Ask students for an answer to an exercise.
  • Ask students to provide the next step in a procedure.

The questions we construct sometimes involve the intersection of two or even three different question types, e.g., Guiding and Factual Questions, Probing and Guiding Questions, Probing and Factual Questions and Probing, Guiding and Factual Questions.

Summary

1 Probing Question
  • Q2
 The questions provided assist students to explain which of the problem solving strategies used is the most correct.
2 Factual Questions
  • Q3
  • Q12
 The questions provided assist students in clarifying or extending an understanding of the properties of the limit laws of the given function, e.g., polynomials and logarithmic functions; provide the next step in a procedure and demonstrate the kinds of limit laws or types of well known limit formulae that should students use.
3 Guiding Questions
  • Q6
  • Q13
  • Q14
  • Q15
 The questions provided assist students in clarifying or extending an understanding (misunderstanding) of the properties of the limit laws of the given function, e.g., rational functions; provide the next step in a procedure and demonstrate the kinds of limit laws or types of well known limit formulae that should students use, e.g., L’Hopital Rule.
4 Guiding and Factual Questions
  • Q1
  • Q4
  • Q5
  • Q10
 The questions provided assist students in justifying the properties of the limit law of the given function, e.g., rational functions, exponential functions, trigonometric functions, and algebraic functions; using prior knowledge (e.g., rationalization, simplification, cancellation, factorization, substitutions in limits, completing the square); applying it to a current problem for finding the limiting value in a step-by-step manner based on a set of specific well-known limit results and mathematical formulae (e.g., Sum of Arithmetic Sequence formula).
5 Probing and Guiding Questions
  • Q7
  • Q8
  • Q16
  • Q17
  • Q20
 The questions provided assist students in verifying the limiting value of the given problem value in a step-by-step manner and matching all information in a correct sequential order by recalling important prior knowledge of mathematical results such as a trigonometric identity/inequality or the concept of a floor function or the sum of an arithmetic sequence formula or a well-known theorem (e.g., Sandwich theorem, Part II of the Fundamental theorem of Calculus, Newton and Leibnitz Rule).
6 Probing and Factual Questions
  • Question 19
 The questions provided assist students in elaborating on their thinking for finding the limiting value of the given problem value in a step-by-step manner and giving a reason why the answer is obtained.
7 Probing, Guiding and Factual Questions
  • Q9
  • Q11
  • Q18
 The questions provided assist students in verifying the limiting value of the given problem value in a step-by-step manner and matching all information in a correct sequential order by recalling important prior knowledge of mathematical results such as trigonometric identities/the power series of exponential and logarithmic/trigonometric functions/the inverse matrix method/a well-known limit formulae and giving a reason why the answer is obtained.

Lab Assignments

Please click the links below to download the lab assignment and check its suggested solutions.

Homework Assignments

Please click the links below to download the homework assignment and check its suggested solutions.

Examination Schedule

Please note that

Schedule of final examination is:

Important dates to remember \( \cdots \)

Final

Date & Time: December 14, from 10:00 am - 12:00 pm
Room: Yasumoto International Academic Park LT7

Course Calendar

The Calculus Project Teams, Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.