![]() ![]() 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). 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). 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. 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. The questions provided assist students to explain which of the problem solving strategies used is the most correct. 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. Ask students to provide the next step in a procedure.Ask students for an answer to an exercise.Ask students for a specific fact or definition (Vacc, 1993).The criteria we use for designing factual questions are: Ask a sequence of factual questions that provides ideas or hints that scaffold or lead toward understanding a concept or completing a procedure.Ask students to think about or recall a general heuristic or strategy (Polya, 1947).Ask for a specific answer or ask for the next step of a solution when students are confused or stuck.The criteria we use for designing guiding questions are: ![]() Ask students to justify or prove their ideas.Ask students to use prior knowledge and apply it to a current problem or idea.Ask students to explain or elaborate on their thinking.The criteria we use for designing probing questions are: ![]()
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