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128 11 MULTIDIMENSIONAL EXPANSION OF THE ALGORYTHMICS... Using questions is an effective way to stimulate the recall of prior knowledge, promote comprehension, and build critical thinking skills. Well-worded questions can stimulate students to think about a topic in a new way. Effective teachers are able to formulate questions to fit the cognitive level of the students (Hattie, 2012). Other characteristics of the effective use of questions are: careful phrasing and word clarity; creating psychologically safe environment; appropriate sequencing and balance; properly calibrated wait time (Tofade, Elsner, & Haines, 2013). 11.3.2 Exploring searching strategies from an algorithm complexity perspective After students have successfully orchestrated the studied searching algorithms, they are prepared (the required psychologically safe environment has been created) for analysing them from the perspective of complexity (skill 5). It is plausible, for example, to assume that they will be able to answer the below questions regarding best and worst cases with respect to searching algorithms. Additionally, as we mentioned above, students can also ask the software tool to generate best/worst case inputs for the searching/sorting algorithms. We suggest the following question sequence: — How many comparison operations does the linear search algorithm imply for the sample presented in Figure 11.2? — How many comparison operations does the binary search algorithm imply for the sample presented in Figure 11.3? — What is the “best case” with respect to the linear search algorithm? (The value we are looking for is located in the front of the list; only one comparison is needed to be found.) — What is the “worst case” with respect to the linear search algorithm? (The value we are looking for is missing from the list.) — What is the “best case” with respect to the binary search algorithm? (The value we are looking for is the middle element of the list; only one comparison is needed to be found.) — What is the “worst case” with respect to the binary search algorithm? (The value we are looking for is missing from the list.) If students possess the necessary mathematical knowledge, the teacher should continue with the following questions (the graphical representation of the corresponding functions could also be illustrative): — How many comparison operations does the linear search algorithm imply (for a list with n elements) in the “best case”? — How many comparison operations does the linear search algorithm imply (for a list with n elements) in the “worst case”?
