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All of these questions and responses were given in a whole class setting. The video segment analyzed begins with the open-ended question, “What does a circle look like?” and ends after the students discover how to find the length of the radius using the Pythagorean Theorem.

The second data collected was the number of correct and incorrect answers on the exit tickets for Day 1. These exit tickets were analyzed to see if the questioning strategies used in the lesson led to student understanding of a circle. There were a total of 26 exit tickets collected, each containing two questions. The students were asked to write the equation for a circle in the first question and to draw a translated graph of a given equation of a circle in the second. Examples of the exit tickets are in Appendix B. The number of correct and incorrect responses is recorded in Table 5.

Table 5: Tally of Questions on Day 1 Exit Ticket

Question 1 Question 2 Points Earned

Correct 23 11 5 points each

Incorrect 3 15 0 points

The responses to question 1 show that 88% of the students got this question correct. However, there were 15 incorrect responses (58%) to question 2 on the exit ticket. Table 5(a) records the number of incorrect responses which were translated using the correct number of units, but were graphed in the incorrect quadrant. All of the results from question 2 indicate that 42% of the students correctly graphed the given equation. Of the 58% of students who answered incorrectly, 60% correctly identified the number of units of translation on each axis, but moved the center in the incorrect direction. This shows that 77% of the students understood how to ascertain the correct number of units to translate a graph, but there was confusion concerning which direction to move the graph. Upon review of the video, it was noted that very little time was devoted to graph translation because the teacher assumed the students already understood this concept.

Table 5(a): Tally of Errors in Question 2 on Day 1 Exit Ticket

Correct Units, but incorrect quadrant 9

Incorrect Units and/or incorrect quadrant 6

The third data analyzed was a transcript of a portion of the video for Day 2. In this part of the lesson, the teacher is guiding the students to understand the differences between the major and minor axes of an ellipse, and what “a” and “b” represent in the equation for an ellipse. There is also questioning concerning the graph of an ellipse and what happens when “a2” and “b2” are reversed in the equation. This portion of video includes evidence of student understanding since a student is explaining how to orient a graph of an ellipse based on the equation.

A series of open- and closed-ended questions were asked in a whole class setting in order to guide the students to an understanding of this conic section. The video transcript from Day 2 reveals that the questioning strategy employed was composed of 84% open-ended questions and only 16% closed-ended questions. There...

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