A Reflection on the Process and Value of Studying Our Own Professional Growth Step 4: Administer the Pre-Test and Analyze the Results Using my objectives for the lesson, I formed identical preand post-tests that focused on testing students' mastery of these objectives (see Figure 2). I administered the pre-test at the end of my colleague's lesson on inverse functions. This gave me a little time between their college algebra class and my class to look over my students' pre-test answers. I found that most of my students were able to draw the inverse of a function on a graph and find a simple inverse algebraically, but most struggled with question three which asked students, "Explain the relationship between inverses." Half of my students left this question blank, and a few had incorrect answers like, "a one to one which means you want to see if 2 functions are inverses of each other." Three students had answers that showed they had some understanding of inverses: One student brought up opposites, another said they undo each other, and the third mentioned switching the domain and range. I was excited to see how their explanations might deepen after participating in my lesson! Step 5: Teach! I was looking forward to seeing how my students would respond to my lesson. The video introducing Dolbear's Law was effective in capturing my students' attention (WTHI-TV, 2016). They were interested to know how Dolbear figured out the relationship between temperature and cricket chirps and were enamored by the featured biology professor's enthusiasm for science. The video seemed to propel them into starting the group work assignment. Unfortunately, my students struggled with the basic task _c of substituting C = 60 into T = 4 + 40 and finding the related T-value. They also struggled with graphing the line. Luckily, this was a great platform to review prior concepts, and the students eventually worked together to complete the assignment. Once students graphed the line for the function and its inverse using the patty paper (see Figure 3), we held a class discussion about the relationship between a function and its inverse. After folding their patty-paper graphs over the line y = x, they were asked, "What do you notice?" Students responded that inverses are reflections. When I reminded students that the dotted line graphed on their patty paper was y = x, they were quick to see why the reflection takes place. One student offered, "Independent becomes dependent and the dependent becomes independent, so x and y switch." As we continued the discussion, I could see the value of using a real-world example to help students deepen their understanding. One student said, "We're just taking a different perspective," when explaining how the two formulas were different. They were able to see that we were still looking at the same relationship, and the same function, but we were switching the independent and dependent variables. Figure 2: The Identical Pre- and Post-Test Questions with One Student's Post-Test Answers Figure 3: Graphing on Patty Paper www.txmathteachers.org Fall/Winter 2020 | 9http://www.txmathteachers.org

Texas Mathematics Teacher Fall/Winter 2020 - No label

Texas Mathematics Teacher Fall/Winter 2020 - 2

Texas Mathematics Teacher Fall/Winter 2020 - 3

Texas Mathematics Teacher Fall/Winter 2020 - 4

Texas Mathematics Teacher Fall/Winter 2020 - 5

Texas Mathematics Teacher Fall/Winter 2020 - 6

Texas Mathematics Teacher Fall/Winter 2020 - 7

Texas Mathematics Teacher Fall/Winter 2020 - 8

Texas Mathematics Teacher Fall/Winter 2020 - 9

Texas Mathematics Teacher Fall/Winter 2020 - 10

Texas Mathematics Teacher Fall/Winter 2020 - 11

Texas Mathematics Teacher Fall/Winter 2020 - 12

Texas Mathematics Teacher Fall/Winter 2020 - 13

Texas Mathematics Teacher Fall/Winter 2020 - 14

Texas Mathematics Teacher Fall/Winter 2020 - 15

Texas Mathematics Teacher Fall/Winter 2020 - 16

Texas Mathematics Teacher Fall/Winter 2020 - 17

Texas Mathematics Teacher Fall/Winter 2020 - 18

Texas Mathematics Teacher Fall/Winter 2020 - 19

Texas Mathematics Teacher Fall/Winter 2020 - 20

Texas Mathematics Teacher Fall/Winter 2020 - 21

Texas Mathematics Teacher Fall/Winter 2020 - 22

Texas Mathematics Teacher Fall/Winter 2020 - 23

Texas Mathematics Teacher Fall/Winter 2020 - 24

Texas Mathematics Teacher Fall/Winter 2020 - 25

Texas Mathematics Teacher Fall/Winter 2020 - 26

Texas Mathematics Teacher Fall/Winter 2020 - 27

Texas Mathematics Teacher Fall/Winter 2020 - 28

Texas Mathematics Teacher Fall/Winter 2020 - 29

Texas Mathematics Teacher Fall/Winter 2020 - 30

Texas Mathematics Teacher Fall/Winter 2020 - 31

Texas Mathematics Teacher Fall/Winter 2020 - 32

Texas Mathematics Teacher Fall/Winter 2020 - 33

Texas Mathematics Teacher Fall/Winter 2020 - 34

Texas Mathematics Teacher Fall/Winter 2020 - 35

Texas Mathematics Teacher Fall/Winter 2020 - 36

http://www.brightcopy.net/allen/txmt/66-02

http://www.brightcopy.net/allen/txmt/66-01

http://www.brightcopy.net/allen/txmt/65-02

http://www.brightcopy.net/allen/txmt/65-01

http://www.brightcopy.net/allen/txmt/64-02

https://www.nxtbook.com/allen/txmt/64-1

https://www.nxtbookmedia.com