Texas Mathematics Teacher Fall/Winter 2020 - 9

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

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Texas Mathematics Teacher Fall/Winter 2020

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