Texas Mathematics Teacher Fall/Winter 2020 - 8

A Reflection on the Process and Value of Studying
Our Own Professional Growth
Step 2: Decide on the Objectives for My Lesson and
Formulate a Research Question
When choosing objectives for my lesson, I kept in mind
our standardized curriculum as well as the objectives of
the inverse function lesson to be taught in my students'
college algebra class the hour prior to my co-requisite
class. I also needed to make sure my students would be
successful in completing their homework assignment,
which is regulated. My objectives for my students were
the following. Students will be able to:
* algebraically determine the inverse function when
given a function in algebraic form,
* graph an inverse function by reflecting over the line
y = x,
* state the relationship between the domain and range
of a function and its inverse,
* describe in words the relationship between a function
and its inverse, and
* explain in words why we switch the variables when
finding the inverse function.
My research question was: How do students'
understandings of inverse functions change after
participating in my lesson on inverse functions?
Step 3: Develop the Lesson
My third step was to design my lesson plan based on
my literature review and chosen objectives. I focused
my lesson on the real-world function I re-discovered as
part of my literature review-Dolbear's Law-which is
the relationship between temperature and cricket chirps.
I would introduce the lesson with a short video about
Dolbear's Law and have students work in groups on
an activity I created. Dolbear's Law states that T= _c4 + 40
where T is estimated temperature in degrees Farenheit
and C is the number of cricket chirps per minute
(WTHI-TV, 2016).
In part one of the activity, students would identify the
independent and dependent variable in Dolbear's Law,
state the domain and range, and graph the function. In
part two of the activity, students would investigate the
inverse of Dolbear's Law as they solve algebraically for
C, identify the independent and dependent variables,
determine the domain and range, and graph the inverse
(see Figure 1). Finally, I would give each group a sheet of
patty paper, or tracing paper, pre-printed with horizontal
and vertical axes and a graph of y = x (or T = C in our
case) as a dotted line. Students would graph both
T = _c4 + 40 and its inverse on patty paper to see that an
inverse function is the reflection over the line y = x.

Figure 1: A Student's Work on Part Two of the
Groupwork Activity
After completing the groupwork, we would discuss our
findings and bridge the gap to connect our findings to
what our book includes about switching the variables
to find inverses algebraically. Next, student-volunteers
would come to the board to work on finding the inverse
of a function algebraically. We would then discuss how
we could know if two functions were inverses. Using this
information we would work on an activity which invovles
matching various algebraic representations of functions
and their inverses to their graphs. For closure, I planned to
use a think-pair-share activity with the following questions: What are the main ideas for inverse functions? What
are the properties of inverses?

"One student brought up opposites, another said they undo each other, and the
third mentioned switching the domain
and range."

8

| Fall/Winter 2020

Texas Mathematics Teacher



Texas Mathematics Teacher Fall/Winter 2020

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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