Notebook Entry
I. Date: 5-30-14
NAME
II. Duration of Tutoring Session: 45 minutes
III. Circle the Mathematical Process(es) practiced during this tutoring session. Then, explain how you met
those standards in Parts IV and V below.
1. Employ processes for problem-solving, reasoning, or modeling (for example, respectively, Polya’s
Process, Deductive Reasoning, Inductive Reasoning, or the CCS Modeling Flow Chart).
2. Reason inductively, conjecture, and generalize toward a problem solution or mathematical model.
3. Reason deductively, and use logic to affirm conjectures, arguments, generalities, or mathematical
models.
4. Logically affirm limitations of conjectures, arguments, solutions, and models.
5. Generalize and specialize appropriately in solutions, arguments, and mathematical models.
6. Demonstrate precision and attention to detail.
7. Logically and mathematically connect mathematical and scientific constructs.
8. Mathematize (quantify) and logically construct arguments.
9. Logically and mathematically critique the arguments of others.
10. Represent mathematical ideas in multiple ways.
11. Recognize and make use of mathematical structure in order to simplify, streamline, specify problem
solutions, algorithms or mathematical models, or to generalize mathematical or logical statements.
IV. Supporting Artifact
1. Briefly state the content focus of your tutoring session.
Conceptualizing log functions as inverses of exponential functions. (SIMULATION)
2. Mathematical Processes
i) Reason Deductively
a) Briefly describe how your tutee met a process you circled in Part III.
We calculated several problems using logarithm calculations, where inverse relations helped
solve the problem. Example: Solve 2.3 = 10x+1. My tutee was able to use the log10 function to
find the value of the variable x, showing herself that the log function is the inverse of the
exponential g(x)=10x.
b) Briefly describe how you enabled your tutee to demonstrate the process you circled in
Part iii.
After spending several minutes reviewing how exponential functions have logarithm inverses, I
demonstrated the algebra associated with functional inversions. My tutee was then able to
solve homework problems, requiring both exponential and log operations, respectively.
ii) Generalize and Specialize Appropriately
a) Briefly describe how your tutee met a process you circled in Part III.
My tutee and I discussed the definition of “inverse functions” and I showed her examples of
inverse linear functions. I also asked her to graph pairs of inverse linear functions and
exponential-logarithm function inverse pairs and describe the graphical relationship among
such pairs.
b) Briefly describe how you enabled your tutee to demonstrate the process you circled in
Part iii.
My tutee was able to relate more generally to inverse functions, noting that they have their
ordered pairs, reversed and their graphs, symmetric about the graph of y=x. She remarked
that not all functions could have inverses unless some ordered pairs of a function were not
included in the graph (domain restriction).
iii) ______________________________
a) Briefly describe how your tutee met a process you circled in Part III.
b) Briefly describe how you enabled your tutee to demonstrate the process you circled in
Part iii.
V. Reflection
After reflecting on your tutoring session, comment on how you might have made it better.
If I had more time with this tutee, I would discuss restricting the domains of functions that were not
invertible, given that they were defined on large domains. For example f(x)=x2, defined on the set of
all real numbers, is not invertible unless its domain is restricted. Generalizing the concept of
invertibility of functions might would have made the notion function a bit more concrete, while
showing that not all mathematical relations are functions. Making this connection also shows that
functions belong to a general class of ordered pairs, called relations.