Notebook Entry
I. Date
Duration
II. Circle the NCTM Standards practiced
during this tutoring session. 
Then, explain how you met those standards
below.
1. Problem-Solving
2. Reasoning and
Proof
3. Communication
4. Connections
5. Representation
6. Use technology
III. Artifact
Briefly describe the focus of your tutoring session.
My pre-calculus tutee needed help with conceptualizing log functions as inverses of exponential functions.
We calculated several problems using logarithm calculations where inverse relations helped solve the
problem.
Example: Solve 2.3 = 10x+1
IV. Reflection
1. At the end of your session, ask your tutee the following questions. Then ask yourself the same questions.
Briefly note both yours and your tutee’s responses.
1. What went well during this tutoring session?
2. What could have improved this tutoring session?
Tutee Responses
1. I was able to see how logs “cancel”
Exponents.
2. I was a bit fuzzy on the inverse function
Concept.
Tutor Responses
She could do the inverse problems on her own at the end.
She confuses composition of inverse functions with
Multiplicative inverses equaling 1.
2. Precisely and accurately describe how you met the NCTM standard(s) in this tutoring session. Use the NCTM
Standards Rubric (on back) to guide you.
At the end of the session, my tutee was able to verbally reason through log and exponentials to solve inverse
problems when the base was new to her, thus demonstrating her ability to conjecture, generalize, and reason
through inverse arguments with logs and exponents.
V. Self-evaluation: Briefly, what did you learn from this tutoring session?
The inverse function concept is a more subtle idea than mechanically employing inverses to solve problems.
Next time I will try to make the idea of composing inverse functions to get the identity function more clear.
NCTM Process Standards Rubric
Instructional programs from prekindergarten through grade 12 should enable all students to—
1. Problem Solve
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build new mathematical knowledge through problem solving;
solve problems that arise in mathematics and in other contexts;
apply and adapt a variety of appropriate strategies to solve problems;
monitor and reflect on the process of mathematical problem solving.
2. Reason and Prove
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recognize reasoning and proof as fundamental aspects of mathematics;
make and investigate mathematical conjectures;
develop and evaluate mathematical arguments and proofs;
select and use various types of reasoning and methods of proof.
3. Communicate
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organize and consolidate their mathematical thinking through communication;
communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
analyze and evaluate the mathematical thinking and strategies of others;
use the language of mathematics to express mathematical ideas precisely.
4. Make Connections
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recognize and use connections among mathematical ideas;
understand how mathematical ideas interconnect and build on one another to produce a coherent
whole;
recognize and apply mathematics in contexts outside of mathematics.
5. Use Multiple Representations
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create and use representations to organize, record, and communicate mathematical ideas;
select, apply, and translate among mathematical representations to solve problems;
use representations to model and interpret physical, social, and mathematical phenomena.
6. Use Technology
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to aid computation;
to conceptualize mathematical ideas;