This document summarizes an interview about a mathematical tug-of-war problem. The problem involves three rounds of tug-of-war between groups of differing strengths. The student was able to correctly solve the problem and show their understanding through symbolic and pictorial representations. The interviewer concluded the student has a strong conceptual understanding of operations. Areas for improvement in future interviews are identified, such as asking more probing questions to fully examine the student's thinking.

1. CLINICAL INTERVEIW
POWERPOINT
Xiaobo She
Texas Tech University

2. Interview question:

A Mathematical Tug-of-War
(Adapted from Math for Smarty Pants by Marilyn Burns; Little, Brown &
Company)
The problem is to use the information given to figure out who will win the
third round in a tug-of-war.
Round 1: On one side are four acrobats, each of equal strength. On the
other side are five neighborhood grandmas, each of equal strength. The
result is dead even.
Round 2: On one side is Ivan, a dog. Ivan is pitted is against two of the
grandmas and one acrobat. Again, it‟s a draw.
Round 3: Ivan and three of the grandmas are on one side and the four
acrobats are on the other.
Who will win the third round? Write an explanation of your reasoning.

3. Reasons for choosing this question:

The definition of “problem solving” -- the means by which individuals

take skills and understandings that they have developed previously
and apply them in unfamiliar situations (Krulik, Rudnick, & Milou,
2003)
NCTM standards for problem solving:

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.

(NCTM, 2000, p. 256)
NCTM standards for algebra:

 Relate and compare different forms of representation for a
relationship;
 Develop an initial conceptual understanding of different uses of
variables;
 Use symbolic algebra to represent situations and to solve problems,
especially those that involve linear relationships;
 Model and solve contextualized problems using various
representations, such as graphs, tables, and equations.

4. To examine the student‟s conceptual understanding of

„operation sense‟ by analyzing her ability to interpret and
translate among these three representations (Huinker,
1987).
Real-world
representation
Concrete and
Symbolic
pictorial
representation
representation

5. Jean’s solutions:
Symbolic pictorial connection
Real-world  symbolic connection

6. Conclusion:

The student has be equipped with content literacy.

The student was able to solve the questions correctly with pictorial

and symbolic representations.
Based on her interpretation of each representational form and

solution, I arrived at the conclusion that this student has mastered the
conceptual understanding of „operational sense‟.
Changes for the future interview:

Ask more relevant questions to investigate students‟ content literacy,

such as “Can you explain what „a draw‟ means?”
More in-depth questions need to be asked to probe students‟

thinking, such as “Can you explain why you get the solution?” or
challenge her by giving her a false solution.

7. What I learned from this interview:

Raising good questions is critical to conduct an effective interview.

“ A good question may mean the difference between constraining
thinking and encouraging new ideas, and between recalling trivial
facts and constructing meaning” (Kamii & DeVries, 1978; Kamii &
Warrington, 1999; Schwartz, 1996; Stone, 1993).