1. A Diagnostic Interview
by Mary Jane Cruz
as part of EDCI 5372 (Assessment Issues in Math/Science
Education), a Texas Tech University course

2. 2
Concepts
Interviewee
 The student selected was a Hispanic female.
 She was 10 years of age.
 She was a 4th Grade student at an
elementary school in the Texas Panhandle.
 Division
 Long Division algorithm

3. 3
Clinical Interview Questions
 The student was asked to (1) compute 81÷3, (2)
model 81÷3, and (3) create a word problem that
involved 81÷3 in the solution process.
 Purpose: illustrate concept of division by translating among
the different representations (Huinker,1993; Liedtke,1988)
 In addition, the student was asked to compute more
problems such as 552÷4 and 2708÷6.
 Purpose: demonstrate understanding of algorithm
(Liedtke,1988)
 Finally, the student was asked to solve the following
application problem: A teacher orders 48 pencils for the 9
students in her class. If each student is to receive the same
number of pencils, how many pencils will each student get?
 Purpose: conduct a miscue of analysis (Bryant,1996)

4. 4
Examples of Interviewee’s Thinking
 Student was able to
successfully
compute the problem as well as
check her answer. (see
illustration)
 Student was not able to model
81÷3 using her choice of
manipulative, base-ten blocks.
(see video)
 Student was able to create a
word problem and solved it by
modeling. (see illustration)

5. 5
Examples of Interviewee’s Thinking
 Student was able to successfully
use the long division algorithm
when the dividend was a 3-digit
number but was not able to do so
when the dividend was a 4-digit
number. (see illustration)
 Student did read, interpret, and
solve the word problem
successful. She found the
solution by modeling. (see
illustration)

6. 6
Modes of Reasoning
 The student has a basic understanding of the concept of division.
Although she was not able to model division when asked, she did
use modeling to solve each word problem. And she was able to
easily create a word problem. Thus, her skill of translating among
the different representations of division is not fully developed and
needs some work.
 Although the student had a basic understanding of how to use the
long division algorithm, when presented with a novel situation she
was not able to adapt (as seen when she could not solve division
problems involving 4-digit dividends).
 No breakdowns were found when the student decoded the given
word problem. She read every word correctly and was able to
successfully solve the problem. It was interesting that she solved
the problem by modeling rather than using the division algorithm.
This may go back to her weakness in translating among the
different representations.

7. 7
Changes for Future Interviews
 Not have so many tasks
 Student got tired
 Present novel situations using 3-digit dividends too
What I Learned
 Knowing a concept is more than just getting the right
answer
 Translating among the different representations
 Applying concept to novel situations
 Very difficult to question effectively in an interview
 Need more practice