Tracy Dobie
Jonathan Lesser
April 28, 2011
CTA Report Template (Part 3):
Student Interview
Choosing the Prompt/Problem
(Q1) Which problem or prompt will you give students?
(Q2) What are you hoping to get out of the student interview? (i.e., assess prior ability or
test an instructional tactic)?
In order to assess students’ prior knowledge, as well as access students’ typical or
routine ways of solving problems, we asked the students to think aloud as they solved
two different fraction comparison problems. We also prompted the students to think
about and explain ways of solving the problems other than their initial strategies. The
problems we provided to the students were as follows:
Which fraction is larger: 3/5 or 4/7?
Which fraction is larger: 35/76 or 47/99?
In addition to asking students to solve fraction comparison problems such as the ones
above, we asked the students to think aloud as they tried to develop a real life word
problem using the fractions 3/5 and 4/7. The goal of this question was to assess how –
and whether – students relate the fraction problems they see in school to their own
lives.
Selecting Students
(Q3) Which students will you interview?
We interviewed two 5th grade students. Neither of these students expressed a strong
interest towards mathematics or fractions. The students also found math to be both
easy and hard, varying with the problem.
Think aloud / Interview
Please see video files of the interviews and image files of the scratch work.
Coding / Identification of errors and omissions
Please see DobieLesser_NoviceInterviewCoding.xlxs
Debriefing
A significant finding that emerged from the data was that both of the novices were
equipped with limited approaches to solving the fraction comparison problems. While
both students were able to get the right answers, they both immediately began
performing a standard algorithm once the problem was read (student 1: lines 7, 23;
student 2: lines 7, 27). The experts, on the other hand, began by considering different
facets of the problem that could possibly have lead to simpler solutions than finding a
common denominator. As the novices lack this strategy for reasoning through the
problem, they may fail to recognize other ways of solving different fraction problems that
might be more efficient than their standard algorithmic approach.
Furthermore, the novices lacked an ability to come up with alternative ways to solve the
problem (student 2: 14-16, 35). The novices seemed to rely exclusively on problem
solving strategies that they were taught explicitly as opposed to being able to reason
about fractions through other means, even when provided with alternative approaches.
Student 1 stated that representing the second fraction problem graphically would be
“harder because this [the LCM algorithm] is the first way that I learned” (33), while
student 2 stated that she couldn’t solve the first fraction problem using a number line
because “we haven’t learned how to do that” (22). This is in contrast to our experts, who
were able to use adaptive strategies to solve the problem using a number line despite
not having generated that as a possible solution.
In addition, the novices seemed to be familiar with other quick mnemonics to solve
problems that run counter to the type of essential understanding laid out by the experts.
Our second expert stated that one of the requisites for understanding fraction
comparison problems is to know that each whole is divided up into “equal” parts, and
that “larger” or smaller “pieces” do not hold comparative meaning. Student 2, however,
started to outline a strategy to compare fractions based on the size of the pieces as
derived from the denominator size, but quickly became confused and didn’t know how
to capitalize on her proposed strategy (student 2: 14-15).
Regarding motivation to work with fractions and perceived ability to solve fraction
problems, the novices echoed two salient beliefs about mathematics that we view as
problematic. Student 1 stated that she does not like fractions: “I don’t think there’s a fun
way to learn fractions” (47), while student 2 stated, “I don’t love math because I’m not
great at it” (47). Student 1’s statement implies she is not engaged with the material she
is currently learning, while student 2’s statement implies that she has a low selfconception of her mathematical abilities, leading to a negative view of the subject. It is
important to keep in mind, however, that these statements were made despite the fact
that both students were able to accurately perform the operations to yield the correct
answers in both of our think-aloud problems.
We may be able to infer from this that while students are being taught how to solve
fraction comparison problems, they are not really taught about fraction comparison
problems; there is a lack of understanding apparent in their actions and responses. Both
students stated that they do not encounter fractions in their everyday life (student 1: 40,
student 2: 42), while they both agreed that their parents and teachers probably interact
with fractions in their lives. The students’ current school experiences are absent of
connections between the work they are doing and their everyday lives, yielding
dissociated mathematical procedures and disinterested students. The experts, on the
other hand, were able to recall several examples of fraction problems they encounter in
their everyday lives (in addition to numerous alternative strategies for solving fraction
comparison problems), likely contributing their status as “experts” who can solve
fraction problems with confidence and enthusiasm.