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School Psychology Quarterly,
Vol. 13, No. 4, 1998, pp.
322-331
Improving Students' Perceptions
of a
Mathematics
Assignment
by
Increasing Problem Completion
Rates:
Is
Problem Completion
a
Reinforcing Event?
Patricia Logan
and
Christopher
H.
Skinner
Mississippi State
University
Sixth-grade students were given
8
minutes
per
assignment to work computation problems
on
a
mathematics assignment containing
25
four-digit
by
one-digit problems (control
condition)
and an assignment containing
25
similar problems plus
nine
interspersed one-digit
plus one-digit problems (experimental condition).
As
expected, total problem completion
rates were higher on the experimental assignment. When presented with
a
choice
for
their
third assignment, significantly more students chose
the
experimental assignment, even
though
it
contained more problems. Current results showed that interspersing additional
tasks that take relatively less time
to
complete
can
improve students' preference
for
assignments without reducing assignment demands (i.e., watering down
the
curricula).
Discussion focuses on future applied and theoretical research related
to
task completion
as
a reinforcing event, schedules of reinforcement, student preference, and student choice.
Researchers have investigated teachers' preference
for
academic
and
behavioral
interventions (Elliott, Witt,
&
Kratochwill,
1991;
Gresham, 1989; Martens, Peter-
son, Witt,
&
Cirone, 1986).
The
applied value
of
this research
is
based
on the
assumption that teachers
are
more likely
to
choose
to
implement interventions
if
they find them highly acceptable. Within educational settings, students, like
teachers, also choose
the
behaviors
in
which they will engage.
For
example,
students
may
choose
to
engage
in
assigned academic behaviors, passive nonaca-
demic behaviors, and/or socially inappropriate disruptive behaviors (Lentz,
1988;
Winett
&
Winkler, 1972).
If
students
are
given academic assignments that they
prefer, they may
be
more likely to choose
to
engage in assigned academic behaviors
(Dunlap
&
Kern, 1996).
Relative rates of reinforcement
is
one variable that has been shown
to
influence
students' choice
of
academic behavior (Mace, McCurdy,
&
Quigley, 1990;
Mar-
tens
&
Houk, 1989; Martens, Lochner,
&
Kelly, 1992; McDowell, 1988; Myerson
& Hale, 1984;
Neef,
Mace,
&
Shade, 1993;
Neef,
Mace, Shea,
&
Shade,
1992;
Address correspondence
to
Christopher
H.
Skinner,
P.O. Box
9727, Mississippi State,
MS
39762;
E-mail: cskinner@colled.msstate.edu.
322
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ASSIGNMENT PERCEPTIONS 323
Neef,
Shade, & Miller, 1994). For example, Martens, Lochner, and Kelly (1992)
showed that
as
experimenters increased
the
discrepancy between rates of reinforce-
ment for on-task versus disruptive behaviors, the probability of the student engag-
ing in the behavior under the thicker schedule of reinforcement increased in direct
proportion to relative rates of reinforcement for both behaviors. Other researchers
manipulated relative rates of reinforcement for two sets of appropriate academic
behaviors and found that students preferred or were more likely
to
choose to engage
in academic behaviors that resulted in the thicker schedule of reinforcement (Mace
etal., 1990; Neef etal., 1992; Neefetal., 1993; Neef etal., 1994).
Another set of variables that may influence whether students choose to engage
in assigned work are the requirements, demands, or effort associated with the
different behaviors. When given a choice of two behaviors, if all else is equal (e.g.,
reinforcers, schedule of reinforcement), students are more likely to choose to
engage in behaviors that require less effort to complete (Hay,
1981;
Horner
&
Day,
1991;
Skinner, Belfiore, Mace, Williams-Wilson, & Johns, 1997).
The effort required to complete an academic assignment can be altered both
qualitatively and quantitatively. Quantitatively, educators can reduce the number
of tasks associated with an assignment. For example, teachers could reduce the
number of pages of required reading, the number of computation problems that
must be completed, or the number of times a spelling word must be written (Kern,
Childs, Dunlap, Clark, & Falk, 1994). Two procedures that rely on quantitative
changes for their effectiveness are overcorrection (e.g., Foxx & Jones, 1978) and
contingent skipping (Lovitt & Hansen, 1976). Educators can also decrease aca-
demic demands or effort required to complete an assignment by removing difficult
and/or time-consuming aspects of an assignment and substituting them with tasks
that require less effort. For example, Cooke, Guzaukas, Pressley, and Kerr (1993)
exposed students to two types of
assignments;
assignments with 100% new items
and assignments with 70% known items and 30% new items. Results showed that
students preferred the academic assignments with only 30% new items.
One concern with reducing assignment demands is that this strategy may also
reduce academic achievement levels (Dunlap & Kern, 1996). Roberts, Turco, and
Shapiro (1991) compared the number of new words students learned when the ratio
of known to unknown words was altered. Conditions included 90% known and
10%
unknown, 80% known and 20% unknown, 40% known and 60% unknown,
and 50% known and unknown. Results showed that students learned more new
words as the percentage of unknown words increased. Other recent experiments
based on instructional ratios have yielded similar results (Cooke et al., 1993;
Roberts & Shapiro, 1996). The probable cause of this decrease in learning rates,
when unknown items are replaced with known items, is the decrease in learning
trials or opportunities to respond (Albers & Greer, 1991; Gettinger, 1985; Green-
wood, Delquadri, & Hall, 1984; Skinner, Fletcher, & Henington, 1996).
Researchers have shown that increasing rates of teacher-delivered reinforcement
or altering assignments to reduce academic demands can be used to improve
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324 LOGAN AND SKINNER
students' preference for an academic assignment and also improve their academic
classroom behavior (Dunlap et al., 1993; Kern et al., 1994; Mace et al., 1990;
Martens & Houk, 1989; Martens et al., 1992; Neef et al., 1993; Neef et al., 1992;
Neef et al., 1994). However, each strategy may have some applied limitations.
Increasing relative rates of teacher-delivered reinforcement can be resource and
time consuming (Hall, 1991; Neef et al., 1994). Qualitative and quantitative
reductions in assignment demands can reduce learning rates (Cooke et al., 1993;
Dunlap & Kern,
1996;
Roberts & Shapiro,
1996;
Roberts, Turco, & Shapiro, 1991).
Recently, researchers combined both of these strategies in an attempt to improve
students' perceptions of an assignment, without increasing rates of externally
delivered reinforcement or reducing assignment demands (Skinner, Fletcher, Wild-
mon, & Belfiore, 1996; Skinner, Robinson, Johns, Logan, & Belfiore, 1996).
Skinner and colleagues proposed that when independent seat-work required stu-
dents to complete many distinct tasks in the absence of any immediate feedback
(e.g., mathematics computation assignment with many different problems), com-
pleting one of those tasks was an immediately reinforcing event. If this hypothesis
was true, then researchers reasoned they could increase rates of reinforcement by
adding, not substituting (e.g., Cooke et al., 1993), relatively briefer tasks. In their
first experiment, Skinner, Robinson et al. (1996) exposed college students to a
control assignment containing 16 three-digit x two-digit multiplication problems
and an experimental assignment containing 16 equivalent problems plus six
additional interspersed, briefer (i.e., one-digit x one-digit) computation problems.
Students then rated the two assignments and picked one for homework. Total
problem-completion rates were significantly higher on the experimental assign-
ment. Therefore, if problem completion was a reinforcing event, more students
should have preferred the experimental assignment. Results showed significantly
more students chose the experimental assignment for homework, and, although it
contained more problems, students ranked the experimental assignment as requir-
ing less effort and time to complete. Subsequent experiments were conducted to
determine what characteristics of the interspersed problems caused these improve-
ments in assignment perceptions and preference. Results showed that neither
novelty effects (Skinner, Robinson et al., 1996, Experiment II) nor problem ease
(Skinner, Fletcher et al., 1996) could account for these findings.
If students are given assignments that they prefer, they may be more likely to
chose to engage in those assignments (see Dunlap & Kern, 1996 for an excellent
review and applied synthesis). Previous investigations conducted with college
students suggest that adding and interspersing brief tasks may be a resource
efficient procedure that could improve how students perceive assignments without
reducing assignment demands. However, previous studies were limited because
the participants (i.e., college students) completed tasks (i.e., mathematics compu-
tation) that were not part of their curricula (Skinner, Fletcher et al., 1996; Skinner,
Robinson et
al.,
1996). The purpose of the current study was to extend this research
by determine if adding and interspersing additional brief computation problems
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ASSIGNMENT PERCEPTIONS 325
would improve elementary students' perceptions of an assignment that was part of
their curricula.
METHOD
Participants and Setting
Parental consent and student assent was solicited from all 39 students assigned to
both sixth-grade classrooms in a rural public school located in a mid-south school
district. Over 80% of the students in the district were African American and more
than 75% qualified to receive free lunch. Standardized test scores showed that the
students in the district scored, on average, over one standard deviation below the
national mean on mathematics achievement subtests. Thirty-one students returned
signed consent and assent forms. During the course of
the
study, one student was
eliminated due to noncompliance in following directions (performing incorrect
operations). The resulting pool of 30 participants had an average age of 12 and
consisted of
9
females and
21
males. Four of the participants were Caucasian and
26 were African American. The experiment was conducted in the cafeteria of the
students' elementary school following their regularly scheduled 15-minute after-
noon break.
Materials
Students spent
8
minutes working on two different mathematics assignments. Each
assignment was printed on one side of a single sheet of paper that contained a title
in bold, large letters followed by mathematics computation problems. Both the
experimental and control assignments contained 25, four-digit x one-digit (4x1)
multiplication problems. The steps in solving this type of problem were taught by
the students' teachers as part of their standard curricula just before this experiment
was implemented. The experimental assignment contained an additional nine,
one-digit + one-digit
(1
+
1)
addition problems that were presented following every
third 4x1 problem. The difficulty level of the 4x1 problems across assignments
was equated by altering the sequence of numbers in the four-digit factors. For
example, the first problem on the experimental assignment was 9 x 5693 and the
first problem on the control assignment was 9 x 9365.
Experimental Procedures
Students were given a packet that contained four
pages.
The first page consisted of
demographic information (name, age, sex). The two assignment sheets were then
presented in counterbalanced order across students to control for sequence effects.
The final page of the packet was designed to collect choice data and the students'
perception of time and effort for each assignment. Upon completion of the demo-
graphic information, the students were informed that they would have 8 minutes
to complete as many problems as they could on the first assignment without
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326 LOGAN AND SKINNER
skipping any
problems.
Students were instructed
to:
(a) work
as
quickly
as
possible
without making errors, (b) work horizontally across the assignment sheet from left
to right, and (c) raise their hand if they finished before being told to stop. The
students were given the same instructions for the second assignment.
After working on both assignments for 8 minutes, the students completed the
final page of the packet. Step-by-step verbal instructions were given to the students
in completing the three questions on the final sheet. The students indicated which
assignment would require the most time and which assignment would require the
most effort to complete from start to finish by circling the appropriate response.
Preference data were gathered by informing students that they would be required
to complete one additional assignment of their choice (either experimental or
control). They were informed that the problems would not be the same as those
they had just completed but would contain the same type, number, and sequence
of problems.
Experimental Design, Dependent Variables, and Data Analysis
Procedures
A within-groups design was used to compare each student's performance across
the assignments, as well as analyze their choice and ranking data following
exposure to both assignments. Counterbalancing the order of the assignments was
used as a means of controlling for sequencing effects. Efforts to reduce multiple-
treatment interference were enacted by clearly defining the different conditions
with a title that described the type of mathematics problems on each assignment
(i.e.,
the experimental assignment was titled "Mixed: Multiplication and Addition"
and the control assignment was titled "4x1 Multiplication") and by rereading
directions before each assignment (Barlow & Hersen, 1984).
Performance data collected and analyzed included: (a) the total number of
problems completed, (b) the number of 4 x 1 problems completed, and (c) the
percentage of 4 x
1
problems accurately completed on each assignment. Partially
completed final problems were not included in computing the percentage of
accurately completed 4 x
1
problems. Matched pairs f-tests were used to test for
differences across the two assignments on each performance variable. Chi square
goodness of fit was used to test for difference on assignment: (a) choice, (b) effort
rankings, and (c) time rankings. All tests were conducted with/> < .05.
Interscorer Agreement
Interscorer agreement was obtained by having a second experimenter inde-
pendently score and record, across
20%
of the assignments, the number of problems
completed and problem accuracy for each problem completed. Mean assignment
interscorer agreement was 100% for problems completed and 93% for problems
correct. The disagreements on problems correct were caused by difficulty in
reading some of the students' handwriting.
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ASSIGNMENT PERCEPTIONS 327
TABLE 1. Problem Completion Rates and Accuracy Levels For the Control and
Experimental Assignments
Control Experimental
Mean SD Mean SD
Number of Total Problems Completed 13.73 4.28 17.00 5.20
Number of 4 x
1
Problems Completed 13.73 4.28 12.93 4.26
Percent of 4 x
1
Problems Completed Accurately 63.74 30.06 68.48 29.30
RESULTS
Means and standard deviations for the number of problems completed, the number
of 4 x 1 problems completed, and the percentage of 4 x 1 problems completed
accurately are displayed in Table 1. Matched pairs Mests showed students com-
pleted significantly more total problems
[t(29) =
5.00,/?
<
.001] on the experimental
assignment than on the control assignment. No differences were found on the
number of 4 x
1
problems completed
[t(29) =
1.70, NS] or the percentage of 4 x 1
problems completed accurately [t(29) = .23, NS]. These results showed that the
experimenters were successful in their attempt to increase total problem-comple-
tion rates by interspersing the additional
1
+
1
problems. Data on 4 x
1
problems
completed and accuracy levels also showed that interspersing these additional
problems did not influence students' performance on the target 4x1 problems.
Summary data on students' choice of assignments, and perceived effort and
time to complete assignments are presented in Table 2. Chi square goodness of
fit showed significantly
[%
(1) = 6.57,p
<
.02] more students selected the control
assignment as requiring more effort. Although two students failed to circle their
choice for their third assignment, significantly
[%
(1) =
9.14,/?
< .01] more
students chose to do the experimental assignment as their additional assignment.
No difference was found for perceived time to complete assignments [x (1)
=
0.00, NS].
DISCUSSION
In the current study, total problem-completion rates were higher on the experimen-
tal assignment. After exposure to both assignments, significantly more students
TABLE 2. Choice, Effort, and Time Rankings, for Control and Experimental
Assignments
Control Experimental
N % N %
Choice 6 21 22 78
Most Effort to Complete 22 73 8 27
Most Time to Complete 15 50 15 50
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328 LOGAN AND SKINNER
reported that the experimental assignment would take less effort to complete than
the control assignment and chose the experimental assignment over the control
when asked to select an additional assignment. These findings suggest that the
students preferred the longer assignment over the shorter assignment. Although
these results appear to be counterintuitive, they support earlier research which
showed that college students preferred assignments when additional brief problems
were added and interspersed (Skinner, Fletcher et al., 1996; Skinner, Robinson et
al.,
1996).
The purpose of this study was not merely to replicate earlier findings, but also
to extend those findings. Previous studies were limited because the participants
(i.e.,
college students) completed tasks (i.e., mathematics computation) that were
not part of their curricula (Skinner, Fletcher et al., 1996; Skinner, Robinson et
al.,
1996). In the current experiment, 4 x 1 problems were selected because
teachers reported that the students had acquired, but not yet mastered, the skills
associated with solving these computation problems. The average accuracy
levels on target problems (i.e., 4 x 1) was 66%. This shows that the participating
students had acquired (well over 0% accurate), but not yet mastered (64-68% is
barely passing in most classrooms) 4 x 1 computation (Daly, Lentz, & Boyer,
1996;
Haring & Eaton, 1978). Because independent seat-work is often assigned
after students have acquired a skill in order
to
help them master that skill (Skinner
& Schock, 1995), this study was less contrived and more ecologically valid (Hall,
1991) than earlier research.
Although assignment choice and perceived effort data supported previous find-
ings,
no significant differences were found on time rankings. When asked to select
the assignment that would require the most time to complete, 50% selected the
experimental and 50% selected the control assignment. These findings differ from
previous research where college students rated the experimental assignment with
the additional brief interspersed problems as requiring less time to complete
(Skinner, Fletcher et al., 1996; Skinner, Robinson et al., 1996). Future researchers
should investigate why college students ranked these assignments differently than
sixth-grade students with respect to time required to complete the assignments.
Perhaps developmental differences in time concepts or perceptions could explain
these results.
Future researchers also should address several other methodological and theo-
retical limitations of this study. In the current study: (a) procedures were imple-
mented by a graduate student, not the students' teacher, (b) no grades were given
contingent upon performance, and (c) students were given only one opportunity to
choose and rank assignments. To enhance the applied value of the current findings,
future researchers should use teacher-directed procedures (e.g., independent seat-
work following teacher-led group instruction) and repeated-measures designs (e.g.,
multiple baseline, reversal, and/or withdrawal designs) to determine if students
would continue to choose assignments with additional interspersed brief tasks on
a day-to-day basis. The external and educational validity of the current findings
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ASSIGNMENT PERCEPTIONS 329
also should be assessed by testing the effects of interspersing additional brief tasks
across students, tasks, and settings. Another limitation of the current study is that
it failed to address the effects of interspersing briefer problems on student out-
comes. Because previous research has shown that academic behavior can be
improved when students are given assignments they prefer, researchers should
investigate the effects of interspersing additional brief tasks on other dependent
variables, including on-task levels, persistence, learning rates, disruptive behav-
iors,
and assignment completion levels.
The current study and previous investigations have been based on the following
proposed causal chain: (a) during independent seat-work, completing a discrete
academic task is an immediately reinforcing event, (b) increasing problem com-
pletion rates will consequently increase rates of reinforcement, and
(c)
this increase
in rates of reinforcement will improve students' perception of the assignment.
Because students completed significantly more problems on the experimental
assignment and significantly more students chose the experimental assignment
over the control assignment, the current findings and previous investigations
(Skinner, Fletcher et al., 1996; Skinner, Robinson et al., 1996) indirectly support
this hypothetical causal chain. However, researchers have yet to demonstrate
directly that completing a task is a reinforcing event. Therefore, the causal mecha-
nism responsible for the current findings can only be inferred. Even if completing
a task is a reinforcing event, it is not clear if task completion is negatively
reinforcing or positively reinforcing. Completing a task may be a conditioned
positive reinforcer because it has been paired with other reinforcers (e.g., praise)
in the past (Sulzer-Azaroff & Mayer, 1986). The Premack Principle also suggests
that task completion may be positively reinforcing because assignment completion
may be linked to the opportunity to engage in high probability behaviors, as
opposed to assigned behaviors (Premack, 1965). Research on contingent skipping
(e.g., Lovitt & Hansen, 1976), overcorrection (e.g., Foxx & Jones, 1978), and
decreasing academic demands (e.g., Dunlap et
al.,
1993;
Kern et
al.,
1994) suggest
that task completion may be a negatively reinforcing event for many students.
Future researchers should attempt to determine clearly and directly the causal
mechanism(s) responsible for the current findings.
If students learn by doing, then having them escape or avoid academic demands
through misbehavior (Dunlap & Kern, 1996) or merely being quiet and docile
(Winett & Winkler, 1972) can eventually result in learning and/or behavior
problems. The current experiment suggests that interspersing brief problems may
be a way to enhance student preference for assignments without reducing academic
demands (i.e., watering down the curricula). School psychologists and other
educational researchers should continue to conduct research on student choice and
procedures designed to make academic assignments more acceptable to students
without reducing learning rates (Turco & Elliott, 1986). A strong data base is
emerging which suggests that these procedures have the potential to reduce or
ameliorate learning or behavior problems (Dunlap & Kern, 1996).
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330 LOGAN AND SKINNER
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Action Editor: Terry B. Gutkin
Acceptance Date: April 27, 1998
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