For adults with disabilities, quality of life is enhanced with
improvements in life skills such as social interaction, employment,
money management, community adjustment, independent living,
self-determination, personal choice, recreation, physical and material
well-being, civic responsibility, psychological well-being, and personal
satisfaction (Hughes, Eisenman, Hwang, Kim, Killian, & Scott, 1997).
However, many individuals with developmental disabilities are not
adequately prepared to live and work in their community (Brown, 2000;
Frank & Sitlington, 2000; Patton, Cronin, & Jairrels, 1997;
Rusch, Szymanski, & Chadsey-Rusch, 1992). With an increase in
advocacy for improved postschool outcomes, the importance of preparing
students to live independently and interact within their community has
gained attention (Lehmann, Bassett, Sands, Spencer, & Gliner, 1999).
Further, with the inception of supported employment services in 1986,
more individuals with developmental disabilities have entered
competitive, employment positions in community-based settings (Revell,
Kregel, Wehman, & Bond, 2000).
Competitive employment has, in turn, led to these individuals
assuming responsibilities for managing and using money independently
(Moon & Inge, 2000). Also, the recent emphasis on self-determination
as an important educational outcome has resulted in less reliance on
caregivers and a greater focus on facilitating the independence of
individuals with disabilities (Agran, Blanchard, & Wehmeyer, 2000;
Field & Hoffman, 2002; Zhang & Stecker, 2001). The quality of
community integration and participation by individuals with
developmental disabilities is seen as a function of independent
community competencies (Benz, Lindstrom, & Yovanoff, 2000).
One general set of skills necessary to function successfully in the
community is the ability to manage money (Browder & Grasso, 1999).
Being able to earn, budget, and spend money is an integral part of
independent community functioning. The ability to engage in such skills
greatly enhances an individual's ability to independently use
various community-based services (e.g., riding public transportation,
eating in restaurants, making purchases). The importance of teaching
community skills, particularly purchasing skills, has been widely
reported in the literature (e.g., Alcantara, 1994). The majority of the
research on purchasing skills has focused on teaching essential money
skills within purchasing routines.
The need to promote independent purchasing by individuals with
developmental disabilities is clear. To date, there have been two major
practitioner-oriented reviews of the literature on functional math
instruction as it relates to the use of money by individuals with
developmental disabilities (Browder & Grasso, 1999; Morse, Schuster,
& Sandknop, 1996). Although the reviews have provided some
evaluation of the effects of money and purchasing skill instruction or
raised issues for consideration, none has offered a comprehensive,
quantitative synthesis of the overall effects of purchasing, money
skills instruction, or the effects of the various instructional
strategies. Rather, the reviews offer information that is important for
educators to consider when teaching functional math. For example,
Browder and Grasso's review of money skills instruction provided
several recommendations for practice, which included (a) simplifying the
use of money task with adaptations or bypass strategies (e.g.,
calculators, money envelopes); (b) providing direct instruction using
prompting and fading strategies, such as time delay and least intrusive
prompt procedures; and (c) training and assessing generalization in
community contexts. In addition, Morse et al. summarized the research on
grocery shopping skill instruction for persons with moderate to profound
intellectual disabilities. This review identified the need to introduce
purchasing skills as early as elementary grades and continue instruction
throughout the school years. It also indicated the need to examine the
relative effectiveness of various strategies for teaching grocery
shopping skills as well as to identify factors (e.g., instructional
settings) that promote generalization. Both reviews also indicated the
need to go beyond money or purchasing skills and consider other related
skills instruction (e.g., social skills, menu planning, nutrition
lessons, and checkbook and ATM machine use).
In summary, there are two important reasons to review the complete
functional math/money skills and purchasing skills literature. First,
the results from studies of money skills and purchasing skills differ in
many ways (e.g., type of purchase, participant characteristics), and it
is important to assess how and to what extent differences across studies
are associated with differences in treatment effects. Second, from a
practical perspective, relatively little is known about what common
components (e.g., prerequisite skills, skill objectives) characterize
effective instructional models of purchasing and money skills.
Therefore, our meta-analysis synthesizes research on functional
mathematics/purchasing skills instruction for individuals with
developmental disabilities and analyzes the relationship between
treatment effectiveness and various study features (e.g., participant
characteristics, purchasing and functional math/money instructional
strategy, generalization programming). Meta-analysis allows researchers
to quantitatively aggregate information while considering the magnitude
of treatment effects across different studies. As such, it serves to
identify effective strategies and address relationships between
treatment effectiveness and relevant mediating variables (e.g., Glass,
1977; Kavale, 1984; Kavale & Glass, 1984). The following research
questions were addressed in this study:
* How effective is purchasing skill instruction for individuals
with developmental disabilities?
* Is intervention effectiveness related to student characteristics
(i.e., grade, classification label, or entry skills)?
* Does the type of instructional approach differentially influence
independent purchasing skill acquisition by individuals with
* Are treatment outcomes related to instructional features (e.g.,
money skill adaptation, instructional setting)?
* What is the effect of the instructional approach on skill
* What is the effect of the instructional approach on skill
LITERATURE SEARCH PROCEDURES AND INCLUSION CRITERIA
We first conducted broad computerized searches of the literature on
money or purchasing skill instruction for students with developmental
disabilities using the following databases: Educational Resources
Information Center (ERIC) database (1978 to 2003) and PsychLit database
(1967 to 2003). Descriptors for the computerized searches included
"purchasing skills," "functional math," "money
management," "next dollar strategy,"
"community-based instruction," "disabilities," and
Second, we conducted manual searches of journals that were included
in articles reported in the Browder and Grasso (1999) study. Finally, we
conducted an ancestral search of studies using the reference lists of
identified articles as well as the two review articles. More than 350
abstracts and summaries were read during the preliminary stage of the
review process. Two of the authors independently read the study
abstracts to determine whether the articles met the criteria for
inclusion. To judge the appropriateness of each article, we evaluated
studies using five criteria. First, studies had to include an
intervention to teach purchasing skills. Second, the recipients of the
intervention were identified as individuals with developmental
disabilities (mild, moderate, severe, profound mental retardation;
autism; multiple disabilities; or dual diagnoses).
Third, single-subject or group research design studies with some
form of experimental control were included in the review. Fourth,
studies had to provide baseline and treatment data or pretest and
posttest data that allowed for the computation of effect sizes. Fifth,
only studies published in English were included in this review. We did
not explore other sources of the literature (e.g., Dissertation
Abstracts International) in a systematic fashion or contact active
researchers in this area for unpublished studies. As such, this review
may represent a potential bias toward published studies versus
unpublished articles (Lipsey & Wilson, 1993); thus, conclusions
based on the review should be viewed as tentative.
Many of the studies reviewed did not meet our eligibility
requirements. The reason for excluding studies was primarily a failure
to investigate interventions that taught money or purchasing skills.
Instead, excluded studies mostly investigated strategies to (a) write
checks (LaCampagne & Cipani, 1987), (b) select lower priced items
using number lines (Sandknop, Schuster, Wolery, & Cross, 1992), (c)
utilize automatic banking machines (McDonnell & Ferguson, 1989), or
(d) understand the value and compare money amounts (Stith &
Fishbein, 1996). In addition, two group design studies (i.e., Matson,
1981; Westling, Floyd, & Carr, 1990) that reported pre- and posttest
scores only were not included in the review, because effect sizes for
these two studies could not be calculated. In the end, a total of 28
single-subject design studies met all requirements and were selected for
CODING STUDY FEATURES
Study features that were coded included participant characteristics
(i.e., grade, classification label, and entry skills) and purchasing
skill instructional features (i.e., purchasing instructional strategy,
money skill adaptation, type of purchase, error correction procedure,
length of instruction, and instructional setting). In addition,
generalization and maintenance effects were also evaluated.
Grade. This variable describes the grade level of the study
participants and was separated into three categories: elementary and
middle school (Grades K-8), secondary (Grades 9-12), and postsecondary
Classification Label. This variable comprised three categories: (a)
mild and moderate mental retardation, (b) moderate and severe mental
retardation, and (c) other disabilities (i.e., autism, severe emotional
disorders, dual diagnoses). Because most studies included a mixed group
of participants (i.e., mild and moderate or moderate and severe), it was
not possible to separate moderate disabilities from mild or severe
disabilities, resulting in an overlap of disabilities in the first two
Entry Skills. This variable referred to whether or not the
participants in the studies began with preexisting functional
mathematics skills and included three categories. Two of the three
categories were defined as whether participants entered the study with
money recognition skills (i.e., able to name and count dollar bills and
coins) or had community experiences (but did not necessarily have the
experience to handle money or recognize specific values of money). In
addition, we coded a third category: participants' entry skill
information was not reported.
PURCHASING SKILL INSTRUCTIONAL FEATURES
Purchasing Instructional Strategy. To evaluate the effectiveness of
different instructional strategies, interventions were categorized as
either modeling and/or verbal instruction or faded prompt procedures.
Modeling and/or verbal instruction was defined as the instructor or
videotapes/photo slides modeling the skill, providing verbal
instructions, and/or role-playing the desired purchasing skill. Faded
prompt procedures referred to instructional techniques that incorporated
a system or schedule of fading of teacher delivered prompts to the
natural discriminative stimuli, such as in a system of least prompts,
most to least prompts, or constant/progressive time delay.
Money Skill Adaptation. Money transaction is one of the key
components of a series of skill steps in purchasing skill instruction.
To explore the relationship between instructional effectiveness and
various money skill adaptations, three classes were assigned to this
variable: (a) simplification, (b) next-dollar strategy, and (c)
calculator use. Simplification involved providing students with a money
number line or other means such as matching money to preprinted cards to
assist with money payment. Another form of simplification included
providing the participant with an envelope containing a predetermined
amount of money needed to make a purchase. Next-dollar strategy involved
counting out the next dollar to the amount to be tendered during a cash
purchase transaction. The cents pile method was included in this
category. It involves an additional step in the next-dollar strategy.
Specifically, the student is taught to put one dollar aside for cents,
count out the requested dollar amount, and combine the two piles to give
to the cashier or instructor. Calculator use referred to using a
calculator as a means to figure out the total cost or to make a decision
as to whether or not one has enough money to make the purchase.
Type of Purchase. We coded three categories for this variable. They
included (a) restaurant ordering, (b) grocery or shopping center
purchases, and (c) vending machine use or money payment instruction
only. Five studies involved money payment instruction only (e.g., Colyer
& Collins, 1996) and were clearly distinguishable from other
purchasing skill studies. For example, participants in studies involving
money payment were presented with the price of an item and asked to pay
the appropriate amount of money. These studies were combined with
vending machine use studies, because they share common features in terms
of an exclusive focus on money skill instruction.
Error Correction Procedure. Error correction procedures were coded
into three categories. These included (a) verbal feedback and/or
modeling, (b) physical guidance (i.e., participants repeated the correct
behavior with instructor's physical guidance), and (c) no error
correction procedures reported.
Setting. To examine the relationship between instructional settings
and outcomes, we coded the environment in which the instruction took
place as follows: (a) simulated/classroom settings, (b) community
settings (in vivo instruction), and (c) simulated plus in vivo (i.e.,
instruction in both simulated and community settings).
Length of Treatment. Treatment duration may influence participant
skill acquisition and maintenance. We coded this variable as either long
(more than 15 sessions) or short (15 or fewer sessions).
Generalization. Skill generalization to novel settings, people,
times, and stimulus universe are typically targeted for generalization
programming (e.g., Scruggs & Mastropieri, 1994). When studies
assessed and included graphed generalization data to allow for the
calculation of generalization treatment effects, we coded the
interventions into two categories: (a) programmed for generalization
(e.g., general case instruction) and (b) not programmed for
Maintenance. To evaluate the extent to which the intervention
influenced skill maintenance, we coded studies that assessed and
presented maintenance data for which calculation of treatment effect was
possible into two categories: maintenance probes collected 1 month or
less after the termination of the intervention or probes collected
beyond 1 month after the intervention.
COMPUTATION AND ANALYSIS OF TREATMENT EFFECTIVENESS
Because all studies in this meta-analysis employed a single-subject
research design, a nonparametric procedure (i.e., the percentage of
nonoverlapping data [PND]) was used to estimate treatment effectiveness
(Scruggs, Mastropieri, & Casto, 1987). Although parametric
approaches have been used to calculate effect size (e.g., the
standardized mean difference), graphic display of results and a limited
number of data points, especially during the baseline, present problems
in using parametric procedures to quantify single-subject data and to
perform reliable and valid analysis of the effect size. Therefore, PND
was chosen as the effect size measure. Interpretations, based on the
interpretative framework for PND articulated by Scruggs and Mastropieri
(1998), are as follows: (a) > 90% is a large effect, (b) 70% to 90%
is a moderate effect, (c) 50% to 70% is a low effect, and (d) < 50%
is not effective.
Specifically, PND was calculated by dividing the total number of
data points in the treatment phase that exceeded the highest baseline
data point by the total number of data points in the treatment phase. In
the case of multiple baseline studies, individual PND scores were
aggregated to obtain an overall treatment effect. The dependent measure
used for effect size calculation was common across all studies (i.e.,
the number/percentage of correct responses). Specifically, the
number/percentage of correct responses for task analysis steps was
measured when the intervention included a long sequence of purchasing
routine. In contrast, the number/percentage of correct responses (i.e.,
payment) to items with different prices was measured when the training
focused on the money payment skill.
After PND was calculated, results were analyzed with each coded
variable as the independent variable. Kruskal-Wallis H, a nonparametric
test that allows for multiple independent samples comparison, was used
to test for significant differences among categories for each
independent variable. In addition, because of the nonparametric nature
of the PND measure and given that it is often not normally distributed,
median PND was chosen as the central tendency measure of the treatment
effects. The median is less likely to be skewed by "outliers"
(Scruggs et al., 1987).
Most studies investigated one intervention strategy, and therefore,
each study yielded one PND score for skill acquisition. However, two
studies (McDonnell & Ferguson, 1988; McDonnell, Horner,&
Williams 1984) compared purchasing instructional effectiveness when
training was conducted in different settings (e.g., simulated or real/in
vivo). As such, two and three PND scores were obtained from the
McDonnell and Ferguson (1988) and McDonnell et al. studies,
respectively, for each intervention strategy examined. Because these
multiple interventions and their corresponding PNDs were setting
related, we only included multiple PNDs from each of these comparison
studies into the categorical comparison analysis when
"Instructional Setting" was an independent variable. For the
analysis of all other variables on skill acquisition, we aggregated the
PND scores in each of these comparison studies to produce a single PND.
In addition to skill acquisition PND scores, maintenance and
generalization PND scores were separately calculated and analyzed. It
must be noted that one study (Sprague & Horner, 1984) compared three
strategies (i.e., single case, multiple case, and general case
instruction) to promote skill generalization. Therefore, three
generalization PND scores were obtained from this single study when PNDs
for generalization were analyzed.
The first author coded all studies and calculated the PND. A second
rater independently coded 32% of the studies. Interrater agreement was
obtained by dividing the total number of agreements by the total number
of agreements plus disagreements multiplied by 100. The interrater
agreement for the coding of study features was 97%, with a range of 95%
to 100%. Effect size agreement was 96%, with a range of 92% to 98%.
Disagreements in calculating PND were primarily due to problems in
deciphering some of the graphed data points, which in turn made it
difficult to judge whether or not a specific data point in intervention
overlapped with baseline data.
OVERALL STUDY CHARACTERISTICS AND TREATMENT EFFECT
Table 1 presents the characteristics of the comparisons for the 28
single-subject design studies. Twenty-six of these studies used a
multiple probe or baseline design and two studies employed a
multielement alternating treatment design. The 28 studies were published
from 1978 to 2000. A total of 115 participants were included in these
studies. Participants' ages ranged from 6 to 74. Twenty-three
studies reported participants' IQ scores with ranges of 10 to 75.
In sum, the 28 single-subject studies yielded an overall moderate effect
(PND = 87%; range = 59% to 100%) for purchasing skill instruction.
MODERATOR INFLUENCES ON THE EFFECT OF PURCHASING SKILL INSTRUCTION
Table 2 presents an overview of treatment effects and the number of
studies or interventions in each category with regard to sample
characteristics, instructional features, and other variables. Potential
variables such as participant characteristics (e.g., grade, disability
label, entry skills) and instructional features (e.g., instructional
setting, type of instruction/adaptations, error correction procedures)
were analyzed to examine their impact on purchasing skills instruction.
Participant Characteristics. The majority of the studies (n = 14,
50%) involved secondary school participants (Grades 9-12) and six
studies (21%) included postsecondary students (i.e., over the age of
21). In addition, five studies (18%) included elementary school
participants (i.e., Grades K-5), and three (11%) comprised middle school
participants (i.e., Grades 6-8). Given the limited number of studies in
the elementary and middle school categories, these two categories were
combined when categorical comparisons of the 28 single-subject studies
were conducted. Results of these comparisons did not indicate
statistically significant differences among grade levels on the
treatment. Regarding the disability category, only one study (4%)
involved participants with mild disabilities. Four (14%) studies
included participants with mild to moderate disabilities, and three
(11%) studies consisted of participants with moderate disabilities. The
majority of studies included participants with a mixture of moderate and
severe disabilities (n = 12, 43%) or severe disabilities (n = 5, 18%).
In contrast, only three studies (10%) involved participants with autism
or severe behavior disorders. Categorical comparisons of studies
analyzed revealed no statistically significant differences among
disability categories in terms of purchasing skill instruction effects.
When participants' preexisting money skills were examined,
differences among categories were statistically significant, [chi
square](2) = 6.49, p = .04. A post hoc Mann-Whitney test indicated a
statistically significant difference (p = .02) only for the first two
categories. Specifically, the treatment effect for participants with
money recognition skills (n = 9, PND = 94%) showed a large effect,
whereas that for participants with previous community experience only (n
= 10, PND = 85%) indicated a moderate effect.
Instructional Features. Moderate effects were found for the
different purchasing instructional strategies, and the differences
between modeling/verbal instruction (n = 9, PND = 85%) and faded prompt
strategies (n = 18, PND = 89%) were not statistically significant.
Further, when interventions involving time delay (n = 4, PND = 87%) were
separated from those involving a system of least prompts (n = 14, PND =
91%), the differences were not statistically significant. In contrast,
results for money skill adaptation (e.g., simplification, next-dollar
strategy, calculator use) indicated statistically significant
differences, [chi square](2) = 7.70, p [less than or equal to] .05.
Further, the post hoc Mann-Whitney test revealed a statistically
significant difference between simplification (n = 13, PND = 95%) that
indicated a large effect and next-dollar strategy (n = 9, PND = 85%)
only, p = .03, which was moderately effective.
It should be noted that results for the two studies (Gardill &
Browder, 1995; Marholin, O'Toole, Touchette, Berger, & Doyle,
1979) included in the "Other" category (median PND = 82%)
indicated a moderate effect. The study by Gardill and Browder taught
participants to discriminate among three stimulus classes (a vending
machine item, snack, and lunch) and pay the money accordingly (i.e., use
75 cents for a vending machine item, a $1 bill for a snack, and a $5
dollar bill for a lunch purchase). This was the only study (PND = 83%)
that taught stimulus discrimination as a strategy to bypass the required
money computation skills, which is different from the other money skill
adaptation categories (e.g., simplification, next-dollar). The study by
Marholin et al. also was included in the "Other" category,
because it did not report the strategies used to help with the money
payment part of the purchasing instruction (PND = 81%).
When instructional effectiveness across three different purchase
types (i.e., restaurant ordering, grocery/shopping center purchases, and
vending machine use/sole money payment instruction) was examined,
results indicated statistically significant differences among the three
categories, [chi square](2) = 6.20, p [less than or equal to] .05.
Further, the post hoc Mann-Whitney test indicated statistically
significant differences between grocery/shopping center purchasing (n =
13, PND = 94%) and vending machine use/money payment only (n = 8, PND =
83%), p = .04. Post hoc analysis also indicated that when restaurant
ordering and grocery/shopping center purchasing were combined, a
statistically significant difference was found between this combined
category and the vending machine use/sole money payment category, [chi
square](1) = 4.91, p = .03. No statistically significant differences
were found between restaurant ordering (n = 6, PND = 91%) and
grocery/shopping center purchasing. Both types of purchases were seen to
be highly effective.
Categorical comparisons indicated a statistically significant
difference for error correction procedures, [chi square](2)= 11.07, p =
.00. Further, post hoc analysis showed a statistically significant
difference between error correction involving verbal
instruction/modeling that demonstrated a moderate treatment effect (n =
10, PND = 84%) and physical guidance, which was highly effective (n =
15, PND = 92%), p = .04. Regarding intervention duration, even though
long treatments (i.e., more than 15 sessions, n = 15, PND = 90%) were
highly effective when compared to short treatments (i.e., 15 sessions or
fewer, n = 13, PND = 86%) that showed a moderate effect, the differences
between these two categories were not statistically significant.
However, analyses for instructional settings showed a statistically
significant difference between training conducted in simulated plus in
vivo settings (n = 11, PND = 94%) and those in simulated settings only
(n = 11, PND = 85 %), p = .03.
Generalization. A total of 18 studies that collected and graphed
generalization data resulted in 21 PND scores, with a moderate
generalization effect (PND = 86%; range = 0%-100%). Results indicated
that interventions that programmed for generalization (n = 10, PND =
95%) were highly effective when compared to those that did not program
for generalization (n = 11, PND = 83%), which revealed a moderate
effect. However, the difference between the two categories was not
statistically significant given the limited generalization database.
Maintenance. A total of 19 studies collected and graphed
maintenance data. Overall, results indicated high maintenance effects
(PND = 100%; range 67%-100%) for these studies. When maintenance effects
were analyzed in terms of the extent to which learned skills were
maintained, results indicated no statistically significant differences
between studies that conducted maintenance probes within 1 month after
the termination of the intervention (PND = 100%) and studies that
conducted probes beyond 1 month (PND = 100%).
HOW EFFECTIVE IS PURCHASING SKILL INSTRUCTION FOR INDIVIDUALS WITH
In general, results of this meta-analysis suggest that purchasing
skill instruction is moderately effective (PND = 87%; range = 59% to
100%) in teaching individuals with developmental disabilities to make
independent purchases. Based on the studies that provided maintenance
and generalization data, results indicated that participants were able
to maintain the learned skills (median PND = 100%) for at least 1 week
to a maximum of 5 months (e.g., Storey, Bates, & Hanson, 1984) and
generalize to new contexts (median PND = 86%).
IS INTERVENTION EFFECTIVENESS RELATED TO STUDENT CHARACTERISTICS?
Participants' grade levels and disability categories did not
have an influence on purchasing/functional math skills instruction.
However, it must be noted that we did not separate the category of
moderate disabilities from mild or severe disabilities. As such, the
first two categories of disabilities used in this meta-analysis were not
mutually exclusive, and this may possibly explain the statistically
nonsignificant results. In addition, the third category (i.e., autism)
included only three cases that may have contributed to the low
statistical power of finding differences.
In contrast, participants' relevant entry skills were related
to purchasing skill effectiveness. Specifically, those studies that
involved participants who were able to recognize and count coins or
dollar bills yielded greater treatment effects than those that involved
participants who had community experience only or lacked experience or
prerequisite skill knowledge. This finding suggests that money skills
may be a key component in the purchasing routine, because participants
who had these prerequisite skills fared better than those without them.
Although several purchasing skill interventions adopted some kind of a
modification (e.g., prepared money envelopes, money number line,
next-dollar strategy) to bypass money skills, participants with
prerequisite money skills responded better to purchasing instruction
than those without these skills. Our results are consistent with
recommendations from a previous review by Browder and Grasso (1999),
which not only indicated that providing students with opportunities to
practice money skills both in the community and classroom is important,
but also that students with prerequisite skills acquire purchasing
skills more efficiently.
WHICH TYPE OF INSTRUCTIONAL APPROACH IS MOST EFFECTIVE WITH REGARD
TO INDEPENDENT PURCHASING SKILL ACQUISITION BY INDIVIDUALS WITH
Results of our study do not support the findings in the literature
about the relative importance of prompting and fading strategies when
compared to other instructional procedures (e.g., Browder & Grasso,
1999; Morse et al., 1996). Both instructional strategies of
modeling/verbal instruction and the faded prompt procedure yielded
similar PND scores. It is important to note that both categories
included a variety of strategies. The first category (n = 9) included
not only preresponse strategies (e.g., modeling, verbal instruction,
role-playing, videotape presentation), but also postresponse strategies
(e.g., verbal feedback). Because of the limited number of PNDs in this
category, further analyses were not conducted. In contrast, the second
category included least-to-most prompting or most-to-least prompting
strategies as well as time delay.
Purchasing skills in the identified studies ranged from teaching
money skills only (e.g., cash register payment) to vending machine use,
restaurant ordering, and grocery/shopping center purchases. These skills
require quite different purchasing activities that involve a different
number of task steps. As such, it might be the case that different
strategies are beneficial for teaching different types of skill chains.
For example, whereas preresponse modeling might be appropriate for
shorter chained skills, the system of least prompts might be necessary
for skills that involve a long list of steps. Modeling and role play may
be critical for training in a simulated setting, but may not be
appropriate in a real setting. Therefore, it is important to analyze the
nature of the skill to be taught and choose an instructional strategy
that does not stigmatize individuals with disabilities. At the same
time, it is important to consider both the effectiveness and efficiency
of the strategy.
ARE TREATMENT OUTCOMES RELATED TO INSTRUCTIONAL FEATURES?
Results of this meta-analysis revealed that different types of
purchasing instruction yielded different treatment effects. In general,
grocery/ department store shopping and restaurant ordering instruction
yielded higher PND scores than those for vending machine use or money
payment instruction only. It should be noted that grocery/department
store shopping as well as restaurant ordering typically involved
numerous steps other than money payment. For example, the task analysis
steps for shopping in a grocery store may include as many as 32 steps
(e.g., walks to store entrance door, goes through the door, walks in the
store, ... exits store). In such cases, when the participant learned any
of these steps, the dependent measure (i.e., number of steps correct) in
the treatment phase would show improvement over the baseline. In other
words, the improvement in the dependent measure may not reflect money
skill learning, which is only one component among a long list of task
analysis steps in the entire purchasing routine.
Regarding money skill adaptation, results indicated that when
purchasing instructional strategies involved simplification strategies
(e.g., prepared money envelopes) to bypass money skills (e.g., Smeets,
1978), the treatment yielded higher PND scores than those that provided
less support for money skill instruction, such as the use of the
next-dollar strategy, which skips only the cents counting step. This
finding regarding the importance of money skill adaptation is supported
in the literature, which indicates that simplification strategies may
reduce the overall academic demands of money use (Browder & Grasso,
1999; Morse et al., 1996). However, with respect to calculator use, this
category failed to show any differentially statistically significant
treatment effects when compared to the other categories, despite the
large PND score of 91% for this category. This finding may be explained
by the low number of studies (n = 4) involving calculator use. It must
be noted that participants in these studies were taught to use the
calculator either to figure out the exact purchasing amount or to make
sure that the purchases did not go over the budget limit.
Money skills play a major role in the whole purchasing process or
are the sole focus in studies on vending machine use or payment skill
instruction only. In these studies, when the participant missed the
money transaction step, the PND score, which is the measure of the
treatment effect, was dramatically influenced. In fact, the PND score in
these studies is a more direct measure of money skill as compared to
studies that teach a considerable number of task steps other than money
skills in the purchasing process. In summary, the results suggest
relatively lower treatment effects when the task or training focused
exclusively on money skills. This finding indicates the need for
additional work in this area and supports previous research
recommendations about expanding instruction to include all skills
associated with money management (Browder & Grasso, 1999; Morse et
Results of this review also suggest that treatments that involved a
terminal level of error correction procedure (i.e., physical guidance)
yielded higher PND scores than those involving only verbal instruction
or modeling. Physical guidance to correct errors ensured opportunities
for learners to repeat the correct behavior and therefore facilitated
skill acquisition. Verbal instructions or modeling alone may not be
enough to shape appropriate purchasing behaviors. It is critical that
instructional planning carefully address the level of error correction
needed for the student to learn the appropriate response.
Instructional setting is another variable to consider when
providing purchasing skill training, especially with regard to cost
effectiveness and efficiency. Will students learn purchasing skills in a
simulated setting (e.g., classroom) or does the skill have to be trained
in the real setting? Results of this meta-analysis suggest that
combining simulated and in vivo training yielded better results. It may
be the case that certain prerequisite and critical skills (e.g.,
functional math skill to deal with money transaction) are better trained
in a simulated setting with a better control of the learning environment
than in a real setting. For example, conducting mass trials of a single
skill (e.g., money payment) may not be feasible in a real setting. As
such, it is important to balance instruction by providing opportunities
for learning in both the classroom and community. Beginning a lesson
with classroom money skill instruction may better prepare students for
the expectations of the natural setting.
Finally, the number of training sessions did not appear to be
related to purchasing skill instructional effects. A plausible
explanation for this finding is that purchasing interventions identified
in these studies varied to a large extent in terms of the complexity of
target skills taught. Purchase skills taught ranged from simple one-item
purchase with or without a bypass money skill adaptation (e.g.,
predetermined dollar amount) to more complex multiple item purchasing
with or without money skill adaptation. As such, sessions needed to
reach training criterion may vary dramatically as a function of the
WHAT IS THE EFFECT OF THE INSTRUCTIONAL APPROACH ON SKILL
Based on the results of 18 studies that reported generalization
data, a moderate generalization effect (PND = 86%) was found. Of the 18
studies, about half of the interventions (n = 10) programmed for
generalization yielded a large treatment effect (PND = 95%). This
finding indicated that participants readily generalized the learned
purchasing skills to novel settings, supporting previous research
recommendations of programming for generalization throughout instruction
(Browder & Grasso, 1999; Morse et al., 1996). However, the results
of the meta-analysis failed to show significantly different
generalization effects between interventions that programmed for
generalization and those that did not program for generalization. It
should be noted that interventions that programmed for generalization
varied in the studies reviewed. They included stimulus generalization,
in which training involved presenting various purchasing items'
price range and verbal statement of the price (n = 6, PND = 89%) and
setting generalization, in which training involved various sites where
the purchasing skill would be applicable (n = 4, PND = 98%). Although
interventions that programmed for generalization, especially those for
setting generalization, yielded a large treatment effect (PND = 98%) and
interventions that did not program for generalization produced a
moderate treatment effect (n = 11, PND = 83%), nonparametric analyses
failed to show statistical significance. It is plausible that the
limited number of cases in each subcategory may have masked treatment
effects. It must be noted that 5 of the 10 studies that did not provide
graphed data needed to calculate generalization PNDs noted partial skill
generalization (see Table 1). Interestingly, all five studies reported
successful applications of the stimulus generalization strategies, which
seem to add further to the importance of generalized instructional
WHAT IS THE EFFECT OF THE INSTRUCTIONAL APPROACH ON SKILL
MAINTENANCE OVER TIME?
About 61% of the studies (n = 19) reported maintenance data, and
findings indicated high maintenance effects (PND = 100%). In addition,
the results indicated that maintenance effects did not decrease with the
increase of elapsed time. Specifically, maintenance effects acquired
within a 1-month period were not significantly different from those
obtained beyond 1-month follow-up (up to a maximum of 5 months). Again,
this result should be interpreted with caution given the limited
Although results of the meta-analysis indicated that purchasing and
money skill instruction revealed moderate-to-high effects for students
with developmental disabilities, the present synthesis is limited in
several ways and should be interpreted cautiously. First, the PND
measure may not be sensitive in evaluating the magnitude of treatment
effects, because it only counts whether or not the treatment data points
overlap with the baseline data points. For a single data point, PND will
only consider it as either a hit or miss (i.e., overlap or not overlap)
rather than how much it hit or missed. In addition, the PND does not
address changes in trend from baseline to treatment performance.
Further, the PND measure can result in a ceiling effect, because the
largest possible treatment effect defined by PND is 100%. Therefore,
this technique might not have sufficient power to find all potential
differences when categorical comparisons are conducted. Second, because
of the limited database, only main effects of each variable (e.g.,
grade, purchasing instructional strategies) were analyzed for
categorical comparisons. Further within class analysis for possible
interactions among variables were not conducted because of the limited
number of cases.
In summary, the effects of purchasing skill instruction for
students with developmental disabilities are encouraging. On the basis
of this review, we draw some tentative conclusions about how to promote
purchasing skills for individuals with developmental disabilities and
offer some specific recommendations and directions for future study
based on the key findings of our review,
IMPLICATIONS FOR PRACTICE
Our analysis of the studies reviewed indicates that although
modeling/verbal instruction and prompting procedures are equally
effective in enhancing purchasing skill performance, a strong foundation
in functional mathematical skills (e.g., coin recognition, counting) is
required for enhancing competent performance by students with
developmental disabilities (Morse et al., 1996; Schloss, Kobza, &
Alper, 1997). This would require having the necessary prerequisite money
recognition skills to effectively respond to purchasing instruction.
Money skills appear to be a difficult part of purchasing routines for
students with developmental disabilities given the demands of basic
academic skills. Therefore, additional instruction in this area is
Second, it would be beneficial to teach or apply money skill
adaptations to bypass the money skill in purchasing routines when these
prerequisite skills are lacking. Our review suggests the contribution of
simplification strategies (e.g., prepared money envelopes) over the
next-dollar strategy on purchasing skill performance for students with
Third, our review suggests that tasks that involved relatively more
independent money handling (e.g., vending machine use) were seen to be
difficult for participants with disabilities, indicating the need for
additional work to identify effective ways to increase the magnitude of
purchasing skill effects for a range of purchasing tasks.
Fourth, there also appears to be a need for providing both
simulated and in vivo instruction. Simulated practice on purchasing
skill routine and prerequisites skills in the classroom prior to
instruction in the natural setting (e.g., community) may contribute to
both the effectiveness and efficiency of the intervention.
Fifth, our results suggest that physical guidance, as a corrective
feedback procedure, is relatively more effective than either verbal
instruction or modeling. This indicates the relevance of actual guidance
not only for reducing errors, but also for providing a coherent
illustration of how to complete the task.
RECOMMENDATIONS FOR FUTURE RESEARCH
Although the majority of the research on purchasing skills has been
conducted with secondary school students, relatively few studies
involved elementary and middle school students, indicating the need for
additional research with this population. Undoubtedly, money skill
acquisition for secondary students who are making the transition to the
real world is critical. In fact, it is an essential community living
goal and commonly included as one of the IEP transition goals for
students with developmental disabilities. However, the need for early
functional math skills (e.g., purchasing, money) instruction in the
elementary grades is necessary for increased functional competence in
Second, continued research is required to address the effects of
independent community functioning skill instruction for subgroups of stu
dents with developmental disabilities. Clearly defining the population
(mild, moderate, severe MR) is seen as critical to interpreting study
findings. Many of the studies in this review included a mixture of
disability categories. Therefore, further investigation of the effects
of purchasing skill instruction for subgroups of students with
disabilities, who differ in functional competence and verbal strengths,
Third, additional research is needed to systematically examine the
separate effects of various instructional procedures (e.g., modeling,
verbal instruction, role-playing, videotape presentation, verbal
feedback, least-to-most prompting, most-to-least prompting, time delay)
on purchasing skill performance. Fourth, continued research is required
to assess generalization and maintenance of the skills given the limited
database. The practice of teaching and assessing on an ongoing basis for
maintenance and generalization is important. Presenting opportunities
for students to apply the learned skills in new situations and contexts
is especially important for students with developmental disabilities.
Finally, a direction for future study relates to access to the
general educational curricula for students with moderate and severe
disabilities. Although the 1997 reauthorization of the Individuals with
Disabilities Education Act (IDEA, 1999) with regard to access to the
general curriculum for students with developmental disabilities has
generated some confusion, researchers in severe disabilities are
unequivocal about the need for continued focus on functional life skills
(community and money management skills) for these students (Browder et
al., 2003). Intensifying instruction on functional life skills (e.g.,
money management) that builds on basic academic skills, for example,
represents one means of accessing the general education curriculum.
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YAN PING XIN
Colonial Intermediate Unit 20
CAROLINE M. DIPIPI-HOY
Easton Area High School
YAN PING XIN (CEC Chapater #70), Assistant Professor of Special
Education, Purdue University, West Lafayette, Indiana. EDWARD GRASSO,
Supervisor of Special Education, Colonial Intermediate Unit 20, Easton,
Pennsylvania. CAROLINE M. DIPIPI-HOY (CEC Chapater #905), Easton Area
High School, Bethlehem, Pennsylvania. ASHA JITENDRA (CEC Chapater #905),
Professor of Special Education, Lehigh University, Bethlehem,
Send correspondence to Yan Ping Xin, Purdue University, Beering
Hall of Liberal Arts and Education, Department of Educational Studies,
100 North University Street, West Lafayette, IN 47907-2098 (e-mail:
Manuscript received October 2003; accepted January 2004.
Studies Included in the Purchasing Instruction Review
Participant Entry Skill; Skill
Author Description Objective
Aeschleman & 4 secondary Visited grocery
Schladenhauffen students with stores as part of
(1984) severe CBI plan(s);
disabilities; CA = purchase groceries
17-18; IQ = 27-35 for a brown bag
Alcantara 3 elementary Prior informal
(1994) students with training in grocery
moderate MR; shopping, but
CA = 8-9; IQ = shopping skills not
NA. yet acquired;
purchase a grocery
Browder, Snell, 4 elementary Able to match
& Wildonger school students coins; select coins
(1988) with moderate to for vending
severe MR; CA machine
= 9-12; IQ = 31-54 purchasing.
Colyer & 4 secondary Able to distinguish
Collins students with among one, five,
(1996) mild/moderate and ten-dollar bills
MR; CA = 12-15; and count to 15; use
IQ = 40-60. next-dollar strategy
to make payment
when presented with
Denny & Test 3 secondary With community
(1995) students with experience but no
mild/moderate dollar bill
MR; CA = 17; recognition skills;
IQ = 39-72. use next-dollar
strategy with one,
five, and ten-dollar
bills to make
Frank & 4 elementary NA; count coins
Wacker (1986) school students using a number
with mild MR; line to make
CA = 11-13; IQ = purchases.
Fredrick- 2 secondary Able to recognize
Dugan, Test, & students with and give correct
Vam (1991) moderate to amounts for all
severe MR; coins and paper
CA = 18-20; IQ denominations; use
= 36-40. a calculator to make
Gardill & 3 middle school Limited monetary or
Browder students with math skills, failed to
(1995) severe behavior learn next-dollar
disorders; CA = strategy;
12-13; IQ = 45-57. discriminate
between 3 stimulus
classes (a vending
snack, and lunch) to
Gaule, 3 secondary Able to name coins,
Nietupski, & students with their values, and
Certo (1985) moderate to count to 15; use an
severe MR; CA adaptive shopping
= 17-20; IQ = 33-36. aid to purchase
Haring, Breen, 6 middle school NA; acquire and
Weiner, students with generalize
Kennedy, & autism and independent
Bednersh severe MR; CA purchasing
(1995) = 10-16; IQ = responses.
Haring, 3 secondary NA; generalize
Kennedy, students with purchasing skills
Adams, & autism; CA = 20; across community
Pitts-Conway, IQ = NA. settings.
Marholin, 4 adults with NA; purchase an
O'Toole, moderate/severe item and pay for a
Touchette, MR; CA = 39-63; meal.
Berger, & IQ = 25-53.
Matson & 3 adults with Able to perform
Long (1986) mild/moderate self-help skills,
MR; CA = 32-53; count numbers to
IQ = 53-69. 100, count money
read food prices,
and read sight
words; use a
calculator to make
McDonnell 4 secondary students NA; purchase snack
(1987) with severe MR; CA food by handing
= 16-18; IQ = 10-34. cashier a dollar bill
for items worth less
than a dollar.
McDonnell & 6 middle school Able to identify #'s
Ferguson students with 0-9 and rote count
(1988) moderate and to 10; make
severe MR; mean generalized
CA = 12; IQ = 43-54. purchases at
McDonnell, 4 secondary Able to rote count
Homer, & students with from 1-10 and
Williams, moderate and recognize #'s from
(1984) severe MR; CA = 0-9; make
16-19; IQ = 36-50. generalized
McDonnell & 4 adults with NA; purchase two
Laughlin severe MR; CA = snack food items at
(1989) 26-43; a supermarket and a
IQ = 23-30. fast food restaurant.
Morse & 10 elementary NA; make grocery
Schuster students with purchases.
(2000) moderate MR; CA
= 6-12; IQ = 40-57.
Nietupski, 4 elementary Able to discriminate
Clancy, & students with and name coins,
Christiansen moderate MR; CA affix values, and
(1984) = 7-10; IQ = 44-51. label numbers to
100; use a picture-
prompt prosthetic to
Nietupski, 4 secondary Able to recognize
Welch, & students with coin names and
Wacker, moderate and values, count
(1983) severe MR; CA = pennies to 17, and
14-20; IQ = 32-57. name #'s 0-9; use a
pocket calculator to
Schlein, 1 secondary No number
Certo, & student with severe recognition skills;
Muccino, MR; CA = 16; pay for the bowling
(1984) IQ = 32. game, purchase a
drink and a snack
Schloss, 6 secondary school Recognize numbers
Kobza, & students with from 0-5 at a
Alper (1997) moderate to severe minimum; use peer
MR; CA =14-17; tutoring to teach the
IQ = 32-52. next-dollar strategy.
Smeets (1978) 3 adults with NA; pay exact
moderate and amounts of money
severe MR; CA = using a calculator.
20-29; IQ = 35-46.
Sprague, & 6 secondary NA; use prosthetic
Horner (1984) students with card to make
moderate and purchases from a
severe MR; CA = vending machine.
15-19; IQ = NA.
Storey, Bates, 6 adults with NA; purchase coffee
& Hanson severe MR; CA = by handing a dollar
(1984) 25-74; IQ = 10-59. bill to the cashier
and waiting for
Test, Howell, 2 adults (in Expt. Able to count
Burkhart, & 1) and 3 high consecutively to 20
Beroth (1993) school students (in with one-to-one
Expt. 2) with correspondence;
moderate and purchase a snack
severe MR; CA = using the one-more-
16-24; IQ = 31-46. than strategy.
Van den Pol, 3 secondary NA; purchase at a
Iwata, students with restaurant by
Ivancic, Page, moderate and mild rounding up the
Neef, & MR; CA = 17-20; meal cost to the
Whitley IQ = 46-75. nearest dollar.
Wissick, 3 secondary Participants
Lloyd, & students with shopped at grocery
Kinzie (1992) moderate to severe store as part of CBI
MR; CA = 12-17; plan; purchase
IQ = NA. snack items in
Adaptations, Study Design
Aids, Task & Procedural
Author Simplification Fidelity
Aeschleman & Picture prompt A multiple
Schladenhauffen for item probe across
(1984) selection and participants;
strategy. fidelity: No.
Alcantara Grocery item Multiple
(1994) photographs, baseline
dollar amount. settings;
Browder, Snell, Coin card for Multiple
& Wildonger matching. probe across
(1988) subject pairs;
Colyer & Next-dollar Multiple
Collins strategy. probe across
Denny & Test One-More-Than Multiple
(1995) technique baseline
with the across
Frank & Coin matching Multiple
Wacker (1986) cards and baseline
number line. across
Fredrick- Picture prompt Multiple
Dugan, Test, & money card probe across
Vam (1991) and pocket participants;
Gardill & Photos of Multiple
Browder money baseline
(1995) amounts and across
the purchase participants;
Gaule, Adaptive Modified
Nietupski, & shopping aid multiple
Certo (1985) with money probe across
line. skill cluster;
Haring, Breen, Multiple probe Provided with
Weiner, across settings; prespecified
Kennedy, & procedural amount of
Bednersh fidelity: No. money to
(1995) make a
Haring, One dollar Multiple
Kennedy, more payment baseline across
Adams, & strategy. participants;
(1987) fidelity: No
Marholin, NA Multiple
O'Toole, baseline across
Berger, & procedural
Doyle (1979) fidelity: No.
Matson & Pocket calculator Multiple
Long (1986) and paying an baseline
amount of money across
greater than settings;
McDonnell Shopping cards. Multielement,
McDonnell & Next-dollar Multiple-
Ferguson strategy. baseline
McDonnell, Next-dollar Multiple
Homer, & strategy, slides, probes across
Williams, and flashcards. participants;
McDonnell & Predetermined Multielement,
Laughlin dollar amount alternating
(1989) (two $1 bills). treatment
Morse & Predetermined Multiple
Schuster amount of probe across
(2000) money within participants;
envelope and procedural
pictorial fidelity: No.
Nietupski, Coin card. Multiple
Clancy, & probe across 3
(1984) machines and
Nietupski, Pocket Multiple
Welch, & calculator and probe across
Wacker, picture prompt participants;
(1983) money card for procedural
calculating fidelity: No.
Schlein, Picture card Multiple
Certo, & and baseline
Muccino, predetermined across skills;
(1984) money amount. procedural
Schloss, Next-dollar Multiple
Kobza, & strategy and baseline
Alper (1997) money cards. across subject
Smeets (1978) Pocket Multiple
Sprague, & Prosthetic card. Multiple-
Horner (1984) baseline
Storey, Bates, Provided with Multiple-
& Hanson $1 bill for probe across
(1984) payment. participants.;
Test, Howell, One-more-than Multiple
Burkhart, & strategy with baseline
Beroth (1993) the cents-pile across
modification. behaviors and
Van den Pol, Round up to Multiple
Iwata, next dollar, use baseline
Ivancic, Page, fingers to across
Neef, & determine the participants
Whitley money amount and skill
(1981) that should be components;
received, and procedural
matching fidelity: No.
Wissick, Photos and Multiple
Lloyd, & wrappers of baseline
Kinzie (1992) grocery items. across
Intervention Description; Acquisition
Length; Error Correction; Results:
Author Setting, PND
Aeschleman & Mnemonic training for 85%
Schladenhauffen making shopping list,
(1984) verbal instruction, & role
play; 13 sessions,
Alcantara Videotape viewing, on-site 99%
(1994) prompting, and
reinforcement; 16 sessions;
least to most prompts; 3
classroom, school meeting
room, and 3 community
sites--grocery store, drug
store, and convenience
Browder, Snell, Time delay, combined 86%
& Wildonger gesture, and verbal
(1988) direction; 11 sessions;
modeling; classroom and
public recreational site.
Colyer & System of least prompts and 73%
Collins instructive feedback; 22
(1996) sessions; modeling; school
classrooms or coach's
Denny & Test Verbal instruction & 84%
(1995) modeling, opportunities for
mixed practice; 27 sessions;
modeling; school library.
Frank & NA; 27 sessions; NA; 100%
Wacker (1986) classroom; no details
provided, just mentions
Fredrick- Progressive time delay, 88%
Dugan, Test, & general case strategy to
Vam (1991) sample the range of stimuli;
5 sessions; NA; school
library, department store.
Gardill & Time delay, multiple 83%
Browder exemplars of stimuli, &
(1995) stimulus prompt (money
picture); 29 sessions;
modeling; classroom, staff
lounge, school cafeteria.
Gaule, Least-to-most prompt 95%
Nietupski, & procedure; 14 sessions;
Certo (1985) verbal to physical guidance;
classroom and a
Haring, Breen, System of least prompts 97%
Weiner, during in vivo training;
Kennedy, & instructor modeling during
Bednersh videotape answer and
(1995) question sessions; 33
sessions; modeling; 7 stores
for each participant
Haring, Least-to-most prompting 77%
Kennedy, procedure, videotaped
Adams, & generalization training; 26
Pitts-Conway, sessions; verbal to partial
(1987) physical guidance;
classroom and one real
setting (school cafe or
convenience store); video
training occurred in school
library or home
Marholin, Graduated prompting, 81%
O'Toole, modeling, corrective
Touchette, feedback, reinforcement,
Berger, & behavioral rehearsal, and
Doyle (1979) time-outs; 11 sessions;
modeling; day program
workshop, bus, and
Matson & Verbal instruction, 94%
Long (1986) modeling, feedback, social
and tangible reinforcement,
participant modeling, and
classroom and a
community grocery store.
McDonnell Constant time delay or Time delay:
(1987) increasing prompt hierarchy 97%;
training; 17 sessions; Increasing
modeling; community fast - prompt
food restaurant and hierarchy:
convenience store. 94%
McDonnell & Next-dollar pretraining, GC in vivo:
Ferguson general case (GC) in vivo 100%
(1988) or GC simulation plus in GC simulated
vivo training; 6 sessions; plus in vivo:
modeling; classroom and 3 94%.
McDonnell, Classroom role playing Flash card:
Homer, & (RP) with flashcards of the 0%;
Williams, purchase amount, Slides: 40%;
(1984) classroom RP with slides of Slides plus in
cash registers showing vivo: 100%.
different amounts, and RP
with slides & in vivo
training; 9 sessions;
modeling & physical
guidance; classroom and a
McDonnell & Backward chain or Backward
Laughlin concurrent chain training, chain or
(1989) decreasing prompt concurrent
hierarchy; 24 sessions; chain
physical guidance; training: 99%.
and fast-food restaurant.
Morse & In vivo training using 82% (data
Schuster constant time delay and available for 8
(2000) simulation training with participants
pictorial story board; 12 who
sessions; modeling; completed
classroom and grocery study before
store. the end of the
Nietupski, Modeling, picture 72%
Clancy, & prosthetic card; 13
Christiansen sessions; modeling
(1984) followed by student
junior high school, and
community shopping mall.
Nietupski, Modeling the use of the 100%
Welch, & picture prompt money card
Wacker, and the subtraction
(1983) calculator procedure; 31
sessions; verbal to physical
guidance; school office.
Schlein, Verbal prompt and 86%
Certo, & feedback; 20 sessions;
Muccino, modeling to physical
(1984) guidance; community
Schloss, Least to most prompts, peer 92%
Kobza, & tutoring, general case
Alper (1997) instruction; 12 sessions;
Smeets (1978) Modeling & reinforcement; 75%
40 sessions; modeling; a
simulated special room.
Sprague, & Most to least prompt 87%
Horner (1984) system, single case vs.
multiple case vs. general
case instruction; 6 sessions;
modeling to physical
guidance; classroom, high
school hallway, community
recreation facility, hospital
lobby, laundromat, and a
public lunch room.
Storey, Bates, System of least-to-most 99%
& Hanson prompts with social
(1984) reinforcement; 11 sessions;
Test, Howell, Verbal instruction and 85%
Burkhart, & modeling; 12 sessions;
Beroth (1993) verbal & model prompts;
participants' homes and
Van den Pol, Simulated training using 86%
Iwata, modeling and role-playing
Ivancic, Page, with social reinforcement;
Neef, & 19 sessions; instructive
Whitley feedback and remedial
(1981) trials; classroom.
Wissick, Interactive videodisc 90%
Lloyd, & simulation, modeling, and
Kinzie (1992) verbal prompts, least
prompts strategy; 16
sessions; verbal to physical
guidance; high school
Author PND PND
Aeschleman & Post-training Majority of the
Schladenhauffen scores were skill components
(1984) maintained for 3 of showed
the 4 participants generalization to
for at least 5 two new
months: 100%. environments:
Alcantara All participants After training in 2
(1994) maintained skills 2 stores, all students
weeks post- increased their
training: 100%. level of
performance in the
3rd store during
was not assessed.
Browder, Snell, Maintenance Generalized skills
& Wildonger probes taken 2-3 to untrained sites:
(1988) weeks later were 78%.
available for 2 of 4
Colyer & 2 of the 4 2 out of the 4
Collins participants participants
(1996) maintained skill generalized skills
for up to 4 probe to the community:
sessions: 75%. 50%.
Denny & Test All three students 2 out of 3 students
(1995) maintained taught improved their
skill for 10 weeks: purchasing skills
100%. in one community
site: Data not
Frank & Maintained skills Generalized skills
Wacker (1986) over a 4-week to the school
interval: 91%. store: 94%.
Fredrick- Both participants Purchasing
Dugan, Test, & maintained newly behaviors
Vam (1991) acquired skills generalized to 2
over a 4-week untrained
period: 100%. community sites:
Gardill & NA 2 of the 3
(1995) generalized to
the third showed
Linear graph data
Gaule, Newly acquired NA
Nietupski, & skills were
Certo (1985) partially
maintained over a
Haring, Breen, A majority of Generalized to
Weiner, participants novel stores:
Kennedy, & maintained skills 3 86%
Bednersh weeks later: 100%.
Haring, Participants Generalized to 3
Kennedy, independently community
Adams, & purchased items stores before
Pitts-Conway, for a majority of video training of
(1987) the probes at 1 these stores:
week and 2 weeks 17%; After video
after training: training: 100%.
Marholin, NA Generalized
Touchette, purchasing skills
Berger, & to untrained
Doyle (1979) restaurant: 88%.
Matson & Gains by all Skills generalized
Long (1986) participants to an untrained
maintained at a store: 100%.
McDonnell NA NA
McDonnell & NA Both strategies
McDonnell, NA Generalized
Homer, & performance in
Williams, 5 untrained
(1984) grocery stores:
Flash card: 0%;
Slides plus in
McDonnell & Maintenance data NA
Laughlin available for 3 of
(1989) the 4 participants
Morse & 6 participants who 6 participants
Schuster reached criterion improved their
(2000) maintained skills performance in a
for up to 6 weeks: similar store
100%. with one session
Nietupski, Skill maintenance Partially
Clancy, & occurred for 3 of generalized to
Christiansen the 4 participants untrained
(1984) up to 6 weeks: vending
100%. machines: Data
Nietupski, Maintenance data Training in
Welch, & were available for school
Wacker, 3 of 4 generalized to
(1983) participants: supermarket for
100%. all participants:
Schlein, NA Generalized to
Certo, & similar
Schloss, NA 5 out of 6
Kobza, & students made
Alper (1997) purchases in
Smeets (1978) NA NA
Sprague, & 18 months after Single case:
Horner (1984) study, 5 of the 6 67%
students were still Multiple case:
carrying a 50%
prosthetic card General case:
and regularly 95%.
using quarters to
Data not graphed.
Storey, Bates, All participants Generalization
& Hanson maintained skills was assessed
(1984) at both a 2-month across two
and a 5-month similar sites and
follow-up one dissimilar
assessment: site: 83%.
Test, Howell, All 3 students in All 3 students in
Burkhart, & Expt. 2 Expt. 2
Beroth (1993) maintained skills successfully
11 weeks later: purchased a
100%. snack in a food
court: Data not
Van den Pol, Newly acquired All participants
Iwata, skills were generalized skill
Ivancic, Page, maintained 1 year to community
Neef, & later: 100%. restaurant (e.g.,
(1981) Burger King):
Wissick, Participants Participants
Lloyd, & maintained skills made purchases
Kinzie (1992) for 5 weeks: 67%. at a local
Note. CA = chronological age in years; CBI = community-based
instruction; Expt. = experiment; IQ = intelligence quotient;
MR = mental retardation; NA = not available.
Summary of Purchasing/Functional Mathematics Intervention Effects
by Study Features
Study Feature n PND Range
Elementary & middle 8 92 72-100
Secondary 14 87 59-100
Postsecondary 6 90 75-99
Mild and moderate 8 86 72-100
Moderate and severe 17 88 59-100
Other (e.g., Autism) 3 83 77-97
Entry Skills *
Money recognition 9 94 73-100
Community experience 10 85 59-99
None reported 9 87 77-100
Purchasing Instructional Features
Purchasing Skill Instructional Strategy
Modeling/verbal instruction 9 85 72-100
Faded prompt procedure 18 89 59-99
Not reported 1 100 NA
Money Skill Adaptation *
Simplification 13 95 72-100
Next-dollar strategy 9 85 59-97
Calculator use 4 91 75-100
Other 2 82 81-83
Type of Purchase *
Restaurant 6 91 81-99
Grocery/dept store 13 94 59-100
Vending machine/$ skill only 8 83 72-92
Error Correction **
Verbal instruction/modeling 10 84 72-99
Physical guidance 15 92 59-100
Not reported 3 94 88-100
Length of Treatment
Short 13 86 59-99
Long 15 90 73-100
Instructional Setting *
Simulated 11 85 0-100
In vivo 9 87 72-100
Simulated + In vivo 11 94 75-100
Programmed for generalization 10 95 40-100
Not programmed for generalization 11 83 0-100
Probes taken within 1 month 9 100 75-100
Probes taken beyond 1 month 10 100 67-100
Note. n = number of PND scores; PND = percentage of nonoverlapping
data points; (a) = only 21 interventions reported generalization
data; (b) = only 19 interventions reported maintenance data.
* p < .05; ** p < .01.