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1. EDUCATION AND TREATMENT OF CHILDREN Vol. 37, No. 3, 2014
Pages 371–391
An Investigation of the Look-Ask-Pick
Mnemonic to Improve Fraction Skills
Gregory E. Everet
Jennifer D. Harsy
Stephen D. A. Hupp
Jeremy D. Jewell
Southern Illinois University Edwardsville
Abstract
The current study evaluated the efects of the Look-Ask-Pick (LAP) mnemon-
ic on the addition and subtraction of fraction skills of 3 general education
sixth graders. Following identiication of fraction skill deicits, participants
were taught to add and subtract fractions with like denominators, unlike de-
nominators where one divides evenly into the other, and unlike denominators
where one does not divide evenly into the other. Using a concurrent multiple
baseline across participants design, results indicated increases in both percent
problems correct and digits correct per minute for all participants during the
LAP intervention. Gains were also sustained at 3-week maintenance. Results
are discussed in terms of extending previous LAP mnemonic usage.
Keywords: Fractions, Mnemonics, Mathematics, General Education Students
As the Individuals with Disabilities Education Improvement Act of
2004 (IDEA, 2004) places emphasis on the assessment of student
response to research-based interventions, school-based professionals
are increasingly tasked with identifying empirically based techniques
for varied academic skill deicits, including mathematics. Although
the general pace of math research has increased recently, most studies
target basic computation abilities of elementary-aged children (Mac-
cini, Mulcahy, & Wilson, 2007), with less empirical atention paid to
higher-level, conceptual skills such as fractions. According to the Na-
tional Mathematics Advisory Panel (NMAP, 2008), half of all middle
school and high school students struggle with fraction knowledge
taught in elementary grades, with at least 40% of middle school stu-
dents lacking a foundational understanding of fraction-related con-
cepts. Based on such high levels of fraction-speciic diiculty, the
identiication of efective instruction procedures designed to improve
fraction skills of at-risk students is important.
Address correspondence to Gregory E. Everet, Ph.D. Southern Illinois University Ed-
wardsville, Department of Psychology, Alumni Hall, Box 1121, Edwardsville, IL 62026-
1121; phone: (618) 650-3284; fax: (618) 650-5087; e-mail: geveret@siue.edu

2. 372 EVERETT et al.
Fractions are foundational for a variety of higher-level math con-
cepts including probabilities, proportions, ratios, and algebra (Brown
& Quinn, 2007; Butler, Miller, Crehan, Babbit, & Pierce, 2003). Fre-
quently viewed as some of the most challenging topics taught in
school with competence often not gained until high school (Siegler
et al., 2012), fractions are considered by the NMAP (2008) as neces-
sary prerequisites for workforce participation. Given their importance
in both academic and real-world situations, it is not surprising that
fractions have received extensive coverage in the recent Common
Core State Standards in Mathematics (National Governors Associa-
tion Center for Best Practices & Council of Chief State School Oicers,
2010). According to the Common Core, an understanding of fractions
as numbers should begin in grade 3, with students being proicient in
adding and subtracting fractions with like denominators in grade 4,
unlike denominators in grade 5, followed by multiplication and divi-
sion of fractions in grade 6.
Although understanding fractions is of foundational impor-
tance for continued success in mathematics (NMAP, 2008), relatively
few studies have directly investigated techniques to improve fraction
performance (Maccini et al., 2007; Templeton, Neel, & Blood, 2008)
and surprisingly few interventions exist for students struggling with
these concepts. As an example, in a recent review of fraction-specif-
ic research, Misquita (2011) located only 10 studies published from
1990 to 2008, with eight of these being group design studies and only
two employing single-case design methodology. Such low numbers
indicate a lack of relevant fraction research; additionally, eight of the
published studies were conducted with students who had an iden-
tiied academic or emotional/behavioral disability rather than those
without a disability in general education. Although the importance
of targeting those with a disability label (e.g., learning disability, in-
tellectual disability, emotional disability) is clear, fraction-speciic
research should also target general education students who are cur-
rently struggling and at risk for future math diiculties in an atempt
to remediate current concerns and to prevent future diiculty.
Methodologically, past intervention research has targeted frac-
tion skills through varied means including (a) manipulatives and/or
pictures (Butler et al., 2003), (b) anchoring instruction to real-world
problems (Botge, Heinrichs, Mehta, & Hung, 2002), (c) employing di-
rect instruction techniques (Scarlato & Burr, 2002), and (d) strategy-
based instruction facilitated via cue cards (Joseph & Hunter, 2001)
or a mnemonic (Test & Ellis, 2005). Mnemonic strategies, deined as
devices or techniques to strengthen memory (Scruggs & Mastropieri,
2000), are a beneicial means of strategy instruction though which

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LOOK-ASK-PICK MNEMONIC
students encode and recall factual information in an atempt to im-
prove classroom performance (Mastropieri & Scruggs, 1998). As stu-
dents with disabilities face increased academic diiculties and are
more likely to require specially designed instruction, past mnemonic
interventions have largely targeted this population (Wolgemuth,
Cobb, & Alwell, 2008) rather than those in general education and at
risk for further diiculty. Much like previous mathematics research
in general, mnemonic-speciic interventions have largely addressed
computation-speciic skills including addition and subtraction
(Manalo, Bunnell, & Stillman, 2000), multiplication (Greene, 1999;
Zisimopoulos, 2010), and division (Cade & Gunter 2002). Although
the application of mnemonics to students with an identiied disabil-
ity makes sense, there is no empirical reason why such instructional
practices could not also beneit at-risk students currently struggling
with the recall of factual information (e.g., addition and subtraction
of fractions).
Regarding fraction-speciic mnemonic usage, Test and Ellis
(2005) provide the only example in which fraction skills were ad-
dressed via a mnemonic technique. Speciically, Test and Ellis em-
ployed a irst-leter mnemonic, LAP, for solving addition and sub-
traction of fractions: (a) “Look at the sign and denominator, (b) Ask
yourself the question, ‘Will the smallest denominator divide into the
largest denominator an even number of times?’ and (c) Pick your frac-
tion type” (p. 4). Intervention was conducted with 6 middle-school
students who were classiied as either intellectually disabled or learn-
ing disabled. LAP instruction involved modeling and practice of the
strategy, with student pairs using lash cards and games to practice
both the mnemonic terminology and its usage to solve three difering
types of addition and subtraction of fraction problems. Type 1 prob-
lems were those with like denominators. Type 2 problems had unlike
denominators where one divides evenly into the other. Type 3 prob-
lems had unlike denominators where one does not divide evenly into
the other. Results indicated improvements for ive of the six students
in knowledge of the LAP mnemonic and percentage of problems
solved correctly; however, the study did not include luency-based
outcome metrics (Axtell, McCallum, Bell, & Poncy, 2009; Poncy, Skin-
ner, & Axtell, 2010) or target general education students at risk for
further mathematics diiculty. As suggested, mnemonic-based strate-
gies may aid in the recall of factual information, including the steps
required to solve addition and subtraction of fractions for students
with an identiied disability. However, because students in general
education also struggle with factual recall, the identiication of inter-
ventions to target such at-risk students is important.

4. 374 EVERETT et al.
As such, the current study was designed to add to the fraction-
based mathematics intervention literature by extending the work of
Test and Ellis (2005) in targeting addition and subtraction of fractions
through use of the LAP mnemonic. The purpose of the current study
was to investigate the efects of the LAP mnemonic on percentage
problems correct and digits correct per minute of three students in
general education at risk for further math diiculty. It is through the
preventative targeting of general education students and the collec-
tion of digits correct per minute that the current work extends and
updates the original Test and Ellis LAP investigation. Such changes
are important so as to investigate the utility of a previously efective
intervention with a difering group of participants and collecting out-
come data widely recognized in math intervention research.
Method
Participant Selection and Screening Procedures
In order to target fraction skills, a two-stage screening process
was employed to identify students who were luent with grade level
mathematics, but who had diiculty with addition and subtraction of
fractions.
First, participants had to obtain a median score at or above
the Instructional level across three sixth grade multi-skill AIMSweb
Mathematics Computation probes (Shinn, 2004), which allow for cur-
riculum-based measurement of mathematics by assessing luency in
addition, subtraction, multiplication, and division. Curriculum-based
measurement of mathematics has been found to be a reliable (e.g.,
both internal consistency and test-retest coeicients above .80) and
valid (e.g., median criterion-related coeicients ranging from .74 to
.83) measure of basic computation skills (Christ, Scullin, Tolbize, &
Jiban, 2008). Here, the sixth grade AIMSweb Mathematics Compu-
tation probes used were normed on more than 32,000 sixth graders
(Pearson Inc., 2008). This irst screening step was important so as to
identify participants who were not currently experiencing diiculty
with basic math luency skills.
Second, participants had to obtain a median score below Instruc-
tional placement across three experimenter-generated probes contain-
ing only addition and subtraction of fractions. These probes were cre-
ated using the Superkids Math Worksheet Creator website (Superkids
Math Worksheet Creator, n.d.). For screening, the fraction-speciic
worksheet consisted of 18 problems, with three addition and three
subtraction problems for each of the three fraction types. Like Test
and Ellis (2005), the three fraction types were (a) like denominators

5. 375
LOOK-ASK-PICK MNEMONIC
(Type 1 fractions), (b) unlike denominators where one divides evenly
into the other (Type 2 fractions), and (c) unlike denominators where
one does not divide evenly into the other (Type 3 fractions). This sec-
ond screening step was important so as to identify participants who
were currently experiencing diiculty with addition and subtraction
of fractions.
In order to provide for uniform decision making across both
screening steps, classiication determinations were based on the recent
work of Burns and colleagues (i.e., Burns, Codding, Boice, & Lukito,
2010; Burns, VanDerHeyden, & Jiban, 2006) who classiied sixth grade
Instructional placement as scores of 24–49 digits correct per minute
(DCPM). This is in line with, although somewhat more stringent, than
the widely used Instructional placement outlined by Deno and Mirkin
(1977) and Shapiro (2004). Screening proceeded in this way because
there are no uniform normative scores applicable to both multi-skill
AIMSweb probes and the experimenter-generated probes. More spe-
ciically, although normative scores are available for AIMSweb probes
(i.e., 20 DCPM is the cutof for Instructional placement), they are not
available for or applicable to the experimenter-created probes. In or-
der to make fraction-speciic screening decisions, the current two-
stage screening process employed empirically derived sixth grade
norms applicable to a wider variety of mathematics probes.
Participants and Seting
Three 11-year-old general education sixth-grade students met
the screening criteria and participated in the study. All were irst
referred by their mathematics teachers for services related to skill
deicits in the addition and subtraction of fractions and then were
screened according to the two-stage screening process. Participants
were Melinda and Danielle, Caucasian females, and Jason, a Cauca-
sian male. Individual screening results were: (a) Melinda—64 DCPM
on AIMSweb probes, 7 DCPM on fraction probes, (b) Danielle—42
DCPM on AIMSweb probes, 2 DCPM on fraction probes, and (c) Ja-
son—50 DCPM on AIMSweb probes, 7 DCPM on fraction probes. All
participants, who had no educational classiication/diagnoses or med-
ical problems at the time of the study, atended the same rural, public
elementary school in the Midwest, with approximately 500 students
in grades K–6 and approximately 98% Caucasian student population.
All sessions were conducted by the second author, a master’s level
school psychology intern completing requirements for the Specialist
in School Psychology (i.e., S.S.P.) degree, in an unoccupied classroom
free from distraction.

6. 376 EVERETT et al.
Materials
Materials used during the LAP intervention included LAP
mnemonic lashcards and a quiz as well as 7-problem and 18-prob-
lem fraction-speciic worksheets. The LAP Mnemonic lashcards and
quiz were designed to allow the participants practice with the tech-
nique and judge mnemonic knowledge prior to practicing with the
intervention worksheets. The 7-problem fraction-speciic worksheets
contained at least one addition and one subtraction problem of each
fraction type and were used during each intervention session to allow
participants practice solving problems while verbally explaining to
the interventionist their application of the LAP strategy. The 18-prob-
lem worksheets used during all intervention and probes sessions con-
sisted of three addition and three subtraction problems for each of the
three fraction types. During intervention sessions, they were used to
allow for independent participant practice absent verbal explanation
of their application of the LAP strategy. During probes sessions, the
18-problem worksheets were used to collect outcome data to judge
LAP intervention efectiveness. All fraction-speciic worksheets were
created using the Superkids Math Worksheet Creator website and in-
cluded single-digit by single-digit addition and subtraction of fraction
problems randomized with diferent numerals so as to provide a wide
variety of fraction practice.
Dependent Measures
In order to determine intervention efects, two dependent mea-
sures were assessed approximately twice weekly, including percent-
age of problems correct (PPC) and DCPM. PPC was calculated for all
baseline, LAP fraction instruction, and maintenance sessions using the
18-problem fraction worksheets by dividing the number of fraction
problems completed correctly by the number of problems atempted
and multiplying by 100 to obtain a percentage. Only those problems
that contained both a numerator and denominator were counted as an
atempted problem.
The second dependent measure, DCPM, was computed by di-
viding the number of digits correct by the number of seconds alloted
for each probe and multiplying by 60. DCPM was calculated during
all baseline, LAP fraction instruction, and maintenance sessions as a
luency measure on those 18-problem fraction-speciic probes created
from the Superkids website.
During all data collection sessions, only the interventionist and a
participant were present in a one-on-one interaction. Each participant
was given 3 min to complete the 18-problem fraction-speciic work-
sheet.

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LOOK-ASK-PICK MNEMONIC
Research Design
The efects of the LAP fraction intervention on both PPC and
DCPM were evaluated using a concurrent multiple baseline across
participants design (Hayes, Barlow, & Nelson-Gray, 1999). Follow-
ing screening, the sequence of conditions for each participant was (a)
baseline, (b) LAP fraction intervention, and (c) 3-week maintenance.
Data analysis included visually analyzing data for both PPC and
DCPM across all participants in addition to calculating means and
standard deviations for both dependent measures.
Decisions to start the intervention phase for a participant were
based on (a) the individual participant’s baseline level for both PPC
and DCPM data rather than placing more importance on one depen-
dent measure over another or meeting a numerical (i.e., mastery) cri-
terion, and (b) evidence of intervention efectiveness for participants
already in intervention. For example, when considering Melinda’s
PPC and DCPM intervention data together, Danielle was moved to
intervention even though Melinda’s intervention data were on the
decline. As Melinda’s PPC data were well above her baseline data
(which was stable at 0 across all three sessions) indicating a treatment
efect, Danielle was moved to intervention. This phase change is a de-
parture from many multiple baseline methodologies in that one might
not have begun intervention with Danielle while Melinda’s irst three
intervention data points displayed a decreasing trend. However, be-
cause Danielle displayed 0 PPC correct during all baseline sessions
and Melinda obtained at least 50% PPC during the irst 3 interven-
tion sessions, it was determined that Melinda experienced positive
intervention efects, thus bringing Danielle into intervention. A simi-
lar decision was made regarding moving Jason to intervention when
Danielle’s DCPM data, although displaying an upward trend, had not
yet stabilized above baseline. In this case, similar to Melinda’s data, as
Danielle’s PPC data were well above baseline it was decided to move
Jason to intervention.
Experimental Condition and Procedures
Baseline. Baseline was conducted to establish each participant’s
current skill level regarding addition and subtraction of fractions (i.e.,
using the 18-problem fraction worksheets) prior to LAP intervention
implementation. In addition, all participants continued to receive
their regular math class instruction, which was based on Prentice
Hall Mathematics: Course 2 (Charles, Illingworth, Reeves, Mills, &
Branch-Boyd, 2008), a curriculum that includes numerous fraction-
based concepts including simpliication, mixed numbers, and various
operations. Speciically, participants continued to receive all other

8. 378 EVERETT et al.
math-related content during daily math lessons, including teacher
lectures and both large and small group instruction, as part of their
general education curriculum with classroom topical coverage focus-
ing on grade level concepts including ratios and percentages, with no
coverage of mnemonics.
LAP fraction intervention. Through the use of the LAP mnemonic
“(a) Look at the sign and denominator; (b) Ask yourself the question,
‘Will the smallest denominator divide into the largest denominator an
even number of times?’; and (c) Pick your fraction type” (Test & Ellis,
2005, p. 4), participants were taught to solve the three types of addi-
tion and subtraction of fraction problems outlined above. For all ses-
sions, intervention included teaching steps designed to instruct in the
appropriate usage of the LAP mnemonic (i.e., lash card review and
LAP quiz) and use of the mnemonic to solve addition and subtrac-
tion of fraction problems (i.e., practice on 7-problem and 18-problem
worksheets). Time required to complete all intervention components
totaled approximately 30 min per session with approximately (a) 10
min devoted to lash card review and LAP quiz, (b) 10 min devoted
to student practice on the 7-problem worksheet, (b) 5 min practice on
the 18-problem worksheet, and (d) 3 min for LAP fraction instruction
outcome data collection.
LAP mnemonic instruction. Mnemonic skill building was facili-
tated at the beginning of each intervention session through lash card
review and quiz completion. Each intervention session began with
participants individually reviewing lash cards (while supervised by
the interventionist) containing the problem-solving steps outlined by
the LAP mnemonic. Flash cards were printed so that one leter (i.e.,
L, A, or P) of the procedure appeared on one side of the card, with
the corresponding action associated with the leter appearing on the
other. Review included having participants read the lash cards orally
while the interventionist ofered verbal guidance on each component
of the mnemonic.
Following lash card review, participants then completed a
7-question LAP quiz that asked questions about the mnemonic and
its use. Speciic questions included: (a) three asking what each leter
of the mnemonic stood for and suggested (e.g., “What does L stand
for and suggest you do?”; with similar questions for the leters A and
P); (b) one asking for participants to identify the denominator of an
example fraction, as the denominator is important in both the L and
A steps of the procedure (e.g., “What is the denominator for 7/9?”);
and (c) three asking speciic fraction type in an example fraction (e.g.,
“What fraction type is 1/6 + 1/2?” with similar questions for each of
the other two fraction types). There was no speciic mastery criterion

9. 379
LOOK-ASK-PICK MNEMONIC
required for quiz completion and the questions remained in the same
order from session to session. Following quiz completion, the inter-
ventionist provided brief verbal feedback to participants regarding
their performance. Flash card review and quiz completion were de-
signed to instruct participants in the meaning and usage of the LAP
procedures prior to actual problem solving.
Fraction problem solving. Following completion of the LAP quiz,
participants then completed a 7-problem practice worksheet that
contained at least one addition and one subtraction problem of each
fraction type. During worksheet completion, participants were re-
quired to verbally explain to the interventionist the steps of the LAP
technique while solving each individual problem. In order to ensure
participants practiced correct problem completion, when errors were
made the interventionist completed the problem while explaining
each step and the appropriate LAP application. The participant then
reatempted the missed problem until it was solved correctly.
For example, to complete the problem 1/6 + 1/2 (a Type 2 prob-
lem), participants’ explanation similar to the following was required.
“L: I look at the sign and denominator and know the fraction is an
addition problem with unlike denominators. A: I ask myself the ques-
tion, ‘Will the smallest denominator divide into the largest denomina-
tor an even number of times?’ Yes, 2 will divide into 6 an even number
of times. P: So, I pick a Type 2 fraction.” In addition to describing the
mnemonic, participants also described the steps required to solve the
problem. As this example refers to a Type 2 addition problem, the cor-
rect explanation included something similar to the following. “I know
that 2 is smaller than 6, so I’m going to keep the 6 on the botom. I
know that 2 can go into 6 three times, so I multiply the 2 by 3 and get
another 6 on the botom. Now, I multiply the 1 on top by 3 to get a new
fraction (i.e., 3/6). Now I add the top numbers (i.e., 1 + 3) to get the top
of the answer and I keep the 6 on the botom.” In numerical notation,
the solution for this as described is: 1/6 + 1/2 = 1/6 + (1/2 x 3/3) = 1/6 +
3/6 = 4/6. Although only one example solution is included for illustra-
tion purposes, all problems on the 7-problem worksheet were solved
in this manner. This illustrative statement also serves as an example of
the manner in which the interventionist taught correct fraction prob-
lem solving and/or modeled problem solution during error correction
procedures. Any mistakes related to either verbal explanation of the
LAP mnemonic or its use to arrive at the correct problem solution re-
sulted in immediate error correction and appropriate modeling of this
type by the interventionist.
During the irst intervention session, interventionist modeling
(using verbal explanations of the type provided above) preceded

10. 380 EVERETT et al.
student atempts so as to teach correct problem-solving techniques
for addition and subtraction problems of all three types. For all
other intervention sessions, this sequence was reversed with the
participant solving the 7-problem worksheet immediately follow-
ing LAP quiz completion with the interventionist modeling correct
mnemonic usage and problem solving only when the participant
made an error.
Following completion of the 7-problem practice worksheet, in-
dependent participant practice occurred on a separate 18-problem in-
tervention worksheet that contained three addition and three subtrac-
tion problems of each type. Participants completed fraction problems
absent the verbal explanation of their solutions required on the 7-prob-
lem variation. Rather, participants worked silently with intervention-
ist’s feedback and modeling occurring only when participants asked
for it or when an error occurred. No other feedback was provided,
including interventionist’s explanation of problems that participants
left blank and did not atempt to answer. Due to time constraints, par-
ticipants were given 5 min to work on the 18-problem worksheet. By
including interventionist’s feedback for both the 7-problem practice
worksheet and 18-problem intervention worksheet, ample opportu-
nity for correct problem solving was provided.
Probes. Following the completion of each intervention session,
participants were alloted 3 min to independently complete a separate
18-problem fraction worksheet absent any LAP modeling/error cor-
rection procedures.
Maintenance
For each participant, 3 weeks following the discontinuation of
the LAP intervention, data were collected to assess maintenance. Data
collection involved the administration of 18-problem fraction probes
(just as during baseline and LAP fraction instruction) absent the LAP
intervention. Participants were given 3 min for fraction probe comple-
tion.
Procedural Integrity and Interrater Agreement
To ensure procedural integrity, each intervention session was
implemented according to a 7-step protocol outlining required proce-
dures including steps related to LAP mnemonic instruction, fraction
problem solving (including modeling and error correction), and LAP
fraction instruction as described above. Each component of the LAP
intervention was listed on a checklist and checked of immediately by
the interventionist after implementation during all intervention ses-
sions. For all sessions, procedural integrity was assessed at 100%.

11. 381
LOOK-ASK-PICK MNEMONIC
Figure 1. Percent Problems Correct (PPC) for all participants across conditions.
0 2 4 6 8 10 12 14 16 18 20 22 24 26
SESSIONS
PERCENT
PROBLEMS
CORRECT BL LAP 3 Week Maintenance
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Melinda
Danielle
Jason

12. 382 EVERETT et al.
Figure 2. Digits Correct per Minute (DCPM) for all participants across condi-
tions.
0
4
8
12
16
20
24
28
32
36 BL LAP
0
4
8
12
16
20
24
28
32
36
0
4
8
12
16
20
24
28
32
36
0 2 4 6 8 10 12 14 16 18 20 22 24 26
SESSIONS
DIGITS
CORRECT
PER
MINUTE
Melinda
Danielle
Jason

13. 383
LOOK-ASK-PICK MNEMONIC
In addition, interrater agreement was calculated on 33% of all
fraction-speciic outcome worksheets across the experimental condi-
tions by having a second rater trained in scoring curriculum-based
measures independently score the probes to assess both PPC and
DCPM. Interrater agreement for both PPC and DCPM was calculated
by dividing the total number of agreements by the total number of
agreements plus disagreements and multiplying by 100 to obtain a
percent. Interrater agreement averaged 99% (range 98%–100%) for
both dependent measures.
Results
Figure 1 illustrates PPC for all three participants across the ex-
perimental conditions. As is evident, changes in level were observed
immediately following condition changes for all participants. During
baseline, both Melinda and Danielle did not correctly complete any
addition or subtraction of fractions problems, but both evidenced im-
provement in PPC following LAP intervention implementation. Simi-
larly, during baseline, Jason completed no more than 17% of fraction
problems correctly with changes seen following LAP introduction.
During intervention, all participants evidenced sessions during which
they correctly completed 100% of the fraction problems atempted,
Table 1
Descriptive Statistics for Percent Problems Correct (PPC) and
Digits Correct Per Minute (DCPM)
PPC DCPM
Participant M SD M SD
Melinda
Baseline 0 0 7.7 1.2
Intervention 85.2 18.3 16.2 6.5
Maintenance 100 0 24.7 3.1
Danielle
Baseline 0 0 4.3 2.1
Intervention 95.2 10.2 10.8 4.0
Maintenance 100 0 14.7 0.6
Jason
Baseline 2.8 6 5.2 2
Intervention 82.8 10.5 15.9 4.1
Maintenance 89.7 9.1 18 0

14. 384 EVERETT et al.
with no intervention data point falling lower than 50% PPC (i.e., Me-
linda’s second and third LAP data points). During maintenance, all
participants maintained or increased their PPC gains observed during
the LAP condition. Further, both trend and variability metrics support
intervention efectiveness in that for all participants, skill acquisition
was noted through trends that increased and/or stabilized well above
baseline levels (with the exception of slight decreases during the con-
clusion of the LAP condition) with only moderate variability.
Figure 2 illustrates DCPM for all three participants across the
experimental conditions. During baseline, data for all participants
were relatively stable with no individual data point higher than 9
DCPM (i.e., Melinda’s irst baseline point). Such data clearly indicate
substantial luency problems with addition and subtraction of frac-
tions. Following LAP implementation, although immediate changes
in level of DCPM were not as substantial as they were for PPC, data
for all participants showed increasing trends during intervention sta-
bilizing at levels well above baseline performance (with the exception
of Melinda, whose DCPM showed continuous increases even during
the inal three LAP sessions). Such data indicate the more gradual
improvement observed in participant luency (i.e., correctly solving
fraction problems more quickly) than evident for PPC, simply a calcu-
lation of whether a problem was correct or incorrect. Regarding main-
tenance, data indicate that all participants maintained their gains in
DCPM 3 weeks following LAP cessation.
In addition to graphical results, Table 1 displays means and
standard deviations for both PPC and DCPM across baseline, LAP in-
tervention, and maintenance. Such data provide additional evidence
of the changes in both metrics following the introduction of the LAP
procedures. Regarding PPC, with 2.8% PPC during baseline, Jason
achieved the highest mean of fraction problems solved correctly. Dur-
ing intervention, each participant achieved mean PPC of at least 82.8%.
Evidence for the efectiveness of the LAP intervention on DCPM is
also provided by mean increase for all participants across conditions.
Each participant achieved DCPM intervention means more than twice
of those during baseline and maintenance means at least three times
baseline results.
Discussion
Although the identiication of research-based academic inter-
ventions is ever expanding, skill deicits of many types continue to
lack available options for remediation. One such area is addition and
subtraction of fractions; although viewed as being challenging to
teach and understand (Smith, 1995), surprisingly few interventions

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exist for students struggling with these concepts. Of those available,
most involve strategies targeting students with identiied disabilities
(Misquita, 2011) rather than investigating intervention efects with
students without disabilities who struggle in mathematical learning
and who are at risk for further math diiculty. As such, the current
study was designed to add to the math intervention literature by in-
vestigating the efects of the LAP mnemonic to target skill deicits in
addition and subtraction of fractions of three general education sixth
graders without disabilities. More speciically, this study extended
the initial LAP work of Test and Ellis (2005) by including participants
in general education and tracking DCPM as a luency-based depen-
dent measure, in addition to PPC.
In general, current results provide additional evidence of the ef-
fectiveness of the LAP strategy at remediating skill deicits in addition
and subtraction of fractions. This includes evidence of intervention-
ist modeling and providing feedback regarding the steps required
for correct problem solution. Considering both visual analysis and
descriptive statistics, gains were clear in PPC following LAP imple-
mentation with increases maintained at 3-week maintenance check.
Speciically, all participants evidenced immediate and dramatic im-
provement in correctly solving addition and subtraction of fraction
problems following LAP introduction. For Melinda and Danielle,
both of whom completed 0 problems correct during baseline, LAP
techniques improved performance to at least 80% PPC during the
irst intervention session (with equally impressive gains for Jason).
These gains persisted throughout intervention, and although some
LAP data points displayed high variability (i.e., Melinda’s second and
third LAP sessions and Danielle’s second LAP session), all outcomes
were at levels well above those observed during baseline. Increases in
mean PPC from baseline to intervention also support the notion that
the LAP techniques were responsible for participant skill acquisition
in solving fraction problems. Of additional interest is that each of the
participants showed decreases in PPC during the inal LAP session(s).
Although not optimal, due to the impending end of the school year it
was necessary to end LAP data collection so as to allow the opportu-
nity for maintenance data collection for all participants.
In addition to dramatic increases in PPC, the data from this
study also indicate the efectiveness of LAP procedures on DCPM.
Although improvement in DCPM from baseline to intervention was
more gradual in nature, results nonetheless indicate the efectiveness
of LAP procedures at increasing problem solving luency involving
fractions. When compared with the immediate changes in level ob-
tained for PPC, the more gradual DCPM changes are not surprising

16. 386 EVERETT et al.
given that one would not necessarily expect luency to immediate-
ly double, triple, or greater upon intervention implementation, but
rather would expect improvement along a more stepwise progression
(Shapiro, 2004). That is, as each of the participants evidenced diicul-
ty with accurately solving addition and subtraction of fraction prob-
lems, it follows that luency would also be compromised (Haring,
Lovit, Eaton, & Hansen, 1978). However, upon increased accuracy
(i.e., correct problem solution), participants also showed associated
luency increases. Within this context, the relationship between PPC
and DCPM warrants speciic mention in that incorrectly answering
either the numerator or denominator of a fraction resulted in the en-
tire problem being counted incorrect (speciic to PPC), but resulted in
earning credit (i.e., a correct digit where appropriate) for the DCPM
results. This was the case for many of both Melinda’s and Danielle’s
baseline results during which neither participant ever correctly an-
swered both the numerator and denominator of the same problem
resulting in baseline scores of 0% PPC, but who both did earn correct
DCPM during the baseline phase. Because mathematics luency mea-
sures are important metrics through which school personnel judge
teaching or intervention efectiveness, such situations require care-
ful data interpretation. That is, although increases in DCPM through
the correct completion of only one part of a fraction problem do not
lead to the desired outcome of correctly completing the entire prob-
lem (thereby increasing PPC), current DCPM results are important.
As DCPM provide data about individual sub-skills required to solve
the entire problem (e.g., adding two numerators together), their col-
lection allows for the identiication of speciic sub-skills in a way that
PPC does not. Given the broad application of luency-based metrics
as outcome measures in mathematics (e.g., Axtell et al., 2009; Poncy et
al., 2010) and given their utility as sub-skill identiiers, when working
with fractions both DCPM and PPC are important.
Practical Implications
The current study is unique in math intervention research and
adds to this literature in several ways. The irst implication is that this
study is a fraction study that adds to this recognized area of need
(Maccini et al., 2007; Templeton et al., 2008) by speciically targeting
a skill with which many students struggle. Second, participants were
general education students without disabilities experiencing diicul-
ty with fractions. In this way, the LAP intervention may be viewed
as a tool to target students who are at risk for future math diicul-
ties by not only remediating current concerns but also preventing fu-
ture diiculty. This its well within a tiered model of service delivery

17. 387
LOOK-ASK-PICK MNEMONIC
(e.g., as a Tier II or Tier III intervention). In addition, individual gains
resulted from LAP implementation of approximately 1 hr per week
(i.e., 30 min twice weekly) indicating not only intervention efective-
ness but also eiciency. In other words, devoting 1 hr per week to
students with an identiied academic deiciency its well within var-
ied Response to Intervention models for prevention and remediation.
Third, in addition to measuring correct problem solutions (i.e., PPC),
the current study also showed results that relect increases in partici-
pant’s luency during intervention sessions. This contribution is espe-
cially unique in that no other studies have investigated the utility of a
fraction-speciic intervention on measures of math luency. Although
conceptually distinct from luency calculations based purely on math
computation skills (i.e., those employing only the four basic mathe-
matics operations), the inclusion of DCPM provides for an additional
metric with which to judge LAP efectiveness. Fourth, although not a
speciic focus of the study, current results may be framed within the
widely adopted Common Core State Standards in Mathematics (Na-
tional Governors Association Center for Best Practices, 2010), which
include fraction-speciic knowledge by the end of sixth grade.
Limitations and Directions for Future Research
The current study has a few notable limitations warranting dis-
cussion. First, because the current LAP intervention included difer-
ing components (i.e., mnemonic rehearsal, modeling, error correction,
repeated practice), it is impossible to atribute positive outcomes to a
singular factor. As this is only the second study to formally investigate
the LAP mnemonic, future research may target more speciically the
individual LAP techniques to identify those components most respon-
sible for fraction skill improvement. Relatedly, as current LAP tech-
niques involved individual student administration and, therefore, dif-
fered from the peer-based format employed by Test and Ellis (2005),
future research may compare the utility of peer versus individual ad-
ministration. Second, because intervention sessions were conducted
by an interventionist, results from this study indicate improved math
performance only in these “experimenter-created” sessions rather
than in the classroom environment. Future research should atempt
to include LAP procedures into a classroom-based seting. Third, the
current study employed checklists to ensure procedural integrity
rather than direct observation of implementation speciics. Although
such procedures are not optimal, they are frequently employed in
academic intervention research (e.g., Carroll, Skinner, Turner, McCal-
lum, & Woodland, 2006; Poncy, Skinner, & O’Mara, 2006; Reinhardt,
Theodore, Bray, & Kehle, 2009) as measures of treatment adherence.

18. 388 EVERETT et al.
Finally, as current data collection did not include the measurement
of social validity outcomes, no statements can be made regarding the
relevance of improved fraction skills to the daily life of the current
participants. As such, future research should include direct measures
of social validity.
Conclusion
Overall, the present study produced additional evidence regard-
ing the efectiveness of the LAP mnemonic at improving addition
and subtraction of fraction skills with students currently struggling
and at risk for further math diiculty. As fractions are problematic
for many students and their understanding is important for not only
more advanced math concepts but also real-world math applications,
the identiication of research-based intervention strategies to remedi-
ate these diiculties is important. It is for these reasons that future
research should atempt to replicate and extend both the current work
and that of the original LAP intervention as implemented by Test and
Ellis (2005).
References
Axtell, P. K., McCallum, R. S., Bell, S. M., & Poncy, B. (2009). Devel-
oping math automaticity using a classwide luency building
procedure for middle school students: A preliminary study.
Psychology in the Schools, 46, 526–538.
Botge, B. A., Heinrichs, M., Mehta, Z. D., & Hung, Y. H. (2002).
Weighing the beneits of anchored math instruction for stu-
dents with disabilities in general education classes. Journal of
Special Education, 35, 186–200.
Brown, G., & Quinn, R. J. (2007). Fraction proiciency and success in
algebra: What does the research say? Australian Mathematics
Teacher, 63, 23–30.
Burns, M. K., Codding, R. S., Boice, C. H., & Lukito, G. (2010). Meta-
analysis of acquisition and luency math interventions with
instructional and frustrational level skills: Evidence for a skill-
by-treatment interaction. School Psychology Review, 39, 69–83.
Burns, M. K., VanDerHeyden, A. M., & Jiban, C. L. (2006). Assess-
ing the instructional level for mathematics: A comparison of
methods. School Psychology Review, 35, 401–418.
Butler, F. M., Miller, S. P., Crehan, K., Babbit, B., & Pierce, T. (2003).
Fraction instruction for students with mathematics disabili-
ties: Two teaching sequences. Learning Disabilities Research &
Practice, 18, 99–111.

19. 389
LOOK-ASK-PICK MNEMONIC
Cade, T., & Gunter, P. L. (2002). Teaching students with severe emo-
tional or behavioral disorders to use a musical mnemonic
technique to solve basic division calculations. Behavioral Dis-
orders, 27, 208–214.
Carroll, E., Skinner, C. H., Turner, H., McCallum, E., & Woodland,
S. (2006). Evaluating and comparing responsiveness to two
interventions designed to enhance math-fact luency. School
Psychology Forum: Research in Practice, 1, 28–45.
Charles, R. I., Illingworth, M., Reeves, A., Mills, D., & Branch-Boyd,
J. C. (2008). Prentice hall mathematics: Course 2. Upper Saddle
River, NJ: Pearson Prentice Hall.
Christ, T. J., Scullin, S., Tolbize, A., & Jiban, C. L. (2008). Implications
of recent research: Curriculum-based measurement of math-
ematics. Assessment for Efective Intervention. 33, 198–205.
Deno, S. L., & Mirkin, P. K. (1977). Data-based program modiication: A
manual. Reston, VA: Council for Exceptional Children.
Greene, G. (1999). Mnemonic multiplication fact instruction for stu-
dents with learning disabilities. Learning Disabilities Research
& Practice, 14, 141–148.
Haring, N. G., Lovit, T. C., Eaton, M. D., & Hansen, C. L. (1978). The
fourth r: Research in the classroom. Columbus, OH: Charles E.
Merrill Publishing Company.
Hayes, S. C., Barlow, D. H., & Nelson-Gray, R. O. (1999). The scientist
practitioner: Research and accountability in the age of managed care
(2nd ed.). Boston, STATE: Allyn & Bacon.
Individuals with Disabilities Education Improvement Act (IDEA) of
2004, PL 108-446, 20 U.S.C. §§ 1400 et seq.
Joseph, L. M., & Hunter, A. D. (2001). Diferential application of a
cue card strategy for solving fraction problems: Exploring in-
structional utility of the Cognitive Assessment System. Child
Study Journal, 31, 123–137.
Maccini, P., Mulcahy, C.A., & Wilson, M. G. (2007).A follow-up of math-
ematics interventions for secondary students with learning dis-
abilities. Learning Disabilities Research & Practice, 22, 58–74.
Manalo, E., Bunnell, J. K., & Stillman, J. A. (2000). The use of process
mnemonic strategies in teaching students with math learning
disabilities. Learning Disabilities Quarterly, 23, 137–156.
Mastropieri, M. A., & Scruggs, T. E. (1998). Enhancing school success
with mnemonic strategies. Intervention in School & Clinic, 33,
201–208.

20. 390 EVERETT et al.
Misquita, R. (2011). A review of the literature: Fraction instruction
for struggling learners in mathematics. Learning Disabilities
Research & Practice, 26, 109–119.
National Governors Association Center for Best Practices & Council
of Chief State School Oicers. (2010). Common Core State
Standards for Mathematics. Retrieved from htp://www.
corestandards.org/assets/CCSSI_Math%20Standards.pdf
National Mathematics Advisory Panel. (2008). Foundations for success:
Final report of the National MathematicsAdvisory Panel. Retrieved
from htp://www2.ed.gov/about/bdscomm/list/mathpanel/
report/inal-report.pdf
Pearson, Inc. (2008). AIMSweb growth table: Mathematics computation.
Eden Prairie, MN Edformation, Inc.
Poncy, B. C., Skinner, C. H., & Axtell., P. K. (2010). An investigation
of detect, practice, and repair to remedy math-fact deicits in
a group of third grade students. Psychology in the Schools, 47,
342–353.
Poncy, B. C., Skinner, C. H., & O’Mara, T. (2006). Detect, practice, and
repair (DPR): The efects of a class-wide intervention on ele-
mentary students’ math fact luency. Journal of Evidence-Based
Practices for Schools, 7, 47–68.
Reinhardt, D., Theodore, L. A., Bray, M. A., & Kehle, T. J. (2009). Im-
proving homework accuracy: Interdependent group con-
tingencies and randomized components. Psychology in the
Schools, 46, 471–488.
Scarlato, M. C., & Burr, W. A. (2002). Teaching fractions to middle
school students. Journal of Direct Instruction, 2, 23–38.
Scruggs, T. E., & Mastropieri, M. A. (2000). The efectiveness of mne-
monic instruction for students with learning and behavior
problems: An update and research synthesis. Journal of Behav-
ioral Education, 10, 163–173.
Shapiro, E. S. (2004). Academic skills problems: Direct assessment and in-
tervention. (3rd ed.). New York, NY: The Guilford Press.
Shinn, M. R. (2004). Administration and scoring of mathematics compu-
tation curriculum-based measurement (M-CBM) and math fact
probes for use with AIMSweb. Eden Prairie, MN: Edformation,
Inc.
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Clas-
sens, A., Engel, M., & Chen, M. (2012). Early predictors of
high school mathematics achievement. Psychological Science,
23, 691–697.

21. 391
LOOK-ASK-PICK MNEMONIC
Smith, J. (1995). Competent reasoning with rational numbers. Cogni-
tion and Instruction, 13, 3–50.
Superkids math worksheet creator (n.d.). Retrieved from htp://www.
superkids.com/aweb/tools/math/fraction/basic.sht
Templeton, T. N., Neel, R. S., & Blood, E. (2008). Meta-analysis of
math interventions for students with emotional and behav-
ioral disorders. Journal of Emotional and Behavioral Disorders,
16, 226–239.
Test, D. W., & Ellis, M. F. (2005). The efects of LAP fractions on ad-
dition and subtraction of fractions with students with mild
disabilities. Education & Treatment of Children, 28, 11–24.
Wolgemuth, J. R., Cobb, R. B., & Alwell, M. (2008). The efects of mne-
monic intervention on academic outcomes for youth with dis-
abilities: A systematic review. Learning Disabilities Research,
23, 1–10.
Zisimopoulos, D. A. (2010). Enhancing multiplication performance
in students with moderate intellectual disabilities using peg-
word mnemonics paired with a picture fading technique.
Journal of Behavioral Education, 19, 117–133.

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