ST (Spatial Temporal) Math®: Impact on student progress

ST MATH – IMPACT ON STUDENT PROGRESS
Spatial Temporal Math® and its Impact on Student Progress
at the Middle School Level
Marianne McFadden

ST MATH – IMPACT ON STUDENT PROGRESS 2
Abstract
This paper studies the impact that the implementation of ST (spatial-temporal) Math®, a visual
support software intervention, has on progress for under-performing middle school students of
two suburban districts in central Pennsylvania. Both schools serve a culturally diverse student
body, but the smaller school has a larger percentage of economically disadvantaged families.
Seventh and eighth graders currently or formerly using the program are being studied along
with their teachers who implement the program as they see suitable for their particular classes.
Two differing surveys focusing on program effectiveness have been administered to these
students and their teachers. Additionally, state test scores for 2013 and 2014 are compared to
determine whether use of ST Math® software impacts learning Math. The study, beginning
with the teacher and Math coordinator surveys in June 2014, continued into the fall with the
student survey and data analysis of updated standardized test scores and demographics.
During the study, my role is substitute teacher/observer – I implement the program according
to the classroom teacher’s plans and help students with lessons while observing student
progress. The study’s findings indicate that the ST Math® program is effective in helping
students to understand difficult, abstract Math concepts, but has not had an effect that is at all
similar to the impressive results that were published with studies done by the program’s
creators. Also, although surveyed students respond favorably to the program, many have cited
other programs as more helpful than ST Math®. Lastly, it was found that surveyed teachers did
not utilize the teacher mode, a feature designed to introduce effective strategies.
key terms: spatial-temporal, blended learning model , self-efficacy, scaffolding approach, teacher-
efficacy, working memory, executive function

Introduction
While studying effective methods of teaching and learning Mathematics, it is customary to
find skilled teachers actively searching for ways to help students better understand difficult
concepts in order to improve progress and success. Likewise, students who are willing to put
time and effort into their studies often look for short cuts and/or multiple ways to learn
concepts that pose a challenge. Teachers who actively utilize a variety of classroom aides
usually feel fairly confident that these tools enable students to better understand material that
can frustrate even the most talented students.
Manipulatives or tangibles can help to ‘unpack’ tough concepts by making the abstract more
comprehensible, and many students become more successful in processes by using such
tangibles. These manipulatives give concrete meaning to abstract processes, thus allowing the
student to tackle problems with greater ease. In a similar way, games and puzzles that
encourage critical thinking help to sharpen analytical skills that are required in higher level
Math courses. Lastly, tools such as the graphing calculator allow for quick, slight graphical
alterations and in doing so, enable teachers and students to quickly explore what effects
multiple variations have on overall results.
Although classroom tangibles, puzzles, games, tools, and software certainly have helped in
the teaching of Math at all levels, from pre-kindergarten through college level Math, very few
tools or programs have actually trained students to understand how abstract concepts actually
make sense. This paper examines one such program that presents the abstract visually and in a
creative, game-like way. The program, known as ST Math® (meaning spatial-temporal), was

developed by MIND Research, an institute that conducts neuroscience research in an effort to
improve educational methods. In conjunction with researchers at the University of
California at Irvine (UCI), the institute claims that developing and training of the brain’s innate
“spatial-temporal” (ST) reasoning ability lies at the basis of creative thinking and intricate
problem-solving. Additionally, since adept ST ability allows the brain to hold visual, mental
representations in short-term memory and manipulate them in space and time, thinking
multiple steps in advance becomes possible and effortless (mindresearch.net). Many of the
skills, processes, and strategies in higher mathematics require well-developed ST skills for
achievement.
The ST Math® software learning tool presents concepts visually so that students see how
correct answers actually work. The rationale is that if concepts make sense through visual
representation, then foundational Math skills are developed so success in working with them is
inevitable – deeper understanding accomplishes this. Since its inception, the ST Math®
program has gained in popularity and studies on student progress have revealed impressive
results, especially through the studies conducted by UCI in the Los Angeles area.
Two local districts in South Central PA are participants in the study detailed in this paper:
Spartan School District and Midstate Township School District (both pseudonyms). This paper
studies how the implementing of ST Math®, a visual learning support program, impacts
progress for under-performing students within the middle school classroom in the participating
districts. My research focuses on the styles of the ST approach. By examining published studies
on student progress while using the ST Math® program, conclusions are drawn about the
effectiveness of the program. Additionally, further conjectures are made with respect to the

program’s ability to enhance student success with higher level courses in Math as well – a topic
of interest to me, an experienced Math teacher at the secondary level, and to all teachers who
strive to help students realize their academic potential through effort and perseverance.
The program has gained popularity and the media has conveyed its purpose and
effectiveness through many videos, some of which are listed below:
https://www.youtube.com/watch?v=7odhYT8yzUM
(Teaching Math Without Words – CEO of MIND Research, Matthew Peterson on TED Talks)
https://www.youtube.com/watch?v=7g8pmwLuZxM (mindresearch.net: Welcome to ST Math®)
https://www.youtube.com/watch?v=WjOcf8bblLA (MIND Research: Transforming Math Learning)
https://www.youtube.com/watch?v=5QJ1KeLHAiE (Linear Equations – Animated Tour)
Literature Review
Matthew Peterson, the co-founder of MIND Institute Research, believes that the way Math is
being taught needs to be revised in order to meet the needs of the diverse students that are
attending schools today. He believes that the skills taught in Math class should apply across
subject areas in solving non-routine problems. While most Math software interventions and/or
remedial programs normally offer the student the correct answer after a few failed attempts,
they do little, if anything, to build mathematical depth of knowledge, problem-solving skills, or
perseverance in seeing difficult problems to completion (Peterson, 2011).
Michael Martinez, a professor of education at UCI, discusses the critical need for the U.S. to
raise achievement levels in Science, Technology, Engineering and Math (STEM) in order to
increase the amount of young people entering those fields and to increase international
competitiveness (Martinez, n.d.).

Martinez agrees with Peterson in stating that since traditional math education is heavily
reliant on terminology, memorization, and long procedures, many students find higher-level
Math courses a particular challenge. Therefore, a new approach, the spatial-temporal
approach, may more closely suit today’s learner’s needs, especially those who become
frustrated with traditional teaching styles, and particularly those who have learning disabilities
and/or are English language learners (Martinez, n.d.).
Spatial-temporal (ST) reasoning, Martinez explains, is a highly intuitive way of learning basic
concepts (Martinez, n.d.). When applied as a focus skill in teaching and learning, the learners
are required to exercise their reasoning ability as they are presented with concepts as patterns
that are represented by images or transformations of images. Additionally, since pattern-
finding through mental imagery is a natural ability of the human mind, ST Math® methodology
may help students gain much greater levels of proficiency in Math (Martinez, n.d.).
MIND Research Institute developed the ST Math® program software to include interactive
exercises that consistently inform the user how and why the math embedded in them works.
The student user moves through the exercises and is required to test hypotheses, learn from
errors, and view pictorial explanations of both correct and incorrect responses. The program
presents challenge as fun in an effort to encourage students to become life-long learners
(Peterson, 2011).
An independent education consultant from Florida noted in her review that the program
offers self-paced, language-independent, mastery-based games designed to teach math
concepts. Some features include: a) internet accessibility, including iPad and Android access,
b) the generating of reports of class and individual performance and progress through the

program, c) lessons aligned to grade level curriculum standards (including common core) that
gradually increase in difficulty with immediate feedback to every question’s response, d) pre-
and post assessments embedded within each module, and e) programs available at every level,
including a K – 5 program as well as a secondary level intervention for below level performers
(Finley, 2013). Other reviews have noted that a specific version, ST Math® + Music,
incorporates lessons that teach music theory mathematically, where lessons are based on
symmetry in order to enhance student thinking and reasoning by encouraging students to think
visually and several steps ahead (Fratt, 2007). Likewise, another review of ST Math® + Music
asserted that including music in the program strengthens the part of the brain that is utilized in
solving problems in math (Royal, 2007).
In discussing implementation methods, Nisbet
and Luther, both of the MIND Research Institute,
describe how well the program fits the blended
classroom set-up since it promotes individualized,
customized learning and can be utilized within the
online instruction rotation – see figure 1 (Nisbet &
Luther, 2012, p. 5). The blended learning model is discussed within the action research and is
utilized in the two middle schools studied in this paper. In emphasizing the importance of
utilizing the teacher mode feature in incorporating
whole class instruction, Nisbet and Luther note that
class discussions on strategies help teachers to lead
students in making ties between the program

content and procedures learned in traditional lessons. Furthermore, they assert that although
students apply skills as much in traditional classes as they do in ST Math® lessons, the
experience and connections have far greater emphasis in ST Math®, and those features
probably make up for the fewer practice sessions (as compared to traditional) that ST Math®
presents – see figure 2 above (Nisbet & Luther, 2012, p. 15). Finally, the ST Math® Training
Manual itself reiterates what Nisbet & Luther note about
the teacher mode feature – utilizing the feature is crucial
in getting students to articulate strategies when posing
such questions (discussion starters) as: What is
happening in the puzzle? (Explain it!), and: How will this
work on the next problem we display? The schematic (figure 3, left) is offered in the training
manual as a visual for posting in the room for frequent reference, in guiding students to make
careful choices that are derived from analytical thinking (ST Math® Training Manual, 2012, p.
36). More discussion on the teacher mode feature surfaces within the action research itself.
Several reviews and reports of progress are available for the ST Math® program. Some,
summarized below in table 1 reflect successes in many districts in various parts of the country.
TTAABBLLEE 11 –– DDIISSTTRRIICCTT SSUUCCCCEESSSSEESS WWIITTHH SSTT MMAATTHH®® TTHHRROOUUGGHHOOUUTT TTHHEE UUSS
LLOOCCAATTIIOONN//GGRRAADDEE LLEEVVEELL AACCHHIIEEVVEEMMEENNTT SSOOUURRCCEE
Phoenix, AZ
- intermediate school
state test (ST Math® users) in 2012 increased by 3
percentiles; whole district scores in 2012 fell by 1
percentile
(District Administration Custom
Publishing Group, 2013)
Elgin, IL
- 3
rd
through 5
th
grade
ISAT - state test - rose from 51% (proficient &
advanced) in 2005 to 84% in 2007
(Royal, 2007)
Los Alamitos,CA
- elementary school
CST (state test) scores rose from 78% percentile
(proficient) to the 99
th
percentile – over 6 yrs
(Fratt, 2007)
Chicago,IL
- elementary school
ISAT rose 13% (ST Math® users) from 2010 to 2011;
ISAT rose 6.7% (non-ST Math® users) from ’10 to ‘11
(mindresearch.net, 2011)
Los Angeles, CA
- elementary school (LAUSD)
CST (state test) scores rose 11.7 % over 2 yrs for ST
Math® users; scores rose 6.4% for non-users
(mindresearch.net, 2011)

In the research that considers the effects of implementing
ST Math® as a curricular intervention program, Schenke,
Rutherford, and Farkas (2014) respond to the dismal findings of a 2007 study on the
effectiveness of educational technology that indicated that there was no difference between
the treatment and control groups (Dynarski, Agodini, Heaviside, Novak, et al, 2007). The
Schenke research team, supported by grants from the Institute of Education Sciences (IES) and
by graduate research grants from the National Science Foundation (NSF), conducted a two-year
randomized control trial of ST Math®, for grades 3, 4, and 5, within fifty-two Southern California
public schools. These schools were eligible to participate since they fell in the bottom one-third
of the achievement distribution, as measured by the state standardized test, or the CST.
Demographics describing these schools include: student enrollment of more than 85%
FFIIGGUURREE 66 –– GGRROOWWTTHH IINN PPEERRCCEENNTTAAGGEE OOFF LLAAUUSSDD SSTTUUDDEENNTTSS ((CCAA))
GGRRAAPPHHIICCAALL RREEPPRREESSEENNTTAATTIIOONNSS OOFF GGRROOWWTTHH OONN SSTTAATTEE SSTTAANNDDAARRDDIIZZEEDD
TTEESSTTSS IINN CCAALLIIFFOORRNNIIAA OOVVEERR TTWWOO YYEEAARRSS,, CCOOMMPPAARRIINNGG PPEERRFFOORRMMAANNCCEE OOFF
SSTT MMAATTHH SSTTUUDDEENNTTSS TTOO NNOONN--SSTT MMAATTHH SSTTUUDDEENNTTSS.. ((mmiinnddrreesseeaarrcchh..nneett))
FFIIGGUURREE 44 AANNDD FFIIGGUURREE 55 –– CCHHIICCAAGGOO RREESSUULLTTSS
Comparisons given by
mindresearch.net for Chicago’s Public
Schools (CPS) after two years of use
in various schools. Figure 4 indicates
that ST Math schools met standards
at a rate that was twice as much as
those who were not ST Math users,
and figure 5 indicates a four times as
much growth for user schools as
compared to non-user schools.
.

minorities with 91% of the students receiving free or reduced lunch. The Schenke team used
these schools in their study with ST Math® as the intervention program being examined for
effects on student achievement.
Schenke’s team described ST Math® as a software program developed by the MIND
Research Institute “to teach mathematical concepts through spatial representations,” where
learning is approached through “a series of game-like activities that are directly tied to relevant
state standards for Mathematics” (Schenke, Rutherford, & Farkas, 2014, p. 217). The focus of
their study on this intervention was to understand how alignment of standards to content
within the ST program affects student achievement. The team noted some of their beliefs
about the Dynarski study and analyzed specific aspects of the study. Among some of their
theories, and in response to the Dynarski study, Schenke’s team offered reasons why the 2007
study produced dismal conclusions:
a) mixed findings may have been related to the curriculum design of a particular
intervention; thus the team’s recommending short, targeted interventions aligned to
state/district curriculum to yield the greatest effect, and
b) the failure of classroom teachers to scaffold the use of technology and/or integrate
the scaffolding technique into daily lessons and assignments; thus their recommending
adopting scaffolding as a best practice for consistent success
(Schenke, Rutherford, & Farkas, 2014).
Additionally, the Schenke team cited the 1995 TIMMS claim that average U.S.
Mathematics lessons offer insufficient challenge and often over-emphasize procedural
methods. In response to these claims, the researchers supported standards-based instruction.
This curriculum design allows for discovery learning with the use of relevant activities that lead
to understanding and achievement without rigorous procedures and memorization. The team
stated that the content of the ST Math® program is aligned to state standards, and their studies

showed that the program allows students to work at their own pace. Furthermore, the
researchers analyzed the games in the program and found that almost 60% of the games were
aligned to the strand labeled as Number Sense – or the ability to understand the magnitude of
numbers and to approximate and manipulate numerical quantities (Schenke, Rutherford, &
Farkas, 2014). In asserting that early number sense is critical for later success in higher
Mathematics, the ST Math® program development and emphasis on advanced
conceptualizations of number support the students’ later ability to handle more difficult
concepts, including place-value and part-whole relationships (dealing with fractions). Lastly,
the researchers asserted that the pictorial and symbolic representations of numbers found in
the program further improve number sense ability of the students. The Schenke team
considered the program to be a game-like number sense intervention, with its goals clearly set
on improving number relationship skills. Furthermore, the team emphasized throughout their
paper that an assessment that is most closely aligned to the content of any intervention would
produce the most reliable results; therefore the team strongly suggested that the standardized
(state) test would be the least likely measure to be used as a success indicator. Instead, the
team favored the teacher-made or company-made test (company creating the intervention) as
the appropriate tool for evaluating student growth and progress.
In reviewing some of the points and observations made by the Schenke team, it is
unclear whether the team accessed any progress indicator, other than the CST (which they
clearly stated would be the least likely reliable indicator). Since they favored teacher-made
tests, it would have made sense to have had made comparisons between the ST Math® group
and non-ST group with respect to regular in-class tests (compare average time to take the test

and actual results, too). Also, it is unclear whether these results are generalizable, since only a
specific type of under-performing school district was eligible for the study. Average and above
average students were not considered to be fairly represented in the study.
Another research team, Rutherford, Hinga, Chang, Conley, and Martinez, did a similar
randomized field trial within fifty-two Orange County, California schools in 2011. This team,
(which also included Rutherford from the Schenke group) was funded by the IES and supported
by the NSF as well. Based on the belief that students of the 21st
century need to develop
methods to solve complex problems, and in stating that U.S. students are falling behind other
top industrialized nations, the team emphasized “the need for novel and highly effective
approaches to increasing math achievement” (Rutherford, Hinga, Chang, Conley, & Martinez,
2011, p. 2). Additionally, the researchers claimed that by raising motivation, academic
achievement was sure to increase as a result, and the student’s expectancy (or self-efficacy)
would increase as well. The Rutherford team asserted that self-efficacy influenced effort,
perseverance, resilience, and the choosing of tasks (Rutherford, Hinga, Chang, Conley, &
Martinez, 2011). Therefore, those students who have developed high self-efficacy for problem-
solving in math would persist longer in problem-solving situations and this persistence would
lead to greater math learning. Although the team pointed to several factors that lead to
increasing self-efficacy, the one sure factor that both ST Math® program does well and teachers
should practice regularly is provide students with process goals and feedback. The team
assured the reader that the program’s strength lies in the fact that each student response is
followed by feedback (a visual representation showing the student’s correct response
matching a picture of identical length) and each incorrect response is followed by an animation

illustrating a method to correctly find the answer (Rutherford, Hinga, Chang, Conley, &
Martinez, 2011). Lastly, these researchers also pointed to the scaffolding approach, as the
Schenke team did, in allowing students to experience success on lower levels, then providing
support to push through failures when attempting harder-leveled problems (so that setbacks
do not become overwhelming).
In reviewing some of the points of the Rutherford study, it is unclear whether these
results are generalizable since again the focus groups were in California. Furthermore, neither
study indicated any idea as to whether these students would be “followed” in order to
determine long-term effects due to exposure to the program, a feature that I would consider
most important in assisting students to be successful in higher levels of Math. Again the CST
took center-stage and was made to be a major factor in determining immediate – not long-term
– success. I would feel much more confident if either or both teams considered continuing with
studying the same students for a few consecutive years. If I were given the opportunity to
participate in a similar study, I would most definitely follow a group of ST Math® students well
into their high school years, and examine both the level of difficulty of their Math courses as
well as their achievements in their math classes.
In a third related study headed by Natalie Tran of the California State University at Fullerton
and her team of thirteen researchers (three of which were from the MIND Research Institute),
elementary teachers of grades 3, 4, and 5 in western U.S. were randomly assigned to a control
or treatment group to study the effects of ST Math® usage on (student) self-efficacy, teacher-
efficacy, outcome expectancy, and instructional practices, where hierarchical linear modeling

was used to analyze data collected (Tran, Schneider, Duran, Conley, Richland, Burchinal,
Rutherford, et al., 2012). The Tran team reiterated previous definitions of efficacy as the:
“beliefs individuals hold about their own abilities to perform a particular kind of task… affect
the level of effort that individuals exert, their persistence in working through challenges,
their resiliency when experiencing failures, and their means of coping with change.”
(Tran, et al., p. 340).
These researchers also continued with a detailed explanation of teacher-efficacy, as they
defined it to be the teacher’s view of his or her own capabilities as a teacher. This self-
judgment can be influenced by many factors, including: the teacher’s preparation for the
profession, the level of student success, the amount of effective teacher-student interaction
occurring, the teacher’s confidence in implementing a new program or strategy, and strength of
content knowledge (Tran, et al.). Since many of these factors can change depending on specific
circumstances, so could teacher-efficacy as well, in response to the situation. While self-
efficacy is self-judgment on one’s own capacity to perform a task, the Tran team defined
outcome expectancy as “a judgment of the likely consequence such a behavior will produce”
(Tran, et al., p. 341), so self-efficacy logically precedes outcome expectancy. The importance in
studying these concepts lies in the belief that high teacher-efficacy should lead to high outcome
expectancy and positively influence student performance, which would produce high student-
efficacy (Tran, et al.).
The researchers continued with a short defense supporting computer-based instruction (CBI)
as an enhancement to learning that, when combined with video-based instruction (rather than
text), is positively associated with student achievement . The Tran group briefly described a
quasi-experimental study that showed (through performance on the state standardized test)
that individually personalized CBI improved students’ attitudes towards Math and enhanced

the performance of lower-level skills in Math. Additionally, the audio-based CBI programs that
incorporated spatial contiguity were found to have favorable effects as compared to non-
contiguous models of CBI (Tran, et al.).
The Tran team then related the CBI findings with ST Math®, a spatial contiguous program
with an audio component as well. In describing a randomized experimental design, the team
reported that students in grades two through five were randomly assigned to either a
treatment or control group, where the treatment group received at least two 45-minute
sessions of ST Math® each week during regular Math instruction while the control group just
had regular Math instruction. While the primary study revealed that ST Math® had a positive
impact on student achievement on the state test, the CST, a secondary study made by the team
examined if the program had a “similar impact on teacher beliefs about their efficacy and
classroom practices” (Tran, et al., 2012, p. 342). The team applied multi-level statistical
modeling to the study to estimate the effect of ST Math® on teachers’ self-efficacy, outcome
expectancy, and instructional practice. The sample consisted of the 339 elementary school
teachers in diverse classrooms in which the student body was 83% Latino, 61% English language
learners, and 83% on the free/reduced lunch program. Student data in 2008-09 indicated that
students in this county performed higher than other students in the state in science, math, and
language arts.
The teachers’ data set consisted of a 40-question questionnaire for both the treatment and
control group, with an additional 28 questions added to the ST Math® teacher users – questions
focusing on implementation of the program, impact on improved instruction, and support
received in using the program (stmath2010teachersurvey.questionpro.com, 2010). A

hierarchical linear model was used to estimate the relationship between teachers’ participation
in ST Math® and self-efficacy, outcome expectancy, and the use of scientific reasoning in their
teaching. Factors having no significant effects on teacher efficacy and outcome expectancy
included: years of teaching experience, student enrollment in free/reduced lunch and
percentage of students identified as ELL. Results indicating positive correlations between
factors are listed as the following (Tran, et al., 2012, p. 346):
a) strong positive correlation between ST Math® participation and the integration of ST
Math elements into the formal curriculum, b) time spent on ST Math® was positively
correlated to the integration of ST Math® elements into the formal curriculum, c) significant positive
correlation between teachers’ usage of scientific reasoning and (Math) outcome expectancy, and d)
significant positive correlation between outcome expectancy and teacher efficacy.
In summarizing the results, Tran’s team offered the diagram to the left, figure 7, as a cyclic
representation that shows the relationship
among the factors discussed thus far, in
relation to the ST Math® program (Tran, et al.,
p. 348). The diagram clearly indicates that
allocating time spent on the program together
with integrating it into daily lessons
encourages student achievement, thus positively impacting instructional practices (including
increased scientific reasoning), teacher efficacy, and student motivation and attitudes. The
team devoted a whole section in the study to explaining how the teacher’s role in ST Math®
implementation (and CBI in general) differs from the traditional teacher’s role – with CBI the
classroom evolves from the traditional teacher-centered setting to a student-centered class,
where students working at their own pace engage teachers one-on-one as teachers offer

tailored assistance to those students who request it. The team recognized the importance of
further study on the implications that CBI has had on the effective teaching and learning of
Math.
The team closed the discussion with a few points they saw as limitations to the study,
including: a) the lack of other valuable data sources such as teacher interviews and classroom
observations during regular ST Math® sessions – sources that could shed light upon how
teachers’ beliefs and instructional practices may change as a result of ST Math®
implementation, b) effects of CBI instruction that are limited in this study to the use of ST
Math® only, therefore limiting generalizing conclusions about CBI, c) the small sample size,
which limits generalizing conclusions to the general population, and d) the issue that teacher
efficacy and instructional practices take time to develop and change over time; longitudinal
data is required in a multi-year intervention in order to document changes over time. Tran’s
group concluded the study and discussion with emphasis on the importance of preparing
today’s and future teachers for more student-centered instructional practices, including CBI, as
a result of technological advancements that influence the delivery of instruction.
In reviewing the major points in this study, it was reassuring to read the limitations that the
group made on their own about their own study. I need to add only a few points. First, some
team members were from the MIND Institute, and while they could have been a help in
explaining any problems encountered with the program that they developed, they may have
been responsible for any bias that may have existed during the study and/or in formulating
conclusions and recommendations. Additionally, once again the schools in the study were
located in California, so all three studies offer no variation as far as location (and culture) is

concerned. Similar schools most likely do things in similar ways. Also, I was glad to read that
teacher interviews and classroom observations were considered important to the team, even
though they did not use the tools as part of their evaluation method.
The next study is one that was conducted by Jennifer Long and Elizabeth van Es, both from
UCI. Their research focused on how professional development (PD) that is designed to support
teachers’ implementation of the ST Math® program impacts the success of the program. Two
aspects were studied: a) what effects the PD had on teachers’ self-efficacy, and b) the effects
the PD had on students’ ease of access and subsequent success with the program (measured by
how much of the program each student completed and what level of proficiency was indicated
on their standardized test scores).
The study included 406 teachers of a single grade, grades two through five, from 50 schools
and began in the spring of 2013. It was not stated what part of the country the schools were
located. Based on the assumption that PD can influence teachers’ strategies and confidence in
a new intervention or practice, Long and van Es studied whether PD could influence teacher
change – change in approach and intensity in implementing the ST Math® intervention. The
goal, then, was to understand if participation in ST Math® PD could influence teacher self-
efficacy, and in return influence their students’ success with the program (Long & van Es, 2014).
The team took into consideration that inexperienced and first-year teachers could lack a
depth of knowledge for teaching Math and this could reflect in a low self-efficacy. If the
teacher portrays a lack of confidence, then it might have negative effects on student success.
Additionally, many teachers, including the experienced, find it difficult to work with abstract
math concepts. Since ST Math® embraces instruction through visualizations, most teachers

would need PD that: a) addresses how to effectively implement the program by building a set
of strategies that correspond to the visual demands of the problems the students are asked to
solve, and b) provides teachers with technical implementation skills (Long & van Es, 2014).
The 406 teachers in the study completed a survey with questions pertaining to three
categories: amount of ST Math® PD they participated in and their rating of the PD’s usefulness,
a rating of their own self-efficacy on implementing the program, and the percentage of their
students who advanced through the software to completion of the program. Results of the
study (models to analyze the results were not discussed in this abstract) revealed that positive
correlations existed between the following factors: the amount of PD received and teachers’
confidence in implementing the program, and the percentage of students completing the
program and teachers’ self-efficacy (for every one-point increase in self-efficacy there was a
6.4% increase in the percentage of students who finished their program). The full paper, which
is not available yet (as of December, 2014), should reveal the 2014 CST results of these
teachers’ students and discuss relationships the CST results have with respect to professional
development, teacher background, self-efficacy factors, and student completion of the program
(Long & van Es, 2014).
This study, although not available in full form yet, offered the most realistic investigation
since it put some responsibility on the teachers’ attentiveness and fidelity in implementing the
program as it was designed. The only limitation again is that there was no mention of long-
term study on teachers or students – it would have been nice to read that maybe the teachers
would be studied for a few years in order to reveal their progress in implementation. The
researchers were clear on the teacher’s role and the importance of whole-class presentations in

getting students to clearly convey their thought processes as they progress through the
program.
In the last study by David Lee, also of UCI, cognitive abilities were the focus as 918 second,
third, and fifth graders from eighteen schools participated (divided between treatment and
control groups) in order to determine whether ST Math® impacted the improvement of specific
skills. (It was not stated what part of the country the schools were located, but again the CST
was a progress determining tool). These three skills were chosen since they are strongly
associated with math achievement and the instructional approach of the ST Math® program:
working memory, executive function, and spatial ability. In defining working memory (WM),
Lee described WM as a “skill that permits manipulation of information as students process
complex multiple steps in math problem-solving” (Lee, 2014, abstract). Lee described spatial
skills as the ability to visualize and mentally rotate objects, two tasks often associated with
mathematical performance. Lastly, executive functions (EF) were defined as “a set of skills
involved in focusing and directing attention” (Lee, 2014, abstract). Lee related the relevance of
these skills to the theoretical approach of the intervention in the following ways: a) Since
students encounter this multi-step problem-solving through ST Math® ’s game-like nature, WM
may be strengthened by successful progression through the program at a challenging level that
coincides with the developmental level of each student, b) Spatial skills are practiced
throughout the scope and sequence of the ST Math® program’s exercises, and c) Students
moving through the program’s exercises are required to perform task-switching (EF) as they
adjust to new and more complicated games (Lee, 2014, abstract).

In this study, since tasks within the program are presented as nonverbal, visual concepts, it
was hypothesized that consistent progress through the intervention may improve students’
visual-spatial skills. Likewise, since the program has a game-like nature, it was also
hypothesized that consistent progress may improve attention control and memory. If these
hypotheses could not be proven true, it was then hypothesized that these skills served as
mediators and moderators of the program on achievement in Math – that is, those students
who already exhibited ability in spatial skills may benefit more from the program’s emphasis on
spatial representations (Lee, 2014, abstract). Cognitive data was collected in the spring, 2011
as follows. WM was assessed with backwards digit span, EF with a measure of inhibitory
control and task-switching (known as Hearts and Flowers), and spatial ability was assessed
through simple rotation tasks. Finally, Math performance was assessed through the CST.
Regression analyses indicated that all three cognitive skills predicted math performance when
controlling for gender, ethnicity, ELL status, and free/reduced lunch status. Results of the
regression analysis of post-test differences in these skills indicated that the program did not
have an effect on the improvement of these skills, where effect sizes were small and
statistically non-significant. The hypothesis that progress through the program would improve
math performance by strengthening these three cognitive skills was not supported by the
results of the study. Lastly, evidence was not found supporting the hypothesis that the effect of
ST Math® varied across levels in cognitive skill; its effect appeared to be consistent across levels
of cognitive function within the sample tested (Lee, 2014, abstract).
Although Lee sort of stands alone with his non-supporting evidence of the effectiveness of
the program, I chose this study since it offered a little variety in what was actually evaluated;

that is, the actual underlying skills that lead to better achievement in Math, from the very basic
to the very challenging of courses. Unfortunately, Lee did not discuss whether there was any
consideration in conducting his study with older students, and then continuing with them for a
few years as well (maybe 7th
graders, then continue for three years or more). Lee seemed
unclear as to whether any classes were evaluated on their performance on their regular
coursework (comparing results from ST users to non-users), so there may have been positive
results that were not identified. Lee’s full paper (not available as of November, 2014) should
reveal more information that cannot be revealed from the abstract alone, even though the
abstract was quite descriptive. Table 2 below is offered as a summary of the above five studies:
TTAABBLLEE 22 –– SSUUMMMMAARRYY OOFF MMIINNDD RREESSEEAARRCCHH AANNDD UUCCII SSTTUUDDIIEESS OONN SSTT MMAATTHH®® EEFFFFEECCTTIIVVEENNEESSSS
RREESSEEAARRCCHHEERRSS//AAFFFFIILLIIAATTIIOONN((SS)) SSTTUUDDEENNTTSS AANNDD//OORR TTEEAACCHHEERRSS FFOOCCUUSS//TTHHEEMMEESS OOFF SSTTUUDDYY
Schenke, Rutherford, Farkas;
University of California at Irvine (UCI)
third, fourth, and fifth graders
Southern California
 2 yr randomized control
 85% minorities; 91%
free/reduced (F/R) lunch
 alignment of standards to ST Math®content
 importance of teachers’ scaffolding when
using CBI
 de-emphasis of standardized test as
indicator of progress; favor teacher-made
or company made assessments
Rutherford, Hinga, Chang, Conley, Martinez;
UCI
52 Orange County schools
Southern California
 importance of feedback in raising self-
efficacy
 importance of support given when facing
failure in order to deal with setbacks and
overcome them
Tran, Schneider, Duran, Conley, Richland,
Burchinal, Rutherford, Kibrick, Osborne,
Coulson, Antenore, Daniels, Martinez;
UCI, MIND Research Institute, Orange
County DOE, California State University
339 elementary teachers and
second through fifth graders
 83% Latino; 61% ELL; 83% F/R
lunch
 teacher-efficacy as changing in response to
adapting to new program and influenced by
student success
 integration of ST Math® into daily lessons
 need for 1 on 1 assistance in CBI in order to
transition to student-centered class
Long, van Es;
UCI
50 schools; 406 teachers of grades
2, 3, 4, and 5
 teachers surveyed
 completion of ST prescribed
lessons regarded as relevant
measure in the study
 professional development as influencing
teacher confidence in implementing new
programs
 fidelity of implementation, especially for
programs that offer innovative approaches
Lee;
UCI
918 teachers of grades 2, 3, and 5
 progress measured through
CST and three tests of cognitive
skills
 effect progress through ST Math® has on
improvement of working memory,
executive functions, and spatial ability
(cognitive skills)

In comparing study designs, all research teams considered the California State Test (CST)
results to measure the success of the ST Math® program, with Rutherford’s team reporting that
on the average the treatment students scored 16 points higher than the control group
(Rutherford, Hinga, Chang, Conley, & Martinez, 2011). Also, in assessing motivation, the
Rutherford team used a 7-point Likert-type scale, and results indicated that the effects of ST
Math® were “partially mediated by increased expectancy for math success among treatment
students” (Rutherford, Hinga, Chang, Conley, & Martinez, 2011, p. 10). Similarly, surveys were
utilized in the Long study to determine how teachers reacted and implemented what they
learned in their professional development.
Since ALL the researchers had connections to UCI either as professors, graduate researchers,
or collaborators from MIND, I am most confident that they had many similarities in their
professional discussions about the implementing and evaluating of the ST Math® program.
Their studies were extremely similar to each other, so much so that I had a difficult time in
determining whether they were indeed the same exact study. In noting this, I can conclude
that they would all agree that since CST scores improved (no matter what other evaluative tools
were used), then the program should be deemed as successful. Since Lee’s results were not as
impressive as the others, he may be the researcher who would return with another research
topic and again investigate, but with a differing focus (other than cognitive skills). His was the
only study that evaluated something very specific, not just the overall increase in state test
scores. All the other teams seemed to focus on some aspect of implementation methods, and
not just specific student skills as Lee did. That doesn’t make his findings less important, but I

think it’s a concern, and if I were he, I’d return with a different approach and possibly different
schools and age level.
The studies presented above offer me differing approaches to evaluating achievement.
Schenke’s team modeled measuring success through raised standardized scores while
emphasizing alignment of intervention content to standard-based curriculum. Rutherford’s
team called for measurements that also considered the student’s increased motivation, which
leads to improved self-efficacy, increased perseverance, and likelihood for success in
increasingly challenging math concepts. Additionally, Tran’s team and Long’s team offered me
a better understanding of fidelity of implementation (through effective, valuable PD), so in the
final months of my research (2014 – 15 school year) I have become more closely in tune with
how the teachers I work with use the program. Preliminary experiences with them over the
past few years have shown me the variety that exists in their implementation beliefs (both
schools use the blended classroom with the rotational model, discussed previously in this
paper). Lastly, because of Lee’s study, I believe that if I had my own students, I would make
sure to keep up with the regular classroom assessments (evaluate regular test scores and
compare ST users to non-ST users). My study addresses many aspects in evaluating student
improvement that is attributed to ST Math® intervention in conducting research in answering:
How does the implementation of ST Math® (spatial-temporal), a visual learning support
program, impact progress for under-performing students within a middle school classroom?
Methods: Action Research, Data Collection, Data Analysis
Methods of Action Research
A mixed methods approach is used in this action research since the data collection
instruments are both qualitative and quantitative in nature. In order to evaluate the impact

that the ST Math® program has on progress for under-performing middle school students,
qualitative data was collected from teacher and student surveys. Additionally, quantitative
data was collected in the form of Math PSSA and Keystone Algebra I scores in conjunction with
other relevant comparative statistics regarding changes occurring from 2012 to 2014 in school
performance rating, academic growth, and demographic changes with respect to ethnicity, the
economically disadvantaged , English language learners, and learning support and gifted
students. Both the qualitative and quantitative data are considered in evaluating the results.
Methods of Data Collection
TTAABBLLEE 33 –– MMEETTHHOODDSS OOFF DDAATTAA CCOOLLLLEECCTTIIOONN IINN AACCTTIIOONN RREESSEEAARRCCHH ,, TTEESSTTIINNGG SSCCOORREESS,, AANNDD DDEEMMOOGGRRAAPPHHIICCSS
IINNSSTTRRUUMMEENNTT((SS)) GGIIVVEENN//RREESSUULLTTSS OOBBTTAAIINNEEDD TTAARRGGEETT SSOOUURRCCEE
AACCTTIIOONNRREESSEEAARRCCHH
ST Math®
Teacher
Survey ((AAPPPPEENNDDIIXX DD))
June, 2014
Math Teachers at
Spartan MS and
Midstate MS
creation: questionpro.com
survey: http://questionpro.com/t/AK5PUZRHnG
results: http://questionpro.com/s/1-2479121-3887048
ST Math®
Coordinator
Survey ((AAPPPPEENNDDIIXX FF))
Math Coordinators
at Spartan SD and
Midstate SD
survey: http://questionpro.com/t/AK5PUZRH3O
results: NO responses from coordinators
ST Math®
Student
Survey ((AAPPPPEENNDDIIXX GG))
November, 2014
7th
and 8th
grade
students at
Spartan MS and
Midstate MS
survey: http://questionpro.com/t/AK5PUZRuNW
results: http://questionpro.com/s/1-2479121-4026937
TTEESSTTIINNGG&&DDEEMMOOGGRRAAPPHHIICCSS
Math PSSA and
Keystone
Algebra I Exam
taken: Spring, 2013 and
Spring, 2014
results: May 2014 and
November 2014 7th
and 8th
grade students
at
Spartan MS
and
Midstate MS
www.paschoolperformance.org and
www.schooldigger.com
Comparison of
Spartan &
Midstate: (’12-’13
and ’13-’14)
 school performance
rating
 PVAAS/AAGE
 extra credit rating
 special populations
statistics obtained:
May 2014 and
November 2014
www.paschoolperformance.org
District
Demographics,
(’12-’13 and
’13-’14)
available October 2012,
then October 2013
Spartan SD and
Midstate SD
www.spartan.org,
www.midstatesd.net, and
www.factfinder2.census.gov

In researching the question, “How does the implementation of ST Math® (spatial-temporal),
a visual learning support program, impact progress for under-performing students within a
middle school classroom?” the matrix above summarizes the methods of data collection utilized
in this study. As shown, qualitative instruments designed specifically for this study are
considered with both demographic and quantitative, standardized (state) test results in
evaluating the effectiveness of the ST Math® software intervention. Reoccurring themes
revealed in the data are discussed as part of the analysis of the data.
Beginning with the qualitative instruments, I created both teacher and curriculum
coordinator surveys online, through the questionpro.com free survey website. The survey links
were emailed to all fifteen Math teachers and both district Math coordinators at Spartan
Middle School (pseudonym) and Midstate Township Middle School (pseudonym) on June 8,
2014. Both surveys are presented in their entirety in Appendix D (teacher) and in Appendix F
(coordinator), and results for the eight teacher responses received are presented in Appendix E.
Neither coordinator responded to the survey (as of December, 2014). Both surveys include
questions (mostly Likert-type) on frequency of student use, achievement level of student users,
extent of teacher training, method of implementation (whole class vs. individualized),
observable student overall gains in Math progress, and participant’s input regarding limitations
and critiques of the program. Questions for both surveys were developed by using the 2010 ST
Math® survey as a guide (retrieved from questionpro.com, at
www.stmath2010teachersurvey.questionpro.com). A student survey was developed over the
summer, 2014 with questions – mostly Likert-type – of the student’s own self-assessment of his
or her progress and gains in Math due to consistent use of the ST Math® program and/or other

Math software that the student believes to be instrumental in his or her progress in Math
overall. Additionally, students are also asked to rate the different parts of their hybrid model
(direct instruction, collaborative group, and independent work) in deciding which is most
influential in assessing his or her own growth in Math. Students in both seventh and eighth
grades were surveyed in November, 2014; some were second-year users of the ST Math®
program. The survey is presented in its entirety in Appendix G (student), and results for the
ninety-five student responses received (respondents were from Spartan MS only; Midstate did
not respond) are summarized in Appendix H.
While Appendix A (Spartan) and Appendix B (Midstate) describe general district
demographics, the quantitative instruments are the 2013 and 2014 Math PSSA and Keystone
Algebra I scores. Both sets of scores have been retrieved and are presented in Appendix C as a
comparative matrix of the two schools’ proficient and advanced percentage rates for PSSAs and
Keystones. The scores for the tracking tools from both school years (2013 – ‘14 and the first
semester of 2014 – ‘15) were not requested (but was planned) since neither coordinator
responded to initial attempts and neither principal followed up with my request to invite
coordinators to complete the survey at the beginning of the 2014-‘15 school year.
As far as setting is concerned, both schools are located in South Central PA, approximately
twelve miles apart; a descriptive comparison of the two districts is offered as Appendix C.
Although both districts have a diverse student body and are fairly similar in percentages of
students receiving free/reduced lunch, Midstate Twp MS has a much larger enrollment than
Spartan MS and Midstate’s boundaries hinge upon a large city while Spartan is set in a much
more rural environment. While Spartan is considered as under-resourced, Midstate is

considered as well-resourced. The individual demographics information in Appendices A and B
indicate that the area Midstate serves has a much higher economic status than the area served
by Spartan (see housing prices, educational level, percentage of college graduates, for
example). Additionally, while the percentage of students who scored at the proficient or
advanced levels are fairly similar between the districts (see Appendix C, 2012-13 school year),
when noting the extra credit received by each district for advanced (only) scores, Midstate
ranks much higher than Spartan, thus giving Midstate a performance score almost ten points
higher than Spartan’s (rating 92.1 vs. 82.6). However, in comparison, when noting the same
rating type for the 2013-14 school year, results and ratings change greatly, especially for
Midstate. Comments on these differing results will be considered in the findings and discussion
section. Lastly, the percentage of gifted students at each school differ by several percentage
points (Spartan at 2.84% and Midstate at 10.97% for the 2012-13 school year), but their
percentages reflecting the economically disadvantaged do not differ much. The state ranking of
the schools in relation to all other middle schools (numbering 745, total) in the state differ
greatly: for 2012-13, Spartan ranks 291st
and Midstate ranks 132nd
. The state wide rankings for
the 2013-‘14 school year were not available yet (with schooldigger.com, as of December, 2014).
I have taught Math as a full-time secondary teacher for over twenty-five years, and the
courses I have taught range from Pre-Algebra to Pre-Calculus; I taught middle school students,
grade 7, full-time for one year. Additionally, I have served as a remediation coordinator for
seven years and have used many types of remedial/tutorial software interventions in
remediating struggling high school Math students. For this reason, I felt comfortable in
choosing this program for evaluation. I currently serve as a daily substitute in both schools in

the study, and since both use the ST Math® program and I am familiar with their unique school
atmospheres and procedures, I have chosen these schools for my study.
I have had friendly, professional contact with both principals and assistant principals when
completing earlier projects within my graduate program, and this project was received similarly
– it has been welcomed as valuable in studying students’ progress, especially within the Spartan
Middle School community.
Data collection instruments were easily administered to Spartan students. I emailed their
principal to ask permission to administer the survey and he posted the survey link on the daily
announcements website. Students easily completed the survey, using their own personal
district-supplied computer. Since Midstate changed their daily schedule to include common
study hall time only occasionally and not daily, the principal could not honor my request in
having the students complete the survey. New teachers to the schools and/or program were
not surveyed, although their initial impressions on the program’s strengths and weaknesses
have been informally discussed during some of my substituting days. Data collected from
teachers who currently use the program is discussed in the data analysis – findings and
discussion section. Informal observations that I have been able to complete (in order to see
how the teachers implement the program – whole class instruction vs. individualized access)
will be evaluated in the findings and discussion section.
Data Collection Tasks - Timeline
An outline of my schedule for implementation of my action research plan:
SSpprriinngg,, 22001144 (May, June)
 develop teacher survey and curriculum coordinator survey through questionpro.com
 administer and collect initial data (online) from teacher survey

 administer and collect initial data (online) from curriculum coordinator survey
(survey was administered on June 8th
, but no responses collected – see revisions below)
 collect 2013 Math PSSA & Keystone Algebra I results for Spartan MS and Midstate Twp MS
(through district websites, paschoolperformance.org, schooldigger.com)
 collaborate with peers in class for ideas on revising coordinator survey (goal: shorten, then
restructure open-ended questions to speed up completion time and encourage responses)
 begin to follow MIND Research Institute through LinkedIn; investigate other companies to
follow that are associated with ST Math® and available through LinkedIn
 register to receive Education Week’s electronic copies of ST Math® press releases
 connect with professionals on LinkedIn who are utilizing ST Math® in their classes
 prepare and submit action research proposal
SSuummmmeerr,, 22001144 (June – August)
 develop student survey to be administered to 8th
grade students at Spartan MS and
Midstate Twp MS in mid-September, 2014
 acknowledge and thank responders (8 responses of 15 invited) for time given to survey
 revise curriculum coordinator survey on questionpro.com to similar length of teacher survey
(NOT completed – principals did NOT offer encouragement in presenting coordinators with
survry
 obtain full manuscripts of the Lee study and Long study (UCI researchers) – not available
 view ST Math® Fractions demo, available through mindresearch.net
 investigate gaining access to ST Math® program (an app) – no independent usage
⇛ ONGOING; CONTINUE INTO FALL:
 read/study ST Training Manual in order to more effectively aid ST Math® students in new
school year and to make more informed observations of the program’s implementation
 investigate/attend training webinars offered for ST Math® (may not be offered in summer) –
none available after school hours
 keep up-to-date with Ed Week’s press releases and LinkedIn’s connections to ST Math®;
read/print relevant information for action research
 investigate the ST Manual’s information regarding symposiums and workshops, possibly for
the fall (partner with teachers from schools in the action research – a possibility)
 read evaluation of LAUSD’s implementation of ST Math® by WestEd (independent education
research company) and research whether they evaluated other districts as well
 view youtube submissions on ST Math®, as well as blog entries (some available in
mindresearch.net), reviews, critiques
EEaarrllyy ffaallll,, 22001144 (September, into October)
CONTINUE last six on-going tasks listed for the summer:
 ST Training Manual
 webinars – none available
 Ed Week; LinkedIn
 symposiums, workshops, professional development, IU13? – none avaialble

 WestEd’s evaluations of ST Math®
 blogs, reviews, critiques
 re-attempt surveying coordinators; maybe set up brief intro interview to discuss goals
of action research
 administer and collect data online (through questionpro) from curriculum coordinator
survey; thank coordinators for time given to research project – principals did not offer help
 administer and collect data online (through questionpro) from student survey – 8th
graders,
second year using ST Math®
 collect 2014 Math PSSA & Keystone Algebra I results for Spartan MS and Midstate Twp MS
(through district websites, paschoolperformance.org, schooldigger.com)
 collect data from any/all progress tracking tools (STAR test at Spartan MS, for example) –
none available
 assist ST Math® students in classes where it is being used
 use planning/prep time to observe other teachers’ implementation styles of ST Math®
LLaattee ffaallll,, 22001144 (October – December)
 continue to assist ST Math® students and actively discuss program with teachers
 organize data in preparation for triangulation (teacher, coordinator, and student surveys,
standardized test scores, benchmarking/progress tracking results)
 triangulate results in accordance with methods of analysis learned in EDG 596; prepare
discussions and conclusions
 review results and write final portions of action research project, including answer to
research question
 prepare and submit action research report
Methods of Data Analysis
Data from both qualitative and quantitative instruments were collected from June, 2014
through December, 2014. Triangulations of data sources were used to analyze the results in
order to draw conclusions, cite implications, make recommendations, and formulate an
informed answer to the research question. In the process, thematic results surfaced in three
categories: methods in the program’s implementation, specific preferences of teachers and
students, and comparative standardized test scores in relation to routine usage of the program.
These themes and supporting evidence are considered in the next section.

Data Analysis – Findings and Discussions
Data collected through action research instruments and testing results/demographics
sources were considered together as triangulation revealed distinct themes.
The first theme that surfaced involves how the schools implement the program and
corresponding concerns that teachers have voiced with implementing the program. While both
schools routinely require their low-achieving students to work on the ST Math® program, most
of my observing during substituting over the past two years has revealed that the work in the
ST Math® lessons is remedial in nature – the lessons attempted do not support current
classroom material being covered. Both schools follow the hybrid (rotational) model for Math
instruction, where the class period is split into three segments of roughly 28 to 30 minutes
each. Rotations are direct instruction, collaborative group, and independent work. ST Math® is
completed during the independent rotation. Only Spartan MS adds a whole-group instruction
portion of about 12 minutes to the beginning of the class, when students learn in a traditional
style during this warm-up time. Spartan uses the hybrid model for all its Math classes, both
high and low abilities. Midstate uses the model only for low-achievers, and their class period
length is similar to Spartan’s 90-minute period, but their average and accelerated classes are
traditional-style (45minutes), not hybrid. Teachers surveyed voiced concerns (see Teacher
Survey results in Appendix E, Table E2) in using the program, shown below as:
Do you believe the program has any
LIMITATIONS? If so, briefly describe.
TABLE E2: CONCERNS VOICED:
 need for weekly time reports
 total minutes, not total puzzles are reported to the teacher
 not clear on how to work some of the puzzles; connections
between puzzles and Math not clear
 students not paying attention to Math in midst of puzzles
 cannot connect puzzles with content taught in class

It is evident, through the concerns voiced in Table E2, that some teachers have a difficult time
connecting the purpose of some puzzles to the content taught in class, so they feel the program
is limited in its use and effectiveness. Additionally, another concern teachers voiced was that
students are not paying attention to the Math embedded in the puzzles. However, in my
observations, I have witnessed just the opposite – I often see students very focused as they
carefully choose pieces to complete a correct response in ‘making a puzzle work’, and if they
have problems, they do ask for my assistance. Some students touch the screen in visualizing
measuring pieces so that the parts fit to make the puzzle whole. I rarely find such focus in
other programs and in some of the other programs students ask fewer questions and make
more guesses. What frustrates me is the fact that students could very well obtain a correct
response in the other programs if they work out the problem presented on paper, but very few
students will do that. Since ST Math® is a visual program, most of the time paper really is not
necessary; visualizations suffice in getting through each puzzle successfully, but since each
response is proven or disproven, immediate feedback increases the chances of the student’s
next response as being correct. Seemingly, this method builds perseverance and concentration
while improving cognitive thinking skills and the understanding of complex concepts.
When asked to comment on use only with low-achieving students, Lucy Bonwaller
(pseudonym), an 8th
grade teacher at Spartan Middle School responded, “Since I teach
Keystone Alg (Algebra) this year, my students think STmath is too childish and simple. They
don't like the ‘games’ and it doesn't address the concepts for Keystone Alg” (Lucy Bonwaller,
email, December 5, 2014). Lucy’s comments suggest that the program was designed solely for

remediation of under-achieving students, thus reflecting the responses of her colleagues
(indicating that 80% of the students using the program are either on level or remedial):
What is the class ability level (or achievement level) of your students - those who are assigned to use the ST
Math® program? (CChhoooossee AALLLL tthhaatt aappppllyy) TTAABBLLEE EE11-- CCLLAASSSS AABBIILLIITTYY LLEEVVEELL
15 total responses:
☑ honors or advanced 13.33%
 20%
☑ accelerated (above average) 6.67%
☑ on grade level 33.33%
 80%
☑ remedial (below grade level) 46.67%
Table E1, shown above, is part of the Teacher Survey results, presented in Appendix E.
In contrast to Lucy’s comments, the UCI and MIND Research studies described in the literature
review support a stronger implementation where alignment of standards to ST Math® content
(the Schenke team’s study), the use of scaffolding (Schenke) and the need for one-to-one
assistance in computer-based instruction in order to transform into a student-centered class
(the Tran team’s study) promote an effective program in which progress is observed.
Furthermore, the program description (in mindresearch.net) includes the claim that the content
in ST Math® software is fully aligned to the standards, including Common Core. I would imagine
that more detailed materials are supplied with a subscription to the program.
The second theme revealed through data analysis centers on preferences expressed by
teachers and students involved with ST Math® and other Math software. When surveying the
teachers, ALL eight respondents answered “no” to the question asking whether they made use
of the teacher mode option available with the ST Math® program. This option, available with
any puzzle within the program, is designed to allow teachers to preview ST puzzles with
students. With this feature, pausing the animation so students can analyze visual feedback
(then explain in their own words what is happening in the puzzle) is an essential strategy for
teachers to explore routinely with students. As the teacher’s manual states, “This can be a

great instructional tool to illustrate important mathematical concepts as ST Math® games are
integrated into classroom lessons.” (ST Math® Training Manual, 2012, p. 18). As mentioned in
the first theme, integration is ‘key’ to success with the program in evaluating it as effective in
enhancing student progress. The Training Manual devotes a whole section to the importance
of teacher mode and emphasizes that its use is imperative in creating a sound, support program
for students to progress.
In examining the “preference” data in the student survey, some surprising results were
revealed as far as which software program is preferred (as most helpful in raising their efforts
and/or achievements in Math) by students and what part of the hybrid model is the most
beneficial to them in contributing to increasing their success in Math. Results are shown as
(Appendix H, student survey results, Tables H2 and H4):
Please check the program that you think helps or helped you the most in Math.
TTAABBLLEE HH22 –– MMOOSSTT EEFFFFEECCTTIIVVEE PPRROOGGRRAAMM
ALEKS 0%
This student response clearly indicates that students
prefer the IXL program over the ST Math® program
when evaluating its effect on their own progress in
Math class.
Compass Learning 6.32%
IXL 64.21%
ST Math® 17.89%
Study Island 5.26%
Other 6.32%  Khan Academy (2 responses)
Please give your HONEST rating for the following statements:
TTAABBLLEE HH44 –– RROOTTAATTIIOONN PPRREEFFEERREENNCCEESS
Strongly
Agree
Agree
Neither
Agree
Nor
Disagree
Disagree
Strongly
Disagree
Cannot
Make A
Judgment
I learn more about Math working on my own
on the ST Math® program than I do when I’m
working in my collaborative group or when
I’m getting direct instruction.
20% 30.53% 24.21% 24.21% 1.05%
I prefer working alone rather than in a group
when doing Math. 30.53% 21.05% 20% 26.32% 2.11%
The way ST Math® shows why my answer is
right or wrong definitely makes Math easier
to understand and is better than having a
teacher or aide explain the Math to me.
15.79% 23.16% 34.74% 25.76% 1.05%
I get more out of working in a collaborative
group than working alone on the ST Math®
personalized program.
46.32% 27.37% 11.58% 11.58% 3.16%

I learn more in direct instruction in Math
than I do when I’m working on my individual
program in ST Math®.
62.1% 18.95% 9.47% 6.32% 3.16%
As indicated in Table H2, the IXL Math program is preferred the most, over and above any of
the other programs – NO other program is even close to the 64% approval rating of IXL Math.
Additionally, table H4 shows that 62% of the students prefer direct instruction over ST Math®
and 46.3% prefer collaborative groups over ST Math®. Therefore, independent CBI is not a
preferred method of learning among those surveyed; instead many students are most
comfortable with traditional-style learning, referred to as direct instruction in the hybrid model.
This preference surprises me since students seemingly respond favorably (in both schools) to
the opportunity to use a computer as part of their daily routine in the classroom. Few students
abuse this privilege and most remain focused during this segment – at least this is what I’ve
consistently observed. Also, the opportunity to work at their own pace helps to remove the
anxiety that is associated with keeping up with the more advanced learners in the room.
The third theme that surfaced while analyzing data focuses on comparative standardized test
scores for the 2012-2013 and 2013-2014 school years in relation to the ongoing use of the
program.
In supporting these results, I had the opportunity, very recently, to informally discuss these
findings (and meanings) with Spartan’s principal, one of Spartan’s Math teachers, and a parent
of a Spartan MS student. The conversations occurred on December 18, 2014, when I was
assigned to Spartan MS as a substitute. I first met Jeremy Solaro (pseudonym, Spartan MS’s
principal) who commented on student preferences when I mentioned the students’ rating IXL
well over and above ST Math® as being the most beneficial as contributing to their progress in

Math. Mr. Solaro believes that IXL’s ‘worksheet look-alike’ appearance affected the students’
choosing it as most beneficial. He pointed out that it is the most straightforward so the
students immediately see the relevance. Also, he commented that the left-brain thinking may
go into overload when attempting puzzle after puzzle, so students naturally lose the connection
between puzzle solving and content being addressed in classroom lessons (Jeremy Solaro,
personal communication, December 18, 2014). Connie Jacobs (pseudonym), an office assistant
at Spartan MS, commented on ST Math® experiences she has had with her son, Peter
(pseudonym), a 7th
grader and ST Math® user at Spartan. She is one of those parents who helps
a Spartan student and finds the experience grueling and time-consuming. Connie noted that
her son frustrates over the fact that hours can be spent on the program before a single
percentage point is awarded – the percentages refer to how much of the program is completed
(in relation to the prescribed curriculum). Students are to complete 25% of their program (or
more) each quarter in order to receive full credit grade-wise for their ST Math® grade. They
also receive an IXL grade, but time spent and credit received in return is easier to handle.
Therefore, some students need to spend many hours at home on ST Math® in order to keep up
with each quarter’s expectations, as Connie explained (Connie Jacobs, personal communication,
December 18, 2014). Lastly, I was fortunate enough to find a 7th
grade Math teacher, Katherine
D’Alfonso (pseudonym), after school and willing to offer remarks about the program. Katherine
confirmed that the students frustrate over the time required to advance in completing the
program’s curriculum, and noted that the IXL program offers students the chance to improve
their scores (measuring correctness, not completion rate) by re-doing the quizzes. Since
students like the option to improve and the IXL program is more straightforward, she wasn’t

surprised that it is preferred over ST Math®. However, Katherine does see the value in the ST
Math®’s approach in training the mind to more deeply understand difficult, abstract concepts
(Katherine D’Alfonso, personal communication, December 18, 2014).
The Long study would be of value here in further emphasizing the importance of effective
professional development in increasing teacher confidence in implementing the program.
Additionally, Long’s team focused on how closely teachers followed the prescribed
implementation plan, including use of the teacher mode in improving student strategies, thus
cutting overall time spent on gaining percentage points towards the program’s completion. The
Long team would recommend that the teacher use the program frequently in whole-group
presentation so students could get an edge on more effective use of their time spent on the
program. Frustration seems to stem from students not being oriented as to what to do when
new challenges are presented. Likewise, the Tran team would recommend a follow-up on
Long’s whole-group instruction with some one-on-one assistance until the student has enough
confidence to sail through some lessons with more ease.
The last theme that emerged from the data analysis centers on the standardized test scores
for the two years that the program has been implemented so far (2012-2013 and 2013-2014).
While Appendix C offers a full comparison of both years and both schools, portions of the
matrix in the appendix are featured below as figure 8 through figure 14, along with comments
pertaining to changes and trends in PSSA and Keystone scores, and percentages as related to
ethnicity for various races, the economically disadvantaged, ELL’s, special ed students, and
gifted students. The figures and their corresponding remarks are offered below:

59.67
91.33
86.2
82.3
81.33
77.33
92.1
82.6
0 20 40 60 80 100
MIDSTATE MS: INDICATOR OF ACADEMIC
GROWTH IN MATH/ALGEBRA I (POINTS)
SPARTAN MS: INDICATOR OF ACADEMIC
GROWTH IN MATH/ALGEBRA I (POINTS)
MIDSTATE MS: PA SCHOOL PERFORMANCE
RATING (POINTS)
SPARTAN MS: PA SCHOOL PERFORMANCE
RATING (POINTS)
SCHOOL PERFORMANCE & ACADEMIC GROWTH
2012 - 2013 2013 - 2014
EETTHHNNIICCIITTYY OOFF SSTTUUDDEENNTT BBOODDYY –– SSEEEE FFIIGGUURREE 99 BBEELLOOWW
White/Caucasian
(comparison of ’12-’13 to
’13-’14 school years)
Spartan MS iinnccrreeaassee of 11..33 percentage points
Midstate MS ddeeccrreeaassee of ..11 percentage points
Minorities
Spartan MS
Hispanic: iinnccrreeaassee of ..0011 percentage points
Black: ddeeccrreeaassee of ..5566 percentage points; Asian: slight decrease
Midstate MS
Hispanic: iinnccrreeaassee of 11..3366 percentage points
Black: ddeeccrreeaassee of ..5522 percentage points; Asian: slight decrease
SSCCHHOOOOLL PPEERRFFOORRMMAANNCCEE AANNDD AACCAADDEEMMIICC GGRROOWWTTHH ((AAAAGGEE)) RRAATTIINNGGSS ((PPOOIINNTT VVAALLUUEESS))
SScchhooooll PPeerrffoorrmmaannccee
Spartan MS rating ddeeccrreeaasseedd by ..44%%
Midstate MS rating ddeeccrreeaasseedd by 66..4411%%
AAccaaddeemmiicc GGrroowwtthh ((AAAAGGEE))
Spartan MS rating iinnccrreeaasseedd by 1188..11%%
Midstate MS rating ddeeccrreeaasseedd by 2266..6633%%
FFIIGGUURREE 88

FFIIGGUURREE 99
0
20
40
60
80
100
SPARTAN: MATH
PSSA/KEYSTONE
(% PROF OR ADV)
MIDSTATE: MATH
PSSA/KEYSTONE
(% PROF OR ADV)
SPARTAN: EXTRA
CREDIT FOR
MATH
PSSA/KEYSTONE
(% ADV)
MIDSTATE:
EXTRA CREDIT
FOR MATH
PSSA/KEYSTONE
(% ADV)
81.65
88.05
52.62
67.28
81.12
85.71
59.84 63.12
PERCENT
MATH PSSA/KEYSTONE
%PROFICIENT AND/OR ADVANCED
2012- 2013 2013 - 2014
MMAATTHH PPSSSSAA//KKEEYYSSTTOONNEE –– %% PPRROOFFIICCIIEENNTT AANNDD//OORR
AADDVVAANNCCEEDD
%% PPRROO OORR AADDVV
(comparison
of ’12-’13 to
’13-’14 school
years)
Spartan
ddeeccrreeaassee of ..5533
percentage points
Midstate
ddeeccrreeaassee of 22..3344
percentage points
%% AADDVV
EEXXTTRRAA CCRREEDDIITT
(comparison
of ’12-’13 to
’13-’14 school
years)
Spartan
iinnccrreeaassee of 77..2222
percentage points
Midstate
ddeeccrreeaassee of 44..1166
percentage points
FFIIGGUURREE 1100

EECCOONNOOMMIICCAALLLLYY DDIISSAADDVVAANNTTAAGGEEDD
Comparison
of ’12-’13 to
’13-’14 school
years
Spartan
percentage points
Midstate
percentage points
EENNGGLLIISSHH LLAANNGGUUAAGGEE LLEEAARRNNEERRSS
Comparison
of ’12-’13 to
’13-’14 school
years
Spartan nnoo cchhaannggee
Midstate
percentage points
FFIIGGUURREE 1111
FFIIGGUURREE 1122

These particular groups with their corresponding comparative statistics were chosen
purposefully since variations in their scores and/or concentrations normally have an effect on
overall performance of the student body. Noting that Spartan’s school performance rating
decreased only slightly in comparison to Midstate (a .3 point decrease versus a 5.9 point
SSPPEECCIIAALL EEDD SSTTUUDDEENNTTSS
Comparison
of ’12-’13 to
’13-’14 school
years
Spartan
percentage points
Midstate
percentage points
GGIIFFTTEEDD SSTTUUDDEENNTTSS
Comparison
of ’12-’13 to
’13-’14 school
years
Spartan
percentage points
Midstate
iinnccrreeaassee of ..9911
percentage points
FFIIGGUURREE 1133
FFIIGGUURREE 1144

decrease), the graphical representations should give some insight as to why Midstate’s scores
dropped dramatically in comparison to Spartan’s. Standard Aligned Systems (SAS) defines the
Annual Academic Growth Expectation (AAGE) indicator as:
… performance measure represents the academic growth of students taking the Mathematics PSSA or
Algebra I Keystone Exam relative to changes in their achievement level/entering achievement during the
reported year. The Mathematics PSSA applies to students in grades 3 through 8. Academic growth
reported for Keystones ONLY includes the scores of students enrolled in a Keystone course at the time
they took the respective Keystone exam for students in the class of 2016 or earlier. For students in the
class of 2017 and thereafter, academic growth reported for Keystones includes the scores of all students
taking a Keystone exam. The Pennsylvania Added Assessment System (PVAAS) Growth Index is the basis
for the Annual Academic Growth calculation. The PVAAS Growth Index is the growth measure (change of
the achievement level for a group of students across grades) divided by the standard error (level of
evidence one has around a particular measure in relationship to the amount of growth made with a group
of students).
…Growth Index is converted to a scale ranging from 50 to 100. If the Growth Index is a zero, then the
school score is 75. If the Growth Index is 3 or higher, the school performance measure score is 100. If the
Growth Index is -3 or lower, the school score is 50. (A score can be no lower than 50.) Performance
measure scores are scaled proportionally within the range of -3 to +3: -3 to -2 (50.0 to 60.0), -2 to -1 (60.0
to 70.0), -1 to +1 (70.0 to 80.0), +1 to +2 (80.0 to 90.0), +2 to +3 (90.0 to 100.0). (pvaas.sas.com, 2014)
Midstate’s dramatic AAGE drop compared to Spartan’s increase gives rise to some concerns –
Midstate traditionally outperforms (by far) many schools throughout the county, but after
glancing at a listing of all the middle schools in the county (while substituting at Spartan MS), it
was discovered that for the 2014 rankings Midstate ranks fifth out of 23 middle schools while
Spartan ranks seventh.
The ethnicity statistics offer little since the white/Caucasian percentages varied very slightly
for both schools in comparison to the previous year. Likewise, the minority percentages varied
slightly as well, even though Midstate’s Hispanic population increased 1.36 percentage points.
As far as passing scores (proficient and advanced) are concerned, Midstate surprisingly
decreased over two percentage points while Spartan’s were almost the same as the previous
year’s. As for the advanced scores only, Spartan’s increased over seven percentage points
while Midstate decreased over four percentage points – very unusual for a district that

normally boasts of increases in achievements, even for the advanced.
As for the economically disadvantaged, once again Spartan’s large increase of over four
percentage points compared to Midstate’s increase of just over one percentage point doesn’t
make sense in relation to the dramatic lack of progress reported for the district. Even the
percentages pertaining to the ELL’s show very little change from the first to the second year in
the study.
When reviewing statistics on special education students, we find, once again, that Spartan’s
increased slightly while Midstate’s decreased slightly – another statistic that doesn’t make
sense when trying to figure what caused Midstate’s scores to suffer as they did.
Lastly, both schools reported a slight increase in the gifted student population, and once
again this should have factored into an increase in the proficient and advanced scores, but
didn’t.
Keeping in mind that many of the studies reported in this paper were completed recently in
California’s Los Angeles area, it is important to clarify that the area’s vastly changing
demographics has had almost an inverse effect on the progress of their students in Math. The
Pew Research Center issued some statistical facts in early 2014, summarized as follows:
YYEEAARR HHIISSPPAANNIICC PPOOPPUULLAATTIIOONN OOFF CCAALLIIFFOORRNNIIAA
1990 25.4%
2000 32.3%
2014 39%
www.pewresearch.org/fact-tank
It is interesting yet alarming to note that while the Hispanic population in California has been
exploding over the past twenty-five years, the state test scores, as indicated in Table 1 and
Figure 6 have been rising dramatically over two years. Seemingly, California’s districts have
found ways to meet the needs of its rapidly changing population; other district could only learn

from their continued successes.
I believe that the five research teams discussed in the literature review could shed some light
upon the situation, especially Midstate’s. Long’s team would most likely call for more in-depth
and rigorous professional development pertaining to the ST Math® program, and in doing so,
would have members of the MIND Research team assist in implementing the program within
actual classrooms. Schenke’s team could be called upon to emphasize the importance of
aligning the standards to the program and could also demonstrate with specific classes how
scaffolding is effective in computer-based instruction. Lastly, Tran’s team could assist in
transforming the classroom into a student-centered class and even help in making the one-on-
one contact with the students as effective and productive as possible. With a more intense and
focused goal, the expert researchers could possibly help both teachers and students use their
resources much more wisely and effectively in raising the achievements of students.
Limitations of the Research
The biggest limitation throughout this study is the fact that I don’t have my own classes since
I am a day-to-day substitute. Because of this I had to continually rely on the generosity of other
teachers and administrators and witness the program’s impact sporadically instead of daily and
consistently. Because of this it has been impossible to observe and comment on qualities such
as growth in perseverance, creativity, effort, motivation, stamina, better questioning and
answering methods, and overall attitude towards challenging concepts. Only teachers, staff,
and parents can make determinations on these qualities since they meet and work with the
students daily. Other limitations to the study include:
 lack of consistent access to the program (only sold to districts, not individuals)
 lack of ability to adjust students’ program to fit individual needs

 lack of access to benchmarking
 lack of consistent collaboration to investigate strategies in using the program
 lack of any professional development available to ‘observers’ (as I am considered)
 lack of longevity – study on the middle schoolers was completed in only two years;
MIND/UCI studies lasted longer and tracked specific classes
 lack of ability to “educate” parents on the benefits of the program – may have had more
favorable response from parents if they had some orientation to the program
 lack of access to individual PSSA/Keystone scores and corresponding PVAAS scores for the
students over the two years of the study (to determine individual growth)
 hybrid model and introduction of ST Math® were concurrent – cannot determine
effectiveness of either if both are new together; both may have effects on each other
 discrepancy between current study and those outlined in the literature review – studies
cited were conducted with elementary (not middle school) students
If any or all of these limitations could have been resolved, then my findings may have had
different interpretations. Therefore, validity may be in question since there are quite a few
limitations cited. Additionally, since the study was conducted on only two years of data and on
students in a very specific demographic area, results cannot be considered generalizable.
Implications and Applications to the Classroom
One of the most important points that materialized through this study is the fact that each
teacher and/or administrator has to determine what best suits the classes they are educating.
Along with that, program decisions should be with a clear purpose in mind. In my work with
remediation programs so far, I have reviewed several types. In determining what a particular
class may need in order to succeed, the teacher should determine what purpose the
intervention (or supplemental program) should serve. Some purposes include: remediation,
extra practice (for state testing or for curriculum support), acceleration/preview, and cognitive
skills development. While the ST Math® program can meet any of the purposes listed, its
strongest purpose lies in aiding in cognitive skill development. The program definitely helps
build perseverance and skills in multi-step problems, thus making the student more able to

attempt challenging problems. Since this is the program’s main aim, perhaps (as some of the
researchers expressed) in measuring growth, tests such as the TerraNova or the test of
cognitive skills (TCS/2 through McGraw-Hill) may seem more appropriate and a truer indicator
of readiness for more advanced Math classes (as compared to considering a PSSA score to
determine readiness).
If we are to serve our students fairly and meet their individual needs as best we can (thus
demonstrating social justice in education), then we need to assess what their individual needs
actually are and take them from where they are presently academically to as far as we can take
them, without overwhelming them to the point of frustration. Personalized computer-based
instruction with one-on-one supports fits nicely into the differentiated environment, where
each student grows at his/her own pace and makes advancements that are specific, not general
for the class as a whole. More and more I am witnessing personalized learning, mostly in the
schools where computers play an essential, daily role in class instruction, and especially in the
hybrid model. This classroom approach seems effective since students know that their goals
are realistic and personalized; therefore they respond more favorably and make consistent
progress towards their specific goals.
Steps in Future Research
If I had the opportunity to continue with this research and take it in any direction (with
unlimited funding), I would first attend professional development sessions on the use of the
teacher mode, then visit classes that use it routinely. This would give me a clear insight into the
benefits of this feature and help me to implement it properly in order to maximize the

program’s effectiveness. I believe the teacher mode unifies the program in the classroom and
helps the student to work the puzzles more quickly and independently.
Next, I would expand usage of the program to ALL ability levels, and begin its use in the
primary grades. Advanced/talented students can be challenged with higher levels in the
program and become even more advanced. This would support their advancement through
very difficult (bonus or brainbuster) problems in class.
Next, I would “follow” students for several years in order to track progress, and compare
their results with those students who had no exposure to the program for the same amount of
years. Studies over several years with the same students yield more valid, generalizable results.
Next, I would design a classroom model that best suits the pace and maturity of the
students. More mature students could probably benefit from the hybrid model daily, while
slower students would benefit from the hybrid only two to three times each week. Frequency
of the hybrid would depend on the complexity of the material being covered.
As far as testing for progress is concerned, I think yearly tests of cognitive skills (like the
TCS/2 by McGraw-Hill) would accurately track progress and help make recommendations based
on ability. Along with these results, I’d consider expanding my research to include investigating
the relationship between cognitive skills development and growth in mathematical ability. This
is a personal curiosity, and I would welcome an opportunity to explore it and then follow the
students to witness their successes in higher Math.
It would be very rewarding to design a program for a class that includes use of the hybrid
model fairly consistently together with software supports such as ST Math®. If given the
opportunity to serve as an instructional coach, I would, after the experience I had with this

research, make sure that the intervention chosen most closely matches the needs of the
students and the purpose of the support, in accordance with the goals of the class.
Conclusion
In addressing the question, ““How does the implementation of ST Math® (spatial-temporal),
a visual learning support program, impact progress for under-performing students within a
middle school classroom?”, the research I conducted on two local middle schools that currently
use the ST Math® program regularly revealed three themes focusing on methods of
implementation, preferences of teachers and students, and results as reflected in standardized
test scores over two years. While most classes that integrate the program use it daily for
remedial purposes, it was discovered that the program’s biggest asset is in its ability to help
students to develop stronger cognitive skills. Additionally, while most teachers surveyed
responded favorably to the program’s use, student surveys indicated that they preferred other
programs, ones that required less time to make advancements and included opportunities to
better their scores in individual assessments. Lastly, the standardized test scores over two
years for these students in the study revealed very little growth in comparison to the studies
conducted over several years by teams hired by the program’s creators, thus raising concerns
about implementation procedures.
In conclusion then, it seems reasonable to state that the program has value when
implemented according to its original purpose – to provide incremental support to the
development of cognitive skills in elementary students over several years of use. Through this
developmental process, students become more equipped to enjoy greater success in Math in
attempting challenging problems that require multi-step procedures.

References
Chicago Public Schools: District Profile of Achievement. (2012). Retrieved from
http://www.mindresearch.net/pdf/Chicago_Public_Schools.pdf.
District Administration Custom Publishing Group. (April, 2013). ST Math® raises both scores
and confidence at Arizona middle school. District Administration, 49(4), 27.
District Report Card (2013). Retrieved from http://www.paschoolperformance.org.
Dynarski, M., Agodini, R., Heaviside, S., Novak,T., Carey, N., Capuzano, I., et al. (2007).
Effectiveness of reading and mathematics software products: Findings from the first student
cohort. Washington, D.C: U.S. Department of Education.
Finley, S. (2013). ST Math®. Internet@Schools, 20(4), 29-30.
Fratt, L. (2007). Music + math = unprecedented proficiency. District Administration, 43(1), 23.
Kibrick, M., Rutherford, T., Burchinal, M. R., Richland, L. E., Conley, A., Long, J. J., ... & Martinez,
M. (2010). The effects of ST Math® on standardized test scores: A randomized field study.
In The Fifth Annual Institute of Education Sciences Research Conference, Washington, DC.
Lee, D. S. (April, 2014). Impact of ST Math® on cognitive abilities. Abstract retrieved from
http://education.uci.edu/news/2014/AERA/impact_STmath.php.
Long, J. J. & van Es, B. (April, 2014). Understanding the relationship between ST Math® teacher
professional development and its impact on students. Abstract retrieved from
http://education.uci.edu/news/2014/AERA/understanding_STmath_pd.php.
Lopez, M. H. (2014). In 2014 Latinos will surpass whites as largest racial/ethnic group in
California. Retrieved from http://www.pewresearch.org/fact-tank.
Martinez, M.E. (n. d.). World-class STEM education: Projects that advance teacher proficiency

and student learning in science and mathematics [PowerPoint slides]. Retrieved from
http://gse.uci.edu/foundation_111609/uci_Found_Martinez.ppt.
Mathematics/Algebra I - Meeting Annual Academic Growth Expectations (2014). Standard
Aligned Systems, Inc. Retrieved from http://pvaas.sas.com.
Midstate School District (2014). District Demographics. Retrieved from
http://www.midstatesd.net.
Nisbet, N. & Luther, D. (2014). Better blends with visual game-based math. Retrieved from
http://mindresearch.net.
Peterson, M. (March, 2011). What’s wrong with math? District Administration, 47(3), 48.
Royal, K. (2007). Mind, music and math. District Administration, 43(12), 18.
Rutherford, T., Hinga, B., Chang, A., Conley, A. M., & Martinez, M. E. (August, 2011). The effect
of ST Math® software on standardized test scores via improvement in mathematics
expectancy. Paper presented at the annual meeting of the American Psychological
Association, Washington, D.C.
Rutherford, T., Kibrick, M., Burchinal, M., Richland, L., Conley, A., Osborne, K., ... & Martinez, M.
E. (May, 2010). Spatial temporal mathematics at scale: an innovative and fully developed
paradigm to boost Math achievement among all learners. Paper presented at the annual
convention of the American Educational Research Association, Denver, CO.
Schenke, K., Rutherford, T., & Farkas, G. (2014). Alignment of game design features and state
mathematics standards: Do results reflect intentions? Computers & Education, 76, 215-224.
School Digger (2013). Pennsylvania school district rankings [Data file]. Retrieved from
http://www.schooldigger.com.

Spartan School District (2014). General district facts. Retrieved from http://www.spartan.org.
ST Math® 2010 Teacher Survey (2010). Retrieved from
http://www.stmath2010teachersurvey.questionpro.com.
ST Math®: K – 5 and secondary intervention training manual (2012). Santa Ana, CA: MIND
Research Institute.
Tran, N. A., Schneider, S., Duran, L., Conley, A., Richland, L., Burchinal, M.,... & Martinez, M. E.
(2012). The effects of mathematics instruction using spatial temporal cognition on teacher
efficacy and instructional practices. Computers in Human Behavior, 28(2), 340-349.
United States Census Bureau (2010). District borough demographics [Data file]. Retrieved from
http://www.factfinder2.census.gov.

APPENDIX A. General District Facts - from district website (Spartan.org/district.cfm)
2013-14 - DISTRICT FACT SHEET
Total Student Population – 3246; enrollments:
 Elementary School 1: 632
 Spartan Middle School: 526
 Spartan High School: 1050
 Spartan Virtual Academy: 45
Aid Ratio: .2882
Per Student Expenditures: $14,360.25
Tuition rate:
 Elementary $9,051.58
 Secondary $9,515.25
Class of 2013 stats: 262 students,
Senior Survey Summary:
 College: 43% (4 years); 12% (2 years)
 Trade/Technical School: 7%
 Deferred Post-Secondary: 10%
 Military: 3%
 Permanent Employment: 25%
Miscellaneous:
 Total school buildings in the district: 5
 Free/reduced lunch: 29.3% (2012, middle school)
 Average number of lunches served per day: 2300
 Number of students transported for non-public schools: 444
 Total teachers with advanced degrees (Master’s and above): 151
Number of Employees:
 Professional: 256
 Administration: 15
 Support Staff: 83
Community Population: 30,059
 sq mi: 95
Financial Information:
 Mileage: 13.841
 Total Assessed Property Value: $2,058,269,700
 Total Budget 2012-13: $44,265,811
 Total Salaries for bargaining unit: $13,688,030.14
 Average teacher salary: $59,851.46
 Starting teacher salary: $43,548

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