Running Head: BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY 1 Back to Basics: Benefits of Developing Basic Math Automaticity University of New England EDU-690 Action Research Project Lynn E. McGee Statement of Academic Honesty: I have read and understand the plagiarism policy as outlined in the “Student Plagiarism and Academic Misconduct” document relating to the Honesty/Cheating Policy. By attaching this statement to the title page of my paper, I certify that the work submitted is my original work developed specifically for this course and to the MSED program. If it is found that cheating and /or plagiarism did take place in the writing of this paper, I acknowledge the possible consequences of the act/s, which could include expulsion from the University of New England.
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Running Head: BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY 1
Back to Basics: Benefits of Developing Basic Math Automaticity
University of New England
EDU-690 Action Research Project
Lynn E. McGee
Statement of Academic Honesty: I have read and understand the plagiarism policy as outlined
in the “Student Plagiarism and Academic Misconduct” document relating to the
Honesty/Cheating Policy. By attaching this statement to the title page of my paper, I certify that
the work submitted is my original work developed specifically for this course and to the MSED
program. If it is found that cheating and /or plagiarism did take place in the writing of this paper,
I acknowledge the possible consequences of the act/s, which could include expulsion from the
University of New England.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Abstract
Many middle school students do not possess automaticity of basic math skills in addition,
subtraction, multiplication and division. Use of ineffective strategies to recall basic math facts,
such as counting on fingers, consume a large portion of working memory, leaving little to no
capacity for higher level mathematical concepts. This action research focused on a triangular
evaluation of select 7th
graders who participated in a numeracy intervention, known as the
Back to Basic Program, to help build mathematical automaticity. Various research-based
strategies were implemented to build fluency, and timed assessments were used to
determine automaticity. Results show conclusive evidence that as students achieved
automaticity of basic math skills, their confidence and attitudes towards learning
mathematics increased. It is recommended that standardized test results be comparatively
analyzed at the conclusion of the school year.
Keywords: automaticity, basic math skills, intervention, mathematics fluency, working
Rationale for Study ................................................................................................................................... 5
Need for research .................................................................................................................................. 5
Problem Statement ................................................................................................................................ 6
Participants and Site .................................................................................................................................. 7
Research Questions ................................................................................................................................... 7
Literature Review .......................................................................................................................................... 9
International Rank of the United States in Mathematics .......................................................................... 9
US Department of Education National Mathematics Advisory Report (2008). ................................. 10
Australian educational research. ......................................................................................................... 10
Automaticity and Fluency ....................................................................................................................... 12
Benefits of automaticity. ..................................................................................................................... 13
Detection, practice and repair. ............................................................................................................ 13
Conclusions of the Literature Review ..................................................................................................... 14
Research Design...................................................................................................................................... 15
Data Collection Plan ............................................................................................................................... 16
Data Validity ........................................................................................................................................... 19
Triangulation of Data. ......................................................................................................................... 20
Appendix C ................................................................................................................................................. 43
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Introduction
Rationale for Study
This action research project was designed, executed and analyzed by Lynn McGee who is
a 7th
grade Mathematics and Science teacher at Graham Middle School (GMS) in Graham, NC.
GMS is one of seven middle schools in the Alamance-Burlington School District. It is a diverse
school whereby more than 80% of the student body receives free or reduced lunch (Title 1).
Currently, GMS is classified as a Focus School for the state of North Carolina as they have not
met their Annual Yearly Progress (AYP) targets, in accordance with the No Child Left Behind
requirements, for two consecutive years. Overall math scores on the 2011-2012 End of Grade
Tests for 7th
grade Mathematics show that approximately 75% of the students are at grade level.
Mathematics teachers at GMS have all observed an alarming behavior in their
mathematics classes. A large portion of students perform basic math skills by counting on their
fingers, drawing tick marks on their papers for performing multiplication, or use other inefficient
strategies for computing basic math facts. Such strategies are being used across the spectrum of
ability ranges which span from the learning disabled to the academically gifted. Many students
cannot perform basic, rudimentary math operations, such as multiplying multi-digit numbers or
perform long division, without a calculator. There is little fluency or automaticity in basic
mathematics.
Need for research. As we enter the 21st century, the United States is no longer the
leader of developed nations in mathematics and science. We are ranked 25th
out of 30
participating countries on the worldwide standardized test, Programs for International Student
Assessment (PISA), in math and science for 4th
and 8th
grade students. Something has drastically
changed over the last several decades in our educational system to cause such lack-luster results.
Why are our students underperforming in math and science? Why are students entering middle
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
school still counting on their fingers to do basic arithmetic? There is very little documented
research originating in the United States on this subject. Educators are not identifying the root
cause of this decline. Instead, our educational system focuses on pushing higher level
mathematics concepts further down into elementary school. Perhaps this is the opposite of what
should happen? Instead of accelerating 2nd
and 3rd
grade students through basic mathematic
skills so that algebraic concepts can be introduced; maybe we should focus on ensuring that
students possess mathematical automaticity before they exit elementary school? This is why
more research is needed in this area. The Australian educational system has focused their efforts
on automaticity of basic math skills for middle school level students, and is now one of the top
ranking countries in the world in math and science.
Problem Statement. A high percentage of the middle school students who attend GMS
do not possess fluency or automaticity in basic math skills of addition, subtraction, multiplication
and division. As students learn new mathematic skills, they should become fluent and be able
to recall facts with accuracy and swiftness. Automaticity results after a student is fluent with
these skills and can recall the facts accurately, timely and with little awareness of the task
according to Axtell, Bell, McCallum, and Poncy (2009). Many GMS students, including the
academically gifted students, use inefficient strategies, such as counting on their fingers, to
perform basic arithmetic computations. Students with Learning Disabilities (LD) are even more
reliant on inefficient cognitive strategies and non-strategic ways of processing information
(Bellert, 2008). Their working memories become consumed with basic mathematical
computations. According to Gagné (1983), as cited in Axtell et al. (2009), mathematical
computations are processed in the working memory which can only process a few computations
at a time. Thus, higher level mathematic calculations, such as algebraic computations, cannot be
completed if the working memory is consumed with basic math computations.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Participants and Site
Participants in this action research were selected from the 7th
grade at GMS in Graham,
NC. One hundred students participated in a numeracy intervention program known as the Back
to Basics Program, specifically designed for this action research. The main function of the
program is to assist students with achieving automaticity of basic math. Sixty percent of
participating students require Tier 2 Response to Intervention assistance. Twenty percent of the
participants are academically gifted and the remaining 20% balance is regular education student.
Twenty of the participating students were designated as Academically and Intellectually Gifted
(AIG) students. They were asked to participate because many of these students still count on
their fingers when doing basic math operations. All three of the 7th
grade math teachers
participated in the implementation of the program. Parents and guardians were also asked to
complete an opinion survey.
Research Questions
1. Is it possible to improve basic math automaticity for 7th grade middle school
students, including those with identified learning disabilities and the AIG students, by
using timed, on-line basic math skills assessments and direct instructional strategies
developed specifically for increasing automaticity?
2. Do timed, on-line assessments with instant feedback increase student automaticity in
basic math skills?
3. What do middle school students consider their most preferred strategies for building
automaticity of basic math skills?
4. Does the improvement of automaticity of basic math skills improve standardized
assessment results for middle school students?
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
5. Does the improvement of automaticity in basic math skills improve middle school
students’ attitudes towards learning mathematics?
Hypotheses
Developing middle school students’ automaticity of basic math skills in addition,
subtraction, multiplication and division via research-based strategies and timed assessments with
immediate feedback will 1) improve student performance on standardized mathematics
assessments, and 2) will improve student confidence and attitudes towards learning mathematics.
Administrative and Institutional Limitations
School administrators strongly supported this action research. Administrators consider
the Back to Basics Program a Tier 2 intervention for students identified via the Response to
Intervention process. Necessary resources, including additional teacher support, were provided
for the program. The main obstacle for this program was the weak computer network
infrastructure. Limited bandwidth and insufficient wireless connectivity are opportunities for
improvement. Administration is aware of these issues and estimates that wireless routers will be
installed by January, 2013 which should alleviate the slow computer response time.
Action Plan
To launch this action research, approximately one hundred 7th graders were identified to
participate in the Back to Basics Program. Participating students were assigned to one of the
three 7th
grade math teachers who instructed, coached and taught strategies to develop
automaticity of basic mathematic facts in addition, subtraction, multiplication and division. The
web-based program, Thatquiz, (Version 2012), was the software program of choice used to
administer timed math drills. The mathematics teachers oversaw and led daily instruction for
participating students, five days per week, during the 45 minute Mastery time period. Data was
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
collected weekly regarding the number of students who become automatic in the respective areas
of addition, subtraction, multiplication and division. Students who attained automaticity of these
four skill areas were rotated to another classroom where they were further challenged by taking
timed assessments for adding and subtracting negative and positive integers, multiplying
negative and positive integers and various other computations involving fractions and decimals.
Literature Review
International Rank of the United States in Mathematics
In 2009, review of United States performance in mathematics literacy on the Programs
for International Student Assessment (PISA) unveiled disappointing statistics for our 4th
and 8th
grade students. The United States ranked 25h in combined mathematics literacy out of 30
countries. Our average score was 9 percentage points below the mean score of all 30 countries
that participated. Although there was a slight increase in performance between the 2006 and
2009 results, there is no significant improvement in mathematical literacy as compared to the
2003 PISA scores according to Fleishman, Hopstock, Pelczar, and Shelley (2010). Table 1
shows the results on the mathematics literacy assessments for all three years of available data.
Many students are not mastering, with speed and accuracy, basic mathematics skills which
include addition, subtraction, multiplication and division (Adcock et al., 2009). As students
enter middle school and high school, those who have not mastered these basic math skills rely on
inefficient strategies, such as counting on their fingers, to determine answers. Unfortunately,
such strategies occupy students’ working memory (short term memory) which has a limited
capacity. Consequently, higher level thinking skills, requiring cognitive capacity within the
working memory, cannot be employed to solve more challenging mathematical concepts (Byers,
2009).
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Table 1
United States Ranking in the Programs for International Student Assessment (PISA)
Year
Mean Score
(30 Participants) USA Score USA Intl Rank
USA
Points Below Mean
2003 500 483 24th 17
2006 498 474 25th 24
2009 496 487 25th 9
US Department of Education National Mathematics Advisory Report (2008). In
2006, President George Bush established the National Mathematics Advisory Panel to advise
how to improve mathematics education in the United States as students’ math achievement is
steadily declining on international assessments in mathematics and science literacy. The
advisory panel concluded that mathematics achievement in the US begins to fall off when
students reach late middle school. Coincidently, this is the time when students begin to learn
algebra. Research shows that success in college and in the workforce is directly related to a
student’s ability to successfully complete Algebra II level mathematics. After hearing testimony
and suggestions from many organizations and individuals, the advisory panel framed their report
on research related to how children learn. Their findings confirm the importance of having
students master their basic math facts until they become automatic and stored in long term-
memory. Only then will this leave room in their working memory to absorb and comprehend
new math skills and concepts (National Mathematics Advisory Panel, 2008).
Australian educational research. Australian educators experienced similar trends with
their educational system. Students with learning disabilities were up to five levels behind their
average achieving peers by the eighth grade (Bellert, 2008). Socioeconomically disadvantaged
students and those living in rural areas comprised a large portion of such underachieving
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
students. Upon further examination, Australian educational researchers identified that their
mathematics curricula, primarily in the lower grades, use a constructivist approach which has
limited benefits for students with learning disabilities. Swanson and Hoskyn (1998), as cited in
Bellert (2008), identified that cognitive strategy instruction using a combination of direct
instruction and strategy instruction is a highly effective approach to use with students who
struggle with attaining automaticity of basic mathematic skills.
One of the most beneficial features of automaticity regarding mathematics is the
augmentation of efficient and effective cognitive processing (Perfetti, 1992) as cited by Bellert
(2008). Conversely, not possessing automaticity leads to labor intensive efforts regarding math
computations students have seen many times before. Bellert and Graham, from the University
of New England in Australia, developed the QuickSmart Program as a response to intervention to
address these shortcomings. Their research disclosed that students must be taught effective
strategies to overcome their roadblocks regarding simple math facts. The initial cohort of 20
students was comprised of 8 average-achieving students and 12 learning disabled (LD) students.
All 20 students were pre-tested to establish a starting reference. The 8 average –achieving
students did not participate in any interventions, but their automaticity abilities were monitored
for comparison with students receiving in QuickSmart interventions.
The QuickSmart Program uses the software package known as Cognitive Aptitude
Assessment Software (CAAS) developed at the University of Massachusetts (Bellert, 2008).
This software records responses of the participants as they speak into a microphone when they
know the answer to a stimulus that appears on a computer screen. Use of this software for the
Back to Basics Program was not possible due to financial limitations and budget constraints for
Graham Middle School.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Australian researchers were also interested if the improvement of automaticity in basic
math resulted in increased standardized test scores. All 20 students in the Australian cohort were
given the Progressive Achievement Tests in Mathematics, Revised (PATMaths Revised), before
and after any interventions were administered. Using a meta-analysis, which combines the
results of many tests to determine the average effect, the means and standard deviations for pre-
tests and post-tests were determined. The resultant effect size was determined to be 0.65
(Bellert, 2009). This suggests that mean scores from the post-PATMath Revised tests were 0.65
standard deviations above the pre-PATMath Revised test scores. This increase in standard
deviation is also known as effect size. Cohen (1988), as cited in Bellert (2008), suggests that
effect sizes of 0.65 are considered medium to large gains. Marzano, Pickering and Pollock
(2001) suggest that an effect size of 0.65 translates to a percentile gain of 24 to 35 on
standardized tests.
Automaticity and Fluency
There is a distinction between automaticity and fluency regarding math basics according
to Adcock et al. (2009). Fluency refers to the ability to respond to stimuli quickly and
accurately. Automaticity refers to the ability to respond to stimuli quickly, accurately and require
little cognitive effort. Many researchers focus only on students with learning disabilities
regarding mathematical automaticity. However, practicing mathematics teachers at Graham
Middle School have detected that even students classified as academically gifted are not fluent
with basic math skills. Research based strategies used to develop automaticity in students with
learning disabilities are also directly applicable for developing automaticity in regular education
students and the gifted. As stated by Graham, Bellert, Thomas and Pegg (2007), “the need for
effective interventions to support middle school students with learning disabilities is clear.”
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
When the working memory of students is freed from basic math computations, higher level
mathematical cognition will occur. The ultimate goal is to improve all students’ automaticity of
basic math skills in parallel with providing essential strategies to retain such skills.
Benefits of automaticity. Results from several research studies from across the globe
regarding the improvement of students’ basic math automaticity have many positive outcomes.
The Australian-designed QuickSmart Program (Bellert, 2008) confirms that when students attain
mathematical automaticity, effect sizes of .65 and higher (24 percentile points growth) are
possible for struggling middle school students on standardized math assessments. Researchers
have also noted that participating students who attain automaticity seem to have an increased
confidence regarding math. Students also seemed to be more willing to participate in math class.
Geary (1996), as cited in Bellert(2009), stated that without intervention, middle school students
will not become automatic with basic math if they do not already possess automaticity,
especially for those with learning disabilities.
An additional positive outcome for students who develop basic math automaticity is their
improved proficiency in performing higher level mathematics. Once the working memory is
freed from laboring basic math computations, they can process higher level math concepts.
Detection, practice and repair. Cates et al. (2003), as cited by Adcock et al. (2009),
suggest that instruction of math basics should be adjusted such that mastered facts are not the
focal point. Only the math facts that are not automatic should be focused upon. As a result,
Axtell, Poncy, and O’Mara (2006), as cited by Axtell, Poncy and Skinner (2010), recommend a
procedure known as Detect, Practice and Repair (DPR) to fortify math automaticity.
The DPR procedure consists of three phases. In the first phase, known as Detection,
students are required to take a pre-test. Math facts are introduced at a metronome cadence of 1.5
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
seconds per math fact. Only those facts not answered during this timed test are focused upon
during the next phase known as the Practice phase. The theory of this technique is to only focus
upon facts that students do not have automatically. Once a fact is rooted in their long term
memory, there is no need to practice it. Axtell, Poncy and Skinner (2010) suggest that during the
Practice phase, students apply the Cover, Copy and Compare (CCC) strategy multiple times
until the students feel they have these facts implanted for automatic recall. The final phase is
known as the Repair phase whereby students take fluency drills or sprints at one minute
intervals. After each one minute sprint, students are given instant feedback on their
performance.
A substantial number of researchers support this technique (Axtell, Poncy & Skinner,
2010) as evidence from this study show that math fluency was enhanced. The mean student
score increased by 63% in a two week period using slightly more than two hours of instructional
time.
Conclusions of the Literature Review
The review of the literature has confirmed that students who lack automaticity with lower
level, basic math facts are hindered from learning higher level mathematical concepts. Cognitive
capacity in humans, also referred to as the working memory, has a finite capacity. Students who
use inefficient strategies to recall basic math facts are using their working memory capacity for
these low level skills and cannot comprehend the more challenging skills. However, if students
develop automatic performance of these lower level tasks, such that they become fast and
routine, the working memory can be opened up for more challenging, higher order thinking and
learning skills. Even though most of the literature on this subject is focused on students with
learning disabilities, the benefits of automaticity can be applied to students of all ability levels.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Perhaps this could be one root cause as to why the United States has fallen behind other
developed nations in mathematics and science literacy.
Students’ attitudes towards learning mathematics and their confidence while learning
mathematics improves as students become automatic. Instead of being embarrassed when called
upon for answers, they are more willing to volunteer in class. There is less of a tendency to have
a defeatist attitude. Conversely, there is a strong need for teachers to identify effective strategies
for students who struggle with their basic math facts. Frequent review of facts and use of mental
math during class without the use of calculators could also benefit students who are not
automatic.
Methodology
Research Design
This purpose of this action research was to determine if building students’ automaticity
regarding basic math skills will improve their performance on standardized mathematics
assessments and improve their confidence and attitude towards learning higher level
mathematics. The Back to Basics Program was developed for this action research to assist
building student automaticity in basic mathematics across the entire spectrum of learning
abilities at Graham Middle School. Students classified as Learning Disabled, Academically and
Intellectually Gifted and those who are in regular education classes participated in the program.
The program was administered by the three mathematics teachers in the 7th
grade at Graham
Middle School. The main component for developing automaticity was the use of computer-
assisted, timed quizzes. As students received immediate feedback from the timed assessments,
various strategies were used to help them master the facts they were struggling with in addition,
subtraction, multiplication and division.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Student testing. Students who participated in the Back to Basics Program worked on
timed, basic mathematics assessments during their 45 minute Mastery block using Thatquiz.org
(Version 2012). There were four independent timed tests in addition, subtraction, multiplication
and division. Each assessment required students to answer 100 problems in a three minute time
period. Students were deemed proficient when they answered 95% of the questions correctly in
the allotted time. The assessments were designed such that students were locked out of the
assessment if they achieve proficiency. Otherwise, students were able to take the assessments an
unlimited amount of times until they reached the 95% proficiency level. Each student that
participated in this action research was asked to complete a Student Opinion Survey.
Quantitative data. Student proficiency data was collected and analyzed each week by
downloading the information from Thatquiz.org (Version 2012). The number of students that
achieved automaticity in each assessment type was tallied weekly. Data regarding cumulative
weekly proficiency were also collected from the Thatquiz.org software (Version 2012).
Qualitative data. Opinion survey data from students, parents/guardians and teachers
were collected using SurveyMonkey software (Version 2012). The Student Opinion Survey
(Appendix A) and the Parent/Guardian Opinion Survey (Appendix B) were designed using ten
subjective questions. Likert Scale values were used so that quantitative results could be
determined (Mills, 2011). Each survey question was analyzed, and the mean values were
calculated for each question. All suggestions from the surveys were categorized and ranked in
frequency charts. A Teacher Evaluation Survey, using Likert Scale questions, was used to
provide feedback and strategies for opportunities to improve the Back to Basics Program.
Data Collection Plan
Data were collected from a variety of sources. Students’ proficiency levels regarding
their automaticity of basic addition, subtraction, multiplication and division were collected via
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
computer timed assessments using Thatquiz.org (Version 2012). These data were compiled into
an Excel spreadsheet for analysis. District benchmark assessment results using Thinkgate
(Version 2012) software and End of Grade standardized test data provided by the NC
Department of Public Instruction will be collected after this action research has been finalized.
Student Opinion Surveys, Parent/Guardian Opinion Surveys and the Teacher Evaluation
Surveys were created using SurveyMonkey (Version 2009) software (Appendix A, B & C). All
surveys incorporate Likert Scale questions which facilitate the conversion of subjective results to
quantitative results. The addition of student views and opinions makes this action survey
somewhat unique as most of the reviewed literature sources reviewed do not consider the
students’ points of reference. As in real world situations, the best solutions lie in the hands of the
workers, or students in this case, and should not be ignored.
Parents and guardians are one of the structural supports in this research. This group is
the most difficult to poll as many parents do not have access to computers or the internet. For
those without internet access, telephone interviews are scheduled to poll parents using the survey
questions taken directly from the Parent/Guardian Opinion Survey (Appendix B). These results
were entered in to the SurveyMonkey (Version 2009) data manually.
When colleagues were asked to provide feedback on the Data Collection Plan for this
action research, one excellent suggestion was to determine the students’ preferred learning styles
and match instructional strategies for learning math facts accordingly. Matching a student’s
learning style to various strategies would most likely have a positive impact on a student
reaching automaticity in math.
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Participants
Select Graham Middle School 7th grade students were chosen for this action research
from two pools of learners. The first 60 students that began the Back to Basics Program were
identified as Tier 2 Response to Intervention candidates by school administration. These
students typically are one to two grade levels behind in mathematics in accordance with the
North Carolina End of Grade standardized test results. Additionally, 20 Academically and
Intellectually Gifted 7th
grade students and 20 regular education students were also included in
this action research as many of these students were noticed counting on their fingers to perform
basic math computations.
All parents or guardians of the students involved in the Back to Basics Program at
Graham Middle School were sent the Parent/Guardian Opinion Survey to determine if they could
detect a positive change in the attitude of their child with respect to learning mathematics.
Although parental consent was not required for this action research per the administration of
Graham Middle School, parents were informed of their child’s progress in the program (Mills,
2011). The principal at Graham Middle School suggested that an automated telephone
communication be sent to all parents advising them of the pending survey.
All three of the 7th
Grade mathematics teachers at Graham Middle School were involved
in this action research and used the same evaluative instruments. Data from all three teachers’
Mastery classes were combined into one database for analysis.
Instruments
The participating students used their student laptops and the Thatquz.org software
(Version 2012) program as the main instrument for this action research program. Opinion
surveys for both students and parents were generated using Survey Monkey (Version 2009)
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
software. The Microsoft Excel spreadsheet software (Version 2010) was used to manipulate data
for analysis and graphing.
Interventions
One systemic intervention implemented early in the data collection phase of the program
involved the installation of a classroom wireless router to permit student computers to connect to
the school’s computer network. Prior to this intervention, limited or nonexistent connectivity to
the internet was preventing student access to the Thatquiz.org (Version 2012) timed assessments
for the Back to Basics Program. The implementation of this intervention resulted in strong
connectivity to the internet in a relatively short period of time. Response time during testing was
greatly improved.
Instructional interventions were implemented when students had 20 or more unsuccessful
attempts on one of the four basic math timed assessments using the Thatquiz.org (Version 2012)
program. Students were required to work in small groups that focus on just the facts that had not
been mastered. Flashcards, manipulatives and activities were used until students felt confident
to resume the on-line timed Thatquiz.org (Version 2012) assessments. Participants were
remediated until they become proficient in all timed assessments. Once a student attained
automaticity in the areas of addition, subtraction, multiplication and division, they were sent to
another teacher to work on higher level skills.
Data Validity
Data validity is an important aspect of teacher-led action research which typically falls
under the umbrella of qualitative research. Since this action research was based in the context of
a program designed for 7th
graders at Graham Middle School, the validity, credibility and
reliability of the research and all associated data are measured by the stake-holders of the school.
Greenwood and Levin (2000), as cited in Mills (2011), suggest that the actions of such
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
stakeholders, based on the results of the research, lend credibility and validity to the research
because actions will be taken in direct response to the findings. Action was taken based on the
results from triangulated data sources. The contexts of automaticity of basic math skills for the
stakeholders of GMS can be extrapolated and transferred well beyond the confines of this
research.
Triangulation of Data. Triangulation of data was designed into this action research by
soliciting the opinions and evaluations of parents, teachers and students. Subjective data were
combined with tangible, concrete formative and summative assessments scores (Mills, 2011),
which resulted in worthy triangulation. As shown in Table 2, multiple data sources are linked to
the research questions.
Peer Review. The data collection plan was given to participating teachers and
administrators for review and feedback. All participants responded favorably to the plan. The
principal suggested that the automated message system be used to notify applicable parents
regarding their child’s participation in the Back to Basics Program. All solicited stake-holders
agreed that the collection of student opinion surveys was a good idea.
Table 2
Data Triangulation
Research Questions Data Source
1 2 3 Do timed, on-line basic math
skills assessments and
direct instructional
strategies improve
student automaticity in
basic math?
Back to Basics
Program assessment
results
Teacher
Evaluation via
survey
(Appendix C)
Student Opinion Survey
(Appendix A)
Does instant feedback
increase student
automaticity in basic
math skills?
Student Opinion
Survey
(Appendix A)
Back to Basics
Program timed
assessment results
Teacher Evaluation via
survey
(Appendix C)
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BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Students’ preferred methods
of building automaticity
of basic math skills?
Student Opinion
Survey
(Appendix A)
General Student
Population
Brainstorming
Sessions
Teacher Evaluation via
survey
(Appendix C)
Does automaticity of basic
math skills improve
standardized
assessment results?
District Standardized
Benchmark
Assessments
Summative
Assessments and
Report Cards
End of Grade Assessments
Are students’ attitudes
towards learning
mathematics improved
by attaining
automaticity?
Student Opinion
Survey
(Appendix A)
Teacher
Evaluation via
survey
(Appendix C)
Parent/Guardian Survey
paper survey
(Appendix B)
Results
Findings-Student Performance
Quantitative Results. Beginning in early September, 2012, 100 select 7th
graders from
Graham Middle School participated in the Back to Basics Program as part of this action
research. Table 3 shows a summarization of the cumulative number of participating students that
ascertained automaticity in each of the four basic math skills of addition, subtraction,
multiplication and division. By the end of the 7th
week, 74% of participating students had
achieved automaticity in basic addition. It is noteworthy that of the 100 participants, 20% were
classified as academically gifted and 60% were considered below grade level in mathematics
requiring Tier 2 Response to Intervention. The remaining 20% were classified as grade-level
ready in mathematics. Figures 2 through 5 show cumulative and individual weekly growth
numbers in each of the four basic math skills: addition, subtraction, multiplication and division,
respectively.
22
BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Figure 1. Weekly cumulative number of Back to Basics Program 7th
grade participants who
achieved automaticity in the basic math skills of addition, subtraction, multiplication and
division.
Figure 2. Weekly and cumulative number of Back to Basics Program students who achieved
automaticity of basic addition skills.
0
10
20
30
40
50
60
70
80
Week1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7
Nu
mb
er o
f S
tud
ents
Addition
Addition-Cumulative
23
BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Figure 3. Weekly and cumulative number of Back to Basics Program students who achieved
automaticity of basic subtraction skills.
0
10
20
30
40
50
60
Week1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7
Nu
mb
er o
f S
tud
ents
Subtraction
Subtraction-Cumulative
Figure 4. Weekly and cumulative number of Back to Basics Program students who achieved
automaticity of basic multiplication skills.
0
5
10
15
20
25
30
35
40
Week1 Week 2Week 3Week 4Week 5Week 6Week 7
Nu
mb
er o
f S
tud
ents
Multiplication
Multiplication-Cumulative
24
BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Due to the limited availability of student laptop computers, not all of the 100 participants
were able to work on the computer timed assessments via Thatquiz.org software (Version 2012).
There were 23-25 computers available every day in just one of the three teachers’ classrooms.
As students reached proficiency in all four mathematic skills, they were cycled out of the
computer classroom and new students were allowed to use the computers. Figures 6 through 9
categorize the percentage of students who passed the assessments with respect to the frequency
of attempts at reaching a score of 95% or better.
Figure 7. The percentage of students out of 52 participants who achieved proficiency in
subtraction in 7 weeks.
Figure 5. Weekly and cumulative number of Back to Basics Program students who achieved
automaticity of basic division skills.
0
5
10
15
20
25
30
Week1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7
Nu
mb
er o
f
Stu
den
ts
Division
Division-Cumulative
Figure 6. The percentage of students out of 73 participants who achieved proficiency in
addition in 7 weeks.
0%5%
10%15%20%25%30%35%
Pro
fici
ent
Stu
den
ts
Number of Attempts to Pass
Addition
25
BENEFITS OF DEVELOPING BASIC MATH AUTOMATICITY
Figure 7. The percentage of students out of 52 participants who achieved proficiency in