benefits of developing basic math...

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

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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

memory

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Table of Contents

Abstract ......................................................................................................................................................... 2

Introduction ................................................................................................................................................... 5

Rationale for Study ................................................................................................................................... 5

Need for research .................................................................................................................................. 5

Problem Statement ................................................................................................................................ 6

Participants and Site .................................................................................................................................. 7

Research Questions ................................................................................................................................... 7

Hypotheses ................................................................................................................................................ 8

Administrative and Institutional Limitations ............................................................................................ 8

Action Plan................................................................................................................................................ 8

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

Methodology ............................................................................................................................................... 15

Research Design...................................................................................................................................... 15

Student testing. .................................................................................................................................... 16

Quantitative data. ................................................................................................................................ 16

Qualitative data. .................................................................................................................................. 16

Data Collection Plan ............................................................................................................................... 16

Participants .............................................................................................................................................. 18

Instruments .............................................................................................................................................. 18

Interventions ........................................................................................................................................... 19

Data Validity ........................................................................................................................................... 19

Triangulation of Data. ......................................................................................................................... 20

Peer Review. ....................................................................................................................................... 20

Results ......................................................................................................................................................... 21

Findings-Student Performance ................................................................................................................ 21

Quantitative Results ............................................................................................................................ 21

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Qualitative Results. ............................................................................................................................. 26

Findings-Parents and Guardians ............................................................................................................. 28

Findings-Teacher Survey ........................................................................................................................ 29

Discussion ............................................................................................................................................... 30

Limitations .................................................................................................................................................. 32

Action Plan.................................................................................................................................................. 34

Conclusions ................................................................................................................................................. 36

References ................................................................................................................................................... 39

Appendix A: Student Opinion Survey ...................................................................................................... 41

Appendix B: Parent/Guardian Opinion Survey ......................................................................................... 42

Appendix C ................................................................................................................................................. 43

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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.

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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

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automaticity of basic subtraction skills.

0

10

20

30

40

50

60


Nu

mb

er o

f S

tud

ents

Subtraction

Subtraction-Cumulative


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


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.


automaticity of basic division skills.

0

5

10

15

20

25

30


Nu

mb

er o

f

Stu

den

ts

Division

Division-Cumulative


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



subtraction in 7 weeks.

0%

10%

20%

30%

40%

50%

0-1 2-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55

Pro

fici

ent

Stu

den

ts


Subtraction


multiplication in 7 weeks.

0%

5%

10%

15%

20%

25%

0-1 2-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50

P

rofi

cien

t S

tud

ents


Multiplication

26


Qualitative Results. Student Opinion Surveys were given to 40 of the Back to Basics

Program participants as these were the first students to work directly on the computer timed

assessments via Thatquiz.org (Version 2012). Surveys were given to these students after the 4th

week of the program. At that moment in the program, 57% of the 40 students polled had

achieved automaticity in the four areas of basic math skills. The remaining 43% of the 40

students surveyed were at various stages of proficiency. Table 3 shows the percentage of

students that agree on the effectiveness of various strategies to gain automaticity of basic math

skills.

Table 3

Effective Strategies for Gaining Automaticity in Basic Math

Strategy Students Who Agree Strategy

is Effective

Mean Scale Score

(5=Highest, 1=Lowest Rating)

Receiving Immediate Feedback 95% 4.10

Timed Computer Assessments

Use of Flashcards

85%

82%

4.05

3.85


division in 7 weeks.

0%

5%

10%

15%

20%

25%

0-1 2-5 6-10 11-15 16-20

Pro

fici

ent

Stu

den

ts


Division

27


Say Facts Out Loud

Repeatedly

70% 3.63

Write Down Facts Repeatedly 65% 3.73

Students were asked to rank their preferred method for learning math facts. Table 4

summarizes the results. When asked for other suggestions, one student recommended homework

as an alternate strategy for learning basic math skills.

Table 4

Students Preferred Methods for Learning Basic Math Skills

Strategy Students Who Chose Strategy as First Choice

Flashcards 25%

Computer Timed Assessments 23%

Math Competitions 20%

Speed Tests, Pencil/Paper 15%

Writing Down Facts

Repeatedly

10%

Saying Facts Repeatedly 5%

Surveyed participants were polled regarding if their willingness to learn mathematics

improved as they achieved automaticity of basic math skills. When asked if they believed that

learning basic math skills without counting on their fingers helped them do better on math tests

and benchmark assessments, 90% agreed or strongly agreed. This resulted in a mean Likert

Scale score of 4.3, with 5 being the highest rating in agreement and 1 being the lowest rating in

agreement. Additionally, 90% of polled participating students agreed or strongly agreed that

learning basic math skills with automaticity helped them enjoy learning math a little better than

before they were enrolled in the Back to Basics Program. This translated to a mean Likert Scale

28


rating of 4.15. Lastly, 95% of polled participants agreed or strongly agreed that learning basic

math facts with automaticity has given them more confidence when learning mathematics. The

mean Likert Scale score for this survey question was 4.43.

Findings-Parents and Guardians

A Parent/Guardian Opinion Survey, Attachment B, was sent home with students. Only

three surveys were returned by the time of this writing. All of the parents that completed the

survey believed their child was able to pass all of the timed proficiency tests in addition,

subtraction, multiplication and division. None of these parents worked with their children

regularly on their basic math skills. When asked if their child used the strategy of counting on

their fingers to perform basic math skills, 67% disagreed or strongly disagreed their child used

this strategy. Two thirds of the parents/guardians noticed an increase in their child’s confidence

and attitude towards learning math since they have been focusing on their automaticity in the

Back to Basics Program. Lastly, parents were asked to rank, in order of preference from 1(most

preferred) to 7 (least preferred), several strategies for learning math facts. Table 5 summarizes

these rankings.

Table 5

Parent/Guardian Opinions on Their Child’s Preferred Strategies for Learning Basic Math Skills

Strategy Parents’/Guardians’ Opinion Their

Child Prefers This Strategy as First Choice

Flashcards 60%

Computer Timed Assessments 30%

Math Competitions 0%

Speed Tests, Pencil/Paper 10%

Writing Down Facts

Repeatedly

0%

Saying Facts Repeatedly 0%

29


Findings-Teacher Survey

A Teacher Opinion Survey, Attachment C, was given to the three 7th

grade mathematics

teachers responsible for working with the Back to Basics Program participants. All polled math

teachers felt their students, who they teach on a daily basis, did not know their basic math facts

with fluency and automaticity. They all noticed that the majority of their students count on their

fingers to do basic math computations, and that the lack of automaticity hindered them from

learning higher level, more complex math skills. When asked if students should be allowed to

use calculators to perform basic, rudimentary math computation, all polled math teachers felt that

calculators should not be allowed. Teachers have also noticed that students who achieve

automaticity have a more positive attitude towards learning math and seem to be more confident

when learning math in their classrooms. Table 6 summarizes each teacher’s priority regarding

their preferred strategy to help students learn their basic math skills.

Table 6

Teachers Preferred Methods for Teaching Basic Math Skills

Strategy Teacher 1 Teacher 2 Teacher 3

Flashcards 1st 1st 1st

Computer Timed Assessments 4th

4th

2nd

Math Competitions 6th

6th 6th

Speed Tests, Pencil/Paper 5th

5th 5th

Writing Down Facts

Repeatedly

2nd

2nd

4th

Saying Facts Repeatedly 3rd

3rd 3rd

30


Discussion

Based on data collected from Thatquiz.org (Version 2012) timed assessments as

summarized in Figure 1, 73% of the 100 active student participants in the Back to Basics

Program are proficient in basic addition after 7 weeks. Additionally, 53% were deemed

proficient in subtraction, 37% were proficient in multiplication and 28% were proficient in

division after 7 weeks. Since there were only 25 computers available during the Mastery block

time period, not all 100 participants could test using the Thatquiz.org software (Version 2012) at

the same time. Therefore, conclusions should not be drawn regarding the speed at which

students acquired automaticity. One of the first research questions posed in this action research

asks if it is possible to improve automaticity for middle school students in addition, subtraction,

multiplication and division through the use of timed on-line assessments. Conclusive,

quantitative data from Thatquiz.org (Version 2012) assessments show positive results in this

area. Student opinion surveys also provide evidence that 85% of the students polled agree or

strongly agree that timed computer assessments helped them achieve automaticity.

When students were asked if they thought that receiving instant feedback on the timed

tests was helpful, 95% of the polled student population agreed or strongly agreed. Students

would write down the facts that they did not answer correctly at the end of each timed

assessment so they could focus on their attention on these to quickly build their automaticity.

This strategy was also cited in the research literature know as Detection, Practice and Repair

recommended by Axtell, Poncy and Skinner (2010). There was no reason to focus on the facts

that were already seated in the student’s long term memory.

Many students in middle school use inefficient strategies for basic math computations,

such as counting on their fingers. When surveyed, 100% of the teachers strongly agree that their

students do not know basic math facts with automaticity, and all feel that the majority of their

31


students count on their fingers to do math. This action research not only focused on teachers’

viewpoints regarding the most effective strategies to help students build automaticity in basic

mathematics, but also focused on what students had to say about their preferred strategies to

build automaticity. It is interesting to compare the student preferred strategies to teachers’

preferred strategies. Parents and guardians had yet an additional set of preferences regarding

preferred strategies. Table 7 summarizes the strategy preferences by ranking them from 1 to 7,

with 1 being the most preferred and 7 being the least preferred. The top three preferred choices

from the students’ viewpoint were the use of flashcards (25%), computer timed assessments

(23%), and math competitions (20%). Teachers voted unanimously that the use of flashcards

was the most effective strategy and none of the teachers felt that math competitions were an

effective strategy for students to learn basic math facts. Although there were only three

Parent/Guardian Opinion Surveys returned, they were united in that the use of flashcards was

their preference followed by timed computer tests and paper/pencil speed tests.

Table 7

Preferred Methods for Learning Basic Math Skills

Strategy Student

Majority

Teacher

Majority

Parents/Guardians

Majority

Flashcards 1st 1st 1st

Computer Timed Assessments 2nd 4th 2nd

Math Competitions 3rd 6th --

Speed Tests, Pencil/Paper 4th 5th 3rd

Writing Down Facts

Repeatedly

5th 2nd --

Saying Facts Repeatedly 6th 3rd --

Other: Homework 7th --

32


Students were surveyed regarding if improving their automaticity in basic math helped

improve their attitude and willingness to learn mathematics. 90% of those polled agreed or

strongly agreed they had an improved attitude about learning math. When asked if they believed

that learning basic math skills without counting on their fingers helped them do better on math

tests and benchmark assessments, 90% agreed or strongly agreed. Lastly, 95% of polled

participants agreed or strongly agreed that learning basic math facts with automaticity has given

them more confidence when learning mathematics. Teachers were also in 100% agreement that

students who had achieved automaticity seemed to have a more positive attitude towards

learning higher level math skills and had a greater confidence in learning math. Teachers

commented that several students who never volunteered to answer questions in the past were

now eager to raise their hand and answer questions during math class.

The timing of this action research precludes having any benchmark data or standardized

assessment data for review to assess if acquiring automaticity helped improve standardized

assessment scores. This is an action for further review and study. However, all three teachers

involved in this action research have noticed a reduction in the number of careless errors when

reviewing formative assessments.

The triangulation of data from students, teacher and parents all yield similar findings. In

order to be successful in math, one must become fluent with the basic facts so that recall

becomes automatic and effortless. Only then can the working memory be freed up so that higher

level mathematics can be processed. The working memory in humans has a limited capacity so

it is imperative that students achieve automaticity in the basics.

Limitations

This action research has been met with just a few limitations. The main obstacles

encountered were due to the technical limitations of the Alamance Burlington School System

33


computer network. At the onset of the Back to Basics Program, students were either unable to

connect to the computer network system or the system response was so slow that their computers

shut down from inactivity. An interim solution was implemented by placing a wireless router in

one of the participating teacher’s classroom which enabled reasonable access to the internet for

participating students. The other two participating teacher classrooms were unable to implement

the temporary solution. Therefore, only 23-25 students per day could participate in the computer

timed assessments via Thatquiz.org (Version 2012). This slowed data collection, but did not

prevent the program from continuing.

A second limitation involved the prohibited student access to SurveyMonkey (Version

2009) which was used to create the Student Opinion Survey. However, when students clicked on

the link to take the survey, they were unable to participate online because the website was

blocked by the school’s firewall. As an alternative approach, paper copies of the survey were

given to students and their data were manually keyed into the SurveyMonkey database. Results

were obtained, but with more manual effort than originally intended.

Another limitation of the action research was the limited involvement of parents and

guardians of participating students. This was no surprise as many school functions requiring

parent/guardian participation are met with mediocre response. Many parents work multiple jobs

and often consider parental/guardian participation optional.

From a global perspective, educators may be reluctant to focus on 2nd

and 3rd

grade math

skills for middle school students. It is surprising that middle school students do not have a good

foundation in basic arithmetic skills. Therefore, educators may be very resistant to spending

time on such low level skills and resort to handing students calculators to do the basics.

Teachers may be concerned that there is not enough time in the day to go back to 2nd

grade skills

as they have a large amount of grade-level math to cover. This mindset is certainly understood,

34


but should not continue if we are genuinely focused on increasing our students’ ability to learn

and master higher level mathematics.

Action Plan

The main action required is to continue this program until the end of the 2012-2013

school year for the 7th

grade. Data collection and analysis should continue until 7th

grade

students achieve automaticity of basic addition, subtraction, multiplication and division. The goal

is to enlist all 7th

grade students in the Back to Basics Program before the end of the school year.

For next year, it is recommended that all grade levels incorporate the Back to Basics Program as

the issue of automaticity, or lack thereof, exists at all grade levels. However, until the internet

infrastructure issue is resolved, it may be physically impossible to incorporate the Back to Basics

Program school-wide.

Several summative assessments are forthcoming over the next several months and scores

should be collected as the program is evaluated for effectiveness in answering the question: Does

the improvement of automaticity of basic math skills improve standardized assessment results for

middle school students? Assessment data should be carefully analyzed for all participating

students in the Back to Basics Program. If data show positive trends in summative assessment

scores, then results will be published to administration immediately. Upward trends in test

scores are paramount and mandatory in order for the United States to remain a competitive and

competent world leader. As concluded from the literature review, strong evidence from the

Australian-designed QuickSmart Program show positive results for Australian students on

international standardized assessments whose scores are far more impressive than the United

States scores. We need to follow their lead and raise our international ranking in math and

science.

35


Table 8 summarizes the Action Plan for this action research for the balance of the 2012-

2013 school year. Presentations regarding the success of the Back to Basics Program are

planned for GMS Administrators and Academic Coaches. A separate presentation for Central

Office Administrators will be scheduled after the End of Grade assessments have been

administered, scored and proper analyses have been completed regarding the Back to Basics

Program.

Table 8

Action Plan

Recommended Action Who Is

Responsible Timing Resources

Continue Back to Basics

Program and cycle as

many 7th grade students as

possible through the

program

Academic

Coaches, Back to

Basics Lead

Teachers,

Administration

Through May 1,

2013

Student Laptop

Computers, All 7th Grade

Students, Thatquiz.org

software, Back to Basics

teachers

Continue the use of

Thatquiz.org

Back to Basics

Teachers

Through May 1,

2013

Student Computers,

Thatquiz.org Software

Continue Use of

Flashcards, Math

Competitions, Writing and

Saying Facts Out Loud

Back to Basics

Teachers

Through May 1,

2013

7th Grade students, math

manipulatives such as

flashcards

Collect results from

Benchmarks, SMI

Assessments and Report

Cards in Jan and Mar, 2013

Administration,

Academic

Coaches, Back to

Basics Lead

Teacher

Jan 15, 2013

April 15,2013

Benchmark Data, SMI

Data, Universal

Screening Data,

Computer w/ Excel

Collect End of Grade

Assessment results in May,

2013

Administration,

Academic

Coaches, Back to

Basics Lead

Teacher

June 1, 2013

EOG Data, Computer w/

Excel

36


Present Results of Action

Research to Graham

Middle School

Administration

Back to Basics

Teachers

Dec, 2012

Mar, 2013

June, 2013

Computer with

PowerPoint

Present Results of Action

Research to Central Office

Administration

Back to Basics

Teachers June, 2013

Computer with

PowerPoint

Conclusions

This action research provides conclusive evidence that many students in the 7th

grade at

Graham Middle School do not possess automaticity of basic math skills in addition, subtraction,

multiplication and division. Opinion surveys show that timed assessments and the use of

flashcards are amongst the preferred strategies recommended by students, teachers and parents to

achieve automaticity of basic math skills. The students who participated in this action research

worked daily for 7 weeks in a math intervention program known as the Back to Basics Program

to help build their automaticity. They used timed assessment via Thatquiz.org (Version 2012),

flashcards, team competitions and unrelenting determination to build their skills. Some students

achieved automaticity quickly whereas others required many hours of repetition and drilling of

the facts. Regardless of the number of attempts each student made on the timed assessments, the

majority of students agreed that their confidence and attitude towards learning math improved as

they become proficient. Teachers unanimously agreed they saw a marked improvement in their

students’ attitudes and confidence in their mathematics classes once automaticity was achieved.

This action research accomplished several important goals. It showed, through concrete

results, that students in middle school need to possess automaticity of basic math so that

cognitive resources and the working memory can be used for higher level math concepts.

Counting on fingers is an ineffective strategy that many middle school students use, even if

37


students are classified as gifted. Administrators and teachers need to allot time during the day to

help all students build this automaticity. Summative assessments were not available at the time

of this writing, but formative assessments using Thatquiz.org (Version 2012) show that it is

possible for all students to achieve automaticity. Immediate feedback is necessary for students to

identify which facts are not known fluently so these can be practiced in isolation. Positive

reinforcement when students successfully complete each timed test fortifies their self-confidence

and their willingness to continue working hard on achieving automaticity.

The next step for this action research is to continue the Back to Basics Program until all

7th

grade students achieve automaticity. Summative assessment scores from benchmark

assessments, report cards, and the End of Grade Mathematics assessment should be tracked and

analyzed for each participating student in the Back to Basics Program. As results become

available in June, 2013, a presentation for administration and applicable Central Office personnel

will be prepared regarding the findings of this action research. If administration chooses to

continue the Back to Basics Program next year, all grade levels should establish a facilitator

monitor and track program results. If successful, the program could then be applied to other

schools in the district that have substandard results on the high-stakes assessments in

mathematics. Offering this program at the elementary school level may also provide

improvements to overall mathematics performance.

The United States needs to embrace radical curricular changes in mathematics in order to

change the trajectory of our rankings on international assessments in math and science literacy.

There are serious consequences in the weakening of our math and science leadership as we enter

the 21st century. We risk losing the technical foundation that has made the United States a world

leader. By strengthening our students in basic mathematics and focusing on building their basic

38


math automaticity, they will be able to comprehend and learn higher-level mathematical

concepts such as Algebra. The National Mathematics Advisory Panel states that Algebra is a

demonstrable gateway to later success in the workforce (National Mathematics Advisory Panel,

2008). We can no longer afford to be complacent with the fact that our middle school students

still count on their fingers. We should not simply hand them a calculator to do simple arithmetic.

As educators, we must stop pushing students along to the next grade level when they don’t have

a solid math foundation. We must stop this downward spiral. We must get back to basics.

39


References

Adcock, W., Luna, E., Parkhurst, J., Skinner, C. H., Yaw, J., Poncy, B., (2010). Efficient class-

wide remediation: Using technology to identify idiosyncratic math facts for additional

automaticity drills. International Journal Of Behavioral Consultation And Therapy, 6(2),

111-123.

Axtell, P.K., McCallum, R.S., Bell, S.M., Poncy, B. (2009). Developing math automaticity using

a class-wide fluency building procedure for middle school students: A preliminary study.

Psychology in the Schools, 46:6, 526-538. doi:10.1002/pits.20395

Bellert, A. (2008). LDA student award winner, 2008 narrowing the gap: A report on the

QuickSmart mathematics intervention. Australian Journal of Learning Difficulties,14:2,

171-183. doi:10.1080/19404150903264310

Byers, T. (2009). The BASICS Intervention Mathematics Program for at-risk students.

Australian Mathematics Teacher, 65(1), 6-11.

Fleishman, H.L., Hopstock, P.J., Pelczar, M.P., & Shelley, B.E. (2010). Highlights from PISA

2009: Performance of U.S. 15-year old students in reading, mathematics and science

literacy in an international context. (NCES 2011-004). U.S. Department of Education,

National Center for Education Statistics. Washington, DC: U.S. government Printing

Office.

Graham, L., Bellert, A., Thomas, J., & Pegg, J. (2007). "QuickSmart": A Basic Academic Skills

Intervention for Middle School Students with Learning Difficulties. Journal of Learning

Disabilities, 40(5), 410-419.

40


Marzano,R.J, Pickering,D.J.,Pollock,J.E. (2001). Classroom instruction that works: Research-

based strategies for increasing student achievement. Alexandria, VA: Association for

Supervision and Curriculum Development (ASCD).

Mills, Geoffrey E. (2011). Action research- A guide for the teacher researcher. Upper Saddle

River, NJ: Pearson.

Department of Education. (2008). National Mathematics Advisory Panel. Foundations for

success: The final report of the National Mathematics Advisory Panel. Washington,

D.C.:U.S Government Printing Office.

Ramos-Christian, V., Schleser, R., & Varn, M. E. (2008). Math fluency: Accuracy versus speed

in preoperational and concrete operational first and second grade children. Early

Childhood Education Journal, 35(6), 543-549.

SurveyMoneky.com (Version 2009) [Computer software].

Swanson, H. (2011). Working memory, attention, and mathematical problem solving: A

longitudinal study of elementary school children. Journal of Educational Psychology,

103(4), 821-837.

Thatquiz.org (Version 2012) [Computer software].

Thinkgate.org (Version 2012) [Computer software].

41


Appendix A: Student Opinion Survey

Strongly

Agree Agree Neutral Disagree

Strongly

Disagree

1. Do you know all the basic math facts (1-10) so that you

can pass all the timed quizzes in the Back to Basics

Program?

2. Do you think the timed math quizzes help you learn math

facts until they become automatic?

3. Do you think the use of flashcards help you learn math

facts until they become automatic?

4. When you do not know a certain math fact, does it help

you to repeat the fact out loud many times (like 10 or

more)?

5. When you do not know a certain math fact, does it help

you to write it down many times (like 10 or more)?

6. When you take the on-line timed quizzes, does it help you

to know which facts you got wrong (instant feedback)?

7. Do you think that learning these basic math facts without

counting on your fingers has helped you do a better on math

tests and Benchmark tests?

8. Do you think that learning these basic math facts has

helped you like learning math a little better than before?

9. Do you think that learning basic math facts with speed

and accuracy has given you more confidence when doing

math?

10. In your opinion, what are your favorite ways to learn basic

math facts with speed and accuracy? Place a 1 beside the most

favored way, a 2 beside the second choice, etc…

_____ Flashcards

_____ Math Competitions

_____ Writing down the facts many times

_____ Saying the facts out loud many times

_____ Doing speed tests on paper

_____Doing speed tests on the computer

_____ Other: ________________

______

42


Appendix B: Parent/Guardian Opinion Survey

Strongly


Strongly

Disagree

1. Do you feel that your child knows all the basic math facts

(1-10) such that they can pass a 100 problem quiz in

addition, subtraction, multiplication and division in 3

minutes time?

2. Do you notice that your child counts on their fingers to do

basic math?

3. Do you work with your child regularly (2 or 3 times a

week) on basic math facts?

4. Do you think the use of flashcards would help your child

learn math facts until they become automatic?

5. When your child does not know a certain math fact by

heart, does it help them to repeat the fact out loud 10 or

more times?

6. When your child does not know a certain math fact by

heart, does it help them to write the fact down on paper 10

or more times?

7. Does your child use a computer at home to learn math

facts?

8. If your child has just recently mastered their basic math

facts by being in the Back to Basics program, have they

become more confident in doing their math homework?

9. Do you think that learning basic math facts with speed

and accuracy has improved their attitude towards learning

math?

10. In your opinion, what are your children’s preferred ways to

learn basic math facts with speed and accuracy? Place a 1 beside

the most favored way, a 2 beside the second choice, etc…

_____ Flashcards






_____ Other: _______________________

43


Appendix C

Strongly


Strongly

Disagree

1. Do you feel that your students know all the basic math facts (1-

10) such that they can pass a 100 problem quiz in addition,

subtraction, multiplication and division in 3 minutes time?

2. Do you notice that your students count on their fingers to do

basic math?

3. Do you feel that students are hindered from learning more

complex math skills if they are not proficient and possess

automaticity in basic math?

4. Do you think a student should be allowed to use a calculator if

they do not know basic math computations and facts?

5. Do you think a student should be allowed to use a calculator to

perform basic math computations on formative assessments?

6. Do you think a student should be allowed to use a calculator to

perform basic math computations on standardized mathematics

assessments?

7. Do you feel that math games on the computer are helpful in

building basic math skill automaticity?

8. Do you think that when students achieve automaticity in basic

math facts that their attitudes and confidence improve with respect

to learning math?

9. Do you feel that all students in elementary school should be

required to pass timed basic math assessments in addition,

subtraction, multiplication and division before entering the 6th

grade?

10. In your opinion, what are the most effective strategies for

students to learn basic math facts with speed and accuracy? Place

a 1 beside the most favored way, a 2 beside the second choice,

etc…

_____ Flashcards






_________

benefits of developing basic math...

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