Developing Math Computational Skills: Enhancing Math Fact Fluency

This study explores the connection between math fact fluency and higher-order mathematics skills, and suggests ways to enhance math fluency through promoting oral activities. It also discusses the needs assessment, additional ways to improve math fluency skills, teaching children with mild intellectual disabilities, and cognitive strategies to involve children in studying math skills.

Running head: EDUCATION
Developing Math Computational Skills
Name of the Student
Name of the University
Author Note

1EDUCATION
Contents
Chapter 1: Purpose.....................................................................................................................2
Chapter 2: Literature Synthesis..................................................................................................4
2.1 Needs Assessment............................................................................................................4
2.2 Improving Math Fluency Skills to Enhance Math Score.................................................5
2.3 Additional Ways to Improve Math Fluency Skills..........................................................5
2.4 Teaching Children with Mild Intellectual Disabilities.....................................................7
2.5 Cognitive Strategies to Involve Children in Studying Math Skills..................................8
2.6 Alternative Measures.......................................................................................................8
2.7: Scaffolding:.....................................................................................................................9
Chapter 3: Method....................................................................................................................11
3.1 Introduction:...................................................................................................................11
3.2 Research Philosophy:.....................................................................................................11
3.3 Methodology..................................................................................................................12
3.4 Study Design:.................................................................................................................13
3.4 Implementation..............................................................................................................14
3.5 Data Collection:.............................................................................................................15
3.6 Confidentiality and Ethical Approval:...........................................................................15
Chapter 4: Evaluation Plan.......................................................................................................16
References:...............................................................................................................................19
Appendix 1: Lesson Planner....................................................................................................26

2EDUCATION
Chapter 1: Purpose
The key goal of the study is to identify the connection between
Math fact fluency as the ability to recall the answers to basic math facts
automatically and without hesitation or counting with fingers. Fact fluency
is gained through significant practice, with mastery of basic math facts
being a goal of both teachers and parents. Additionally, the means of
enhancing the process of math fluency through promoting oral activities
will be considered in the study. The implication for mathematics is that
some of the sub-processes, particularly basic facts, need to be developed
to the point that they are done automatically. If this fluent retrieval does
not develop then the development of higher-order mathematics skills —
such as multiple-digit addition and subtraction, long division, and fractions
— may be severely impaired. Chester A Moore Elementary is located in
the North portion of St. Lucie County, characterized as: low income, less
educated, and primarily composed of children & teenagers. Chester A.
Moore Elementary School is large, whereas 489 students, or 69.8% of
the student population is identify as African-American, making up the
largest segment of the student body. The student to teacher ratio of 17:1
is significantly higher than the average for US public elementary schools
in Florida (14.5).Students may enroll in Pre-K - 5th grade. This green zone
school is a positive learning environment where the whole child is engaged
and inspired by dedicated stakeholders who work together to create and
empower life-long learners. Chester A. Moore Elementary is the school
where excellence is believed and achieved by all.

3EDUCATION
Faculty and staff members embrace students through conferencing
as well as informal conversations throughout the school day. Individuals
are available to translate for families and students that do not speak
English. For students that do not speak English, the teacher assigns
another student that speaks the native language to assist the student
through peer tutoring. Parent teacher conferences are held to learn more
about students' cultures, heritage and backgrounds. Chester A. Moore is a
Kids at Hope school where all children are capable of success and the
faculty and staff is committed to the philosophy of the Kids at Hope
Initiative. Kids at Hope ensure that there is a caring adult in the lives of
the children. The adults on campus serve as those caring adults.
Chester A Moore Elementary is committed to our mission of
providing quality, standards-based instruction by providing the best
possible educational experience for all students in the safest possible
environment.
Chester A. Moore is committed to our vision that all students are
provided with exemplary instruction and learning opportunities in order to
prepare each child to advance to the next level in their pursuits of college
studies and careers.
In setting our goals, we will continue to strive towards higher levels
of student performance by offering a challenging elementary curriculum
that is aligned with rigorous standards delivered through diversified
instructional strategies.

4EDUCATION
Our purpose is to strive to prepare all students to the next level
in their pursuits of college studies and careers.
Students in the computer lab are given opportunities to expand
and demonstrate their knowledge using technology. Students create
multimedia presentations and use various programs and equipment to
advance their skills in mathematics, reading, language arts, and
technology. Students are encouraged to collaborate with their peers to do
such things as conduct research and create presentations which will
enable them to become lifelong learners and have marketable skills. This
year we will also be focusing on our keyboarding skills and we will be
taking some virtual field trips. The school has two computer labs with 35
computers in each lab.
St. Lucie Co. School System adopted a computer program called
IReady Math & Reading which is a reading and math program to help
enhance students learning abilities through multimedia narration,
interaction and animation.
Chapter 2: Literature Synthesis
2.1 Needs Assessment
Need Assessment requires the school to review performance and
early warning systems data in order to develop strategic goals and
associated data targets for the coming school year in context of the
school’s greatest strengths and needs. An online tool was developed,
which includes data visualizations and processing questions to

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support problem identification, problem analysis and strategic goal
formulation.
Although children's use of a variety of strategies to solve arithmetic
problems has been well documented, there is no agreed on standardized
and validated method for assessing this mix. A closer look at a typical
classroom setting will reveal that a teacher has to apply the strategy that
will allow for recognizing the classroom diversity. The latter may
concern the students’ need for self-identification, learning and
acquiring new experiences in terms of communication and
academic life.
Based on the difference in proficiency between Caucasians and
African-American students (ethnicities with the highest and lowest math
proficiency, respectively), Chester A. Moore Elementary School has largely
minimized the disparity in math literacy among different ethnic groups,
but there is still room for improvement.
Though African-American students comprise the largest segment of
the student body at Chester A. Moore Elementary School, they have
achieved the lowest level of math proficiency out of the three ethnic
groups represented at this school.
2.2 Improving Math Fluency Skills to Enhance Math Score
The need for teaching math skills is an integral part of any training
program, and if it is a school education, the initial attention is paid to
mathematical score. (Hodges, McIntosh, & Gentry, 2017). One of the

6EDUCATION
possible and affordable ways to increase the ability of students to perform
both elementary and more complex calculative activities is to attend
extra-curricular classes for the additional workload (Foster, Anthony,
Clements, Sarama, & Williams, 2016). For example, Fosteret al. (2016) is of
the opinion that it is best to start teaching these skills in kindergarten
when using special computer programs and technologies.
Perhaps, this approach can be effective enough. Nevertheless, it is
essential to not only provide children with an appropriate program but
also prepare them for classes in order to assess the degree of interest of
each student in this subject and the desire to learn (McTiernan, Holloway,
Healy, & Hogan, 2016). If it is not done for some reason, for instance,
because of the long absence of a certain child or the lack of desire to
make contact, it is likely that attention should be paid to the variation
methods of teaching. As Burns, Ysseldyke, Nelson, and Kanive (2015)
note, a certain number of repetitions of the studied material should
be carried out in order to more effectively memorize the features of the
mathematical calculations. Moreover, appropriate early training
facilitates faster the memorization of material during late learning periods
in the middle and high school (Nelson, Parker, &Zaslofsky, 2016). Thus,
other methods may also be of interest to tutors to teach their wards
certain skills and thereby help them to adapt to a complex scientific
environment.
2.3 Additional Ways to Improve Math Fluency Skills

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While reviewing the scientific literature to search for relevant, up-to-
date information on the selected topic, it can be noted that many authors
share similar views on methods of intervention. For instance, Duhon,
House, Hastings, Poncy, and Solomon (2015) are confident that a timely
response should be given to any difficulties that arise in the students,
and the method of immediate reaction is true. It is possible that this
approach can be of good use.
If it is the question of the success of the chosen strategy, opinions
may also diverge. Schutte et al. (2015) raise the issue of how it is best to
teach children of mathematical literacy: massively or selectively and
come to the conclusion that each of the ways has its pluses. For example,
Jacob and Parkinson (2015) argue that the relationship between individual
and group learning is quite strong, and even despite the effectiveness of
individual lessons, students can get all the necessary knowledge in the
classroom.
It is also significant for not only the child but also the tutor to be
interested in achieving success in teaching his or her students and plan
wards’ success (Cai, Georgiou, Wen, & Das, 2016). It is important to reveal
the interest and inclination of the child to mathematics since early
childhood because later in school, students will face rather hard tasks
(“Help your child,” 2016). If such work is properly conducted, it is likely
that this science will entice children and will not bring difficulties in
solving more and more advanced tasks (Green, Bunge, Chiongbian,
Barrow, &Ferrer, 2017). The ways to achieve effective results can be

8EDUCATION
different. For instance, Bartelet, Ghysels, Groot, Haelermans, and Maassen
van den Brink (2016) note the importance of advanced homework
aimed at in-depth training of the material covered and the consolidation
of appropriate skills. Crawford, Higgins, Huscroft-D'Angelo, and Hall (2016)
suggest using electronic tools to make the learning process as
advanced and modern as possible since practically all modern children
and students have access to the Internet and electronic gadgets. For
instance, according to Eaton (2013), the fastest and the most efficient
way to teach math can be achieved through games and various
computer applications. Therefore, as it becomes clear, many authors
have different opinions but agree on the issue that much depends on
teachers themselves.
2.4 Teaching Children with Mild Intellectual Disabilities
There are quite different strategies for teaching children with mild
mental disabilities, which are mentioned in the scientific literature. For
example, Swanson (2015) proposes to develop individual programs for
training various mathematical skills: memorization, classification
operations, etc. According to Purpura, Reid, Eiland, and Baroody (2015)
in the case a small mental disorder has been detected in the child in early
childhood, training math should not be stopped. On the contrary,
teaching initial math skills should be conducted to help the child adapt
in the future.
For children with mild intellectual disabilities, Foster, Sevcik, Romski,
and Morris (2015) propose the use of specific phonological procedures

9EDUCATION
aimed at accelerating the assimilation of certain mathematical
phenomena and training prior knowledge. In general, this method is quite
innovative because children not only learn the basics but also train
particular cognitive skills that are necessary for ordinary life. Thus,
Duncan (2017) offers to transform classes into a full-fledged game
where the child has the right to choose and can, together with parents or
teachers, engage in the basics of math through fascinating activities. A
slightly different approach is suggested by Cozad and Riccomini (2016)
who consider digital-based work with children with some mental
disabilities as one of the primary sources of gaining important knowledge,
monitoring the performance of students, and adjusting the learning
process in parallel. One of the useful skills that can be practiced with
children of almost any level of ability is teaching the basics of addition
and subtraction (Wise, 2016). Such work can certainly be conducted by
almost any child and at the same time will be of significant benefit to the
further learning process.
2.5 Cognitive Strategies to Involve Children in Studying Math Skills
One of the ways to help children who have difficulties with
mathematics is to use certain cognitive strategies (Bugden, DeWind, &
Brannon, 2016). The effectiveness of this approach to learning is
confirmed by quite a few authors. For example, Özsoy and Ataman (2017)
claim that honing specific skills contributes to faster further response to
similar tasks and thereby helps the child. The task of a qualified teacher,
as Chandran (2015) remarks, is to help children cope with anxiety caused

10EDUCATION
by difficulties and assist them in adapting the scientific environment that
is new for them.
Specific interventions are offered by Musti-Rao and Plati (2015) who
consider several ways of teaching, including both self-study and teacher-
led lessons. Thus, Liu, Kallai, Schunn, and Fiez (2015) also talk about
individual training of skills and suggest improving mathematical fluency
by using computer-based education. However, this method is partially
challenged by Powell and Fuchs (2015) who see successful work only in an
individual approach to each student and are confident that all
implementations should be conducted under the direction of a responsible
teacher. Perhaps, that is why Clements and Sarama (2016) conduct a
positive correlation between the cognitive skills of children and their
ability to study exact sciences. In other words, the higher the motivation
and preparedness of a child are, the more likely it is that his or her
success in mathematics will be high enough.
2.6 Alternative Measures
As alternative ways to improve students’ mathematical skills,
different mechanisms can be used. For instance, Brendefur et al. (2015)
suggest referring to a special assessment system that is more relevant
for older children and can also be applied in higher education. With the
help of such a mechanism, the student can get full information about his
or her problem topics and pay extra attention to specific rules for
improving the learning outcome. Reisener, Dufrene, Clark, Olmi, and
Tingstrom (2016) propose to use visual aids and other digital tools that

11EDUCATION
can show the peculiarities of certain mathematical calculations outside
the box, that is, through comparisons with other scientific fields.
Finally, Szkudlarek and Brannon (2017) consider a rather old
mechanism for training mathematical fluency, resorting exclusively to the
help of numbers and without the use of language. This method can seem
quite difficult to study, especially at the initial stage. Nevertheless, as
practice shows, the cognitive nature of the human is specific enough, and
such a method of learning can be very successful (Szkudlarek and
Brannon, 2017). Thus, both alternative and traditional methods can be
effective, and it is essential to responsibly approach work and not be
afraid to resort to different ways of training in order to help children,
adolescents, and adults to better adapt to the scientific environment.
2.7: Scaffolding:
Scaffolding utilizes a range of teaching approaches that can help the
student to develop their academic skills, and help them understand their
subjects and also provide more independence in the learning process. The
term ‘scaffolding’ can be understood as a metaphor that highlights a
process in which the teacher provides temporary support to the students
which are repeated successively supporting the development of a higher
degree of comprehension and acquisition of skills which can be achieved
independently by the students (Saye et al., 2017). The structure is similar
to physical scaffolding in the process of incremental removal of support,
once they are needed no longer, slowly shifting the responsibility of
learning on the student. This strategy has been considered to be an

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essential aspect of an effecting teaching approach, and have been utilized
by several educators in various degrees of instructional scaffolding while
teaching their students (Gilles, 2014). Studies show that scaffolding can
also help to bridge any gaps in learning (which are essentially the
difference between the knowledge possessed by the students and the
knowledge that is expected to be possessed by them at specific points in
their education (Reynolds & Goodwin, 2016). For example, a student not
able to solve a given mathematical problem which is a part of the
curriculum, the teacher can provide instructional scaffolding to
incrementally improve their skills to solve the same or similar types of
mathematical problems, helping the student to develop the necessary
skills to start solving the problems on their own, and without any need for
assistance. One of the biggest advantage of scaffolding is that it can help
to reduce the negative emotions and negative self perceptions which
might be experienced by the students as a result of not being able to
perform a given task (such as solving a mathematical problem), which can
cause a sense of frustration, intimidation and discouragement while
attempting to perform the task without any help (Kao et al., 2015).
In the process of scaffold teaching, different strategies would be
utilized that can help to support independent learning by the students,
with minimal or no assistance from the teachers. Certain strategies that
have been identified from the review of literature can be incorporated to
support the scaffold teaching such as group based learning,
extracurricular classes and activity based learning, using digital
technologies (such as computer programs and applications), providing

13EDUCATION
advanced homework that requires in depth understanding of the subject
and phonological approaches to help the development of the required
mathematical skills and concepts. In this process, the students can
develop math skills at their own pace, with instructions from the teacher,
and also can assist other students who are facing challenges to cope up
with the learning (Hulstijn et al., 2014). Thus by helping other students,
the skills can be further developed. Moreover, the students would be
given specific math learning softwares, which they can use at home to
complete their homework. Teachers would also provide extracurricular
classes from time to time, in which they would recapitulate and revise the
concepts taught earlier, and teach interesting activities that can help the
students to learn moths faster and in a more interesting manner. During
the extracurricular classes, any challenges faced by the student to learn
the subject would also be shared and addressed, thereby helping other
students as well to learn from each other. Additionally, students who have
acquired a strong concept and understanding of the subject can in turn
assist the weaker students to understand the same, helping them to
develop their skills, without the necessity for an intervention by the
teacher. Computer based games or applications would also help in the
development of independent learning, as the students would be able to
play these interactive games in their free time, refreshing their memories
of the lessons learnt and using them to play the game. The in game
rewards, accolades and rankings can also help to boost the morale of the
students, and motivate them to perform better (Reynolds & Daniel, 2018;
White-Clark et al., 2017).

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Chapter 3: Method
3.1 Introduction:
The purpose of a research method is to outline the process in which the research
would be conducted, the instruments of research that would be used, the research objectives,
and how to reach the goals of the research. The aim of this chapter is to understand the
research philosophy used in the study, understand the strategy of research used and the
methodologies adapted and the research instruments that is utilized in the research.
3.2 Research Philosophy:
A research philosophy can be understood as the set of beliefs regarding the data
associated with a phenomenon (that is how it should be collected, analyzed and utilized). The
terms epistemology vs. doxology outlines the different philosophies of a research process.
Moreover, the aim of a scientific process is to transform something that is believed to be true
into a scientific fact or a known phenomenon that is a conversion from doxa to episteme.
Two main research philosophies that are used in scientific studies are positivism and
interpretevism (Edson et al., 2016). The study in the given scenario would abide to the
positivist approach. This form of philosophy implies that the reality is stable and can be
observed from an objective point of view. and without the necessity of interfering with the
studied phenomenon. In this philosophy it is assumed that a phenomenon should be isolated
and the observations can be repeated. Such an approach also allows manipulating the reality
through variations in single independent variables which allows identifying any irregularities
in the results and helps to develop an understanding of the relationship between the studied
variables and their outcomes. Based on such understanding, predictions can also be made,
that utilizes previously observed and explained results and inter-relations. As such the
philosophy of positivism is considered to be an important and even a vital philosophy in

15EDUCATION
scientific research which can ensure the validity of a scientific study. Authors have also
supported that positivism allows an empirical study, and thus helps to understand the
association between the variables and outcomes in a better manner (Saunders et al., 2015).
3.3 Methodology
The methodology selected for thesis study would be a primary research, in which
students (participants) would be divided in 2 groups, and differential teaching approaches
would be used for each of the group, and the performance of each of the approach would be
analyzed by testing the performance of the students before and after the test. The study would
utilize the primary data collected from the sample population in the form of performance
scores in the pretest and post test. Using the primary data would ensure high degree of
reliability and accuracy of the data, ensure relevance to the context of the study, and provide
a more realistic understanding of the outcomes (Flick, 2015). The experiments helps the
researchers to understand the relationship between specific variables which are being studied
within a specific context using quantitative and analytical techniques and then making
generalizations which can be used in real life and predict the future. However, laboratory
based experiments can also lead to oversimplifications or limit the extent of the relationship
that actually exists in the real world. However, the efficacy of laboratory based studied can be
enhanced through field experiments which helps to understand the learn the real life
scenarios, and how they affect the outcomes of the study (Ledford & Gast, 2018).
3.4 Study Design:
The design of the study is aimed to understand the effects of group based learning
supported by a scaffold teaching approach, requiring minimal support from the teachers
among children aged 8 to 9 years. The study will include the students of Chester A. Monroe
Elementary School from the pre 5th grades. The study would involve 100 students, who

16EDUCATION
would be divided into two groups (Group A and Group B) (Melero et al., 2015). The sample
size would be the representative of the demographics of the school, and would include ethnic
minorities such as Caucasians and African Americans. Each group would have 50 students,
and would be given a specific form of teaching strategy. The study would span for 8 weeks,
during which each group will go through the differential teaching. The comparison of the
result will be done through the analysis of a pre test (taken at the start of the study) and a post
test (at the end of the study). The test will be aimed to quantify the mathematical skills of the
students and compare the performance of each groups. The pre test would also provide the
baseline data that would be used to understand the extent of progress at the end of 8 weeks.
The scaffold teaching technique would be contrasted to the traditional approach of teaching,
in which the teacher would be conducting regular classes that would involve giving lessons to
the student, assessing the understanding gained by the students, and repeating the lessons
whenever necessary. The approach would involve the teachers giving assignments to the
students, which they need to prepare by themselves, but would not include extracurricular
classes, activities or group based learning. The Group A would be provided a traditional
form of teaching, while Group B would be given scaffold teaching that would include all the
components and approaches that have been discussed earlier. Thus, group A would act as the
control and Group B the experiment (Davidson et al., 2014).
The outline of the lesson would be as follows: The Whole Group lesson (Go Math)
would involve engaging the students, teaching and talking to them, practicing problem
solving skills, summarizing the lessons learnt and group studies. The Touch Math strategy
would involve the development of fluency, application of problem solving skills,
development of core concepts and debriefing the students. The structure of these activities is
given below:

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Go Math Touch Math
• Aligned to the Florida Math
Standards
Lesson Outline:
Whole Group Lesson
• Engage - Access Prior Knowledge
• Teach and Talk - Investigate, Draw
Conclusions, & Make Connections
• Practice - Share and Show, Problem
Solving
• Summarize - Essential Question
• Small Group – Response to
Intervention
• Aligned to the Common Core
Standards
Lesson Outline:
• Fluency - 10 minutes
• Application - 8 minutes
• Concept Development - 15 minutes
• Small Group & Center Rotation –
Continue with Problem Set (15
minutes)
• Student Debrief - 10 minutes (Exit
Tickets)
3.4 Implementation
The study will be carried out in the form of a combination of an experiment and
general research. Particularly, the participants aged 8-9 will be split into two groups (group A
and Group B), the first one being taught math in a traditional manner using, whereas the
second one will be provided with the teacher’s scaffolding assistance (Eisenhamer et al.,
2016). Additionally, the students in the second group will be suggested to assess each other’s
tests based on a rather basic and very simple grading scale developed specifically for this
purpose. Two set of tests will be conducted; the former one will be delivered to the students
prior to the experiment, whereas the second one will be administered to each of the groups
afterwards. As soon as the tests are completed, a statistical analysis of the two evaluations
will be conducted in order to identify the differences in the performance rates among the
members of the two groups. As far as the second part of the research is concerned, it will be
carried out as a general research, with the evaluation of the latest research papers on the
subject matter.

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3.5 Data Collection:
The study was designed to understand if scaffolding and group based learning can
improve the mathematical and computational skills among students. The data was collected
from the pre test, conducted at the beginning of the study which would test the mathematical
and computational skills of all the participants at the starting of week 1. At the end of week 8,
another test would be conducted (post test), which will re evaluate the mathematical and
computational skills of the student. During the eight weeks of intervention, the students
would be given tasks to add and subtract numbers (single, double and triple digits, ranging
from 0 to 999). The tests would be filled out by the students and filed to be analyzed later.
3.6 Confidentiality and Ethical Approval:
Prior to the study being conducted, an approval would be sought from the educational
and ethical council as well as from the administrative authorities of the school. Also, each
students would be given a letter with an informed consent form, addressed to the parents or
guardians of the students using appropriate language. Signature would be obtained from the
parents or guardians before reporting the child’s data and including him/her into the study. In
the informed consent letter, the purpose and procedure of the study would be outlined
(Petrova et al., 2016). The parents or guardians would also be informed that they can
withdraw their children or ward at any point during the research without risking any adverse
effects. All data would also be kept strictly confidential in accordance with the Federal and
State laws as well as the Universal Policies of ethical research. Confidentiality would be
maintained and assured by setting up a code, which would use randomized numbers to
identify each participant in the study, and the same codes would be used to collect and record
the data from the tests, and then stored in a secured location accessible only to the researcher.
The data would be given both physical security through securing the access points (such as

19EDUCATION
computers and data collection sheets) and digital security in the form of encryption and user
authentication protocols. After the completion of the study, the codes would be destroyed
(Walliman, 2017).
Chapter 4: Evaluation Plan
The outcomes of the experiment will be evaluated with the help of a set of criteria for
the performance quality of learners. Particularly, for the hypothesis of the study to be proven,
the students in Group B will have to display a significant progress as opposed to the learners
in Group A. Though a minor variance may occur in the specified setting, it will be required
that the difference between the average score of the students in the two groups in question
should differ significantly (Rijcke et al., 2016).
The evaluation will consist of several stages. Particularly, the variance and the
standard deviation in the aspects such as math facts and the ability of the learners to
comprehend the text that they have read will be estimated. As far as the speed of math
fluency is concerned, the number of basic math facts per minute will be considered the key
evaluation parameter. Engage NY provides the rigor needed to be successful on the MAFS.
The tests will supposedly help both identify the effects of the specified strategy and inform
teacher on further steps that will need to be taken to improve the learners’ skills.
In each of the pretest and post test, sets of mathematical computational activities
would be given. The activities would include addition and subtraction of single, double and
triple digit numbers (from 0 to 999). The test would measure the following aspects: accuracy
of the answers (that is the number of answers given correctly), the score of the test and the
time taken to complete the test. These factors would be compared to the results from the post
test, to understand the extent of improvement in the skills of the students. Care would be
taken to ensure that the calculation tasks given in the pretest and post test involves different

20EDUCATION
numbers, but at the same time having the same complexity to solve. Given below is a chart
that would be used in the collection of the data from the pre test and post test:
Measured variable Pre-Test Post-Test
Accuracy of answers
Score
Time taken to
complete
This chart would be used for each student, and an aggregate table would also be
prepared to understand the possible trends in the data in both the groups (Group A and Group
B). Comparing the data from group A and group B would help to identify whether the
scaffolding training provided to group B have resulted in any improvement in the
performance of the students. The assessment questions are attached in the appendix.

21EDUCATION
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Beaulieu, J. (2015). Developing a comprehensive mathematical assessment tool to
improve mathematics intervention for at-risk students. International Journal for
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Bugden, S., DeWind, N. K., & Brannon, E. M. (2016). Using cognitive training studies to
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Future of Children, 26(2), 75-94.

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Cozad, L. E., &Riccomini, P. J. (2016). Effects of digital-based math fluency interventions
on learners with math difficulties: A review of the literature. Journal of Special
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Appendix 1: Lesson Planner
Week
Day
Addition Skill Subtraction Skill Strategy
1.1 Beginners math
practice
Beginners math
practice
Introduce and explain TouchMath with
peach ring candy and Dots. Explain and
model the addition skill using physical
representation.
1.2 Beginners math
practice
Beginners math
practice
Review addition skill. Use randomly
generated numbers to
create computations and be able to answer
the computations
Within three minutes.
1.3 Beginners math
practice
Beginners math
practice
Use grocery fliers to gather numbers to add;
focusing on single-digit numbers. The
students will be given three minutes to
complete the addition computations.
1.4 Beginners math
practice
Beginners math
practice
The students will create and answer addition
computation word problems. The students
will be given five minutes to complete the
computations. The students will also be
given a weekly summative test to determine
knowledge gained.
1.5 Beginners math
practice
Beginners math
practice
Practicing learnt strategies
2.1 Single digit
numbers 1-10
Single digit numbers 1-
10
Addition/Subtraction with counting on
statement
2.2 Single digit Single digit numbers 1- Addition/Subtraction with counting on

29EDUCATION
numbers 1-10 10 statement
2.3 Single digit
numbers 1-10
Single digit numbers 1-
10
Addition/Subtraction with regrouping statement.
2.4 Single digit
numbers 1-10
Single digit numbers 1-
10
Addition/Subtraction with regrouping statement.
2.5 Single digit
numbers 1-10
Single digit numbers 1-
10
Practicing learnt strategies
3.1 +1, +2, +0 in ones,
tens, hundreds, and
thousands place
value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement
3.2 +1, +2, +0 in ones,
tens, hundreds, and
thousands place
value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
3.3 +1, +2, +0 in ones,
tens, hundreds, and
thousands place
value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
3.4 +1, +2, +0 in ones,
tens, hundreds, and
thousands place
value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.

30EDUCATION
3.5 +1, +2, +0 in ones,
tens, hundreds, and
thousands place
value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Practicing learnt strategies
4.1 +1, +2, +0 in ones,
tens,
hundreds, and
thousands
place value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement
4.2 +1, +2, +0 in ones,
tens,
hundreds, and
thousands
place value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
4.3 +1, +2, +0 in ones,
tens,
hundreds, and
thousands
place value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
4.4 +1, +2, +0 in ones,
tens,
hundreds, and
thousands
place value
-1, -2, -0 in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
4.5 +1, +2, +0 in ones,
tens,
-1, -2, -0 in ones, tens,
hundreds, and
Practicing learnt strategies

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hundreds, and
thousands
place value
thousands
place value
5.1 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement
5.2 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
5.3 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
5.4 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
5.5 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Practicing learnt strategies
6.1 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement

32EDUCATION
6.2 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
6.3 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
6.4 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
6.5 Doubles in ones,
tens, hundreds, and
thousands
place value
Doubles in ones, tens,
hundreds, and
thousands
place value
Practicing learnt strategies
7.1 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement
7.2 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens, hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
7.3 Near doubles in Near doubles in ones, Addition/Subtraction with regrouping statement.

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ones, tens,
hundreds, and
thousands
place value
tens,
hundreds, and
thousands
place value
7.4 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
7.5 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens, hundreds, and
thousands
place value
Practicing learnt strategies
8.1 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Addition/Subtraction with counting on
statement
8.2 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Addition/Subtraction without regrouping
statement.
8.3 Near doubles in
ones, tens,
hundreds, and
Near doubles in ones,
tens,
hundreds, and
Addition/Subtraction with regrouping statement.

34EDUCATION
thousands
place value
thousands
place value
8.4 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Addition/Subtraction with regrouping statement.
8.5 Near doubles in
ones, tens,
hundreds, and
thousands
place value
Near doubles in ones,
tens,
hundreds, and
thousands
place value
Practicing learnt strategies

35EDUCATION