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.

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.

Our purpose is to strive to prepare all students to the next level in their pursuits of college studies and careers.

Literature Synthesis

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.   

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 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.

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 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.

Needs Assessment

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 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.

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 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.

Improving Math Fluency Skills to Enhance Math Score

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 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.

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 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.

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 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 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).

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.

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 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).

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).

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 5^th grades.  The study would involve 100 students, who 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:

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)

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.

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.

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 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).

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 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.

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