Pedagogy

This applied dissertation was submitted by Adel Abdalla under the direction of the persons listed below. It was submitted to the Fischler School of Education and Human Services and approved in partial fulfillment of the requirements for the degree of Doctor of Education at Nova Southeastern University.

This applied dissertation is designed to provide teachers an intervention program for elementary students to help them improve their academic performance in Mathematics. The After-School Mathematics Tutorial Program is evaluated in the context of an elementary school in South Florida in order to measure it effects on male and female students, in terms of academic achievement. A mixed methods research design will be implemented to holistically evaluate the impact of this tutorial program on the students. The research will follow the Sunshine State Standards for Mathematics to determine academic achievement.

Statement of the Problem
The No Child Left Behind (NCLB) Act of 2002 has placed tough responsibilities on the public school system to guarantee that all children succeed. Taking into consideration this expectation and requirements, it is obvious that closing the achievement gap at all grade levels and between male and female students is essential. Research has shown that mathematics academic achievement has posed a great problem for female students compared to male students, and for the lowest 25 of students as a whole at the identified elementary school in south Florida.

The After-School Mathematics Tutorial Program (ASMT) program needs to ensure that the academic needs of both males and females in fourth grade in a south Florida elementary school are being adequately addressed. Research studies have made it very clear that the differences in achievement of males and females in mathematics is a problem that needs to be investigated in order to understand the genders effect on the academic mathematics achievement. It is also a challenging concern for our society to study, investigate, document, and address the gender mathematics differences in early ages of our students. Therefore, this applied dissertation comes at the opportune time, in relation to program credibility and funding opportunities.

Background and Significance of the Problem
The primary focus of this applied dissertation is to evaluate the practices implemented in the context of an After-School Mathematics Tutorial Program (ASMT) at work in an elementary school setting. Fennema (2000) pointed out that during the last three decades, the need to continue studying and researching about gender and mathematics must continue in order to deepen ones understanding of what and how this discourse can be achieved. An understanding of gender and mathematics will improve by research and engaging the whole community in this discourse.

Research studies on the differences between male and female students achievement in mathematics began almost 60 years ago. It is important to study the differences in gender achievement in mathematics if the gap between genders in mathematics continues to exist. Newsweek magazine, December 15, 1980, (as cited in Hyde, Fennema, Ryan, Frost,  Hopp, 1990) carried the headline Do Males Have a Math Gene They subsequently replied to the affirmative. However, some researchers and investigators claimed that the environmental factors could affect the students achievement, but not the biological factors (Hyde et al., 1990).

The ASMT is designed to service students between the ages of nine and 10. Participants were chosen based on the needs as determined by one or more of the following criteria (a) a group of 14 female students who scored a level 1 or 2 on the Florida Comprehensive Assessment Test (FCAT) for mathematics administered in 2006 (b) a mixed group of 20 male and female students who scored a level 1 or 2 math FCAT administered in 2006 (c) a group of 17 male students who scored a level 1 or 2 on math FCAT administered in 2006. It was calculated that 41 students enrolled in this program. The programs measurable objectives include (a) providing tutoring and enrichment to assist 70 or more of its participants in obtaining and maintaining a level 3 in mathematics, and (b) 70 of the participants will increase one level or more in mathematics by the end of the program. The three groups will compete to get the best results.

This elementary school will be referred to as an elementary school in a south Florida school district. The students in this school came from middle class socioeconomic background. The population of this school for the 20052006 academic session was 650 students.

In accordance with the state of Floridas A Plan, the elementary school being studied earned a grade of D for the 2001 and 2003 school years a grade of C for the 2002, 2004, and 2005 school years and a grade of B for 2006 school year. In the 2006 school year, in the area of reading, 54 of the students who participated in the FCAT were at or above grade level, 59 made a years worth of progress, and 66 of struggling students made one years growth.

In the area of mathematics, 48 of all the students who participated in the FCAT were meeting high standards in math, and 68 were making learning gains in math. In the area of writing, 85 of all students were meeting high standards. The 2005-2006 Adequate Yearly Progress (AYP) indicted that the lowest 25  students need improvement in mathematics (Florida Department of Education, 2006). It is clear that ASMT program should play an important part to improve the mathematics academic performance of the lowest 25  students.

The student population in the elementary school being studied is 2.5 White, 39.3 Black, 34.6 Hispanic, and 0.6 Asian. In the grades 3-5 population, 98.7 of the students are classified as economically disadvantaged, 43 are students with limited English proficiency (LEP), and 20.8 are classified as students with disabilities (SWD) (Florida Department of Education, 2006).

Deficiencies in the Problem
Over the years, the belief that boys do better in mathematics than girls has remained consistent. Brynes and Takahira (1993) declared that males have scored an average of 46 points higher than females on the Scholastic Aptitude Test mathematics exam. These findings and their implications have been recognized for years. Teachers and parents mirror this thinking. Fennema (1975) stated that for over 50 years males have achieved higher levels in mathematics than females. It seems that for males, mathematics has been a necessity, while in the mean time, for females it has not. Is it lack of self-esteem Or is it just a saying which we have inherited from the past generations
Secada (1989) asserted that females, more than males, doubt their ability in mathematics. It is repeatedly stated that female students have no self-confidence when it comes to their abilities in mathematics. Crawford, Herrmann, Holdsworth, Randall, and Robbins (1989) explained that classroom studies have shown that the belief that male students achieve better in mathematics than female students is in place by the time children enter the third grade. It is obvious that this problem started at an early stage of schooling. Lummis and Stevenson (1990) declared that by the time children enter kindergarten, parents expect girls to do better at verbal tasks and boys to do better at mathematics. This means the belief is common throughout society, schools, and among researchers.
This applied dissertation will evaluate the increased level of fourth grade students to indicate whether or not the ASMT program is effective on the three groups of student and the impact of the program. This applied dissertation is to evaluate the program. A product portion of the Control, Input, Process, Product (CIPP) Evaluation Model checklist will be used to determine the extent to which the goals of the program have been achieved. Evaluating the impact of the program and measuring the goals, the resulting data are used to make decisions about continuing or modifying the program.

Today a whole new era of tutoring has evolved. Specifically, a major question regarding tutoring to be answered in the circumstance of public education is, What is the definition of a tutoring program in a Title I school Under the NCLB Act, local districts have received more federal funding than ever before. Title I of the Elementary and Secondary Education Act allocates a large portion of these funds for grants to improve the academic achievement of the disadvantaged. The school districts and schools have the latitude to determine how this money will be used (United States Department of Education, National Center for Education Statistics, 2003). The only mandate of the law is obtaining the same result to have all students proficient in every core subject area. It is necessary to check what the recent statistics indicate about this problem.

The U.S. Department of Education, National Center for Education Statistics issued a table of comparison of fourth- through eighth-grade mathematics performance in 2003 which showed that in the United States, in fourth grade, the total average is 518 male 522 female 514, and in eighth grade the total average is 504 male507 female 502. Eventually, these numbers indicate that there is a gap in performance and achievement in mathematics between male and female students in America.
Fierros (1999) showed that in general the cross-country analyses revealed few gender differences in the 8th grade with increasing gender differences in mathematics achievement favoring males developing by the 12th grade. Some researchers declared that it is only a slight difference. The difference started to decrease roughly in eighth grade. The research has gone further claiming that females tend to do better in mathematics than their male counterparts.

Another perspective is that the math FCAT is a multiple-choice question test. Whether or not the expected difference is due to the nature of the exam itself becomes a questionable matter. Ryan (1996) indicated in a study of 6,000 fourteen-year-old students on an international mathematics test, that males scored better on algebra and geometry, but females performed better on arithmetic, though all questions were presented in a multiple-choice question format. Actually, that reason probably would be seen as a component of the problem which needs to be addressed.

The applied dissertation needs to indicate if it has an effect on the achievement of the female or the male students. Yang (2003) declared that the male students showed more positive motivational beliefs in physical science than the female students, and female students exhibited more positive motivational beliefs in reading than the male students. These various opinions about what females or males aptitudes are, and why, is evidence of an existing problem in this particular area.

Some other researchers approached the problem from different view points. Bielinski and Davison (1998) reported a sex difference by item difficulty interaction in which easy items tended to be easier for females than males, and hard items tended to be harder for females than males. Others declared the opposite. Eccles and Wegfield (1985) stated that unfortunately, by the time critics pointed out that even in the same classroom, boys and girls may have very different experiences. Eccles and Wegfields study did not explain why this happened. There was no explanation about these tendencies of the females or the males. Different findings about the problem have been studied in detail, but in a different period of time. This applied dissertation will find out about the elementary stage as it is important to know about what is happening at that early age.

Finally, there are many research studies that deny the whole problem whether in elementary or in middle schools. For instance, DeClerico (2002) claimed that there are no significant gender differences in achievement in any of the subject areas of mathematics, science, and language arts on the New Jersey Elementary School Proficiency Assessment or the New Jersey Grade Eight Achievement Assessment.

Definition of Terms
Adequate Yearly Progress (AYP) - Adequate Yearly Progress is the minimum level of performance that school districts and schools must achieve each year as determined under the federal No Child Left Behind (NCLB) Act.

After-School Mathematics Tutorial Program (ASMT) - The key goal of Math Tutoring is to provide problem-solving experiences that build students understanding of specific math facts and skills.
Control, Input, Process, Product (CIPP) Evaluation Model  this is a checklist used to determine the extent to which the goals of the program have been achieved.

Florida Comprehensive Assessment Test (FCAT) - the standardized test used in the primary and secondary public schools of Florida.

National Council of Teachers of Mathematics (NCTM) - a public voice of mathematics education supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development and research.

Sunshine State Standards (SSS) - broad statements that describe what a child should know and be able to do at every grade level. These standards cover seven content areas social studies, science, language arts, healthphysical education, the arts, foreign language, and mathematics.

Purpose of the Study
The purpose of this applied dissertation is to investigate and compare the academic achievement between genders in mathematics for a group of fourth-grade students in the identified elementary school in south Florida.  The applied dissertation will assess the participation in the ASMT program and also the results of participation in the program.

A school or school district that does not meet the states definition of adequate yearly progress (AYP) for two years (school wide or in any subgroup) is considered to be in need of improvement (United States Department of Education, 2002). The 2005-2006 (AYP) Report of the identified elementary school in south Florida indicated that Hispanic, LEP, and SWD students in the selected elementary school in south Florida need improvement in mathematics. It is very clear to the elementary school that their ASMT program plays a very important part in improving the mathematics academic performance of male and female students. This applied dissertation is to evaluate the ASMT program at the identified elementary school in south Florida.

Also, this applied dissertation is to investigate and compare between genders academic achievement in mathematics of fourth-grade students. It will assess the results of participation in the ASMT program. It will also evaluate the after-school program to determine if it is more effective with a class consisting of females only, or with a mix of males and females. Due to educational needs, there is a tremendous necessity for a program evaluation of the curriculum framework and instructional practices to determine who is benefiting more, whether it is female students, male students, or both at an elementary school in south Florida.

Chapter 2 Literature Review
Introduction
The study was created to evaluate the practices that were employed in After-School Mathematics Tutorial Programs in elementary schools. There was a significant achievement gap that led to the creation of the No Child Left Behind Act of 2001. The performance gaps were observed between genders that emerged 60 years ago (Hyde et al., 1990). The last three decades experienced an increasing need to study and research gender and mathematics in order to address this gap (Fennema, 2000).

There was a significant need to enrich the existing literature because the gaps between genders still exist, especially in the context of the mathematics field.  Lalley and Miller (2006) stressed that despite the efforts to meet the needs of low-achieving students, they still continued to represent a significant portion of the population in the schools, wherein four to seven percent of the students were low achievers in the mathematics subject alone.

This section would provide the scholarly groundwork for this research. The discussion would begin with an understanding of what mathematics is and the role that it played in the field of education. The chapter would also address what research studies have to say about the current trends in assessment and the professional development of teachers. Furthermore, the discussion involves current views of student performance in terms of intervention strategy effectiveness, student achievement and gender patterns. Finally, the role of tutoring would also be addressed in relation to its influence in student achievement.

What is Mathematics
Modern mathematics curriculum has changed over time. It has become a subject that was more complex than just arithmetic (Zevenbergen, Dole  Wright, 2004). More than 100 years ago, mathematics entailed computation of tasks involving large amount of numbers, long division, square roots of non-square numbers and so on. It was in the early 1960s when the new maths entered the curriculum, representing the shift in most Western countries (Zevenbergen et al., 2004). Decades passed and more forms of reforms influenced the curriculum, such as the inclusion of problem solving wherein students were expected to be more creative in their thinking. Technology played a more significant role in the curriculum in the 1980s as software programs were constantly created.
Mathematics was about being aware of recurring ideas and relationships among mathematical ideas. It was described as the study of patterns and relationships (Zevenbergen et al., 2004). When a learner receives knowledge from one area, one should be able to link it to other mathematical concepts and principles. The capability to view types of patterns and relationships was a key factor in how students learn and appreciate mathematics. Mathematics could also be considered as a way of thinking, seeing and organizing the world (Zevenbergen et al.). It was beneficial to understand mathematics as a dynamic discipline, which could be used to interpret much of the world. Through this body of knowledge, one could organize and analyze events in systematic ways.

Mathematics was also considered as a language. There was a time wherein mathematics was viewed as a disparate discipline. Presently, students were taught to learn and to understand the language of mathematics in order to appreciate it (Zevenbergen et al., 2004). Furthermore, it was also considered as a tool that could solve everyday problems. The more competent a person in this field, the more problems one could solve and, in some cases, the better one could cope in the real world (Zevenbergen et al.). It was also viewed to be a source of power. Mathematics was behind most inventions in modern history, such as the space rocket that was sent to the moon and the atomic bomb. Moreover, it was viewed as an access to professions of high status, wealth and power.
Developing nations were observed to empower the youth to be good at mathematics because they knew of the benefits that such knowledge could provide them as individuals and as citizens of the country (Zevenbergen et al., 2004). In the same manner, many Western countries also recognized the problems that were associated with a decreasing interest that students have in taking up more advanced mathematic subjects.

The examination of the nature of cognitive development that was related to mathematics difficulties of young students involved the number sense, which was defined as the movement from the initial development of basic counting abilities to a more sophisticated understanding of number relationships, patterns, operations and place values (Bryant, Bryant, Gerste, Scammaca  Chavez, 2008). There were essential elements of the number sense that included counting, number knowledge (i.e. quantity discrimination, counting sequences, among others), number transformation (i.e. addition, subtraction, verbal and nonverbal calculations), and estimations (i.e. group size).
In 2005, the National Council of Teachers of Mathematics (NCTM) declared a vision of a future wherein all students will have access to rigorous and high quality mathematical instruction, as well as a curriculum that will be rich in mathematical instruction, which will provides students with opportunities to learn important concepts and procedures about the subject (Paul  Miller, 2007). They urged educators to purse new directions in mathematics education that would help students move out of a narrow and highly procedural set of experiences to one that was closer to a more challenging mathematical instruction.

According to Luowenberg (2001), the mathematics education community should actively seek to improve the teaching of this subject in the country. Reforms were often perceived to bring about widespread impact because of the critical significance of this subject in the achievement of academic success for the students. The subject should be presented with an understanding that it was a skill that provided high standards for progress and accomplishment (Luowenberg, 2001).

Seo (2003) pointed out that the development of appropriate early mathematics education programs would help children get ready for more advanced mathematical subjects wherein most failures come from. Children, especially those from low-income households, often have difficulty with school mathematics and science. This should be the focus for intensive early mathematics education that would provide the foundations for preparations.

Professional Development
    In the times wherein the students of today lived, there were different elements that brought changes to society, work, school and life. Variables, such as technology, globalization, the information age, and different patterns of family, leisure, and work, brought changes to the society, in comparison to that of past generations.  The curriculum in schools needed to be relevant to the changes in the wider society in order to ensure that these institutions of academic learning were adequately preparing students for the world beyond the school (Zevenbergen et al., 2004).  Students grow up in technology-rich environments in which they no longer have to get up and change the channels of their television sets.

Mathematics education in the modern time needed to be relevant given the nature and importance of this subject in the larger society. The students need to develop mathematical ways of viewing and interpreting the world and they need to enhance their problem-solving skills. More than that, the students need to have a disposition for utilizing the subject to solve the problems they were confronted with (Zevenbergen et al., 2004).

Thus, school teachers need to adopt new pedagogies that would cater for the diversity in the classroom and would be relevant to the new generation of students. Old models of seated individual work from traditional mathematics instruction possibly created problems for students progress in the subject (Zevenbergen et al., 2004). A number of students often voice out negative feelings and misleading learnings about the subject due to their encounter with the outdated models of instruction.
The mathematics curriculum that was started before the 1960s focused on arithmetic and operations. Most of the models of instruction for the subject developed after this in the Western countries, which arose after the Sputnik era, when the race to the moon was translated to the race of intellectual superiority among the nations and mathematics were considered as the linchpin for success (Zevenbergen et al., 2004).

The new mathematics paved the way to a lock-step approach to teaching the subject with hierarchies in orders and sequences in teaching. The decade after that saw a revival of the mathematics curricula. It was influenced by arguments of logic and reason, despite the fact that they were not research based (Zevenbergen et al., 2004). The hierarchal approach to teaching mathematics was described by the use of the skill, drill and kill approach, to be followed by application and problem solving. For most mathematics teacher, this had become a way of life. Much of what was written in the reforms in the 1970s was based on insignificant research foundations and raised questions to the validity of this curriculum (Zevenbergen et al., 2004).

The recent times reflected the realization that such approaches did not result in positive learning outcomes. Researchers argued that all students learn from their 10 years or more compulsory schooling was the fact that they cannot be good at mathematics (Zevenbergen et al., 2004 Burns et al., 2006). The countries that did not implement this approach, such as Netherlands, were described to have new methods and approaches of teaching the subject. They focused on teaching students to think mathematically that enabled the learners to draw on understandings and build on them, as they progressively move towards more abstract and formal mathematical processes (Zevenbergen et al., 2004).

According to Adams (2000), there were many approaches that could be used to teaching mathematics to young children and many theories of learning addressed how they could be empowered to learn the subject. More than the chosen method, it was the childrens varied learning styles, strengths, experiences and perspectives that significantly impact the success of teaching the subject. In order to achieve the goal of helping children develop mathematical competencies, it was important to recognize that children have multiple means of learning or intelligences.

Howard Gardners multiple intelligence theory described that the children employed different intelligence in learning situations (Adams, 2000). Children could have one or more intelligences, which could serve as a mechanism for learning and lead to the development of a cognitive ability.
According to the NCTM in April 2000, new principles and standards for school mathematics should be put in place. The standards contained five content-oriented approaches and five process-oriented ones (Adams, 2000). They functioned as a framework for using multiple intelligences that children could utilize in mathematics learning. The multiple intelligences theory provided a platform by which learners diverse problem solving characteristics and strengths could be evoked.

Other contemporary approaches to teaching mathematics encouraged two aspects, which were content and pedagogy (Zevenbergen et al., 2004). Content referred to intellectual integrity of the subject wherein students learn, apply and appreciate it. This was where deep learning and deep knowledge were critical to learning experiences. In this way, students could make connections between the subject they learned and other curriculum areas, as well as the world beyond education. Children should have the foundational understanding that this subject was an informing discipline that had importance and relevance to many spheres of life and aspects of society.

On the other hand, pedagogy related developing supportive environments wherein student diversity was reflected and practices were developed in accordance to this recognition. Approaches recognized that the different background and knowledge that students bring to the classroom were to be used for the enrichment of knowledge (Zevenbergen et al., 2004). This was highly associated with the recognition and utilization of multiple intelligences in individuals.

The mark of good pedagogy was the development of inclusive practices to develop and extend the students learning and confidence for the utilization and practical application of the principles of the subject. The classroom is a place that should value and appreciate the benefits of the different backgrounds and capabilities of the mathematics students. The development of inclusive practices should enhance intellectual integrity among the students (Zevenbergen et al., 2004). Furthermore, teachers must be able to express their perception of value for the students, as well as their belief that each student could develop skills in mathematics.

According to Zevenbergen and his colleagues (2004), productive pedagogies were those that were about high intellectual engagement and helping students see and make connections it is learner-centered, where each individuals knowledge and culture is valued, and learners feel supported in their learning.

Lloyd and Frykol (2000) pointed out that the differences in instructional methods that the prospective teachers were expected to use in schools and the experiences that they had as students of mathematics were perceived as opportunities by which mathematical and pedagogical ideas could be reviewed. Teachers also needed to experience for themselves a greater understanding for the subject in terms of exploring, guessing, testing, estimating, arguing and proving.

Overall, before the teachers could teach through new modes of instructions, they need to learn mathematics in a manner that encourages them to active engagement with mathematical ideas. It was true that if they were not exposed to this, all they would know would be how they were taught in their own time. It was quite possible that teachers would merely repeat the classroom instruction that they were exposed to, even if it included imposing trauma on the students to learn mathematical concepts and principles through blackboard drills and similar activities.

Unfortunately, this was a reality for teachers, as most possessed weak knowledge and narrow views of the subject and the pedagogy that included conceptions of mathematics as a closed set of procedures (Lloyd  Frykhol, 2000). These included viewing teaching as telling and learning and accumulation of information. It was important to apply reform themes that could be enacted in the classroom of future math teachers. These conceptions need to be challenged and developed in such a manner that it would radically eliminate the skill, drill and kill approach for teaching mathematics.
According to Copple (2003), teachers that worked in early childhood settings needed to undergo extensive training. The task of improving and setting the foundations for what a young child could believe about mathematics would be critical for the childs future. The efforts to improve the quality of the curriculum and instruction in the early years could make a difference in society. However, the dark reality was there were hundreds of thousands untrained early child educators, along with a host of teachers with basic early childhood training but little preparation in relating and teaching mathematics (Copple, 2003).

Preservice teachers need to engage in new conceptions regarding the subject, especially in the context of middle schoolers (Lloyd  Frykhol, 2000). They needed to be exposed to school reform-oriented curriculum materials that would help them recognize new perspectives about the subject, even if it would entail learning unfamiliar mathematics using pedagogical methods that they have not experienced when they were still studying. This involved training preservice teachers to accept unconventional methods of teachings in order to enable students to learn and understand the subject from a different and a more impassioned perspective.

It would be highly beneficial for the least trained personnel to be exposed to the core messages for mathematics education (Copple, 2003). Furthermore, early childhood educators should provide fruitful direction for children to explore mathematics in the developing or identifying of materials that they might find interesting, but could develop their mathematical skills. It was without a doubt that the educators knowledge and skills were vital to educational effectiveness.

In order to improve the mathematics curriculum, it was critical for the teachers to improve their own learning curve and for them to receive new materials in learning the new mathematics (Copple, 2003). Teachers needed to know relevant mathematics lessons that would work well with children. It was advantageous to provide children with lessons that they could experience with real life application in their age. In order to do this, individual assessment of what the children were interested in and what they were capable of doing would make a significant improvement. It was also important for teachers to avoid underestimating the range of the young mathematics learner and their interests for the subject (Copple, 2003). It was easy to fall into this trap because of the negative personal experiences the teachers have had during their time.

According to Zevenbergen and his colleagues (2004), teachers commonly dreaded issues of behavior management that were associated in teaching mathematics classes. They knew that few students considered mathematics as an enjoyable subject due to the backlash of the drill, skill and kill approach to teaching.  Many elements of productive pedagogies were commonly absent in todays classrooms. Students would be unengaged in deep learning about and through mathematics (Zevenbergen et al., 2004). It was also discovered that while students undertook the most activities during mathematics classes, they did not engage much in any deep mathematical learning. This highly explained the construed misbehavior of children during mathematics classes, because they were bored with the subject and the pedagogy was ineffective.

It was important to consider the changes that teachers could make. It was not the schools that could make a difference for the students, but the individual teachers (Zevenbergen et al., 2004). Teachers have a powerful influence over the students, in terms of what and how they learned in the classrooms. The provision of an appropriate learning environment, wherein the content and pedagogy matched the background, needs and interests of the students could make students want to learn the subject and make them understand and use it as well.

Furthermore, it was important for teachers to change their attitudes towards the subject as well. While they dread the childrens behavior towards the subject, they also need to change their beliefs towards the ability and the interest of their class for mathematics. The most important influences on learning included the teachers belief that not only selected students could learn mathematics but everyone could (Zevenbergen et al., 2004).  The values and stereotypes that teachers carried could be interpreted and implemented in the way teachers teach their classes.  Thus, when teachers believe that their students were unable to learn mathematics due to their background, behavior, and even gender this would ultimately impact the learning environment that constructed the expected outcomes (Zevenbergen et al., 2004).

Tanner and Jones (2001), as well as Ray and Elliot (2006) stressed on the relationship of teacher behavior to classroom behavior. It was important for teachers to be able to create a classroom atmosphere that encourages learning. The way a teacher addresses the classroom pre-empt misbehavior and can encourage learning. Thus, it was critical for teachers to show that viewing their students to be bright and excellent, especially in the mathematics subject is one of the ways by which students will mirror this behavior. Furthermore, teachers should avoid declaring that the subject was hard and that it was a subject that would be the students waterloo in the future. This could create an atmosphere of tension and dislike for the subject.

Tutoring
Since middle school is a critical time in a students academic progress, the preparation and their performance during this time needed to be ready for advanced studies in critical thinking.  Flores and Kaylor (2007) pointed out that there were significant gaps in the students understanding of certain mathematical concepts, areas that were defined to make use of critical thinking skills.  The performance of the students in mathematics classes could be understood in different manners, which included the intervention programs, student achievement and gender patterns. These areas would be analyzed to understand the existing trends that were available in mathematics achievement.
According to Wasik, Bond and Hindman (2002), tutoring was a common after-school activity that provided children with additional avenues for instruction in subject areas wherein they were either struggling with or trying to excel in. Tutoring programs were noted for their significance, especially in high-poverty neighborhoods wherein limited in-school resources were available and unable to meet the needs of numerous children. Unlike other after-school experiences that focused on enrichment, leisure activities and purely custodial care, tutoring in mathematics had a strict focus on academic emphasis.

This academic focus, presented many challenges for schools and community organizations in trying to establish programs that would reinforce concepts that were presented during school or teaching new information. Usually, well-trained professionals were ideal tutors. However, given the budget of schools in poverty-stricken communities, they could not be afforded. Instead, the schools needed to challenge organizations in the schools and in the communities to establish programs serviced by volunteers (Wasik, Bond  Hindman, 2002).

In the context of solving word problems, tutoring provided both calculating and mathematical cognition skills (Fuchs et al., 2008). Even if word problems were required for correct calculation for a solution, students needed linguistic competencies in order to master this. This created difficulties in the academic achievement for students in using mathematics, as a critical tool for academic and real life challenges.

Tutoring has become on of the most common prevention system for academic difficulties and failure (Fuchs et al., 2008). Students that failed to respond to general education, enter secondary prevention. In most research studies, secondary prevention involved one or more rounds of tutoring. Those that failed to improve through such strategies could be recommended for tertiary interventions that made use of intensive instruction that was typically individualized in programming (Fuchs et al., 2008).
There was an increasing need to adapt a model of academic enablers wherein one should contribute to academic achievement, through the provision of additional skills and attitudes that could be taught explicitly in order to increase student learning (DiPerna, Elliott, Volpe, 2002). This should not be considered exclusively for assessment or intervention strategies alone. It was something that should be presented in prevention services.

Davenport, Arnold and Lassman (2004) also described how tutoring was one of the most successful programs for low-achieving students. It emphasized that prevention was better than remediation. Instruction in this setting was designed to increase the amount of time engaged in the learning processes of the subject.  Mastery of the subject required more time for the student to be exposed to the subjects concepts and principles.

Furthermore, since tutoring was more hands-on and individualized, children could choose among activities that the teacher had prepared or the ones they have initiated by themselves. When children were able to make choices about learning, it would become more meaningful, interesting and function for them (Davenport et al., 2004). It was also possible for tutoring sessions to allow more interactive tasks that involved students more deeply in the learning process.

The current studies that explored the effects of a direct instruction program that was implemented with middle school students who were at-risk for failure in mathematics, reflected significant improvement skills as a result of participant in the fraction program (Flores  Kaylor, 2007).  This program showed that children were able to master fractions over a course of seven weeks that took away the existing structure of the classroom and implemented a more tutorial-type of learning. According to Flores  Kaylor (2007) the performance of the student increased significantly.  Furthermore, the corrective mathematics program, which consisted of modules for specific skills such as addition and multiplication, showed the option for freedom of choice according to the needs of the student (Flores  Kaylor). Thus, students could be grouped according to their individual needs and different concepts and skills could be mastered in an effective manner.

Performance
Lauzon (2001) noted that there had been considerable effort over the years that had expanded in attempts to explain the mathematics achievement gender gaps. Biological explanations have been tapped in order to explain the differences between the males and the females when it came to performance on assessments. This was something that interventions could not easily resolve. There was a danger in cultivating mathematics learning gender disparity for children as they mature into adults (Lauzon, 2001).

In another perspective, Boaler (2002) described the differential learning styles of boys and girls. Girls, because of their so-called preferred learning styles and ways of working, experienced the greatest disadvantages. The underachievement and non-participation of girls in mathematics had become established in the recent years and as a result, equity concerns had been pointed out and initiatives for raising girls achievements were implemented (Boaler, 2002).

The major difference could be observed in the top five percent students in the United States, in England, as well as in many other countries (Boaler, 2002). It showed that five boys to every four girls attained the highest grades. On the other hand, girls only made of 35 percent of the top percentile in these countries (Boaler, 2002).  The attribution theory focused on the girls anxieties and their tendency to attribute their failure to their lack of ability, and psychologists used this to suggest how female students could do better in class. Moreover,  girls experienced that they are at disadvantage when it came to their schools mathematics teaching (Boaler, 2002).

Yang (2003) revealed that the male students showed more positive motivational beliefs in physical science than did the female students, and female students exhibited more positive motivational beliefs in reading than did the male students. These various opinions about what females or males aptitudes are signaled the existence of a problem in the performance of these students. Bielinski and Davison (1998) reported a sex difference by item difficulty interaction in which easy items tended to be easier for females than males, and hard items tended to be harder for females than males.

On the other hand, Eccles and Wegfield (1985) argued that unfortunately, by the time critics pointed out that even in the same classroom, boys and girls may have very different experiences. Eccles and Wegfields study was not able to provide validity and evidence for this conclusion. Different findings about the problem have been studied in detail, but in a different period of time. Despite the studies that discussed the academic achievement gap, especially in the subject of mathematics, there were still limited research that widely discusses the role of interventions strategies in the performance of girls and boys.

Assessment
The aim of educational assessment was to produce information in order to assist in educational decision-making. This process involved administrators, policymakers, the public, parents, teachers and students themselves. Not one of these consumers of assessment information should be taken for granted. In an age of information, educational assessment systems should gather information about individual students, group of students, teachers of students, and programs for students from a different range of sources, not just tests (Lesh  Lamon, 1992 Bredekamp, 2003).

Furthermore, the information should contain multidimensional profiles of the different achievements and abilities, and descriptions of relevant conditions under the profiles mentioned. The information must be displayed in a simple, yet relevant manner in order to address the concerns of the different decision makers and their decision making processes.  There was no single source of information that could serve all purposes and there was no single characterization of students or groups that was appropriate for all decision making issues.

In a technology-based society, assessment opportunities were influenced by the fact that reports could achieve simplicity without having to sacrifice information to a single number (Lesh  Lamon, 1992). Simplicity could be attained through the use of computer-based, graphics-based, interactive and inquiry oriented assessments that focused on specific questions from specific people in a specific circumstances. The alternative approaches to assessment were not based on the fact that there was simply a need to develop new modes of assessment. Instead, the concern for education assessment methods was to change the substance of what was being measured (Lesh  Lamon, 1992).

According to Lesh and Lamon (1992), new types of response to interpretation procedures needed to be developed in order to indentify profiles of strengths and needs for the students. New data analysis models and procedures were also needed based on the assumption that was considered with the accepted viewed on the nature of mathematics, learning and real world-relevant problem solving.
New types of learning progress reports needed to be created for a simple assessment that integrates information from different sources, focus on patterns and trends in data and inform different decision-makers and decision-making issues. Furthermore, there needed to be a certain level of awareness and priority for the new decision making issues that include topics such as accountability and diagnostic analysis of learning progress, with a conscious emphasis on equity and validity (Lesh  Lamon, 1992).
According to Burns, Vanderheyden and Jiban (2006), mathematics performance assessment was considered to be more complex because of the relative paucity of data that supported technical properties of decision-making in this subject. Assessment tools for educational decision making needed to meet a certain criteria with technical data for each purpose by which the assessment tool was used. The reliability of the test data with which the academic growth was measured requires estimations through alternate-form or test-retest methods. This reflected how current standards for assessment called for evidence of validity in the assessment data (Burns et al., 2006).

In the context of the assessments in this subject, it was critical to provide a match between student performance and the instructional techniques employed (Burns et al., 2006). The apparent lack of data in examining assessment of instructional level for the subject suggested the need to empirically investigate the technical adequacy of decisions based on instructional ranges in the subject. It was important for assessments to uphold reliability and criterion validity of the fluency and accuracy criteria in order to identify the instructional level for mathematics (Burns et al., 2006).

There were also difficulties with traditional, norm-referenced tests as measures of student achievement, especially in the discipline of mathematics (Westport et al., 2001). These tests inadequately measured students performances due to the sole utility of multiple-choice options, which isolated facts, definitions and procedures. These tests were described as an anathema to mathematical reform because it perpetuated the focus among teachers, administrators and policymakers on basic skills that were bound to be presented in a linear and fragmented fashion (Westport et al., 2001). Tests would be the focus for teaching the subject, instead of actual learning objectives.

Alternative forms of assessments should be considered, such as the portfolios, performance tasks, observations and student interviews, because they offered different avenues for documenting the substantive mathematical understanding. At the same time, they supported and reinforced the changes in classroom instruction that were badly needed.

The FCAT is a multiple-choice question test.  There were questions and whether or not the expected difference was due to the nature of the exam itself becomes a questionable matter. According to Ryan (1996), 6,000 fourteen-year-old students wrote an international mathematics test, it was seen that males scored better on algebra and geometry, but females performed better on arithmetic, though all questions were presented in a multiple-choice question format.  In reality, the reason was viewed as component of the problem, which needed to be addressed. There was a research gap regarding the effect on the achievement of the female or the male students.

The chapter has presented the empirical background on which this study will be conducted. There were significant issues in the discussion of the achievement gap when it came to students performance in the subject of mathematics. This subject perhaps presented a unique challenge in terms of curriculum, assessment and intervention strategies.

The chapter has presented the nature of mathematics and its importance in the academic success of the student. Professional development for classroom instruction provided significant attention in this study. It also presented tutoring as a strategy for preventing failure in the subject. Furthermore, assessment and performance research were also considered in relation to the mathematics achievement gap.

Research Questions
1. Is the ASMT program at an elementary school in south Florida effective in increasing students mathematics academic achievement
2. Is the ASMT program at an elementary school in south Florida more effective with a female student group
3. Is the ASMT program at an elementary school in south Florida more effective with a male student group
4. Is the ASMT program at an elementary school in south Florida more effective with a combined group consisting of male and female students


Chapter 3 Methodology

The increase accountability that NCLB placed on public school systems created literatures that addressed the achievement gap at all grade levels. In this research the context of the gap focused on the disparity of academic performance between male and female students. The mathematics subject posed a significant disparity between female and male students. There was insufficient research that provided significant knowledge regarding the mathematics achievement disparity between male and female students. The purpose of this research was to investigate and compare the academic achievement between the genders for fourth-grade students in the selected elementary school in south Florida. There was also a need to present a viable intervention strategy that could close the achievement gap between male and female students.

Participants
An elementary school in the South Florida school district was the setting for this study. The students at this school come from a middle class socioeconomic background. There were 650 students that made up the population of this school for the school year 2005-2006.

In accordance with the state of Floridas A Plan, the elementary school being studied earned a grade of D for the 2001 and 2003 school years a grade of C for the 2002, 2004, and 2005 school years and a grade of B for 2006 school year. In the 2006 school year, in the area of reading, 54 of the students who participated in the Florida Comprehensive Test were at or above grade level, 59 made a years worth of progress, and 66 of struggling students made one years growth.

In the area of mathematics, 48 of all the students who participated in the FCAT were meeting high standards in math, and 68 were making learning gains in math. In the area of writing, 85 of all students were meeting high standards. The 2005-2006 Adequate Yearly Progress (AYP) indicted that the lowest 25  students need improvement in mathematics (Florida Department of Education, 2006). It is clear that ASMT program played an important part to improve the mathematics academic performance of the lowest 25  students.

The student population in the elementary school being studied is 2.5 White, 39.3 Black, 34.6 Hispanic, and 0.6 Asian. In the grades 3-5 population, 98.7 of the students are classified as economically disadvantaged, 43 are students with limited English proficiency (LEP), and 20.8 are classified as students with disabilities (SWD) (Florida Department of Education, 2006). The 41 subjects who participated in the ASMT program were fourth-grade students at an elementary school in south Florida.

It was in a community where most of its population relied on seasonal work, either in farming or in a sugar factory. The school has a population of 650 students. It has 59 teachers certified in the elementary education. The teachers who taught in the ASMT program were two males and one female. One of the male teachers was the researcher who is an ESOL teacher and has 26 years of teaching experience. The tutors overall have a stellar academic math performance and produced better general results on the standardized math test (Nazzal, 2002).

The students participated in the ASMT program during the fall semester of school year of 2006-2007. The sample of this comparison will evaluate the program. The 41 participant students were divided into three groups. There were 14 female students in the first group and 10 male students in the second group. The third group contained 17 students of 9 male students and 8 female students. All of the students had been chosen randomly from the list of students who had scored a level 1 or 2 on the 3rd grade math FCAT published in the 2006 school year.  

Participants were between the ages of 9 and 10. Participants were chosen based on the needs as determined by one or more of the following criteria (a) a group of 14 female students who scored a level 1 or 2 on the Florida Comprehensive Assessment Test (FCAT) for mathematics administered. (b). a mixed group of 20 male and female students who scored a level 1 or 2 FCAT administered mathematics in 2006 (c) a group of 17 male students who scored a level 1 or 2 on math FCAT administered in 2006.

Instruments
In order to examine the effectiveness of the ASMT program model on students achievement at an elementary school in south Florida, Stufflebeam (2003) suggested a production portion of the (CIPP) evaluation method approach, using data from the 2007 school year, from the participants current report cards, the schools AYP Report, and standardized assessments.

The ASMT was designed to service students in 2006
The Sunshine State Standards (SSS) (Florida Department of Education, 1996) contained the benchmarks for the mathematics skills that demonstrate the participants weaknesses. It provided number sense and mathematics operations such as addition, subtraction, multiplication, and division. Lam (2002) reported that in placement tests, males achieved better than females. There was a large gender gap regarding the mathematic achievement at age 16 as compared to the gap seen at age 13. Also, there was a small adverse impact in all mathematics areas. Specifically, there was a slight advantage for males at age 13 and 16 in measurement skills and geometry, and a slight advantage in algebraic functions for females at the same age.

Procedures
All three groups of students were taught the same mathematics concepts by three different instructors. One of the male instructors taught the first group. The other male instructor taught the second group, and a female instructor taught the third group. The lesson plans were identical for the three groups as were all tests. The female group and the male group were the two experimental groups. The control group was the mixed male and female group. Each group received the same interventions and their math achievement was compared in terms of the effect of gender on this achievement.

The classes were held every Monday, Wednesday, and Friday from November 1, 2006 to March 1, 2007. After the tutorial class on each designated day, the teachers had training.  The training consisted of lesson plan format and the collaboration of instructors to ensure the consistency of strategies, delivery methods, matters, manipulative, and materials. This training was to ensure that all after-school teachers were presenting content in the same way. This applied dissertation employed two instruments to generate data collection.

One instrument was the FCAT scores for mathematics for the 2006 school year, which was used to verify the students performance levels prior to the program. This data covered all of the grade level expectations within the mathematics curriculum strand of the (SSS). The other instrument was the math FCAT scores for the 2007 school year, which was used to determine the effect of the ASMT program on the three groups. Every student of the three groups had both instruments to evaluate the impact of the program on each participants achievement. The mean, median, mode, and standard deviation were calculated for the three groups. Each of the measures of central tendency were compared to answer the research questions and to determine which group achieved the highest levels of performance.

Design

The mixed methods (MM) approach was utilized in order to address the research questions that were set in the first chapter of this study. MM research designs make use of the strengths from both of these research methods.

There were several research problems that specifically call for the employment of MM.  Overall, the use of MM will emerge from needs that failed to be address through the use of a single research design. When there is a need for both quantitative and qualitative approaches to be employed, the MM is the preferred design (Creswell  Park, 2007). The integration of qualitative and quantitative data presents a more holistic picture of trends and generalizations. One type of data can be insufficient to tell the complete story thus making the research lack confidence in the findings of his or her study.

In a mixed method (MM) design, the quantitative and qualitative strands of in this study occur in a chronological order.  The qualitative approach came before the quantitative approach. They are planned and implemented in order to address related but different aspects of a basic research question or questions. The MM research used inductive-deductive research cycle, the cycle of scientific methodology, as well as the research wheel (Teddie  Tashakorri, 2009).  This research involved a triangulation approach wherein the procedures undergo twice as much effort and work in order to satisfy the standards of the MM design.

Triangulation is defined as the use of different methods to study a single research problem (Creswell, 2003). For example, sampling procedures in MM studies employ both probability and purposive techniques, which are considered to be unique for an MM, design (Teddie  Tashakorri, 2009). MM data analysis also involves the integration of statistical and thematic techniques.

The quantitative research approach used methods to measure attitudes and rating behaviors (Creswell, 2003). It utilized a post positivist position in obtaining knowledge. Post positivism involved principles of determination, reduction, empirical observation and measurement, as well as theory verification (Creswell, 2003). Since the aim of this study was to analyze the comparative effectiveness of the ASMT based on gender, this research design was implemented. Gender patterns could be understood in the analysis of the comparison of student achievement of the participants.
The presentation of a hypothesis that needed to be tested called for the need to employ the quantitative research method. In a quantitative research, historical precedent existed in viewing theoretical conception as an explanation for a phenomenon. The research was designed to determine whether the gender patterns between the disparity of achievement in the mathematics subject between males and females continued, despite the implementation of the ASMT. It required statistical analysis in order to discover the level of disparity. Based on these data, the research could present valuable strategy to increasing awareness as to the level of effectiveness of ASMT in closing the achievement gap between the males and females.

The qualitative approach served only as a second approach in this study. The quantitative served as the primary and dominant approach. This approach was considered to implement constructivist knowledge claims. It observed behavior. It implemented a narrative design of inquiry.
This approach involved studying the context of the participants. It also involved validation of the accuracy of findings. This approach was included to describe the level of effectiveness of ASMT, in general. It established the framework for the research.   The objective of the research design is to examine the effectiveness of ASMT program model on student achievement for the students of an elementary school in south Florida.

Data Analysis

Qualitative Data Analysis. The first research question was evaluated qualitatively.
Research Question 1 Is the ASMT program at an elementary school in south Florida an effective strategy for increasing students mathematics academic achievement
In an effort to ascertain behavior variations exhibited by the three teachers and the students in each of the groups, the principal and the assistant principal at the target elementary school in south Florida conducted observations as part of running the program. The principal observer reported that students and teachers actual behavior both verbal and nonverbal reflected sound teaching practices for improving student learning.  An ANOVA test was conducted to test the difference between the means of the three groups to reduce the portability of a type-I error, which was the rejection of the null hypothesis even though it was true.

Quantitative Data Analysis. Methods of quantitative data analysis were specific to the last three research questions as well as another part of the first question.

Research Question 2 Is the ASMT program at an elementary school in south Florida more effective with a female student group

The dependable variable was the math FCAT score for the 2007 school year. The covariant was the math FCAT score for the 2006 school year. The female student group was the independent variable.
Research Question 3 Is the ASMT program at an elementary school in south Florida more effective with a male student group

    The dependable variable was the FCAT score for mathematics for the 2007 school year. The covariant was the FCAT score for mathematics for the 2006 school year. The male student group was the independent variable.

Research Question 4 Is the ASMT program at an elementary school in south Florida more effective with a mixed male and female student group

The dependable variable was the FCAT score for mathematics for the 2007 school year. The covariant was the math FCAT score for the 2006 school year. Student groups (male, female, and mixed) are the independent variables.

A comparison of the results was conducted to determine if the groups benefited from the program and if there was a significant difference among the groups. An ANOVA test was employed to assess the difference between the means of the three groups to reduce the portability of a type-I error, which was the rejection of the null hypothesis even though it was true. A product portion of the CIPP Evaluation Model checklist will be used to evaluate the impact of the program.

Program evaluation involved deciding the extent to which the goals of the program have been achieved. In this type of evaluation, measures of goals are developed and administered, and the resulting data are used to make decisions about continuing or modifying the program (Gall, Gall,  Borg, 2006). The evaluation findings were used to gauge the programs positive and negative effects on its beneficiaries, sort out and judge important side effects, examine whether program plans and activities need to be changed, prepare and issue a program accountability report, and make a bottom-line assessment of the programs success.  The evaluation findings were used to contrast similar programs elsewhere to make a bottom-line assessment of the programs significance and success (Stufflebeam, 2003).

The anticipated outcome of this evaluation is to aid the principal, director, and other stakeholders in identifying factors that are important to the programs success. Mainly, this applied dissertation will assist in areas that increase students mathematics academic achievement. It will also clarify the gender differences, and will indicate whether a female student class, a male student class, or a mixed male and female student class benefits better from the program, and if there is a significant difference between the groups. The applied dissertation will also serve as a guideline to track students performances and help in continued funding opportunities to continue the program or not, and also to separate boys and girls, or not. Just as significantly, it will serve as a relevant guide to assist the school district in implementing district-wide after-school tutorial programs.

Limitations

    The research, due to various constraints in time and resources, has several limitations. The methodology employed could have used a much larger sample size to give a more accurate measurement of the variables under studied. The methodology could also be improved a more complex method could be employed to check the validity and accuracy of the data gathered. Finally, the study lacked further and in-depth related review on the specific topic at hand.