I. Organizational Structure


As I am being considered for the position of Superintendent of a large school district I would want to share my views on both education and leadership. However, no matter how important my visions for the education of the children in the district might be; it would be unlikely that they’d be accomplished if I could not exhibit a good strong sense of leadership. Leadership is different from the simple management of a school district, though the two are easily confused.  One may be a leader without being a manager, and many managers could not lead a squad of seven-year olds to the ice cream counter (Gardner, 1989, p. 2).  Bennis and Nanus (1985) offer the distinction that managers do things right, and leaders do the right things (p. 21).   

Among the skills an effective leader must have is the ability to look through any situation using a variety of lenses.  In Bolman and Deal’s book, Reframing Organizations (2003), they posed four main frames for guiding the way leaders look at situations. Using different frames helps one analyze the situation to improve the possibility of clearly defining the situation and arriving at an effective solution.

If we examine each of the four organizational frames, we would most likely see how some school systems  favor one frame over the others and some that combine two or more frames (multi-frame). If we look closely, it is likely that we would find characteristics of each in every particular instance.

The first frame, the Structural Frame is based upon six assumptions:


1.      Organizations exist to achieve established goals and objectives

2.      Organizations increase efficiency and performance through specialization and a clear division of labor.

3.      Suitable forms of organization and control make certain that the efforts of both individuals and units fit together.

4.      Organizations work best when good sense prevails over personal preferences and outside pressures.

5.      Structures must be designed to fit an organization’s circumstances

6.      Problems arise from a lack of structure and can be remedied through analysis and restructuring.


The structural view has two main scholarly roots. The first is the work of industrial analysts bent on designing organizations for maximum efficiency. The most prominent of them, Frederick W. Taylor (1911), broke tasks into minute parts and retrained workers to get the most from each motion and every second spent at work.

The second branch of structural theory stems from the work of the German economist and sociologist Max Weber. Weber wrote around the beginning of the twentieth century when formal organization was relatively new.  His model outlined several major features:


·        A fixed division of labor

·        A hierarchy of offices

·        A set of rules governing performance

·        Separation of personal from official property and rights

·        Technical qualifications (not family or friendship) for selecting personnel Employment as primary occupation and long-term career


I would impress upon my audience the importance of structure; however, individuals comprise an important part of any organization and should therefore always be considered. The Human Resource frame is based upon the following premises:


·        Organizations exist to serve human need rather than the reverse.

·        People and organizations need each other:

o       Organizations need ideas, energy and talent.

o       People need careers, salaries and opportunities.

·        When the fit between the individual and the system is poor, on or both will suffer.

·        A good fit benefits both.


Successful organizations embrace creative and powerful ways to align the needs of both individuals and the organization. A core assumption is treating the workforce like an investment rather than a cost. This attracts better employees who are motivated to do a superior job and results in a better product, in this case, education. Human resource theorists place little emphasis on power, though they often promote the idea of empowerment. Unlike structuralists, they emphasize limits of authority. In an organization like a school district, in addition to the individual employees (faculty, staff and administrators) there are also the students and the parents whose needs must also be considered. I would impress upon my audience my willingness to do so.

In every organization, including school systems, there is a human element that must be examined and dealt with. As was set forth in the human resource frame, human beings each have needs. However, they do not all have the same needs, nor do they have the same ambitions, goals or points of view. Many consider their own interests more important than those of the organization or consider one outcome more desirable than another. Others may agree on a goal, but differ on the means or methodology to attain that goal. We must therefore consider the interaction between individuals or the Political Frame where the focus is not on resolution of conflict, as often in Structural & Human Resource, but on strategy and tactics.

In the political frame, organizations are viewed as living political arenas that host a complex web of individual and group interests. Five propositions summarize the perspective:


1.      Organizations are coalitions

2.      There are enduring differences

3.      Involves the distribution of resources

4.      Scare resources and enduring differences give conflict a central role in organizational dynamics and make power the most important resource

5.      Goals and decisions emerge from bargaining, negotiations, and jockeying for position among different stakeholders


Pfeffer defines power as the potential to influence behavior & change the course of events; since organizations are coalitions and different participants have varying interests and preferences, the question is not how organization should be designed to maximize effectiveness, but whose preferences/interests are to be served by the organization. (pg 225)

I would therefore stress to my audience the importance of the ability to reach agreement when differences arise. While personal preferences and varying interests will always be present, it is imperative that, for the good of the district, differences be worked through.

The Symbolic Frame focuses on how people make sense of the messy, ambiguous world. Meaning, beliefs and faith are central themes and symbols are the basic building blocks of the meaning systems, or cultures, that we inhabit. Some assumptions include:


·        What is most important is not what happens, but what it means

·        Activity & meaning are loosely joined. Events can have many meanings because we all interpret things differently

·        In face of widespread uncertainty and doubt,  people create symbols to reduce ambiguity, increase conviction and find direction

·        Developments are more important for what is expressed than what is produced


Keeping this in mind, I would impress upon my audience the importance of standing for something.

Keeping these four frames in mind, as  addressed my audience, I would ask myself what characteristics do the leaders of the individual school systems exhibit that contribute to the success or failure of the system as a whole. Do they promote an atmosphere of cooperation amongst students, teachers and school administrators or are new ideas and differing opinions suppressed and ignored. Is theirs a top-down, authoritarian style of leadership or are they more egalitarian.

The structural frame establishes clear goals and expectations. Effective organizations have clearly defined goals and responsibilities for its employees. Their policies and lines of authority are clearly defined and accepted. However, how leaders define the goals of the organization and employee responsibilities will determine how they will be viewed and subsequently the degree of success the organization has.

Human resource leaders put employees at the center of the organization. When employees feel connected with the organization and when the organization is supportive of their personal goals, then the employee will generally be committed and loyal in return.

Some leaders translate the political approach into their management style. They intimidate and manipulate subordinates while others prefer to be more diplomatic and resolve conflicts.

The symbolic leader believes that the most important part of leadership is inspiration; giving people something they can believe in. Employees become excited about and committed to an organization with a unique identity, a place where they feel that what they do is really important.

Leaders however should not limit their managerial style to only one or two frames. There are times when each may be appropriate and the challenge for a good leader is to learn to which style is appropriate for the moment. Effective leaders help articulate a vision, set standards for performance, and create focus and direction.  Another characteristic mentioned in many studies is commitment or passion.  Good leaders care deeply about their work and the people who do it.  A third frequently mentioned characteristic is the ability to inspire trust and build relationships. If I were selected to head a school district, I would try to remember all these things and hopefully, through good leadership, accomplish the task set out before me.



II. Policy Analysis


Before addressing Whittle’s comments I’d like to address the issue of poverty in this country for just a moment as it is closely related to many of the problems we experience in education. As with other areas of policy, politics complicates the process and hinders efforts to clearly define the problem of poverty in America. Proponents of social welfare programs often over-estimate the number of poor and maintain that the problem is persistent and requires immediate attention. Those opposing government assistance programs minimize the severity of the problem and maintain that government assistance programs perpetuate poverty by diminishing people’s incentive to go out and work and assume responsibility for their own well-being.

The poverty level for a family of four at the time of the book’s publication according to Thomas Dye was $18,844. According to Dye, approximately 34 million Americans fell below that level with African-Americans and single females with children under the age of eighteen making up the majority of Americans in that category. Liberals criticize the official definition of poverty because income levels include cash income from social welfare programs. If government assistance were to be discounted, they argue the number of Americans below the poverty level would be much higher. Conservatives criticize the official definition of poverty because they say it fails to consider the value of assets belonging to those under the poverty level. They say that some individuals, officially counted as poor, are not and only their current circumstances allow them to meet the criteria. Further, they argue that many individuals under-report their income (work “under the table”) and point out that estimates do not include non-cash benefits such as food stamps, free medical care, and publicly assisted housing. Conservatives claim that if these benefits were calculated as cash, the percentage of people below the poverty level would be reduced.

A larger percentage of Blacks and Hispanics experience poverty than do Whites, Middle-Easterners and Asians. One explanation for this may be the fact that poverty is most common among female-headed, single-parent families and that 45% of all Black families were headed by females as opposed to 14% of white families. Older Americans experience poverty to a lesser degree than do younger Americans. Older people tend to own homes whose mortgages are paid, their medical expenses are paid for by Medicare and their net worth is not taken into consideration when determining eligibility for social assistance. Therefore, as conservatives argue, it is possible to have substantial wealth and still have an income below the poverty level.

Poverty tends to be a relatively temporary phenomenon rather than a permanent one and only about six percent of Americans remain in poverty for more than five years. Poverty is usually associated with a traumatic event or misfortune in one’s life that is eventually overcome. Periods of economic downturn also tend to make the poverty level rise. As poverty tends to be temporary, so to does the assistance that Welfare provides.

Dye also notes discrimination as a factor determining poverty that is largely overlooked by economists. However, while this may have been true in the past, the effects of discrimination on poverty have been largely mitigated by affirmative action programs and anti-discrimination legislation. In most instances, people are in fact poor because they do not possess the skills necessary to compete in a free market society. Poorly educated and unskilled workers are relegated to low-paying, menial jobs.

Social researchers have described the “culture of poverty” as a way of life that is learned by the poor. Characterized by irresponsibility, apathy, indifference, lack of self-discipline and the incentive to work hard, it encourages family instability and the need for immediate gratification and prevents the poor from taking advantage of the opportunities available to them. It gives rise to the liberal assertion that “it’s not their fault.” In 1995, approximately 70% of all births to Black women were to single mothers, compared to 25% of births to White women. While this statistic may account for the higher levels of poverty among Blacks, it also fuels the controversial question of whether lack of money creates the culture or is it something inherent in the individual. Does poverty lead to a breakdown of the family or does a breakdown of the family lead to increased poverty.

Recently, America’s cities have become microcosms of the social problems facing Americans today. The shift of manufacturing and commercial sales jobs to the suburbs has left the cities with a predominance of low-paying, menial jobs. The rise in unemployment and the migration of middle and upper income families to the suburbs has resulted in a rise in the number of poor in the cities.

In light of all this, my question to the writer would be how he would redesign a system of education that would equally provide for all the different ethnic, economic and other special interest groups that would solve all of our current educational woes. Yes, teachers are by comparison underpaid, but as the author correctly points out, the nation is in no position to double their salaries. His figure of $1,000 falls far short of the figure that New Jersey tax payers would have to pay. Property taxes, already through the roof, would put home ownership out of the reach of everyone except the wealthiest.

With regard to funding, Amy M. Azzam, of Educational Leadership magazine wrote “It comes as no surprise that the majority of states provide fewer dollars per student to their highest-poverty school districts than to their lowest-poverty districts and that most states have funding gaps between the schools that have the most minority students and those that have the fewest.” (February 2005, Vol. 62, No. 5) This identifies another obstacle to providing one organizational structure, the unwillingness of lawmakers to provide equitable funding across the board. 

The author then compares redesigning our education system to Boeing and the redesign of one single airplane. I submit that the task of redesigning our educational system is just slightly more involved than that. There are many factors that affect the quality of education in this country. I’ve already mentioned poverty, but there is also the issue of leadership, standards assessment, funding and teacher qualification.

A major step towards achieving what Mr. Whittle’s ultimate goal of improving education was Congress’s most recent reauthorization of the Elementary and Secondary Education Act (ESEA). ESEA is the nation’s major federal law related to education in grades pre-kindergarten through high school. Subsequently being renamed the No Child Left Behind Act (NCLB) of 2001; the Act requires all schools to bring all students to a proficient level in reading and math. When President George W. Bush signed the “No Child Left Behind” legislation into law in 2002, he publicized it as a way to promote academic proficiency among all students and, more specifically, to "close the gap" by the year 2014 between white students and low-income blacks and Hispanics who disproportionately attend poorly-funded, inner-city schools. However, many school administrators have found themselves faced with the task of creating rigorous academic content standards that comply with the mandates set forth in the law. In addition, standardized tests aligned to those content standards and at least three levels of performance have been defined and are used to hold schools accountable. (Wikipedia)

As a matter of policy, NCLB has shifted the impetus for change away from the social factors that have influenced the subjects of history and language; away from both the economic and technological forces that have influenced the fields of mathematics and science. With NCLB, the movement to improve our schools has fallen directly under the influence of policy makers in Washington.

            Critics of NCLB have attacked the law for several reasons. They say that although the law professes to be based on scientific research, “no scientifically based research, or any research, supports the law's mandates” (Bracey). Some consider the requirement that all students be proficient in reading, math, and science by 2014 unrealistic by some and simply ridiculous by others. Some educators are critical of NCLB’s reliance on punishment and argue that standardized testing is not an adequate measure of achievement in all cases. Yet others argue that many underprivileged students have no reason to put effort into standardized tests, even if they are capable of doing well. Why should a student who can't afford college, who goes to a school with no extra-curricular programs and whose teacher has given up on him care about a test score? In order to excel academically, students first need something to aspire to, and that certainly won't come from an environment focused on the mind-numbing task of standardized test taking. (McQuilken, 1/1/2005)

Education Week recently focused on the clash between NCLB's ambitious goals and the shortfall in states’ capacity to meet those goals. As NCLB has been implemented, states have found they have neither the funding nor the staff to respond to many of the law’s requirements and as these requirements increase each year, states find themselves increasingly overburdened. Gene R. Carter, Executive Director, ASCD, wrote in June of 2005 “although No Child Left Behind has placed increased pressure on states to raise student achievement, it has not done enough to support them in responding to that pressure. If we expect more from states, we must raise our support to them, particularly in light of states' recent fiscal woes and the increasing requirements of NCLB each year.” 

            Organizations such as the Association of Community Organizations for Reform Now (ACORN) have criticized the unwillingness of the federal government to fully fund the act. While promoted by President Bush and applauded by both parties, neither the Senate nor the White House has requested funding up to the authorized levels for several programs such as Title I. Republicans in Congress have viewed these authorized levels as spending caps, not spending promises and have pointed out that President Clinton never requested the full amount of funding authorized under the previous ESEA law. (Wikipedia)

Despite the critics, the Act does have several positive aspects. It requires schools and districts to focus their attention on the academic achievement of traditionally under-served groups of children, such as low-income students, students with disabilities, and minorities. Previously, many state-created systems of accountability only measured average school performance, allowing schools to be highly rated even if they had large achievement gaps between affluent and disadvantaged students.

One positive aspect of NCLB and one mentioned by the author was the issue of teacher qualification. NCLB requires that all children be taught by a highly qualified teacher. Although some schools must now hurry to ensure that all their teachers are viewed as highly qualified, but teachers can take additional courses or pass a proficiency test to be considered as such. In addition, New Jersey requires continuing professional development hours. Effective school administrators view this as an opportunity to assist their teachers in continuously growing and expanding their horizons as professionals within the larger learning community.

NCLB is the most recent attempt to address this nation’s lagging educational system and it has proven highly controversial because of its intrusion into the jurisdiction of state and local governments. Much of the criticism aimed at NCLB concerns the standards and fiscal responsibilities imposed upon the states. Recently, the National Education Association (NEA) and several states have filed suit in federal court demanding that Washington to pay for the rules and regulations imposed upon the nation’s public schools. As word of the suit spread across the nation, reaction was immediate.  A Detroit News editorial stated “If the federal government wants to dictate policies to local public schools, it should fork over the money for meeting those mandates.” (April 4, 2005) USA Today wrote, “School districts have been very, very patient, but their patience has run out...budgets have been eaten up by the rules and regulations imposed by this law," NEA President Reg Weaver said.” (April 20, 2005)  And, an article in the Chicago Tribune stated “The nation's largest teachers union and a group of school districts sued the U.S. Department of Education Wednesday, contending the No Child Left Behind act is severely under funded and has forced schools to divert money from worthy programs to pay for the reform's ‘costly absurdities.’” (April 21, 2005).

The author’s idea has merit in that he identifies that there is a problem in our educational system. I believe however that is where the merit stops. There are a great many diverse issues affecting education today, not the least of which is NCLB. Historically, education policy was handled at the state and local levels and that is where the majority of educators would like to see it returned. As education is affected by so many factors, it is inconceivable that any resolution can be a universal one which begs the return to local control. I think that although the intentions of Congress and  the President were good, their solution to the problem was a bit heavy handed.

What the outcome of the current will be, few are willing to speculate, but no doubt the end result will be a shift in policy. Regardless of the outcome of the civil case, opposition to NCLB is becoming too widespread and too vocal and members of Congress will soon have to listen to what their home states are saying lest they find themselves replaced at election time. The road to changing the current policy is led by educators across the country. Characteristic is this statement on NEA’s web site, “the Elementary and Secondary Education Act (ESEA), renamed "No Child Left Behind" (NCLB) in 2001, established laudable goals -- high standards, accountability for all, and the belief that all children can learn, regardless of their background or ability. Unfortunately, the law is seriously flawed and under funded. But the importance of NCLB's goals demands that we work to ‘fix and fund’ the law. NEA is supporting that commitment through public awareness, legislative lobbying, and member empowerment -- working for things children need to be successful.”


III. Curriculum Design


The author states that “one crucial but often overlooked source of the distinctiveness among high-performing schools is philosophy – the beliefs and values that create our sense of what makes life worth living, and therefore what is worth teaching and how we should teach it.” It sounds as if the author is striking a perrenialist note when he talks of what makes life worth living and how those beliefs and values can be lost in our drive for education to be research based.

Describing the clash between progressives and traditionalists as one “not grounded in science, but in history and philosophy and ideology” he goes on to say that we can not solve the dichotomy through empirical means. While empirical research, he notes, is useful, it is subject to interpretation, the correctness of which can be endlessly debated.

Reminding us of the importance of “values, beliefs and culture to education,” the author also notes that we do not take these beliefs seriously when we consider what we want our schools to be or in defining a good education.

In Curriculum Planning: A Contemporary Approach, Forrest Parkay and Glen Hass describe ten issues that will challenge education in the twenty-first century. These are:


·        Increasing Ethnic and Cultural Diversity – The large number of different ethnic cultures are retaining their cultural identity rather than assimilating ours creating a nation with an increasing amount of cultural plurality. 

·        The Environment – Environmental problems such as over-crowding, pollution, over-consumption of precious resources, and the prospect of other natural disasters similar to those we have recently encountered.

·        Changing Values and Morality – Many believe we have lost our sense of morality and values and believe educators should reinforce those issues.

·        Family – The traditional definition of “family” no longer applies to many Americans. In general families are becoming less close knit and more geographically spread out.

·        Microelectronics Revolution – As technology advances in leaps and bounds education must strive to keep pace. To do so, schools will have to embrace technology and ensure teachers do the same.

·        Changing World of Work – In our modern world where job requirements change daily, students will have to be taught to be self-directed learners.

·        Equal Rights – Despite advancement in the areas of racial and gender equality, many feel that our current system of education only maintains the inequality through unequal treatment of minorities and the poor. 

·        Crime and Violence – More and more, crime and violence has invaded our schools. Educators must contend with issues that were only isolated events just a few years ago. Many schools have become fortresses complete with metal detectors and security guards.

·        Lack of Purpose and Meaning – Changes in society, technology, and economic opportunity have deprived many of a sense of purpose. A recent article in the campus newspaper from the University of Washing/Seattle states “In order to excel academically, students first need something to aspire to, and that certainly won't come from an environment focused on the mind-numbing task of standardized test-taking.”  

·        Global Interdependence – Similar to our own nation of diverse cultures, students must recognize the interdependent nature of our world and be aware of the needs and beliefs of others.


The author alludes to these issues when he discusses the difficulties educators have in reaching agreement on an instructional program. He then suggests that if agreement cannot be reached amongst themselves that educators reach out to “parents, students and local citizens” to determine what their needs are and what beliefs and values they share with educators. He states, just as we have learned in our decision making classes that reaching out to the community will create “broad ownership” of the solution and increase its acceptance.

The author warns however that this may lead to segregation, but that schools must determine how much separation by race or gender they are willing to tolerate. Unfortunately, due to the nature of our society, a certain degree of segregation is unavoidable. Schools must be places where students learn that although we are an ethnically diverse people, we must all learn to live together. Ferrero suggests that schools be prohibited from teaching “anti-liberal” values such as race hatred or the “rejection of the secular government.” He states instead that all schools should teach “the principles of the U.S. Constitution and to provide civic education that goes beyond the minimal expectations of tolerance and cooperation.”

One of the basic tenets of perennialism is that education is not an imitation of life but a preparation for it. In light of today’s focus on standards and assessments it seems strange that someone would focus on preparing students for life out in the world aside from the basic staples of reading, writing and mathematics. The author even states that standards are not “misguided,” but that “both common standards and research, along with broadly shared societal ideals, help us define good schooling and provide necessary limits to diversity.”

According to Parkay and Hass, providing for the individual differences between students, the teaching of values, the development of self-understanding and the development of problem-solving skills are four significant curriculum-planning criteria that demonstrate how social forces influence the curriculum. Successful educational programs help students, regardless of of their cultural background or family situations to understand themselves and others more completely. This is imperative in our culturally pluralistic society.

In A Morally Defensible Mission for Schools in the 21st Century Nel Noddings explains the inadequacies of the traditional school curriculum. She declares that schools have largely ignored massive social changes, only responding to some in a piecemeal fashion.  She proposes that education focus around “centers of care” to correct for the problems associated with the traditional curriculum. As was mentioned in my answer to Policy, poverty is a massive social problem that walks hand in hand with our current education dilemma. Noddings states that the traditional liberal curriculum relies too heavily on academic training (ie. NCLB) and that such academic training cannot save people from “poverty, crime and the other evils of current society.” Since some people who perform honest, useful work live in poverty, she labels the traditional school curriculum a moral failure.

The importance of curriculum has not changed. For a curriculum to be relevant its planning should reflect consideration of society’s goals and values keeping in mind the four curriculum bases (social forces, human development, learning and learning styles, knowledge). Despite the recent movement towards higher standards and equalizing opportunity, the author suggests that we need to not forget the other things that can not be measured.



IV. Research Design

Statement of the Problem


How do the current course offerings affect student achievement in Mathematics?


Sub Questions:


Null Hypothesis:

The current course offerings have no affect on student achievement.


Literature Review

The researcher will examine previous literature pertaining to curricular offerings and how they affect student performance in mathematics as well as teacher’s education levels, experience and job satisfaction as they pertain to student achievement. Research will also be studied relating to various subgroups within the school, such as gender, ethnicity, limited English proficiency, and socio-economic status, as to how each group can improve achievement in mathematics. Particular attention will be given to previous studies conducted that indicated no gender differences. Literature regarding parental involvement and its affect on student performance will also be examined.


Importance and Limitations

Importance: The goal of this study is to determine the affect the current curriculum has on student achievement and to determine if it is possible to improve student achievement in mathematics



·        This study will be limited to 500 students and 23 members of the mathematics faculty.

·        The curricular offerings examined will be limited to Calculus and Trigonometry.

·        The study shall limit itself to examining different variables only as they pertain to achievement in mathematics.



This study will involve 500 high school students and 23 members of the mathematics faculty


Data Collection

Quantitative data will be obtained by examining freshman and junior grade point averages along with student’s final grades in Trigonometry and Calculus. These correlation analyses can provide necessary data to determine the success and weaknesses of the high school’s student mathematics achievement. The data must also be stratified to determine any weaknesses in math performance based upon subgroups such as gender, ethnicity, limited English proficiency, or socio-economic status.


 Qualitative data will be obtained through the use of surveys of both faculty and students. Students will be asked to give feedback on their own performance and study habits, the extent to which their parents become involved in their schooling and the effectiveness of teachers. Teachers will be asked to comment on student’s current levels of achievement and to identify any variables that might affect same including their familiarity with the student’s parents. They will also be solicited for their educational backgrounds, level of teaching experience and level of job satisfaction.



Data will be collected through examination of student records and through the use of surveys The following statistical analyses will be conducted:

·        An examination of any correlational relationships between the final grades in Trigonometry and Calculus and the student’s freshman and junior grade point averages

·        Analysis involving matched pairs t-tests to determine the difference in the means of the student’s freshman and junior GPA’s. These analyses can be drilled down further to include demographic differences.

·        Chi Square analyses of the results of the both the student and faculty surveys     


Conclusions and Recommendations

As this study hopes to identify the affect the current curricular offering has on achievement, should it be found that the current curriculum has a positive affect, a recommendation can be made to keep the current curriculum in place. If it is found that the current curriculum has no effect or a negative effect on achievement, a recommendation can be made to look into changing the current curriculum. With the inclusion of the quantitative demographic data and the qualitative data, the possibility exists that some other variable that affects students’ achievement can be identified. If so, recommendations can be made to account for these variables. Such steps might include after-school programs to help students who are performing poorly or increased language instruction to limited English proficient students. Deficits in teacher’s skill can also be identified and steps taken to improve those skills or make replacements where necessary. Adjustments to the curriculum if it is found that certain courses aid performance more than others. As this study is relatively open ended the possibility for its consequences are substantial.



V. Statistical Methods


1.      Here we are comparing final grade data of 500 students (N) for two advanced Mathematics courses (Trigonometry and Calculus) and student’s Junior Grade Point Average (GPA).


Trigonometry and Calculus


·        The r value is .484, which is a low positive correlation

·        The p value is .000, which makes it statistically significant

·        Those students who tend to do well in Trigonometry also tend to do well in Calculus


Junior GPA and Trigonometry


·        The r value is .275, which is positive but implies little if any correlation

·        The p value is .053, which means the result is not statistically significant


Junior GPA and Calculus


·        The r value is .398, which is a low positive correlation

·        The p value is .050, which makes it statistically significant

·        The students who have higher GPA’s tend to do well in Calculus






2. This is a one sample t-test comparing the mean of a recently administered math achievement test against the national average.


·        Mean of the math achievement test is 13.09803, the national hypothesized mean is 13, a difference of .09803.

·        The standard deviation is 6.604590

·        The t value is .332

·        The p value is .740, which is not statistically significant.




While the mean of the student’s scores is .09803 higher than the hypothesized national mean, the t value of .332 is not statistically significant because the p value is greater than .05. As a result we can accept that there is no statistical difference between the student’s mean score and the national mean.

            As a result, I would suggest that the current curriculum is adequately aligned with that of schools across the country. Further research can be done to analyze individual grade/course data to determine if any improvement can be made in the curriculum to improve student performance.



3. From a group of 500 students we are comparing the mean grade point averages for 280 female and 220 male students to determine if there are any gender inequities with regards to GPA scores.


·        The mean for females is 3.2175 and the mean for males is 3.1483, a difference of .0692.

·        Standard deviation for females is .53315, for males it is .49025. Very similar

·        Two statistical analysis were conducted, a Levene’s Test for Equality of Variances and t-tests for two independent samples.

·        F value is 2.314 with a correspond sig. of .129 making it statistically significant. (incorrect, it is not statistically significant)

·        T values were obtained for equal variances assumed (1.492) and for equal variance not assumed (1.507). The corresponding sig. values were .136 and .132 respectively making each statistically significant. (incorrect, they are not statistically significant)




While the t values are statistically significant, the actual difference in the means is minimal. However, I would recommend a closer look at some other factors including student transcripts, extracurricular activities and time spent studying to identify any other contributing factors or problem areas. 



4. Here we are comparing 500 student’s GPA’s using a matched pairs t-test involving students freshman and junior GPA’s to determine the degree of success of three years of program improvements and interventions by the superintendent.


·        The junior GPA mean is 3.2955 and the freshman GPA mean is 3.1871, a difference of .1084.

·        The junior standard deviation is .48365 and the freshman standard deviation is .51535.

·        The t value is 7.323

·        The p value is .000 meaning it is statistically significant





The data shows that there is a statistically significant increase in student’s mean GPA’s over the three years. I would suggest that the school continue its program as it seems to be working.