Independent Study on Alternative Assessment in Mathematics at the Secondary Level in Public Schools

Educational Assessment Methods and Standards Participants Scoring Key Letter to Principal Principal's Questionnaire Teacher's Questionnaire Raw Data It is widely known that testing and assessment have become critical components and indicators for success in today's educational system. This process is widely considered as a feasible means to improve student success and achievement as well as educational outcomes and future potential in educational pursuits and the workforce for millions of students with widely varying levels of skill and ability.

Therefore, standardized assessment does not often reflect the true talents and abilities of the existing student population. Furthermore, assessment standards and testing procedures are often scrutinized for their ineffectiveness in accurately evaluating student promotion and skill development, which lead to future educational pursuits and workforce placement. The primary argument against the current methods of testing and assessment is that the established standards do not accurately reflect the true talent, skills, potential, and problems within the student pool at any given period of time.

Therefore, alternative methods of assessment are a popular topic for debate in today's public schools across the United States and beyond. Specifically, alternative methods of assessment in mathematics will serve as the focal point for the remainder of this study. Statement of the Problem Today's assessment methods and standards are not living up to the expectations that were established when they began to be used as measures of student performance in schools across the country and in U.S.-owned territories.

As school environments continuously change as a result of both external and internal conditions, their students also continue to evolve in terms of skill development and abilities. Therefore, some students may not fit the mold that is generally assumed through typical assessment standards.

As student performance for many individuals continues to decline or remain stagnant at the average level of achievement, it is time to reevaluate current assessment and testing methods to identify ways in which they can be improved to better reflect how students are truly performing in their academic endeavors. As the debate rages on, a number of alternative methods have been proposed, which will be discussed in detail later on in this research study.

In particular, the researcher anticipates the identification and evaluation of alternative assessment standards in mathematics at the secondary school level. Furthermore, an additional component will identify the difficulties and behavioral outcomes that are encountered when alternative assessment methods are introduced into schools where teachers are accustomed to traditional instruments and may not be tolerant of such substitute methods, perhaps as a result of tradition as well as indolence to new techniques that may ultimately make a significant difference in student learning and performance.

Purpose of the Study The proposed independent study will identify the primary methods that are currently under consideration in today's public schools as alternative means of assessment and testing, particularly in the subject of mathematics, an often difficult subject for many students to comprehend and master. Mathematics will be evaluated because in general, it is probably one of the most difficult concepts of all for students to sustain. Specifically, the proposed research will be performed in St. Thomas, Virgin Islands, where only a handful of secondary public schools exist.

Several of these schools are currently in a state of transition and turmoil, as they have recently lost their accreditation and are attempting to identify ways to regain this status. The study will discuss the new methods of assessment in detail and will evaluate their potential effectiveness against the current methods already in place.

Furthermore, the study will isolate the potential repercussions and reactions from teachers in these schools to such alternative assessments, as many of these professionals are acclimatized to the traditional methods of assessment and testing, and may not consider these new methods as effective indicators of student performance, regardless of the transition to a new student paradigm in today's public secondary schools.

These issues will be evaluated in order for teachers and administrative staff at these unaccredited schools to identify ways to regain accreditation as well as to improve student learning and performance as well as future outcomes. Research Question The primary research question that will be evaluated in this study is how the identification of the most effective methods of alternative mathematics assessment that will accurately reflect the talents, skills, and potential of the student population in two secondary schools located in St. Thomas, Virgin Islands.

Background information regarding the primary methods of alternative assessment will be collected and identified in the Review of Literature section. Then, various methods of alternative assessment will be presented to the faculty and administrative staff at the two participant schools through a survey design method. All responses will be collected and evaluated, and judgments regarding teacher attitudes towards alternative assessment will be presented.

The final outcomes will present the most feasible alternative methods of assessment that will make a difference in how students are tested and evaluated in order to promote student success and academic achievement.

Definition of Terms The following set of terms will be referenced throughout the study: Alternative assessment: A form of evaluation that allows teachers to individualize assessment, to mimic strong teaching practices, and to involve teachers more intensely in the assessment process (Glass, 1995) Group tests: Structured much like normal classroom activities, but typically presents a more difficult question or set of questions that must be answered http://www.springfield.k12.il.us,4/25/03) Journals and writing: A form of assessment that utilizes student journals as a means of communication and evaluation of daily progress http://www.springfield.k12.il.us,4/25/03) Non-standardized assessment: The traditional form of assessment found in classrooms, whereby teachers develop questions, evaluate responses, assign homework, monitor projects, and informally make assessments throughout the school day (Glass, 1995) Open-ended response items: A form of alternative assessment that asks students to construct their own answers to questions that may possess a number of possible answers (U.S.

Department of Education, 1996) Performance-based items or events: Activities, tasks, or questions that require students to perform a specific action (U.S. Department of Education, 1996) Projects and experiments: Performance tasks with extended deadlines that may take up to several weeks to complete (U.S. Department of Education, 1996) Portfolios: Student collections of work that can provide assessments of the quality of work over a longer period of time (U.S.

Department of Education, 1996) Questioning and documentation: Observing and talking with students as they work on mathematics tasks http://www.springfield.k12.il.us,4/25/03) Short tasks: A form of alternative mathematics assessment in which students are required to form their own answers by showing their work http://www.springfield.k12.il.us,4/25/03) Student presentations: A method that is used to assess student understanding of a particular topic http://www.springfield.k12.il.us,4/25/03) Test validity: The degree to which the inferences based on test scores are meaningful, useful, and appropriate (Rudner and Schafer, 2002) Chapter 2 Review of Literature An extensive body of literature exists from a wide variety of sources that is directly related to the discussion of alternative assessment, including such federal agencies as the United States Department of Education.

Only a small portion of this literature will be presented in this section, primarily as a result of space limitations. The most significant information that was identified during the preliminary phase of study development will be presented to provide support and evidence related to the research question and problem presented earlier. To begin the review of literature, it is most feasible to discuss the current state of affairs in mathematics in public schools across the United States and its territories.

The publication The Facts About...Math Achievement by the U.S.

Department of Education (2003) provides the following statistical information regarding mathematics education: According to the 2000 National Assessment of Educational Progress (NAEP), only a small percentage of students in grades four, eight, and twelve have improved their math scores Only 25% of fourth and eighth graders possess scores at or above the average, and twelfth grade math scores have not improved since 1996 The No Child Left Behind Act, passed by Congress and signed into law by President Bush in 2001, was developed to improve educational excellence, particularly in math and science education, across the spectrum through a variety of partnerships and collaborations, supported by funding from the National Science Foundation and the U.S.

Department of Education (p. 1). In addition, the act is designed to increase teacher salaries for those that provide instruction in science and mathematics in order to attract a wide range of talented individuals to the profession. A formal definition of alternative assessment is quite significant to the proposed research study.

According to an article by Silbermann (2003) in a publication entitled The Guide to Math & Science Reform by Annenberg/CPB published on the website www.learner.org,"Alternative assessment techniques measure students' understanding of a subject differently than traditional approaches (e.g., standardized, multiple choice, or closed question tests). Typically, students solve problems that allow multiple approaches to the correct solution; a problem may even have several possible solutions. Students are assessed both on their performance and on their thoroughness in communicating their thought processes" (p. 1).

Past studies have demonstrated that when alternative assessments are the utilized method in public schools, students tend to respond positively to these techniques by performing their work more independently, and in group tasks, they will provide their own input to the task at hand (Silbermann, 2003). However, the transition to from traditional to alternative assessments can be tricky at times, particularly when students have become accustomed to conventional methods.

Typically, students initially respond to alternative assessments with confusion and frustration, since they are not sure what is expected of them under this new method. Therefore, teachers that utilize alternative assessment methods are trained to explain the situation and the assignment very carefully before students begin their work on the problem, also known as modeling assessment tasks. This action provides students with a framework for completing the assignment using individual skills, and this model creates student confidence in the tasks being performed (Silbermann, 2003).

However, it is somewhat of a challenge for teachers when performing alternative assessments, as they must be careful not to give the answer to the problem away. Rather, students must develop their own set of skills and find ways to complete the tasks in order to identify the importance of the subject matter (Silbermann, 2003). In order for alternative assessment techniques to become universally successful, support must be available from a variety of areas, including parental encouragement.

The introduction of alternative assessment was as confusing for parents as it was for the students in its early stages, introduced several years ago. However, teachers now realize that providing training sessions for parents to explain the techniques and to reduce the frustration that is experienced when parents are unable to assist their children with homework activities is necessary to improve parental understanding. In addition, when teachers maintain a portfolio of each student's work, parents are grateful as they are kept in the loop regarding their child's progress (Silbermann, 2003).

A discussion of alternative assessment would not be complete without an analysis of the more traditional method, standardized assessment. An article written by Sanders and Horn (1995) entitled Educational Assessment Reassessed: The Usefulness of Standardized and Alternative Measures of Student Achievement as Indicators for the Assessment of Educational Outcomes discusses the various options in detail. Generally, standardized testing has received a negative image in recent years, primarily as a result of public and media perceptions, which are chiefly opinion-based assumptions.

However, as standardized assessment data has changed in response to criticism, it is still the preferred method for most public educational institutions for the following reasons, according to Sanders and Horn (1995): "Standardized test data is ubiquitous. It is readily available, cheap, and abundant. Most often, the scale scores, percentiles, and stanines provided by those who score the tests are duly recorded by the receiving school or system, precisely as received. No further analysis is attempted.

The usefulness of the data is severely limited, and so it is used for very little other than placement and, occasionally, a crude form of program evaluation that is, as critics have rightfully stated, biased by extraneous factors such as socio-economic level, past achievement, and percent of minority students" (p. 3). In order to meaningfully evaluate the data collected from standardized tests, it must be measured by the appropriate indicators, and multiple forms are most feasible.

Some examples include test scores and performance, and if these are measured properly, then the assessment may result in success. Sanders and Horn (1995) conclude that standardized testing "renders viable, inexpensive, reliable, and valid indicators of student learning useful in the assessment of educational entities and student achievement. Alternative forms of assessment are also viable tools for the assessment of student progress and attainment, so long as care is taken to assure their validity and reliability.

Because they are expensive and difficult to develop, administer and score, their usefulness for large-scale assessment is questionable. Should such assessment models achieve comparable reliability and validity as standard measures now possess, they would in effect become standardized, also. There is a question as to whether this is a desirable result. If it is determined that this is the course that should be attempted, the results of assessments of any type that exhibit an appropriate degree of reliability and validity can be used for large-scale assessment.

However, if alternative forms of assessment are used, instead, for the assessment of individual students by in-house assessors, many of the problems listed above may be avoided and the strengths of alternative assessment modes may have the impact desired on the quality of instruction in the classroom" (p. 10-11). This article provides an additional perspective regarding the debate over the most appropriate method of assessment in today's public schools. In many circles, the advent of standardized testing was proposed to create a large-scale reform in the educational system.

In general, learning occurs on an individual basis, with each student gaining knowledge from the subject matter at different levels, depending upon existing knowledge, inherent abilities, and personal characteristics, all of which contribute to individual educational outcomes. An article by Stake (1998) entitled Some Comments on Assessment in U.S. Education evaluates learning and assessment as evidenced throughout the U.S. educational system. According to the author, "Standardized test development is one of the most technically sophisticated specialties within education.

Definitions and analytic procedures, at least at the major testing companies are scrutinized, verified, codified and reworked. The traditional ethics of psychometrics call for extensive construct validation of the measurements to be used in schooling...in the development of assessment instruments by the 50 states, adequate validation has seldom taken place. Instruments have been analyzed statistically to see that they are internally consistent but not that mean what users think they mean.

Presumption that assessments indicate quality of teaching, appropriateness of curricula, and progress of the reform movement - commonplace presumptions in political and media dialogue is unwarranted. Proper validation would tell us the strength or weakness of our conclusions about student accomplishment. Those studies have not been commissioned. The most needed validation of statewide assessment programs has not taken place" (p. 3). According to Stake (2003), assessment dramatically changes the way that teachers provide instruction as well as how students react to that instruction and their required courses.

Many experts believe that assessments promote change in teaching methods, resulting in positive and negative consequences of varying degrees. The long-term results of assessment must be better evaluated in order to truly appraise their outcomes. Furthermore, it has been shown that all findings should not be considered permanent, and in fact, should be considered speculative (Stake, 1998). The importance and frequency of formal assessments have increased in recent years. As a result, schools have become increasingly dependent on these methods to affect the well being of students and schools (Stake, 1998).

Although there are many benefits to utilizing assessment methods in schools, there are also a number of costs, including the following (Stake, 1998): Daily instruction is distracted by assessment requirements and the large focus on scoring Student self-esteem decreases, particularly if students do not perform well on standardized tests Teachers often become intimidated by the rigorous requirements brought about by standardized testing The locus of control within educational boundaries becomes more centralized, reducing individualized student attention Unnecessary stigma is placed upon a particular school, especially when student performance is below average In order to maintain a respectable reputation in the local community, many educators may be tempted to falsify scores that may fall well below the average great deal of the blame that is placed on students when teachers provide poor instruction that results in poor test scores and low assessment characteristics; however, the blame should lie directly with the instructor Educational funding from states is constantly being reduced, and much of this funding is directly related to standardized test performance As assessment standards increase and become more severe, teachers respond by making changes in their own daily habits and increase their preparation for test-taking and other related activities.

In addition, "as the stakes rise, the central authorities are both pressured and authorized to intervene more in teaching responsibilities. A widespread public perception of legislators and school authorities is that they are not knowledgeable or competent in matters of the classroom. With ever-confirming evidence that students continue to be testing poorly, the public is tempted to withhold funds for needed improvement in instruction. There is good evidence that increased funding alone will not greatly change the quality of teaching.

But at the same time, by investing in the assessment of students without investing in more direct evaluation of teacher and administrative performance, the professional people and the elected overseers are partly 'off the hook.' In summary the consequences of assessment are complex, extending far beyond the redirecting of instruction toward state goals" (p. 4). Since assessment is a complex endeavor that results in long-term effects for students and teachers alike.

In general, education serves a different purpose for each individual and its value cannot be easily measured in terms of statistical inferences. Putting this information to practical use also varies from school to school and person to person, and teachers must make significant sacrifices in order to perform the required assessments. This article presents a variety of information that provides additional factual support for the discussion of assessment.

The author's opinion demonstrates that if assessment is not managed properly at the outset, it will be very difficult to manage throughout the process, and its potential value will be questionable, particularly for students and even teachers, who must modify their teaching methods in order to accommodate state mandates and other regulations.

Specifically, in the mathematics arena, an article by Fantegrossi (2001) entitled An analysis of alternative assessment methods with an eye towards their alighment with the NCTM Principles and Standards for School Mathematics and Achieve Inc.'s Foundations for Success middle grades expectations provides a discussion of the ever-changing domain of mathematics assessment.

In 1995, the Third International Mathematics and Science Study (TIMSS) determined that there were serious problems with middle school math and science curricula, because as students finished the fourth grade, their mathematics scores were among the best worldwide, but that by the time these same students graduated from high school, their scores were near the bottom of the rankings (Fantegrossi, 2001).

This data demonstrates that making the appropriate determination regarding alternative assessment is extremely important and may make all the difference in how secondary school students perform and excel in their academic endeavors and in future years. Teachers must make the effort to identify alternative methods of assessment that best fit their teaching styles as well as the student population in question in order to satisfy the needs of their students. Chapter 3 Population The proposed research study is concentrated on a specific geographic area of the U.S.

Virgin Islands, which is comprised of a small group of islands with a population of 123,498 residents, as of July 2002 (World Factbook, 2002). Specifically, the island of St. Thomas is the focus area, where very few public secondary schools exist, since the school-age population is relatively small. The primary components of this research study will concentrate on the student population and assessment methods at two specific schools in order to identify the potential indicators for change and improvement.

As these schools have recently lost their accreditation for a number of reasons, they are reevaluating their current circumstances in an attempt to regain accreditation and to improve student outcomes and performance. Specifically, Charlotte Amalie High School opened in 1920 for junior high students, and in 1930, the implementation of the first twelfth grade class took place. In 1955, the school moved to its current location, where it now provides college preparatory, business education, vocational programs, music, and arts coursework for students, with numerous opportunities to achieve excellence in their educational endeavors.

The primary objective of Charlotte Amalie is to "instill civic and personal responsibility and prepare students to become proficient, life-long learners, competitive workers and responsible citizens able to function in society here and abroad," and the school professes a motto of "To Excel Always" for its students (Charlotte Amalie publication). The mission statement of Charlotte Amalie High School is the following: "The educational mission of the Charlotte Amalie High School is to produce high achievement in all students.

We educate students of varying abilities and backgrounds, and we believe all students can learn and master instructional objectives. As a comprehensive high school, we offer a wide selection of courses, programs, and activities with opportunities for students to develop and excel in academic, vocational and career supportive competencies. We instill civic and personal responsibility and train out students to function effectively in society here and abroad...we seek to maintain an environment where every student can achieve and develop his or her maximum potential.

In this environment, we stress discipline and fairness and are committed to the growth and improvement of our students and our school" (Charlotte Amalie publication).

Charlotte Amalie High School also possesses a philosophical approach to education that is grounded in the belief that "the purpose of education is to provide students with the framework of knowledge and skills necessary to understand, function, and succeed in an ever-changing, global society...this can best be accomplished by focusing on the intellectual, physical, emotional, cultural, moral, and social growth of each student as an individual with unique needs, interests, and abilities...Charlotte Amalie High School aids in the development of each student by offering an extensive number of required and elective courses in academic, vocational, special education, and advanced placement programs.

Emphasis is placed on involving students in intellectual subject matter while teaching problem solving, critical thinking, analytical reasoning, communication, interpersonal and life skills. Further, courses are designed to expose students to a variety of teaching methods suited to their individual needs" (Charlotte Amalie publication). It has been strongly demonstrated through the mission statement and philosophy that Charlotte Amalie High School possesses high aspirations and anticipates successful experiences for its student body.

Ivanna Eudora Kean High School began in 1971 under a different name: The Nazareth Bay Secondary School, admitting both junior and senior high school students. When Bertha C. Boschulte Junior High School opened nearby, Nazareth Bay became a senior high school. In 1975, the school was renamed Ivanna Eudora Kean High School in honor of Ivanna Eudora Kean, an educator in the Virgin Islands for 52 years (Ivanna Eudora Kean publication). Many significant changes have taken place over the past.