Developing Regression Models Of Students Performance In High School Geometry

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Given a rapidly changing world, today's student success hinges on the students' abilities to organize and apply Mathematics in the solution of meaningful problems. According to Osborne (2002), making a valid projection concerning an outcome for a particular individual can be achieved by making prediction models through multiple regressions.

The need to improve the standard of living in Nigeria through the advancement in science and technology has made Government at all levels and stakeholders in education to be more concerned now than ever about the poor performance of students in Mathematics. A study on Some Student Personal Variables as Predictors of Mathematics Achievement in Secondary Schools in Central Cross River State - Nigeria concluded that in tackling poor performance in Mathematics, variables within the learner need to be addressed, as they also contribute to explain or predict learners' performance in Mathematics (Obo, 2007).

Internationally, the Philippines belongs to the bottom five of poor achievers in Math and Science. According to the study by the Trends in International Mathematics and Science Study (TIMSS) in 2003, in the Math Achievement test, the Philippines ranked 41st . According to Tinio (2002), public school students do poorly in diagnostic and achievement tests. He also added that those students who took the exam were prepared by their teachers months before the actual tests, and their teachers had to go to a seminar in PNU (Philippine University of the Philippines) in preparation for the review, but still their performance is poor.

In the local scenario, specifically in Davao Del Sur, Mathematics is one of the weakest subjects having a low performance in the 2006 National Achievement Test and Division Achievement Test (Angco, 2007). Subscribing to the belief that the quality of education is measured by the performance of students, every educator feels the imperative need to identify variables that could be used as a tool in predicting performance in Mathematics subjects.

As of the present, no study has been conducted yet to predict students' performance in High School Geometry in Davao Del Sur. Thus, this study was undertaken to formulate regression models that will help to project future performance in Geometry of the Secondary School Students.

Statement of the Problem

The study was conducted to develop regression models of students' performance in High School Geometry. Specifically, this study sought answers to the following questions:

1. What is the level of the following student variables:

1.1 Study Habits

1.2 Perceived Teacher Support

1.3 Attitude towards Mathematics

1.4 Parent Involvement

1.5 Monthly Family Income?

2. What is the level of Students' Performance in Geometry in terms of:

2.1 Polygons and Space Figures

2.2 Measurement of Polygons and Space Figures

2.3 Relations Involving Line Segments and Angles?

3. Is there a significant relationship componentwise between student variables and performance of students in High School Geometry?

4. What regression models can be developed in predicting Students' Performance in High School Geometry?


The null hypothesis tested in this study was that there is no significant relationship componentwise between student variables and performance of students in High School Geometry.

Review of Related Literature

This section includes varied sources of materials that are viewed in relation to the investigation. The topics are hereby presented to provide a better background and insights of the present investigation.

Student Variables as Predictors

Researchers in psychology and education have always been interested in

determining differences inter and intra-individuals in order to investigate causes and/or effects of some variables (independent) on other variables (dependents), knowing that the individual is the one who decides the outcome of the treatment. It is his nature and the nature of the interaction among his personal variables on one side, and family, and school factors on the other side, which decides how he receives, assimilate, react to the treatment, and produce the behavioral changes (Fawziyah, 2001).

Study habits. Educators and parents long have been plagued by the problem of students' low achievement in school. Many have had the frustrating experience of watching a child undermine his or her chances for a good performance simply by not trying. A student who performs poorly as a consequence of not studying or not completing assignments is usually perceived by his teachers as a hopeless case (Camahalan, 2006). He further added that many students who encounter achievement problems in school frequently warrant the concerned scrutiny of teachers and parents alike. They are victims of pre-judgment that they can do no better.

Study habits are learning tendencies that enable students work privately. Azikiwe (1998) described study habit as the adopted way and manner a student plans his private readings, after classroom learning so as to attain mastery of the subject. According to her, good study habits are good asset to learners because they (habits) assist students to attain mastery in areas of specialization anal consequent excellent performance, while the opposite constitute constraints to learning and achievement leading to failure.

Ikegbunam (1998) pointed that poor study habits as one of the major causes of poor academic performances among Nigerian university students. Efficient study habits can strengthen writing. Professors in the developing countries, such as those in Nigerian universities, should attempt to equip graduates with high level of analytical skills, the capacity for critical reasoning, self-reflection and conceptual grasp and ability to learn autonomously and exercise flexibility of mind.

A research study on "Effects of self-regulated learning on Mathematics achievement of selected Southeast Asian Children" by Camahalan (2006) revealed that students' low achievement in school is related to their poor study habits. It is also indicated that training the students to be self-regulated learners through the Self-Regulated Learning Program (SRLP) will help them improve their Mathematics achievement and study habits.

The said research was based on the conceptual framework that students' low mathematics achievement in school is related to their poor study habits. Thus, the intervention titled "Mathematics Self-Regulated Learning Program" aimed to help selected children from Southeast Asia (the Philippines) improve their Mathematics achievement, Mathematics self-regulated learning, and Mathematics school grade.

Good (1996) defined the term study habits as the student's way of study whether systematic, efficient or inefficient etc. Good study habits are perceived to be the determinants of the academic performance. That is why efforts are made to develop and improve study habits in students. Secondary school students in public schools of Pakistan come from economically poor and average income families. These families face various problems causing emotional disturbance among their children. They have poor study habits hence they show poor academic performance. A great deal of evidence is present to show the positive correlation between study habits and academic achievement.

Ansari (1998) found that study habits and study attitudes are both significant variables which determine the academic performance of the students. Russell and Petrie (1997) have cited a research study aimed to find out the relationship between study habits and student attitude and academic performance (cumulative GPA) of college students. Findings of this study indicate a positive correlation between study attitude, study habit and academic achievement.

National Assessment of Educational Progress (NAEP) in 1994 conducted a study to find out the relationship between study habits and academic achievement. Findings of the study revealed a positive correlation between study habit and academic achievements of elementary and secondary school students.

Onwuegbuzie (2001) also conducted a series of studies to find out relationship between study habits and academic success and reported positive relationship between study habits and academic success. The main objective of the study was to examine the effect of guidance services on students study attitudes, study habits and academic achievement.

Perceived Teacher Support. The teacher is the key person in the teaching learning situation. Hence, he must be a model to all his students in all aspects of life. Students are good imitators, especially the ones, and they usually make their teachers their role models (Calderon, 1998).

He further stressed that the teacher is the manager of the teaching learning situation, the facilitator of learning and the evaluator of the student achievement. Hence, he must possess the mastery of the subject matter upon the principle that one cannot give what he does not have. The teacher should master the methods and tools of teaching. The teacher is like a carpenter. The carpenter who uses old, rusty, and unsharpened tools cannot produce fine furniture. In like manner, the teacher who uses haphazardly outmoded and ineffective methods and tools of teaching cannot produce a good product. But the teacher who combines the best features of techniques and who manipulates with utmost dexterity the tools at hand turn out the most desirable.

Hudley (2002) cited that teacher support seems to be one of the most influential variables that promote higher student achievement. They focused more on students' ethnicity and engagement as factors of achievement, but students who reported feeling more supported by the school community showed more engagement in the learning and greater achievement.

Likewise, Yeung and McInerney (1999) revealed that perceived teacher support made greater impact on students' GPAs and attendance than self-image and even input from family and friends. Surely teachers' ability to influence students' academic achievement translates to their ability to impact their achievement on high stakes tests.

Ewen (2002) emphasized that the question of how to motivate students in the classroom has become a leading concern for teachers of all disciplines. Student motivation and student management are especially relevant to mathematics education in light of recurring questions about how to get more students interested and involved in learning.

If students were provided with everyday situations for practicing and learning the important uses of mathematics, they would develop such skills as "making inferences, evaluating the reasonableness of results and using references to look up what they need to know (Cawelti, 1999).

Swartz (2003) noted that there is a great deal of qualitative and anecdotal evidence from school classrooms that infusion lessons both improve student thinking and enhance content learning. Teachers report that student interest in their learning improves, their understanding of the content they are learning deepens, many students do better on content-area tests, and many students begin using the thinking strategies introduced in these lessons. When using infusion as an approach to teaching thinking and enhancing learning, the learning students engender will prepare them to enter an increasingly complex and technological world with skills that they will need to use information meaningfully, to make sound judgments, and to develop confidence in themselves as thoughtful people.

Skemp (1996) cited that more recent studies with improved methodology which have provided evidences that teachers who have a conceptual or rational understanding of Mathematics, can influence students' learning.

Given that teaching skill is associated with student achievement, school districts and policymakers are interested in how teachers are prepared. While teaching skill is a goal of preparation, usually a credential only requires an academic degree and coursework. Virtually all public school teachers in the United States have at least a bachelor's degree, and many possess advanced degrees (Ashton, 1996).

Greenwald (1996) reviewed a number of studies of the relationship between school inputs and student outcomes. Some school resources, i.e., teacher ability, teacher education, and teacher experience were strongly related to student achievement.

Attitude towards Mathematics. The conceptions, attitudes, and expectations of the students regarding mathematics and mathematics teaching have been considered to be very significant factor underlying their school experience and achievement (Borasi, 2000).

The general conceptions determine the way students approach mathematics tasks, in many cases leading them into nonproductive paths. Students have been found to hold a strong procedural and rule-oriented view of mathematics and to assume that mathematical questions should be quickly solvable in just a few steps, the goal just being to get "right answers". For them, the role of the student is to receive mathematical knowledge and to be able to demonstrate so; the role of the teacher is to transmit this knowledge and to ascertain that students acquired it (Frank, 1998).

Based on the study on the "Roles of Attitudes, Perceptions and Family Backgrounds on Students Achievement in Mathematics", student engagement in mathematics refers to students' motivation to learn mathematics, their confidence in their ability to succeed in mathematics and their emotional feelings about mathematics. Student engagement in mathematics plays a key role in the acquisition of math skills and knowledge - students who are engaged in the learning process will tend to learn more and be more receptive to further learning. Student engagement also has an impact upon course selection, educational pathways and later career choices (Leder,2003).

Reys (1999) asserted that the influence of attitudes, values, and personality characteristics on achievement outcomes and later participation in the learning of mathematics are important considerations for mathematics educators. Teachers not only want students to learn mathematics but also want to be able to enjoy and be confident about the subject. He strongly believed that affective variables such as motivation and self-esteem facilitate or hinder students' learning and achievement in mathematics. Furthermore, affective goals are included in statements of educational objectives for mathematics curricula.

Students' causal attributions are not only fundamental motivational variables but are also critical motivators of their persistence in learning. Optimism, pessimism, and achievement in mathematics were measured in a sample of primary and lower secondary students on two occasions. Although achievement in mathematics was most strongly related to prior achievement and grade level, optimism and pessimism were significant factors. In particular, students with a more generally pessimistic outlook on life had a lower level of achievement in mathematics over time. Gender was not a significant factor in achievement (Kloosterman, 2001)

McLean (1997) investigated attitudes toward learning with regard to their achievement and found that five attitudinal factors were significantly related to academic performance by distinguishing between the attitudes of high and low achievers. Students' attitudes may not only directly affect academic achievement,

but also indirectly influence the effect of other variables, as well.

Abu-Hilal (2000) found that the effect of attitudes passes through the level of aspiration. McLean (1997) and Abu-Hilal's (2000) studies shared consensus with regard to the significance of attitudes in predicting achievement. They further complemented the results of earlier studies, with the former proving that the students' initial attitude towards school was significantly related to academic performance, while the latter found that attitudes predicted their deep approach to learning.

Parent Involvement. In her review of literature on parent involvement and student achievement, Hendrickson (1997) concluded that for now the evidence is beyond dispute: parent involvement improves student achievement. When parents are involved, children do better in school, and they go to better schools. She also noted the following: the family provides the primary educational environment; involving parents in their children's formal education improves student achievement; parent involvement is most effective when it is comprehensive, long-lasting, and well-planned; the benefits are not confined to early childhood or the elementary level; there are strong effects from involving parents continuously throughout high school; involving parents in their own children's education at home is not enough; to ensure the quality of schools as institutions serving the community, parents must be involved at all levels in the school; children from low-income and minority families have the most to gain when schools involve parents. Parents do not have to be well-educated to help.

The research showed that parents can play an important role in strengthening their children's education by participating in their learning and by reinforcing the efforts of teachers and schools.

It is noted that parents can take many positive steps to help their children, including the following: they can encourage students to pursue advanced course work, to invest significant amounts of time in their homework, and to devote more time to reading than to television. An interest in reading and learning can be fostered by reading aloud to children; holding family discussions about reading materials, school work, and current events; and encouraging frequent trips to the library to gather more information about interesting topics. (Mullis,1997).

According to Gianzero (1999), the premise that strong family-school linkages improve children's educational outcomes has acquired almost axiomatic status. Research studies abound documenting the association between parents' involvement in their children's schooling and a host of benefits accruing not only to students themselves, but to their schools and parents as well. Among the documented findings are strong positive correlations between parental involvement in children's schooling and improved student attitudes, achievement, and attendance.

Involved parents reap benefits as well, including increased confidence in their abilities to parent, help their children learn at home, and communicate effectively with schools. For some parents, involvement in their children's education prompts them to pursue further education themselves. Studies reveal that teachers not only hold involved parents in higher regard than uninvolved parents, but they also have higher expectations for their children. (Henderson & Berla, 1997).

Monthly Family Income. Parental occupation may influence student performance in various ways. For example, occupation-related income may determine access to learning opportunities and resources and so play a role in learning outcomes. The education and types of skills associated with different occupations and modeled by parents may motivate students to develop their own skills in particular ways. Parental occupation may also influence how students perceive the value of mathematics learning, their beliefs about the usefulness of mathematics and the learning environment at home (Gianzero, 1999).

In addition, he further stressed out that the longer a child is in poverty, the more deleterious the effect on his or her educational growth. Furthermore, the concentration of poverty within a school can be shown to be harmful to all students in that school whether or not an individual student comes from a poor background. All student poverty is not equal. Students experiencing long-term poverty or who attend schools with high poverty concentrations are much more likely to have educational difficulties than students from families whose duration in poverty is short or who attend schools with low poverty rates. In addition, the findings suggest that many of the same students who experience long-term poverty also attend schools with high poverty concentrations.

Performance of Students in Geometry

Since the establishment of the mathematics standards by the National Committee for Teaching Mathematics (NCTM), researchers have been evaluating these standards on successful implementation strategies and student achievement. One area within these standards focuses on competencies students need to master in basic geometry. The NCTM standards describe geometry as a way to provide students the ability to visualize and work with spatial relationships and estimation. The authors assessed these standards that relate to geometry and looked into the ability of students to estimate angles.

From an early beginning, humans have used graphical representations to communicate ideas. Engineers and other professionals related to science, mathematics and technology have long used geometry and descriptive geometry to find solutions to everyday problems. In fact, geometry can be defined as a science to use graphic representations to find solutions to spatial problems (Pare,1997). These spatial problems require the ability to use spatial visualization to mentally manipulate and interpret visual information in problem solving situations (Wiley, 1995).

Although geometry and spatial visualization play an important role in everyday activities, Perkins (1996) conducted studies that indicate humans are basically poor geometers. The rationale for such a statement came through a series of studies analyzing geometric factors like rectilinearity, symmetry, and extrusion (both linear and curved). Through these research studies, Perkins concluded that the human perceiver does act as a geometer, but a "sloppy" one, and more training is needed to associate geometry to real-world examples so that humans can use geometry accurately and in everyday situations.

Geometry and descriptive geometry are not the only areas requiring student skill development. Estimation plays an important role in everyday life as well. The National Council for Teachers of Mathematics (NCTM) defines estimation as a process involving comprehending a problem, relating the information to data known, making judgments, and verifying reasonableness. Estimation is seen as a process to connect mathematical ideas to the physical world and communicate these ideas through articulation. Harte and Glover (2000) stated that many situations involve estimation rather than precision and that teachers need to help students develop good estimation skills.

Happs and Mansfield (2001) argued that learning to estimate can be difficult, but students with a prior or contemporaneous experiences in measurement (ie. geometry), find it less difficult to apply these estimation skills. Students use of mental imagery, as learned through geometry, will "benefit from opportunities to construct an image in the same way that scientists and engineers construct mental models to serve as useful representations of the phenomena to be understood. But, if students are to develop these skills in estimation, direct linkages to geometry and its use in everyday life must be taught in both elementary and secondary schools.

In 1992, the National Assessment of Educational Progress (NAEP) conducted a series of statewide assessments in mathematics. The assessment focused on both fourth and eighth-grade students in public institutions. North Carolina participated in this voluntary state-by-state assessment with testing in areas of numbers, data analysis, geometry, basic mathematics, algebra, and estimation. North Carolina students performed lower than the national average in all six areas, particularly in geometry and estimation. Once this information was known, the NAEP asked teachers about the amount of time spent on each of the six areas that were assessed. Only twelve percent of North Carolina teachers indicated they place an emphasis in Geometry at the fourth-grade level, and only fourteen percent do so at the eighth-grade level.

Regression Models. Regression models are used to predict one variable from one or more other variables. These provide the scientist with a powerful tool, allowing predictions about past, present, or future events to be made with information about past or present events. The scientist employs these models either because it is less expensive in terms of time and/or money to collect the information to make the predictions than to collect the information about the event itself, or, more likely, because the event to be predicted will occur in some future time (Stockburger,2003).

Ding (2006) considered regression models may be one of the most commonly used statistical analysis techniques in educational research. Typically, regression analysis is used to investigate the relationships between a dependent variable (either categorical or continuous) and a set of independent variables based on a sample from a particular population. Often the particular interest is placed on assessment of the effect of each independent variable on dependent variable, and such an effect is considered as the average effect value across all subjects in the sample.

Turner and Williams (2002) in "Predicting Student Proficiency on the Arkansas Benchmark Mathematics and Literacy Exams" used the data from five semesters from spring grade 1 to 3. The prediction model information was used to identify the SAT-9 scales that were best predictors of future academic performance in fourth grade mathematics and literacy. The study was conducted purposively not to identify the best prediction model but rather to identify the best predictors of future at-risk performance at each grade level.

Kruck and Lending (2003) developed a model to predict academic performance in the first year college level Information System course to explain the performance in an introductory college level financial accounting course. Their research found out that motivation/effort and GPA do predict performance and that prior related courses do not predict performance. Moreover, their model pointed out that the individual's gender affected the academic performance.

Asia's four dragons, Singapore, South Korea, Japan and China, attended Trends in International Mathematics and Science Study (TIMSS) 2003 had excellent achievement in math, but there is the comment and diverseness to effect these countries' math achievement. The study analysis TIMSS 2003 data from grade 8 students of Asia 's four dragons , to comprehend the factors effected students' math achievement in Asia's four dragons, and the difference among the relative variables namely: father' s educational level, mother's educational level, self-confident of student, parents' educational conception, homework time, extra lessons, student consider math is important (Chang,2006).

The result of the abovementioned study is that the factors including parents' educational level, the level of enjoy math, self-confident of student, parents' educational conception, homework time, extra lessons, school climate are predictors in the Mathematics achievement of Asia's four dragons.

The findings of the above studies are relevant to the present investigation inasmuch as all developed regression models predicting the performance of students in mathematics. As a whole, the related literature presented herein provides the foundation of information gathering regarding the variables of the study. The foregoing researches help in establishing the proponents' theoretical basis that will prepare students to do better in Mathematics subjects especially in Geometry and that study habits, perceived teachers support, attitudes toward Mathematics, parent involvement, and monthly family income of students are deemed significant predictors in their performance in High School Geometry.

Theoretical and Conceptual Framework

This study was anchored on the theory of Osborne (2002) which stated that making a valid projection concerning an outcome for a particular individual can be achieved by making prediction models through multiple regressions.

Reyes and Stanic (1996) theorized a pattern effected mathematics achievement factors. They believed that the society influence, mathematics curriculum in school, the activity in class, the attitude of students, and the behavior related to academic achievement, can affect mathematics achievement and they discovered that the comparison between students, will affect their expectation which succeeds in achievement, thus has a higher performance in mathematics achievement.

Ercikan (2002) predicted that various independent variables that include both student personal and environmental variables (students' attitudes toward mathematics, parents' highest level of education attained, self-expectations and the expectations of parents, teachers, and friends, students' confidence in mathematics, home support for learning) can affect to the dependent variables (students' mathematics achievement and participation in advanced mathematics courses).

Okebukola (1992) identified factors like home environment (e.g. Socio-economic background), school environment (e.g. class size, school resources) and quality and quantity of instruction as responsible for students' poor performance in mathematics. Most of these factors are external to the student.

The schematic diagram of the study is shown in Figure 1. The independent variables include the following student variables: study habits, which refer to the adopted way and manner a student plans his private writings, after a classroom learning; perceived teacher support, which refers the way students recognize the guidance and support of the teachers; attitude toward mathematics, which refers to the feeling of the students on the subject Geometry; parent involvement, which refers to the way the parents of the students guide and support them; and monthly family income, which refers to profits and takings of the students' whole family. The dependent variable is the students' performance in High School Geometry which includes the following components: polygons and space figures, which refers to the geometry of shapes and sizes; measurement of polygons and space figures, which refers to the dimensions of

Independent Variable Dependent Variable Output

Figure 1. The Conceptual Paradigm showing the Variables

shapes and sizes; relations involving line segments and angles, which refers to the measurement containing either sides or angles. The expected outputs are the regression models that will serve as predictors of future students' performance in High School Geometry.

Significance of the Study

The results of the investigation can be useful in predicting the performance of students in High School Geometry.

Specifically, the findings will be beneficial to the following:

School Heads. Findings of this study will provide valuable information to school heads for them to reexamine and develop strategic plans that would enable them to enhance the performance of students in High School Geometry. Moreover, they could be able to identify the strengths and weaknesses in the part of the administration, faculty members and students for future improvements.

Master Teachers. The output of the study will provide the master teachers an opportunity to strengthen those weak points of their teachers. Knowing the best predictors on the performance of students in High School Geometry, they could be able to formulate programs that will address the needs of the students.

Subject Teachers. Potential predictors of students' performance in High School geometry can be useful to the members of the teaching force especially on how are they going to improve and strengthen the potentials of their students when it comes to mathematical problems. Results of this study will also disclose the strengths and weaknesses of the instructors' teaching methods and techniques with a view to fitting them to the needs of the students. Finally, this study can provide the faculty insights on the proper motivation of students to improve their academic performance in Geometry.

Students. The results of this research will provide students valuable insights that will motivate them to acquire the knowledge proficiency, mathematical skills and application of Geometry in a reality-based situation. Furthermore, the students will come to realize that they can be successful in achieving high level in Geometry if they could be able to identify the important variables that would predict their performance in Geometry.

Definition of Terms

The following terms relevant in this study, were defined operationally to facilitate better understanding:

Regression Models. Regression models are used to predict one variable from one or more other variables. These provide the researcher with a powerful tool, allowing predictions about past, present, or future events to be made with information about past or present events. In this study, the regression models to be developed are on students' performance in High School Geometry.

Student Variables. As used in this study, these refer to the variables that could predict students' performance in High School Geometry and these are monthly family income, study habits, perceived teacher support, attitude towards Mathematics, parent involvement and monthly family income.

Performance of Students. In the study, it refers to the achievement of students in High School Geometry specifically in polygons and space figures, measurements of polygons and space figures and relations involving line segments and angles.