EFFECT OF COMPARATIVE GRADING IN MATHEMATICS ON STUDENTS’ ACADEMIC SELF-EFFICACY BELIEFS AND ACHIEVEMENT IN ABA EDUCATION ZONE OF ABIA STATE

ABSTRACT

The study  was carried  out  to investigate  the effect  of comparative  grading  on  students’ mathematics  achievement  and self-efficacy  beliefs in Aba  education  zone.  Also, the study explored   the  influence  of  gender  and  interaction   effect  on   comparative   grading   in mathematics achievement of students’ self-efficacy. Four research questions were asked and four hypotheses were formulated and tested at the (P<0.05) level of significance. The study adopted a non – equivalent control group quasi- experimental research design involving one experimental group and one control group. Four co-educational secondary schools in Aba North  Local  Government.  Area  of  Abia  State  were  randomly  selected  and  assigned  to experimental and control group, and used for the study. A total of 200 SS One students (100 males and 100  females) in four intact classes were sampled and used for the study. Two instruments,   Students’   Academic   Self-efficacy   Beliefs   Questionnaire   (SASEBQ),   and Mathematics  Achievement  Test  (MAT).were  used  for  both  pre-test  and  post-test.  Data collected using the instruments were analyzed using descriptive statistics in  answering the research  questions  while  Analysis  of  Covariance  (ANCOVA)  was  used  to  test  the  null hypotheses. The result of the study showed that Students who were exposed to comparative grading achieved  significantly higher than those exposed  to criterion  referenced grading. Also,   there  was  no  significant   difference   between   the  self-efficacy   belief  scores   of male and female students on mathematics.  Based  on  the  findings,  discussions  implications and recommendations of this study, suggestions for further studies were mad

CHAPTER ONE

INTRODUCTION

Background of the Study

Every day people operate one form of math or the other without knowing they are applying mathematical concept. For instant, a carpenter has to measure the length and width of the door or window the carpenter is constructing. Similarly, mothers prepare food using correct quantity of the ingredients without knowing that they are applying math. Likewise, when children are given money to buy something, they will ask for their change after buying depending on how much they are given. All these activities involve math yet when they are put in sentences or in figures, students see it as a very  difficult task. Mathematics  is the science of addition and subtraction which involves everyday activities whether consciously or unconsciously. Math is done from the pre-school where children recite nursery rhymes with numbers. In primary school, pupils do simple addition, subtraction and simple algebra.   From primary, pupils proceed to secondary school where students are expected to write math as one of the core subjects;  in  fact, math is one of the requisite one is expected  to have (credit) before being  admitted  into the university.   This showed  that its important cannot be over emphasized,  our parents that are doing business  apply math even though it is not  written down in mathematical terms. But it is seen in the measurement  they do in the  process of selling fabrics. No one can do without math as it is very vital in our daily lives.

Mathematics is an aged, wide, and deep discipline or field of study that deals with daily activities of human beings (Moursund, 2006; Mikhail, 2006).   Mathematics is as old as human  existence,  throughout  the  history;  humans  have  faced  the  need  to  measure  and communicate  about  time,  quantity,  and  distance.    To  a  layman,  it  is  the  addition  and subtraction of numbers. In   Brouwer’s view, math is the mental  activity which consist in carrying  out construct  one after  the other.   This might  be  why Soyemi  (2005)  said  that

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everybody uses mathematics in one way or the other in solving life problems. Nations that desire  to  forge  ahead  scientifically  and  technologically  cannot  afford  to  toy  with  the mathematical knowledge of her citizenry.

Mathematics  arises  from  many  different  kinds  of  problems  such  as  commerce, architecture and astronomy. It is the idea of math that made the physicist Richard Feynman to invent  the  path  integral  formulation  of  quantum  mechanics   using  a  combination   of mathematical reasoning and physical insight which in turn becomes string theory (Johnson & Lapidus,  2002).     Mathematics   comprises   many   things  such  as  human  endeavour  – measurement  of time (seconds,  minutes,  hours,  days, weeks, months, seasons and years). Equally  measurement  of  distance  is  considered,  and  the  different  systems  of  distance measurement   that  developed   throughout  the  world.  Even  in  art,  music,  and  dances, mathematics play important roles.

There is abundantly history of human development of math and mathematical uses  in our contemporary society.  Mathematics is an indispensible tool that even a layman performs (Abakpa and Iji, 2011).  Mathematics is much more than enrolling in algebra, geometry and calculus during high school. It is about acquiring skills students need to reach their goals in high school in future.

There are so many reasons for students to learn mathematics; math teaches logic and order, teaches life skills, it supports continuing education and career among others  (Elise,

2014).    No  wonder  (Salmon,  2005)  asserted  that  math  is  an  originator  for  intellectual development, scientific discoveries and intervention. As can be seen from above that math is an   interdisciplinary   language   which   explains   the   relationships,   structures   quantities, properties and forms of objects, time, construct and the space. No wonder math is regarded as an indispensible  tool. Therefore,  when students have the  capability to solve mathematical

problems and   get the rightful skills that are needed, there is the tendency that such students will do well in any external examination which in turn leads to academic  self-efficacy in math.

In    spite of the recognition accorded to mathematics due to its relevance,  Elekwa (2010) remarked that students exhibit non-chalant attitude towards mathematics, even when they know that they need it to move ahead in their studies and in life. Such students who have already conditioned their minds that mathematics is a difficult subject are usually not serious in  the  learning  of  mathematics  and  therefore  perform  poorly  in  mathematics  tests  and examination.  Even though the importance  of mathematics  to all aspect  of life cannot  be overemphasized,       researches     show that there is  increasingly poor achievement  in the subject among students in secondary schools as asserted by Awolola (2010). For instance the results of May/June 2012 West African Examination Council of West African Senior School Certificate Examination(WASSCE),  reveals that 38.81 per  cent  candidates record credits in English and Mathematics (Tide,  2012). Similarly, the former education minister, Professor Ruquyyatu  Rufai  (2012), lamented on the poor performance of students in Nigeria. She said that  an  average  of  30%  of  over  one  million  students,  who  sat  for  May/  June  WAEC examination in the last six years, obtained five credits including English and Mathematics. The students’ underachievement  in math has been the chief worry to parents, mathematics teachers, science teachers and curriculum experts across the nation.

Analysis of school certificate mathematics examination results showed that students’ performances  in mathematics are consistently poor, that nothing much has  been achieved. Uwadiae, (2010) reported that less than 42% of registered candidate in SSCE obtain credit pass  in  mathematics.  Even  the  SSCE  results  released  by  WAEC  and  NECO  for  2012 indicated poor achievement of students in mathematics. According to Olunloye (2010), this ugly trend of high failure rate in mathematics is a national tragedy. Therefore, feasible ways

of improving the performance  has remained an area of great concern for researchers.  The deplorable  state of mathematics  achievement  is attributed  to a number of factors  such as attitude of students (Uhumuavbi and Umoren, 2005); lack of instructional  resources (Yara and Otieno, 2010); Instructional techniques (Olulonye, 2010) among others.

Although several measures have been in use to improve the students’ achievement in math, only a little has been achieved. Example,  the 2010, 2011 and 2012 WAEC  results showed that there was about 6% improvement – from 35% to 41%.  In Aba education zone, specifically, in Aba North local Government Area, out of three thousand five  hundred(3500) candidates  that  sat  for math in 2011  WAEC,  only one thousand  four hundred  and  fifty (1450)candidates got credits and distinctions and that represents 41% (Secondary Education Management Board, Aba Zonal office, 2012).

Over the past decades in Nigeria, students’ attitudes to achievement in math seem to have  taken  a  negative  direction.  According  to  Osuji  in  Ali  (2006),  research  studies  on achievement patterns in mathematics  among secondary school students in  Nigeria showed that amid  1979 and 2001, there was a steady annual average  of  1.7%  annual decline  in students’ A1 to C6 grades in mathematics at the West African School Certificate Examination. The  results of November 2006 West African Senior School Certificate (WASSCE) indicated that out of 423,518 candidates  who sat for the  examination,  only 50,065 candidates were seized due to examination irregularities and that represent 85% of the total candidates. The various ways like deploying of security personnel to various centers to checkmate students had not yielded much fruit, executors often ingeniously outwit them (Edukugho, 2007).

Academic achievement or (academic) performance is the outcome of education,    that is, the extent to which a student, teacher or institution has achieved their educational goals.

Academic achievement is commonly measured by examinations or continuous assessment, but there is no general agreement on how it is best tested or which aspects are most important

— procedural knowledge such as skills or declarative knowledge such as facts.

High dropout rates, poor grades and scores among secondary school students seemed to be as a result of wrong orientation to achievement. Dependency on other peoples’ effort seems to have become the order of the day among secondary school students as a result they lose self-confidence, and the spirit of hard work will no longer be there. Students attitudes towards achievement  emerges from some parents or role  models who had achieved much thereby sending out wrong signals that might lower  students’ efficacy by making them to believe that they have it all, therefore have no need to work hard any longer. So students will have such notion at the back of their minds and at the end of the day, they will have nothing to achieve.

The persistent  students’  poor  performance  in mathematics  has  been assumed  to  be highly related to their level of math task persistence and self-efficacy beliefs. The reason is because students’ previous experiences of success or failure in a given field determine their level of    self-efficacy and persistence as regard to tasks that relate to that area (Woolfolk,

2010). So when students have the capability to solve mathematical    problems and get  the rightful skills that are needed, there is the tendency that such students will do well in any external examination, which in turn leads to academic self-efficacy in math.

Students are motivated by grades they receive at the end of a term or semester. When a student scores low grade in any examination, there is the tendency that the student will not be  focused  in  any  academic  activities  especially  those  students  that   are  extrinsically motivated. On the contrary if a student scores high grade in any exam, that student will be motivated the more as the student will be eager to perform more complicated academic task, for instance, if a student solves a math task involving basic operations or algebra taking into

considerations  the necessary steps. It is likely that students’ beliefs about their abilities  to succeed in courses (math and English, for example) might directly impact their performance in those courses. This is in line with Math professor Vaden-Goad (2009) who thought that students  might  be more  motivated  to study and be able to succeed  in introductory math courses if he allowed them to replace early grades with higher ones received subsequently.

Grades are an institutionally required measurement of the students’ demonstration of well defined and communicated learned outcomes (Dave & Robert, 2013).     Grading is the segregation of students according to their proficiencies by way of evaluation. It is a form of assessment, which describes the process of gathering information about  students’ learning including all kinds of ways to sample and observe students’ skill,  knowledge and abilities (Linn and Miller, 2005).   For that reason, it’s useful to consider alternative approaches that might affect not just the motivation to get the grade, but the motivation to learn and develop important skills. Walvoord and Anderson (1998) classify the multiple roles that grades serve: as an evaluation of student work; as a means of communicating to students, parents, graduate schools, professional schools, and future employers about a student’s performance in college and potential for further success; as a source of motivation to students for continued learning and improvement; as a means of organizing a lesson, a unit, or a semester in that grades mark transitions in a course and bring closure to it. Additionally, grading provides students with feedback on their own learning, clarifying for them what they understand, what they don’t understand, and  where they can improve. Grading also provides feedback to instructors on their students’ learning, information that can inform future teaching decisions.

Grading is often a challenge simply because grades are used as evaluation of  student work, it’s important that grades accurately reflect the quality of student work and that student work is graded fairly. Grading with accuracy and fairness can take a lot of time, which is

often in short supply for college instructors. Students who aren’t satisfied with their grades can sometimes protest their grades in ways that cause headaches for instructors. Also, some instructors find that their students’ focus or even their own focus on assigning numbers to student work gets in the way of promoting actual learning.  Given  all that grades do and represent, it’s no surprise that they are a source of anxiety for students and that grading is often a stressful process for instructors (Walvoord & Anderson, 1998).

Parents expect their children to excel, as much importance is attached to grades and grading. With this expectation from parents and guardians, some students prefer short-cut by avoiding intellectual risk to learning. One can see that much emphasis on  assessment can invariably affect the pursuit of excellence, (Maher & Midgley, 1996). In this same note, how people behave can often be better predicted by the beliefs they hold about their capabilities than by what they are actually capable of accomplishing.

Every parent wants to boast the child as “a straight ‘A’ student”; is at the top of  the class”, or on the honour roll”. Example, a man from Minnesota threatened his daughter with a gun for getting two ‘B’s instead of straight ‘A’ on her report card (Daily Sun, 2013). One may wonder what generally determines this prized status. Grade is a symbol that represents the degree to which students have a set of well-defined instructional objectives. Grades which are most often, report cards, are the primary means of measuring a child’s progress through school, “Doing well’ in school is measured by series of letters on a piece of paper: A is great; B is ok; C is not  so good; and D, E or F means that one has failed. Some parents reward students for good grades, either by ascribing a monetary value to each good letter, or taking away privileges for each bad one.

So, for many families, the grade is the goal. One wonders the importance of these grades. Considering Aba as a commercial area where students combine academic work with

business, they lack concentration and at the end, they have low grades; in order for them to maintain their academic self-efficacy, they find means of upgrading their low grades. Some parents on their parts are bribing teachers to upgrade their children’s grades whether they know what they are doing or not. So, one might see that when these students graduate from secondary schools, they find it very difficult to gain admission into the university. Literature reveals that many works have been done in relation to academic self-efficacy and math but nothing much has been done on comparative grading. Having this in mind, it poses a problem for the researcher, hence this research work.

In fact,  grading could be considered  a component  of assessment  which  comprises  a formal, summative,  final and product-oriented  judgment of overall  quantity of worth of a student’s performance  or achievement  in a particular  educational activity, example, and a course.  It  employs  a  comparative  standard  of  measurement  and  sets  up  a  competitive relationship between those receiving the grades. Operationally,  grading is seen as a part of appraisal of overall quality worth of a student’s performance or achievement in a particular education activity. One might think that comparative grading is the use of different types of grading system to assess students’ academic work, that might be true, but in this research work CG is same as norm-referenced grading.

Comparison is the act of finding out the differences and similarities between two  or more things or people.  Comparison can take place whenever there are two or more things at the same time; either for the purpose of having a better understanding  of the  relationship existing between them or for the purpose of having a better choice. Parents at home compare their children’s behaviour; children equally compare their parents as well to know the one that  loves  them  more.  Therefore,  comparative  is  a  comparison     or  an  assessment  of similarities or differences between two or more things relating to, based on, or involving in comparison, or relating to the scientific or historical phenomena, institutions, or objects such

as language, legal systems, or anatomical structures, in an effort to understand their origin or relationships (The American Heritage).   In this study, comparative grading is synonymous with norm-referenced grading and is the major concept in this study.

Several grading systems have evolved over the years. Common among these grading systems are letter grading, 4.0 point scale grading, mastery grading, norm referenced grading and criterion referenced grading system. With the letter grading system, students can receive A, B, C, D, E, or F for 90 percent accuracy or above, 80  percent to 89 percent accuracy respectively in that order, to F grade, which is the least and could be for performance below

60 percent. The 4.0 point scale grading is typically used as a means to calculate a grade point average (GPA) in tertiary institutions. The mastery grading system uses M for mastery, which demonstrates that a student has mastered the standard by showing accuracy 80 percent of the time, P for progressing, which connotes that the student is not quite showing mastery but is progressing. If a student exceeds mastery of the standard he can receive an E and if a student is failing to progress toward mastery, he receives an LP grade. In the mastery grading system, grades are broken down by each content standard, rather than broad subject area, with a score of, E, M, P, or LP given for each standard (CFE, 2012).

Grading brings about competition. One would think that competition would  always lead  to  improved  learning  to  all  students  but  Woolfolk  (2010)  observes  that,  ‘highly competitive  classes may be particularly hard on anxious students,  students who lack self- confidence,  and students  who  are less prepared’.  To woolfolk  (2010),  high standard  and competition  tend  to  be  generally  related  to  increase  academic  learning.  The  two  basic approaches to grading student work are norm-referenced and criterion referenced grading.

In norm- referenced (comparative) grading, a student grade is determined by how well the individual  performs relative to the performance  of all the other students in  the class,

because the highest grades will only be awarded to the highest performing students.  The students are implicitly in competition with one another for a limited number of  the most desirable grades.   Common example of comparative grading are standardized  test such as University and Tertiary Matriculation Examination ( UTME), Scholastic  Assessment Test (SAT), Graduate Record Examination (GRE) or The use Of English as a Foreign Language (TOEFL).  Comparative grading is designed to identify which students have learned the most or the least but may not be able to indicate whether the students have learned enough. More of this will be discussed in chapter two.

By contrast  in criterion-  referenced  grading,  a student’s  performance  is measured  not against  that  of other  students,  but  against  a fixed  standard  of  performance,  such  that  a student’s  grade  reflects  the  degree  to  which  a  student  demonstrates  particular  level  of knowledge or skill, irrespective of other students’ level of achievement. Typical examples of criterion  referenced  tests  are  Medical  Licensing  examination  and  Bar  examination  for Lawyers  (University of North Carolina,  2012).   Criterion-  referenced  (absolute)  tests are designed to indicate whether students have learned enough but may not be able to identify which students have learned the most (Rose, 2011).   Unlike  norm-referencing,  there is no pre-determined  grade  distribution  to be generated  and  a  student’s  grades  are in  no  way influenced by the performance of others (University of Minnesota, 2011).

Theoretically, all students within a particular group could receive very high (or very low)  grades  depending  solely  on  the  levels  of  individuals’  performances  against  the established  criteria  and  standards.  The  goal  of  criterion-referencing  is  to  report  student achievement  against  objective  reference  points  that  are  independent  of  the  group  being assessed.  Criterion-referencing  can  lead  to  simple  pass-fail  grading  schema,  such  as  in determining fitness-to-practice  in professional fields.  Criterion-referencing  can also lead to

reporting student achievement or progress on a series of key criteria rather than as a single grade  or  percentage.  Criterion-referencing   requires  giving  thought  to  expect   learning outcomes:  it  is transparent  for  students,  and  the  grades  derived  should  be  defensible  in reasonably objective terms – students should be able to trace their grades to the specifics of their performance on set tasks. Criterion-referencing lays an important framework for student engagement  with the learning process and its outcomes,  (Centre  for the Study of Higher Education, 2002). Grading may not be all that good to provide feedback because it does not actively  motivate  students,  encourage  them,  and  it  does  not  provide  method  of  student improvement. Similarly, it may not highlight strengths and weaknesses of students.  Students’ beliefs about their abilities to succeed in courses such as math and English directly impact their performance in those courses.

Some factors play an important role to promote or decline academic achievement such as Self- efficacy and gender.  The confident that an individual has to accomplish a given task at a designated level is referred to as self-efficacy. Bandura (1994) asserted that self-efficacy is a person’s belief in their capacity to successfully perform a particular task. These effects are  particularly  apparent,  and  compelling,  with  regard   to  behaviours  affecting  health (Luszczynska   &  Schwarzer,   2005).   Self-efficacy   refers   to  judgments   of  a  person’s capabilities, and is a capability to carry out the actions needed to succeed in a task. It is one of the strongest factors predicting performance in domains as diverse as sports, business, and education. In academic settings, self-efficacy is a strong predictor of performance (Klassen, Krawchuk, Rajani, 2008). Self-efficacy is the measure of one’s own competence to complete tasks and reach goals (Ormond, 2006).

The research of self efficacy goes back to original ideas of Albert Bandura. According to

Bandura (1995), self efficacy is the belief in one’s capabilities to organize and execute the

courses of action required to manage prospective  situations which could be academics  or otherwise. Researchers hypothesize that students beliefs in their ability to succeed in courses or activities  and their  amount of science  self efficacy,  influences  their choices  of school related tasks, the effort they expend on those activities, the perseverance  they show when encountering difficulties, and the ultimate success they experience in their courses. Another definition of self efficacy is the strong belief that a student has that they can succeed in any given task or activity, having the ability to persevere in the face of difficulty, and being able to promote confidence as they meet obstacles. Self efficacy is also known as a judgment of confidence. It is context sensitive, it can be task specific. It is made and used in reference to some type of goal. It is domain specific, and is more of a question of can. Students with self efficacy ask themselves  “Can I do  this?”  There  are four sources of self efficacy that are formed  by students as  described by Bandura(1986,  1997).  The four sources  are mastery experience,   social   persuasion,  physiological   states,  and  vicarious  experience.  Mastery experience is the most influential of the four.

Individuals  have to be motivated  to learn before the actual learning can take  place, during the process of learning and after the task has been learned. In order to  increase a student’s self efficacy beliefs they should surround themselves with positive and encouraging role  models.  This  peer  modeling  works  best  for  all  types  of  students  whether  they  are considered to be gifted, special education, or regular  students. Students need to be taught what it looks like to have high self efficacy beliefs, because many students do not have the proper  role models to teach or  encourage  high self efficacy traits. If students are around people  that are positive  confident  in their  own abilities then that is a very good  way to motivate the students to strive for better. Rewards and positive reinforcement is not a factor that is used when encouraging higher self efficacy beliefs in students. Majority of the beliefs of self worth  and confidence  must be derived from within the student and based on their

knowledge and success at a task. The student should not be confused by receiving rewards for having confidence. Many extrinsic rewards will undermine the effects of self efficacy. It has been  stated  in  research  that  providing  rewards  only  for  participation  in  an  activity  has generally led to decreased interest in that activity (Bates, 1979) and that is not the results that teachers desire in the students that they teach. They want them to continue to have interest in the tasks that are presented to them.

Students can develop their own self efficacy by knowing how they learn best. Once a student is more knowledgeable about their own learning and what works best for them, they will  be  able  to  experience  more  success.  That  student  should  then  focus  more on their strengths, but still attempt to work at the task that are more difficult for them.

When people successfully accomplish a task, their perceived ability to  accomplish  a similar task in the future increases. On the contrary, failure at a task diminishes or decreases self-efficacy and can result to a decline in the likelihood to persist or engage in behaviours related to the original tasks. As it applies to student’s success, when students successfully achieve academic goals, academic self-efficacy is increased and the tendency of achieving future academic goals also increases. There are some variables that may be related to the role of mastery in shaping efficacy beliefs. For instance, age as a variable, with regard to the role of mastery experiences in shaping academic self-efficacy beliefs (Hampton, 1998).Mastery may be more influential for older students because they are more likely to sustain a longer performance   history   and   more  successful  experiences   to  inform  self-efficacy  beliefs compared to  younger students.    Students can have belief about themselves in the area of studying  and  writing,  such  as,  time  for  studying,  and  strategies  used  in preparation  for examination.    When these  are effectively used, there  is the tendency that  such  student’s academic self- efficacy will be enhanced.

Academic  self-efficacy  is defined  as individual’s  perceived  capability in  performing necessary  tasks  to   achieve   goals  (Bandura,   1997).   Academic   self-efficacy   refers   to individuals’ beliefs that are formed    specifically toward  academic (as different from non- academic,  general  social,  emotional,  or  physical)  domains.  This  in  other  word  means individuals’ convictions that they can successfully perform given tasks at designated levels (Schunk,  1991). Poor academic  performance  in sciences  could probably link to low self- efficacy among secondary school performance, the higher their opportunity to compete for lucrative and competitive courses (Mbathia, 2005).  Academic performance is influenced by many  factors,  such as; attitude leads to achievement  (Njuguna,  1998; Owiti, 2001). Self- efficacy influences the choice and engagement in a task, the effort expended in performing it, and the standard of the performance (Bandura, 1997).

Students’ academic self-efficacy is the confidence that students have in them in order to do well in their  academic  tasks.  Similarly,  student  academic  self-efficacy  is  student’s degree of confidence in performing various school related tasks to produce a desired outcome such    as   passing    examination,    (Solberg,    O’Brien,    Villarreal,    Kennel,    &   Davis,

1993).Secondary   school   students   with   high  self-efficacy   approach   difficult   tasks   as challenges  to  be  overcome  rather  than  as  threats  to  be  avoided  (Pajares  &  Schunk,

2001).Reverse is the case for students with low self-efficacy. Students may also believe that despite their perceived capability they will not make a good grade in the class because they do  not  have  a  positive  relationship  with  their  teacher,  (Wilder,  1993).    Operationally, students’  academic  self-efficacy  is the level of self-assurance  students  has in performing different academic activities in order to have good grades in their academic tasks.

Several studies have investigated female students’ choice of courses and careers, and self-efficacy has turned out to be critical predictor. For instance, in the United  States, boys hold more positive attitudes toward mathematics than do girls, ( Kahle, 2003 & Kurth,2007).

These  gender differences  seem to predominate  as students move from the primary to  the secondary school level, (Kanai & Norman, 2007). Some other research (AAUW, 2002; NSF,

2004) studies indicate that gender differences in attitude toward mathematics do not exist in the  primary  grades.  In the  middle  school  grades,  gender  differences  begin  to  appear  in attitudes  toward  mathematics  and  boys  are  more  likely  than  girls  to  find  mathematics interesting (American Association of University Women, 2002). By high school, few young women  consider  mathematics  and  science-related  careers  as  desirably  options.  Experts attribute  this  phenomenon  to  the  fact  that,  during  the  middle  school  years,  adolescents formulate  their  gender  identities  and  career  aspirations  (AAUW,  2002).  Also,  statistics revealed that women are underrepresented in science-related and mathematics-related careers. Women make up a staggering 46% of the labour force in all occupations, but only 22% of the science and engineering labour force (National Science Foundation, 2004). A World Bank study conducted  in 2001 in  Sub-Saharan Africa noted that gender differences are close to being eliminated at the primary school level at least in the region as a whole. However, the disadvantage towards females is still prominent at the secondary school level (World Bank,

2001)

Gender  is seen  by Bassow  (1991)  as  a psychological  term  describing  behaviour  and attributes expected of individuals on the basis of being born either male or female. Gender has a crucial role in performance.   Girls perform as capable as boys in academic tasks but have lower self-efficacy (Pajares, 1996b).However, a study showed that women had a higher ability (Greenglass  & Miller, 1999) to cope with stress, by setting and striving to achieve academic  goals.  This  study  intends  to  help  in  resolving  this  controversy  regarding  the influence of gender in achievement.

Statement of the problem

Parents and guardians expect their children to excel; so much importance is attached to grades and grading. With this expectation from parents and guardians, some students prefer short-cut by avoiding intellectual risk to learning.     How people behave can often be better predicted  by the beliefs they hold about their capabilities  than by  what they are actually capable of accomplishing. The self-efficacy perceptions held determine what individuals do with the knowledge  and skills they have.  Results  showed  that students’  performances  in mathematics are consistently poor, but nothing  much has been achieved. Uwadiae, (2010) reported  that  less  than  42%  of   registered   candidate  in  SSCE  obtain  credit  pass  in mathematics. Even the SSCE results released by WAEC and NECO for 2012 indicated poor achievement of students in mathematics.   In Aba education zone, specifically, in Aba North local Government  Area, out of three thousand five hundred (3500) candidates that sat for math in 2011 WAEC, only one thousand four hundred and fifty (1450)candidates got credits and  distinctions  and that represents  41% (Secondary Education  Management  Board,  Aba Zonal office, 2012).

Considering  Aba  as a  commercial  area  where  students  merge  academic  work  with business, they lack concentration and at the end, they score low grades; in order for them to maintain their academic self-efficacy, they find means of upgrading their low grades. Some parents on their parts bribe teachers to upgrade their children’s grades whether they know what  they are  doing or  not.  So,  one  might  see  that  when  these  students  graduate  from secondary schools, they find it very hard to gain admission into the university. Having this in mind,  it poses  a problem  for the researcher,  hence  the  need  to  investigate  the effect  of comparative   grading   in  mathematics   on  students’   academic   self-efficacy   beliefs  and achievement.

It is very obvious that students who are confident in their academic skills expect high marks on examinations and  expect  the  quality  of  their  work  to  remain   personal and professional benefits. The opposite is true of those who lack confidence. This could be the reason for students who lack self-efficacy in their academic skills envision a low grade even before  they  begin  an  examination  or  enroll  in  a  course.  Discontent  with  the  academic achievement  of  students  in  secondary  schools  especially  in  the  science  subjects  in  the national  examination,  the researcher  is    very   much worried,  hence  the general research question  “what effect does comparative grading in mathematics  have on students’ academic self-efficacy beliefs  and achievement in secondary school?”

Purpose of the study

The  purpose  of  this  study was  to  ascertain  the  effect  of comparative  grading  in mathematics  on students’  academic  self-efficacy  beliefs  and achievement.  Specifically,  it sought to:

1.   Ascertain   the achievement mean scores of students exposed to comparative grading in math and those exposed to criterion referenced grading.

2.   Determine  the  academic  self-efficacy  belief  mean  scores  of  students  exposed  to comparative grading in math and those exposed to criterion reference grading..

3.   Determine the achievement mean scores of male and female students in math.

4.   Ascertain the academic self-efficacy of mean scores of male and female students in math.

Significance of the study

The  significance  of  this  study  is  based  on  the  framework  of    Bandura’s  social cognitive  theory and the expectancy theory of Vroom.  Bandura’s  social  cognitive  theory

states that: in a learning setting there exist reciprocal influences of the three forces (personal, social and behavioural) on each other, relationship of which determine the learner’s level of achievement.  The  study  will  help  to  create  the  level  of  reciprocal  relationship  among personal, environmental and behavioural factors during CG instruction and how such affect achievement and this in turn will help to promote the social cognitive theory. Comparative Grading (CG) allows students to compare with one another in the class based on Bandura’s proposal. Therefore, the investigation and establishment of the effectiveness of comparative grading will help to affirm the theory.

On the other hand the study will be of great importance in strengthening the expectancy theory which states that an individual’s effort will lead to performance, which in turn, will lead to a specific outcome.  Mostly, self-efficacy is based on an individual’s belief about their ability to perform specific behaviours.  This means that a person will decide to behave in a certain way because they are motivated to select a specific behaviour over other behaviours due to what they expect the result of that selected behavior will be. The study will help to establish the level of reciprocal relationship among Expectancy, Valence and instrumentality during classroom instruction and how such affect achievement. This in no doubt will help to uphold the expectancy theory.

Practically,  the findings  of this study will be of great benefits to secondary school principals,  mathematics  teachers,  students,  parents,  community,  ministry  of  education, curriculum planners, and future researchers when published and implemented.

The Finding with the help of the mathematics teachers will assist principals to identify the strengths and weaknesses of the students especially in the course content.  With this in mind  students  attitude  towards  mathematics  will  change  positively  as  their  minds  are channeled  to  actualize  their  dreams  especially  those  of  them  in  sciences.  When  CG  is

effectively done by the mathematics teachers, this will help to boosts students’ academic self- efficacy.

The findings will also equip mathematics teachers with alternative and more effective approach to grading of students in secondary schools. Furthermore, it creates room for good teacher-student relationship in such a way that will prevent students from having mathematics phobia,  when CG is effectively done this in turn helps to boost  students’ academic  self- efficacy. As self-efficacy is boosted, this will in turn help students to achieve their academic excellence.

The findings will help students to have good rapport with their math teacher  knowing that the math teacher does not hate or intimidate any student in the class; rather wants to help them realized their math potentials as they further their academic pursuit. On that note, with CG, students will work harder academically since they have to compete with other students in the class, which in the long run will boost academic  self-efficacy.  And this will facilitate students  to  engage  in  meaningful  academic  activities  instead  of  causing  trouble  in  the community. This will in turn help to improve students’ math performance in the secondary school certificate examination, and other external examinations.

Findings of this study will help parents to be aware of their responsibilities as regards to their children’s academic   performance. Realizing that they are not to force their children to engage in any course or subject they do not have the capability, with comparative grading students will know the important of believing in themselves;  consequently,  academic self- efficacy will be enhanced.

To   the   Ministry of Education (MOE), the research if   efficiently   completed  and published will help to identify areas that need enhancement in the teaching and learning   of mathematics in secondary schools, especially in the number of periods it will be taught in a

day and the time frame.  Again, it will help MOE in decision making as well as in organizing seminars and workshops for math teachers in order to improve their competencies in concepts that  are  difficult,  as the  math  teachers  are  loaded  with  facts  after  the    Workshops  and Seminars (WSs) this will have positive impact on the students, definitely, this will help to increase math academic self-efficacy of students, especially those with high academic self- efficacy to have the confidence that they are capable of achieving their dreams.

With the report from the Ministry of Education, curriculum planners will be able to determine areas that need to be reviewed and recommend new strategies as well as textbooks that  math teachers  should  be used  in order  to  make  teaching  of math  interesting  to  the students. When this is done there is the tendency that students perception about math will increase  thereby  making  students  realize  that  when  once    a  student  masters    any math concept, it becomes part of life to that student, hence  math academic self-efficacy will be boosted.

To the future researchers, the findings of this study will provide them with information for future researches on area of comparative grading. And data from this study will serve as empirical basis for research work.

Scope of the study

The  study  aimed  specifically  to  find  out  the  effect  of  comparative  grading   in mathematics on students’ academic self-efficacy beliefs and achievement. Senior Secondary One (SS1) students in Aba Education zone will be used for the study. The content scope of the study is mathematics. Specifically,  researcher will cover the  following topics: Number system, algebra, fractions among others. The researcher’s choice of number system for the study  is  motivated  by the  fact  that  the  area  has  always  been  identified  as  one  of  the candidates’ area of weaknesses in the Junior WAEC examination in Nigeria, (WAEC Chief

Examiner’s  report  2008-2012).  The  chief  examiner  maintains  that  students  show  poor knowledge   of  algebra,  number  system,   fractions  especially  when  it  involves   halves. Similarly, interview conducted with students showed that students find the topic very difficult because of the fact that letters that are used to represent numbers confuse them.

Research Questions:

The following research questions will guide the study:

1. What are the achievement mean scores of students exposed to comparative grading in mathematics and those exposed to criterion referenced grading?

2. What are the academic self-efficacy belief mean scores of students exposed to comparative grading in mathematics and those exposed to criterion referenced grading?

3. What are the achievement mean scores of male and female students in mathematics?

4. What is the academic self-efficacy of mean scores of male and female students in mathematics?

Hypotheses:

The following hypotheses will guide the study and will be tested   at 0.05  level of significance.

Ho1:    There is no significant difference between the achievements mean scores of students exposed to comparative grading in mathematics  and those exposed to  criterion referenced grading.

Ho2:     There is no significant difference between the academic self-efficacy mean scores of students  exposed  to  comparative  grading  in mathematics  and  those  exposed  to  criterion referenced grading.

Ho3: There is no significant difference between the achievement mean scores of male  and female students in mathematics.

Ho4:  There is no significant difference between the academic self-efficacy belief mean scores of male and female students in mathematics.

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