CHAPTER ONETHE PROBLEM1.
1 IntroductionMathematics is one of the core subjects that areoffered in all pre-tertiary institutions in Nigeria. “It is the science ofstructure, order and relation that has evolved from elementary practices ofcounting, measuring and describing the shapes of objects, it deals with logicalreasoning and quantitative calculation and its development has involved andincrease the degree of idealization and obstruction of its subject matter”(Encyclopedia Britannica, 2013). Kolawole, Oladosu and Ajetunmobi (2013) opinedthat mathematics is an instrument that is used to facilitate the learning ofother formal school subjects, and also very important tool for resolving problemsituations in all disciplines. It is with the realization of the importance ofMathematics education that compelled the Federal Government of Nigeria made Mathematicscompulsory subject at both primary and secondly levels of the Nigerianeducational system (Mathew and Kenneth, 2013).
This compulsory nature of Mathematicscarries with it assumption that the knowledge of the subject is essential forall members of the society. However, this enables most citizens to acquire thebasic Mathematics knowledge and skills for effective contribution to communityand national development. Okereke (2006) opined that Mathematics competence isa critical determinant of the post-secondary education and career optionsavailable to young students.The Nigerian Secondary School Mathematics Curriculumis developed and structured around six main concepts, namely; Algebra; Numberand Numeration; Geometry; Mensuration; Statistics and Probability; and Trigonometry.Trigonometry has long been a standardcomponent of the secondary school curriculum in Nigeria, usually in the latterhalf of the secondary years. Table 1.1 shows the Mathematics Curriculum in Nigeria.Table 1.
1 Distributions of the Curricula ofMathematics at Post-Primary in Nigeria.Course JSI JSII JSIII SSI SSII SSIII Algebra Geometry Mensuration Number and Numeration Statistics and Probability TrigonometrySource: NERDC Abuja (2013) Secondary School Mathematics CurriculumTrigonometry is an important branch of school Mathematicsthat has everyday application in the life of the child, especially inestimation, construction, technology and astronomical relationships (Sidhu, 2006).Trigonometry is the aspect of Mathematics involving the measurement ofdistances, angles, lines and surfaces. The knowledge of trigonometry assiststhe students to appreciate the shapes and situation around their environmentand helps to develop their inductive reasoning skills that become necessaryingredient for learning Mathematics, unlike geometry, trigonometry constitutesa substantial part of the senior secondary school Mathematics, which form agreat part in their assessment (Abakpa, 2011). Despitethe importance attached to trigonometry to our-day-today activities and asagents of nation’s development and wealth creation, student’s attitude andperformance towards trigonometry has not been encouraging. Many factors havebeen identified by Ahmad (2014) as reasons for the poor performance of studentsin trigonometry; such factors include government policies, curriculum planners,examination bodies, teachers’ attitudes, students’ attitudes, home, and lack ofqualified mathematics teachers that will handle the abstract curriculum thatdoes not address to immediate use of trigonometry in everyday life. Apart fromthese, other factors have also been identified, such as poor primary schoolbackground in Mathematics, lack of interest on the part of the students, students’attitude towards trigonometry, lack of incentives for the teachers, lack ofqualified teachers in primary schools, students’ perception that trigonometryis difficult, large class size syndrome, psychological fears of the subject andpoor method of teaching.
Massive and consistent failures of students inmathematics have remained a major threat to its learning. Nworgu (2013)reported that the Federal Government described the poor performance of studentsin mathematics as unacceptable and warns that the trend has to be checked if thecountry has to move forward. Table 1.2 illustrates the performance of studentsin WAEC, 2007-2016 Table 1.2 Performancesof Students in Mathematics in WAEC 2007- 2016 YEAR Total No.
of students Who Sat No. of Students that Obtained Credit & Above (A1 – C6) % of Students with Credit & Above (A1 -C6) No. of Students with (D7-F9) % of Students with (D7- F9) 2007 1,275,330 198,441 15.56 1,076,889 84.44 2008 1,369,142 314,903 23.00 1,054,239 77.
00 2009 1,373,009 425,633 31.00 947,376 69.00 2010 1,351,557 453,447 33.55 898,110 66.45 2011 1,540,250 587,630 38.93 952,620 61.07 2012 1,675,224 819,390 49.
00 852,834 51.00 2013 1,543,683 555,726 36.00 987,957 64.00 2014 1,692,435 529,732 31.30 1,162,703 68.70 2015 1,593,442 544,638 34.
18 1,048,804 65.82 2016 1,544,234 597,310 38.68 946,924 61.32 Source: (WAEC, 2016)It could be observed from Table 1.2 that thestudents’ performance for the period is less than 50% throughout the years withthe exception of 2013 and 2016 in which the performance slightly raised to64.26 and 52.97 respectively. Bearing in mind the importance attached totrigonometry the continued low performance would lead to ripple effects whichundermine the future development of the country.
Generally trigonometry isconsidered by many as uninteresting, boring and difficult. However, the performanceof students depends largely on the quality of teacher’s competence and the use of a widevariety of techniques to change the students’ attitude. In order to complementother instructional strategies which are being used in the teaching andlearning of mathematics, to this end the researcher is of the opinion that ifMathematical-Games and Analogical Instructions are incorporated to complementthe conventional method of teaching Mathematics could help in developmentpositive attitude and improved the academic performance of students.
In every culture children play games as part oflearning to show up in the culture or as a pass-time or leisure. The idea ofusing games to engage students in the process of active learning, over the pastseveral years is well pronounced, Educators have been increasinglyincorporating various games into their teaching curriculum in an effort tocreate a fun and engaging learning environment for students. Games have beenused to teach Science and Mathematics in Nigeria (Azuka, 2005). Datun(2005) viewsMathematical games as activities in the form of puzzles, magic tricks,fallacies, paradoxes or any type of Mathematics which provides amusement orcuriosity. Mathematical games can facilitate the mathematical environment asthey reduce boredom, tension and establish a friendly atmosphere, which allowsfor the growth of interest, skills, attitude and knowledge. Ainsworth and Habgood (2009), opined that whenstudents are engaged in mathematical activities they can succeed where it countin applying their skills and reasoning ability to solve real-life problemsrequiring, mathematical solutions.
One way to arouse students’ interest inlearning mathematics is the integration of mathematical game. Mathematicalgames bring joy to the learners and teachers, helps to break resistance ornegative attitude to learning by reducing tension, it also flushes boredom andproviding an environment for learners to develop interest and acquire skillsand competence in mathematics. Games enhance learners to think mathematically, imbibethe culture of cooperation, competition organization and spirit of individualism(Okigbo and Okeke, 2011). Games do not only help in reducing tension andboredom in class, but also provide an environment where the students candevelop their individual and collective skill and acquire more knowledge. Gamesand mathematics are related because each has rules which involve experience,drill and practical application to real life situation. Analogy is a process ofidentifying similarities between two concepts. The familiar concepts are calledthe analog and the unfamiliar concepts are called the target (Glynn in Nworgu,2009).
According Ruhl (2003) analogy is a comparison of something unfamiliarwith something familiar in order to explain shared principles. The studentscould use this process for comparison between newly introduced concepts(unfamiliar) with the previous concept (familiar) for better understanding.Analogy is when some less familiar domains or abstract concept are made moreunderstandable to the learners are by making references to similar relationsobject or situation with which the learners are familiar. Moreover, Sani (2006)opined that analogy is one the teaching strategies within the constructivistframe that has evidently proved effective in preventing and overcoming poorperformance and wrong perception of the students towards trigonometry.Furthermore, Sani (2006)reported three benefits of the use of analogies as a teaching strategies forabstract concepts, these are:i. itprovides visualization of abstract concepts.ii. Ithelps compare the similarities of the students’ real world with the newconcepts.
iii. it hasa motivational function.Attitudes are psychological orientations developedas a result of one’s experiences which influences a person’s view ofsituations, objects, and people and how to respond to them either positively ornegatively or favourably or unfavourably (Mensah et al, 2013). Attitude is anorganization of beliefs, feelings and behavioral tendencies.
In education, attitude has beenidentified as one of the important elements which determine students’ success(Cetingöz and Özkal, 2009). Attitudes affect the students’ interaction withtheir friends, families, school and lessons. Therefore, positive students’attitude towards trigonometry will add to their academic performance.Academic performance refers to how wella student is accomplishing his or her task and studies (Scortts 2012). Smith, (2010)defined Academic performance as a display of knowledge attained or skillsdeveloped in schools subject designated by test and examination scores or marksassigned by subject’s teachers, therefore, academic performance is the outcomeof education: the extent to which the student, teacher or institution haveachieved their educational goals. In the context of this study, academicperformance refers to observable or measurable behavior of a student in a particularsituation usually an experiment. Kathryn (2010) opined that academicperformance encompasses the students’ ability and performance in all academic disciplinesin a class as well as extracurricular activities. From the on-going,teaching strategies and attitude of students may have effects on the academicperformance of students; therefore, the study intends to find out the “effects of Mathematical-games and Analogical instructionon attitudes and performance in trigonometry among Secondary School Students inZaria, Kaduna State”.
1.2 Statement of the ProblemDespite the relative importance of Mathematics inscience and technology, students’ performance in the subject in both internaland external (WAEC) examination has remained consistently poor (Adolphus, 2011).Mathematics educators are trying to identify the major problems associated withthe teaching and learning of mathematics in the nations’ schools. Many factorswere identified which includes inadequate facilities instructional material, studentsattitudes, poor infrastructure, manpower deficits in schools and the overpopulation of students are among causes of poor performance of students in WAECexamination (Alausa, 2013).It is also observed that, students factor is adirect cause for their success or failure in Mathematics, no matter howprofessional the teachers is, no matter the amount of instructional materialsprovided without the students to exhibits the right attitude and learn with astrong determination for success all other efforts become unproductive, thus, theperformance of students in a subject is determined by the students attitude.The negative attitude of students towards Mathematics and particularly theconcepts of trigonometry tend to create fear and anxiety among students whocontinue to perform dismally as they lack the interest, curiosity and patienceneeded for learning. The report of WAEC (2015) Chief Examiner,Mathematics educators and researchers revealed that most students includingthose who passed Mathematics at credit level and those who failed, haphazardlyattempted geometry and trigonometry questions or avoided them completely.
Instructionalstrategies employed by the teachers’ play an important role in the acquisition of instructional content formeaningful learning. Nigerian secondary schools classrooms are predominantlydominated by lecture method of instruction, which does not encourage students’ active participation and interaction. Studies inmany areas of education have shown that the method of teaching utilized by theteacher is an important factor in students learning and subsequent performancein examination (Obeka, 2014). Inview of the above, the researcher intends to use Mathematical-games and Analogicalinstructions in teaching some selected concepts in trigonometry in order toinvestigate their effects on student’s performance.
In other words, could theuse of Mathematical-games and analogical instruction help to enhance student’s attitudeand performance towards trigonometry?1.3 Objectives of the StudyThe major purpose of thisresearch work is to find out the effects of mathematical-games and analogicalinstructions on attitudes and performance in trigonometry among secondaryschool students in Zaria. Specifically, the objectives of this Study are tofind out:1. the effectsof mathematical-games and analogical instructions on student performance when taught trigonometry.2. the Changein attitude of students’ towards trigonometry when taught using mathematical-games and analogical instructionstrategies. 3.
the effects of mathematical games and analogyinstructions on the performance of male and female students intrigonometry.4. the changeof attitude on students’ gender taught trigonometry with mathematical games and analogy instruction strategies.
1.4 Research QuestionsBased on the stated objectives, the followingresearch questions are formulated for answering:-1. What is the differencein the mean performance scores between students taught trigonometry using mathematical-games, analogicalinstruction and those taught using lecture method?2. To what extentdoes the attitude of students taught trigonometry using mathematical-game, analogical instruction differfrom those taught using lecture method differ?3. How does themean performance scores of male and female students differ when taughttrigonometry mathematical-game and analogical instruction?4. What are thedifferences in attitude change between male and female students taughttrigonometry using mathematical-games and analogy instruction?1.5 HypothesesFrom the research questions four null hypotheseswere formulated and will be tested at P?0.
05 level of significance.H01: there is no significantdifference in the mean performance scores of students taughttrigonometry using mathematical-game, analogical instruction and lecturemethod.H02: there is no significanceattitude change between students taught trigonometry using mathematical-game,analogical instruction and lecture method.H03: there is no significantdifference in the mean performance scores of male and female studentstaught trigonometry using mathematical-game and analogical instruction.H04: there is no significantdifference between the attitude of male and female studentstaught trigonometry using mathematical-games and analogical instruction1.6 Significance of the StudyThe significance of this study lies in itspotentiality of addressing key issues in the teaching and learning ofmathematics as a compulsory discipline as well as being its prerequisites forfurther education. It is expected that the findings of this study willhopefully be useful and uplift the standard of mathematics education.
Specifically, the significance was discussed under the applications and implicationsof the research for students, teachers, curriculum planners, the government andother researchers in the following ways:Students will hopefully developa positive attitude towards mathematics and enable them to know thatmathematics is fun and learners friendly. Thus, have better scores andperformance in mathematics. This study will also be of importance to teachersof mathematics who will find mathematical-game and analogical instructionresult oriented and applicable in their teaching of trigonometry andmathematics in general and thus enable them to employ mathematical-game andanalogical instruction as a guide for developing a wide range of classroomactivities which are capable of making teaching and learning of mathematicsmore meaningful. It is also hoped that the study willhelp the curriculum experts/planners in plans to improve in the standardizationof educational programmes and hopefully extend the frontiers of knowledge andstimulate further researches on teaching and learning of mathematics in Nigeria.Furthermore, it is alsohoped that science and research based organizations like Science TeachersAssociation of Nigeria (STAN), Mathematical Association of Nigeria (MAN),National Educational Research Development Council (NERDC) etc. will find thisstudy useful and will see the need emphasize the use of mathematical-game and analogical instruction inmathematics teaching in secondary schools in Nigeria. The study is significant to extent itis hoped that it will help to improve students attitude and performance in mathematics.The potentiality of mathematical-game and analogical instruction will hopefullymake it easier for teachers to expose pupils to certain mathematical conceptsthat are real and meaningful with much emphasis.
It is also hoped thatthe study will be of benefit to society in that the study will help to improvestudent’s attitude and performance in mathematics. Thereby, the subject and itsallied courses (Engineering, Medicine, and Physics, etc.) will be studied bymany students in institutions of higher learning. This will raise our nation’s potential in the use of Science and Technologyfor capacity building and sustainable growth.
In increase, researchers canutilize the findings of the study as a basis for their inquiry. The researcherbelieves that the findings of the study will make a modest contribution to theexisting body of knowledge and also be useful for further research in mathematicseducation.1.
7 Basic AssumptionFor the purpose of thisresearch, the following assumptions are made, thus:1. The selectedtopics are appropriate for the level of the students used for the research.2. Themathematics teachers are familiar with the use mathematical-games and analogicalinstruction in teaching trigonometry.3. The Studentshave some foundation of trigonometry concept from their previousclass which is needed for the present study.4.
Learning by doingcould enhance and motivate students to improve on their performancein mathematics. 1.8 Scope/Delimitation of the StudyThe research is aimed atinvestigating the effect of two teaching strategies, mathematical game and analogicalinstruction on the academic performance among senior secondary school studentsin the Zaria educational zone. The research is delimited to SSII students of someselected senior secondary schools in Zaria educational zone because SS II arefamiliar with trigonometry concept and more stable class, SS I are just intothe senior secondary and are not familiar with the trigonometry concepts neededfor this study and the SSS III are preparing for their senior secondarycertificate examination (SSCE). The study will cover all aspects of trigonometryand Mathematics SSII for senior secondary schools. The trigonometry topicsselected for the conduct of this study are:1.
Pythagorastheorem 2. Trigonometricratio of special angles3. Angles ofelevation and depression4. Sine and Cosine rule 5. Bearing anddistances These topics were chosenbecause they form part of the SS II syllabus and basic foundation for learningtrigonometry.
Also the WAEC (2015) chief examiners report identified thesetopics as difficult and students’ lack of understanding of the concepts intheir workings.The study will use twoinstruments, which will be developed by the researcher for data collection.Theseare:1.
TrigonometryPerformance Test (TPT) which is made up of 40 structured multiple choicequestions on trigonometry.Trigonometry AttitudeQuestionnaire (TAQ) is a 20- item questionnaire that will be adapted from Limand Chapman (2013) the TAQ will beadministered to both the experimental groups and the control group before andafter the treatment to determine change in attitude of the students towardstrigonometry and mathematics in general .the TAQ will be scored based on Likertfive (5) point scale: strongly agreed (SA), agree (A), undecided (UD) disagree(DA) and strongly disagree (SD).Period of the treatment will last for six weeks