In the present chapter, inside informations of the different phases involved in transporting out the instance survey will be given, including the design of the instance survey, the sample used and the data-collection methods applied in order to light the above research inquiries. Besides, ethical considerations were besides taken attention of in the current survey.
3.2 The Case Study
A instance survey, harmonizing to Robert Yin ( 2003 ) , can be described as a “ narrative about something unique, particular, or interesting ” . This something can either be an person, an administration, a procedure, a plan, a vicinity, an establishment or even, an event.
3.2.1 Elementss of the Case Study
The elements of a instance survey are non fixed as each instance survey is different from each other. Hence, depending on the chosen narrative, the elements will change as the information to be collected and the intent of the instance survey are non the same. However, instance surveies usually describe a plan or intercession put in topographic point to turn to a peculiar job. Neale et Al. ( 2006, p.7 ) provided the undermentioned elements for a instance survey:
Identify the job
Explain why the job is of import
How was the job identified?
Was the procedure for placing the job effectual?
Stairss taken to turn to the job
Challenges and how they were met
3.2.2 Showing a Case Study
Case surveies are said to be flexible as they can be presented in a figure of ways. In fact, there is no definite format to follow. Still, justification and methodological analysis of the survey should be provided every bit good as any back uping information, that is, transcripts of instruments and ushers used in the survey merely like for all rating consequences. A instance survey can be a stand-alone study or can be included in a larger rating study. Neale et Al. ( 2006, pp.10-11 ) suggested the undermentioned outline study whenever a instance survey is presented as a stand-alone study:
How was the procedure carried out? ( Describe the procedure of choosing the instance and informations aggregation beginnings, every bit good as how information was collected. )
What premises are at that place ( if any ) ?
Are there any restrictions with this method?
What instruments were used to roll up informations?
What sample is being used?
The stairss taken to turn to the job
The challenges and how they were met
3.3 Sample Description
The research worker conducted the survey in his topographic point work which is a private fee-paying secondary school. Since the chapter ‘Logarithm ‘ is taught at Form IV degree, the research worker conducted his survey with the Form IV pupils, including male childs every bit good as misss, in order to accommodate his intent of the survey. The sample consisted of 16 male childs and 8 misss of assorted abilities, that is, they are low- , regular- or high-achieving pupils, coming from different societal background. The age group of the sample is between 15 and 16 old ages old. In fact, this peculiar group of pupils was chosen as it would assist the research worker to provide for the diverse needs in acquisition and sharpen the focal point on single strengths and any short-comings in the cognitive sphere. It is deserving indicating out that, antecedently in Form III, the mathematics categories were streamed, that is, the best pupils were in Group I and the low-achievers were in Group II, and non all pupils in the sample were once in Group I.
3.4 Premises of the Study
The research worker assumed the following while transporting out this instance survey:
The sample was representative and equal, that is, the sample had more or less the same features as that of the whole population.
The instance survey did non hold any negative impact on the pupils.
Instrumentality refers to the procedure of roll uping informations at an appropriate clip for the intent of set abouting a survey. Data consists of facts and findings obtained by the research worker from the persons under survey. Data is usually collected by the aid of different tools known as instruments. Some normally used instruments are questionnaires, interviews and standardised trials among others. In this survey, the research worker has made usage of the undermentioned instruments:
The research worker has opted for a triangulation method, that is, the usage of more than one information aggregation method. Triangulation is when “ the strengths of one method offset the failings of the other, so that together, they provide a more comprehensive set of informations. To the extent that the consequences from each method converge and indicate the same consequence, there is triangulation and therefore greater credibleness in the findings ” ( McMillan and Schumacher, 2006, p.6 ) .
Observation is frequently considered to be the best technique in finding the usability demand of those being studied. The research worker has opted to be a participant perceiver since he is transporting out the survey with his pupils. Ethical considerations were taken in to account before get downing the observation. The research worker explained his pupils about the survey being undertaken, its purpose and aims, and in conclusion asked for their blessing to transport out the observation procedure. The research worker afterwards noted down all the jobs faced by the pupils and necessary remedial was applied.
3.5.2 Standardized Trial
The research worker chose to give the standardized trial in the signifier of an aptitude trial whereby the ends were, primo, to mensurate the ability of the participants to work out jobs straight related to the Torahs of logarithm and secondo, to mensurate the ability of the participants to use their cognition of Torahs of logarithm in different state of affairss. This information aggregation tool was chosen for the undermentioned grounds:
The fact that it is standardized renders it to supply the same stimulation, that is, the same jobs are given to all the participants in the sample.
It possesses a strong psychometric belongings. In other words, standardised trials provide high measuring cogency.
Analysis of informations is easy due to the quantitative nature of the informations obtained.
The trial can be administered to a group. Hence, it helps save clip.
The cost of bring forthing standardized trial is low compared to other informations aggregation tools such as questionnaires.
22.214.171.124 Method of Administering the Standardized Trial
Since the research worker was in fact the Additional Mathematics instructor of the male childs mark sample, the standardized trial was administered during the category period. In fact, after being granted permission by the Rector of the school to transport out the research, this standardised was given as an appraisal for the 3rd term of the school calendar. Hence, for the good behavior of the research, this ensures that the pupils would give their best when taking the trial. At the same clip, this guarantees the research worker to hold dependable and valid informations. For the misss mark sample, the standardized trial was administered with the aid of one of the research worker ‘s co-worker in the misss ‘ section.
126.96.36.199 Ethical Issues
Throughout the class of the survey, great attention was taken non to miss regard to any of those involved, be it the school, the direction of the school, the mark sample or anyone who were straight or indirectly related to the research work. First, permission was sought to the Performance Monitoring Office ( PMO ) – who are responsible for supervising the public presentation of pupils at the school – and to the Deputy Rector by the research worker to transport out the standardized trial as an appraisal for the 3rd term. Hence, the research worker was able to maintain the books for the intent of his survey.
Furthermore, before transporting out the trial, pupils were made aware of the purposes, aims and intent of this research. It was made clear to them that the informations received would be kept purely confidential and would be used entirely for the intent of the survey. The pupils were besides informed about the fact that take parting in the survey is merely voluntary.
As for administrating the standardized trial to the misss mark sample, the research worker respected the school ‘s doctrine of segregation of sexes and so, agreement was done with a female co-worker from the Mathematics section to set about the trial with the misss.
188.8.131.52 Justification of Questions in the Standardized Trial
Each inquiry in the standardized trial has been carefully and purposefully been chosen based on the research being undertaken, that is, they will assist the research worker to reply the research inquiries. The tabular array below gives the beginning of each inquiry and the ground for taking the peculiar inquiry:
Beginning of Question
Reason for Choosing Question
Cambridge O-level Additional Mathematics ( June 2009 Paper 2 No. 7 )
To prove for the cognitive of pupils ability in remembering and using the Torahs of logarithm for simple use. Furthermore, the Cambridge O-level study ( 2009 ) states that “ Answers to this inquiry ranged from those with complete truth to those with addled thoughts on uniting logarithms. ”
To prove for the cognitive of pupils ability in remembering and using the Torahs of logarithm for measuring logarithm without the usage of reckoners.
Cambridge O-level Additional Mathematics ( November 2008 Paper 2 No. 5 ( two ) )
To prove for the problem-solving ability of pupils to work out equations affecting logarithm to establish. As for the Cambridge O-level study ( 2008 ) , it states that “ Many campaigners made no effort to reply portion ( two ) , but some who did made small advancement, authorship, and others did non utilize. ”
Cambridge O-level Additional Mathematics ( November 2010 Paper 13 No. 5 )
To prove for the computational accomplishment of pupils in explicating two additive equations from two logarithmic equations with two terra incognitas. Furthermore, the logical logical thinking ability of pupils was besides required in using the conditions for a logarithm to be. The Cambridge O-level study ( 2010 ) states that: “ Some campaigners were rather comfy with logarithms but many would profit from more pattern on this topicaˆ¦.very few realised that a = 1, B = -1 was non a possible solution. ”
Cambridge O-level Additional Mathematics ( November 2011 Paper 12 No. 3 )
To prove for the interpreting ability of pupils between words and mathematics so as formulate an appropriate quadratic equation in three footings. Besides, the Cambridge O-level study ( 2011 ) states that “ Most campaigners were able to obtain the correct consequence which, as stated in the 2nd portion of the inquiry, was meant to assist campaigners. In malice of obtaining a right consequence for portion ( I ) , few campaigners were able to utilize the given permutation right and were therefore unable to obtain the intended three term quadratic equation. ”
Cambridge O-level Additional Mathematics ( November 2010 Paper 23 No. 12 ( I ) , ( two ) OR )
To prove the ability of pupils to stand for informations spatially and thereof formulate an appropriate equation affecting two variables. With respects to the Cambridge O-level studies, it states that “ ( I ) Points were normally plotted with some grade of truth. Some graphs were spoilt by one hapless point taking to a line of best tantrum which caused truth jobs subsequently. ( two ) The truth depended greatly on the quality of the graph with campaigners frequently avoiding reading mistakes by utilizing tabulated values. The better campaigner frequently jumped in one measure from an equation associating to to a right equation affecting and. Some campaigners stopped after the first measure and demand to reflect on the diction which implies an reply of the signifier was required. A important figure falsely wrote an reply in this signifier which should hold been the signifier. ”
Frey and Oishi ( 1995, p.1 ) define an interview as “ a purposeful conversation in which one individual asks prepared inquiries ( interviewer ) and another replies them ( respondent ) ” . The research worker opted to utilize a one-on-one interview manner which was semi-structured. In other words, a set of five inquiries was prepared beforehand but at the same clip further self-generated inquiries were asked based on the respondent ‘s reply in order to obtain clearer reply or to inquire for farther amplification of the reply. The set of inquiries were:
What was your first feeling about logarithm?
What instruction manners were used by the instructor in explicating the different parts of logarithm?
What larning techniques did you utilize?
What difficulties did you brush and what troubles do you still confront?
What proposals would you propose to do the instruction and acquisition of logarithm to be easier?
184.108.40.206 Reasons for Choosing Interview
The research worker opted for interview for the undermentioned grounds:
Interviews are said to be flexible, that is, “ if a respondent has misunderstood a inquiry, the interviewer can clear up, thereby obtaining relevant responses ” ( Babbie, 1992 ) .
The research worker while carry oning his interviews in private ensures that the respondents will give indifferent replies as there is no audience with their equals.
The response rate for interviews is high relation to other informations aggregation tools such as questionnaire.
After carry oning the first interview, necessary alterations can be made to the interview agenda.
220.127.116.11 Justification of Questions in the Interview
Merely like for the standardized trial, inquiries were besides meticulously chosen for the demands of the survey. The undermentioned grounds were behind the pick of the inquiries:
As it is a well-known fact, the first feeling is frequently durable and can merely be changed by appropriate behaviors. So, the research worker was trusting to associate this first feeling with the larning experience of the respondent sing the subject logarithm.
Research has shown that different instruction manners deployed by the pedagogue affect different pupils in different ways ( Wetzel et al. , 1982, p.34 ) . Hence, the research worker is trusting to happen a relationship between the instructor manner used and the jobs encountered by the pupils in the acquisition of logarithm.
Each pupil has a different ability in relation to tilting. However, a pupil may, wittingly or unwittingly, make usage of different larning schemes even though some would reason that one peculiar acquisition manner would be ruling. By and large talking, Wetzel et Al. ( 1982, p.33 ) argues that pupils can be classified as a “ dependent scholar, an independent scholar, or a collaborative scholar ” .
This inquiry will partially assist the research worker to accomplish his aim of look intoing the troubles pupils have. The first portion of the inquiry tries to happen out the initial jobs pupils were confronting and how did they rectify to the jobs and the 2nd portion ought to happen out the jobs that pupils are still confronting after the completion of the chapter.
The research worker is seeking to look for the originative and inventive thoughts of the pupils in heightening the instruction and larning experience in relation to logarithm.
18.104.22.168 Reliability and Validity in the Interview
For the quest for cogency and dependability in his collected informations, the research worker has preferred to transport out his interview one-on-one with the respondents and the same inquiries was asked to each as under the influence of their equals, the respondents may give biased information.
3.6 Statistical Analysis
For the intent of analyzing the collected informations, assorted statistical tools, such as descriptive statistical tools, were used to expose the consequences and thereof, decisions were made.