Abstract
The paper covers a proposal for the study of identification and provision for mathematically gifted and talented students. The proposed study seeks to critically appraise available literature on aspects identification and provision of gifted and talented pupils in mathematics. Moreover, the study intends to appraise and evaluate existing theories on the study topic and determine their applicability in the current times.
Nonetheless, the study seeks to apply secondary research techniques in data and information collection for the research. Secondary research is preferred over primary research methods since the core of the study is to appraise already available literature and existing theories on the topic to determine their reliability to the area of study.
Scope of the Research
This research study covers a critical appraisal of identification and provision for mathematically gifted and talented students who are aged between five to thirteen years as they are believed to be in their school going period at a primary level. To achieve this, the study will narrow its scrutiny on the primary school going students of the United Kingdom as they would serve as the case study in the research.
The study will try to unlock the mystery through exploring already existing literature by making a critical appraisal of what have been initially established on the topic. In addition, theories that relates to identification and provision for mathematically gifted and talented pupils will be appraised and their applicability evaluated on the subject.
Moreover, the study will try to provide a comprehensive review of strategies used to enhance the process of identification and provision for the mathematically gifted pupils.
Literature Review
According to Jensen (1994), gifts and talents include the exceptionally high level performance in a limited field or in a range of endeavors as well as those potential for excellence that are not recognizable.
In relation to this, gifts are assumed to be more straightforward way of measuring aspects of intelligent development such as high level of achievement and intelligent quotient (IQ). Consequently talents are taken to be the highest level of performance in measurable aspects like sport, art which are usually discovered by experts in these fields.
However, some academicians believe that giftedness are a homogenous group that can at times be misidentified which may results to undergoing inadequate or wrong curriculum provision that leads to misplaced or wrong grades (Koshy & Jean, 2011). Nonetheless, gifts and talents are diverse as level of abilities and giftedness is usually different from one individual to another.
Therefore ‘psychonometric tests’ which measure level or degree of intelligence quotient are the best and the simplest taxonomy means of measuring level of giftedness. Intelligent quotient tests are capable of profiling strengths and weaknesses of students therefore able to establish discrepancies that may exist between the sequential and the mental age (Heller, et al., 2000).
However, in relation to giftedness in mathematics, there are several ways that can be used to determine ones giftedness. According to Adams and Wallace (1991), one of the criteria used to establish giftedness in mathematics is the use of ‘off-level testing’ where students are given opportunities to demonstrate their high level abilities in several tests.
Thereafter, these students can then be categorized according to their levels in order to enable them reach their potential in a full gear in an area where they have strength.
Nevertheless, Adey (1999) holds that giftedness in mathematics requires students to undergo pre-testing of new modules of work to judge whether they already know.
Adey adds that they should tackle more challenging and complex activities and the content of their learning materials should contain contents with higher abstraction level. This provides a difference between those who are gifted and the rest since gifted group will show a higher degree of oddity by attaining a higher mark under these peculiar circumstances.
All the same, it is exceptionally understood that high intelligence is the best criteria of determining whether children are gifted. On the other hand, Adimin (2001) holds that giftedness can be developed and nurtured since everyday intelligence can always be improved through practice as the more frequently one does something the better he or she becomes better at it.
Therefore, it is evident that intelligence quotient can be developed and increased through learning and training in any subject or field. In addition, this helps one to attain the highest level of performance in an area which one may be interpreted to have some level of giftedness (Benbow & Lubinski, 1996).
In relation to this, Barnett and Juhasz (2001) provide a case study of Japanese children whose intelligence is believed to be steadily growing due to their longer stay in schools than those of any other country since they continue working hard when they are there.
Therefore, to these Japanese, the notion of giftedness in children is imaginary since they believe that all children have same potential but the difference comes in according to the degree of efforts made by an individual.
Then, it becomes evident that level of intelligence quotient is depended on higher self esteem and it increases where there is a balanced, steady and responsive relationship that are positive rather than encounters that are disconnected (Marchaim, 2001).
Moreover, it is alluded by Blakemore (1999) that all students including mathematically gifted and talented require the opportunity to achieve their optimum potential. However, it is usually a collaborative responsibility of instructors and educators to give instructions and guidance to these kinds of students.
Even so, Chan, (2000) believes that pupils who are talented and gifted in mathematics normally exhibit an extraordinary high capacity of understanding mathematical concepts. Therefore, they should be identified early enough through numerous assessment methods in order to nurture them further so that they can attain their full potential in mathematics as a subject.
Nonetheless, parents, teachers and students themselves are the biggest participants in identification of their talents and gifts in mathematics.
For instance, Coleman (1995) believes that instructors or teachers must analyze, assess and evaluate students overall educational development in conjunction with their mathematics potential, aspirations and achievements in order to determine whether the student is gifted in mathematics as a subject or not.
On the other hand, parents must provide enabling environment to their children who should then be able to explore their talents and gifts (Elder, 2002).
Moreover, students on their own should be able to analyze their potential, passion and ability in relation to mathematical concepts and ideas to determine for themselves whether they have an urge in mathematics which is one way of determining whether one is gifted and talented in the subject.
Characteristics of Mathematically Giftedness and Talents among Students
Students who posses attribute of mathematically giftedness and talents are characterized by several traits which make them distinct from those with no elements of mathematical gifts and talents.
According to Fai (2000), a student who has the ability to formalize mathematical materials and be in a position to isolate it from other content together with being capable of abstracting from concrete numerical forms is said to be gifted and talented in mathematics. Nonetheless, these attributes must be extremely excellent to provide the difference between an average, above average and the gifted and talented student (Marland, 1972).
Furthermore, according to Fox and Zimmerman (1985), students capability to generalize mathematics materials and be in a position to establish what is of chief important and by doing so abstracting from the irrelevant is enough way of demonstrating that one is gifted and talented in mathematics.
A student who does not posses some attributes of mathematical giftedness and talents will not be in a capacity to abstract relevant mathematical materials (Leroux, 2000).
In addition, Freeman (1997) alludes that a student who is mathematically gifted and talented will have a flexible mind where by he or she is able to switch or navigate from one mental operation to another in a sequential or iterative manner. This is a major distinguishing factor since good mathematicians are creative thinkers since mathematics demands creative minds.
Moreover, it is believed that a gifted and talented student in mathematics is likely to have the ability of shortening reasoning process and be able to think in more curtailed structures (Gilheany, 2001).
In relation to this, a student can be identified as gifted and talented in mathematics from evaluation and tests that relate to mental work which requires quick reasoning capacity since such test require one to operate in a curtailed environment.
Provision for Mathematically Gifted and Talented Students
According to Guenther (1995), the purpose of identification process of gifted and talented students is to establish whether students require special educational provision, whether an additional or alternative to regular instruction is needed and to diagnose their special needs.
Nonetheless, these processes must be inclusive and flexible to achieve the desired outcomes. Consequently, the main purpose of provision process for giftedness and talented students in mathematics is to enrich and accelerate their potential so that they may reach their highest possible capacity (Landau, Weissler, & Golod, 2001).
In relation to giftedness and talented mathematics students, it is necessary to have some aspects of provision for mathematically promising students (Hansen, 1992). Therefore, there are several ways that these students can be enriched.
In relation to this, House of Commons (1997) holds that education which comprise learning of mathematics should be a good experience for enriching students as it acts as the starting point in talent development. Under normal circumstances, education provides an appropriated avenue for development of gifts and talents in mathematics since it acts as a nurturing platform.
Besides, it is alluded by Kitano and DiJiosia (2002) that giftedness is normally a domain specific hence provision must take into account aptitudes and special abilities of these students.
This should be prioritized since it can not be taken literally that all gifted and talented children have a strong knowledge framework (Landau, 1990). Furthermore, provision of education in classroom necessitates adaption of developing these talents and gifts in mathematics hence nurturing them further.
Research Methodology
Introduction
Research methodology can be broadly divided into two categories of primary and secondary research methods. According to Belenky (1986), a primary research method is the approach that entails conducting trials, asking questions and later collating the results. In addition, primary research methodology is applied in two forms of qualitative and quantitative approach.
In respect to quantitative research approach, Cranton (1996) opines that the researcher may hold a hypothesis of which the research work seeks to approve or disapprove.
Nonetheless, the kind of data generated in quantitative research can be mathematically analyzed. On the other hand, Daloz (1999) states that qualitative research is usually concerned with feelings and opinions and therefore data collected can not be analyzed in mathematical terms.
Alternatively, secondary research methodology is usually founded on the basis of other people research findings (Alvesson & Deetz, 2000). Therefore it involves gathering of the previous research results of others from online sources such as materials available on the internet or from offline materials such as printed books and reports that can be easily accessed in the library.
In any research study, a researcher is at liberty to either choose to use primary, secondary sources of data collection or a combined use of these two methods during data collection exercise (Bryman, 2001).
However, according to Bell (1999), the choice of any of this method is dependent on the type and kind of the research or at some time, the circumstances at which the research is being conducted. In respect to this research, the researcher will only employ secondary sources in his data collection exercise.
Research Design
In collection of data for this investigation, the researcher will use secondary sources where by literature such as books, articles, journals, committee reports and any other available research that is related to the study topic will be evaluated (Maxfield & Babbie, 1995).
Being a sensitive matter to the education sector and to talent and potential development and growth, there are many related studies that have been undertaken which will be reviewed. In addition, other literatures also exist that relates to identification and provision of mathematically talented students. In relation to this, the researcher will therefore review already available pieces of literature in the research.
Nonetheless, Bryman and Bell (2003) hold that secondary research methods entails using secondary information which consists of several number of sources of data that have been previously collected by preceding researchers. However, the materials to be reviewed must be on the area related to the research topic that have been preserved and archived in a given format.
Some of the secondary sources that may be used in data and information collection in secondary research include the traditional books, journals, thesis and dissertations that are readily available in libraries, information materials that are syndicated, industry studies and government reports that are under control of specific government agencies (Bryman, 2001).
Nonetheless, it is relatively important to acknowledge that secondary sources of information facilitates inexpensive and a quick way of addressing research question than in primary research.
Nevertheless, secondary sources of data collection have been adopted for this research due to the nature of the research that is intended to be carried on the topic. It is understood that identification and provision for mathematically gifted and talented students is a global topic that interests the whole world to explore in order to develop its human resource capital that match its needs, gifts and talents.
These needs have had diverse influences and effects to most countries and therefore it is a world’s topical issue. It is therefore important for the researcher to just review the already available literature that relates to identification and provision for mathematically gifted and talented students rather than going fresh to the field and collecting fresh data from primary sources.
The following are some of the secondary sources that will be utilized in the research.
Secondary Sources
Authorities and Experts in the field of Gifts and Talents Development
According to Chisnall (2004), the best way of learning about a given topic is seeking the knowledge of someone who is well acquainted with the subject area of the topic. In relation to this, it will be relevant for the researcher to seek some information from professionals and academicians who have carried research work and who have practically been involved in the identification and provision for mathematically gifted and talented students.
This will provide theoretical and practical insights of the research topic and hence aid the researcher to derive conclusion and recommendations from an informed point of view (Cassell & Symon, 2004).
In addition, there exist some professional associations that are concerned with identification and provision for gifts and talents development that acts as authority in this field. The research will also seek to obtain information from these sources since they are involved in several instances of identification and provision for mathematically gifted and talented students.
Furthermore, according to Corbetta (2003), every organization usually has recorded data and records that form part of its normal operation. In respect to this, the research will also examine records of psychological and mathematical associations that are in place especially those ones that relates to identification and provision for mathematically gifted and talented students.
Government Publications
There exists several government organizations that have already collected data on the topics related to the subject under investigation. Some of these data are collected on regular basis or at times, they are collected when the need arise for example when a commission of inquiry is formed to investigate into a certain issue.
Therefore, all government publications that relate to identification and provision for mathematically gifted and talented students will be reviewed to provide insight of the study subject.
Earlier Research
Earlier research works exist that relate to the subject under investigation. Their findings and conclusions will also be considered in the investigation.
Commercial Information Services
Several organizations exist that are in business of collecting information and selling it (Denzin & Lincoln, 2003). This kind of information can be rarely found in libraries since they have a commercial value attached to them.
Therefore, the researcher will also conduct these organizations to establish whether they have relevant information that concerns the research topic in question. However, it is imperative to acknowledge that this information sources are always costly and expensive since they are owned by profit making organizations.
Advantages of Using Secondary Sources
By solely employing secondary sources in the investigation, the researcher will benefit from numerous advantages that are connected to their applications. First and foremost, secondary sources are generally available and ready made for use (Newman & Benz, 1998).
However, since information in these sources was generated without the present research in picture, the researcher will plan to tailor information from these sources to the current research.
Another huge benefit of using secondary sources in this research is that these sources are not limited by space and time (Maxfield & Babbie, 1995). For instance, the researcher will be at liberty to review these sources at his own convenient time and place.
The researcher will therefore be at autonomy of collecting data as per his own diary since he will not be pinned down to fit into schedules of other people as it is the case in primary sources where the researcher is obliged to fit into schedules of respondents (Jankowicz, 2005).
In addition, as postulated by Housden (2008), secondary methods of data collection is a much quick and inexpensive and therefore the researcher will be able to benefit from this advantage. In addition, in using this method, the researcher will be particularly interested in getting to understand causes of differences in the level of intellectual quotient that results to some individual being gifted and talented in mathematics than others.
Furthermore, according to May (2001), in using this method, the researcher will be able to narrow down on specific issues that were crucial in identification and provision for mathematically gifted and talented students. This will be achieved through proper formulation of questions that will be searched from online materials on the internet using suitable search engines and from other printed materials.
In addition, books that relates to the subject will be reviewed (Johnson & Duberley, 2000). These will provide enough insight knowledge necessary to enable the researcher to draw authentic conclusions and recommendations on identification and provision for mathematically gifted and talented students
Disadvantages Related to Use of Secondary Sources
Despite secondary sources having a number of benefits, the researcher also acknowledges their deficiency (Patton, 2002). For instance, the researcher understands that there may be a problem of personal bias of information presented in these sources since some of them may lack objectivity in their presentations. In addition, there is also a potential threat of these sources not being available to the researcher.
This is likely to be encountered to literature that is highly regarded as government secret. Such unavailability is likely to hinder data collection process where crucial information can be completely concealed from the researcher.
The researcher is likely to have a lot of difficulties in getting relevant information from the internet. For example, most of the hits to be gotten from the searches may at times be too general or even at times quite irrelevant from the desired information.
Therefore, the researcher will be forced to consume a lot of time in sieving these materials gotten to determine those which are relevant from irrelevant ones (Miller & Brewer, 2003).
Moreover, some of the concepts from these sources may be too complex for the researcher to conceptualize and understand. Therefore, the researcher may consume a lot of time for the researcher since he may devote a lot of time in conceptualizing these concepts provided which may affect the research process especially working behind the stipulated timeframe of the research (Stewart & Michael, 1993).
Evaluation of Secondary Sources
Nonetheless, before using any secondary sources in the research, the researcher will have to evaluate and establish authenticity of the materials. According to Green (2002), not all information that can be obtained from secondary sources is valid and reliable.
It is therefore imperative that information from these materials must be carefully weighted in respect to credibility for their contributions to be considered in the current research. Therefore, the research will consider the following factors in evaluating these materials:
Study Purpose of the Material
Every secondary material has a central purpose on which its study was developed. Usually, the purpose of a given piece of secondary material significantly determines the findings of the study. On the other hand, it is postulated by Hicks (2005) that data collected to further some interests of a given group is not authentic enough to constitute sources of information for the research work.
Nevertheless, level of precision and data collection methods often provides the purpose of the study (Gerrish & Anne, 2006).
In addition, therefore, the researcher will be committed to determine whether the study carried out in the secondary material was done to only confirm a predetermined conclusion or whether the conclusion was based on the information collected. This will provide a good avenue to sieve relevant and authentic secondary sources from those which are not.
The Period Information was collected
Period of time when the information was collected should be put into consideration when evaluating secondary sources. For instance, there might be different factors present in the environment during the time when the research was conducted which are less related or different from the current times.
Therefore, using such sources is likely to provide irrelevant findings that may mislead conclusions and recommendations drawn from the current research topic. According to Bernard (2006), the passage of time changes parameters used to measure a given phenomenon.
Furthermore, information that was collected after a long period of time may in turn be obsolete in the current set up since its relevance might have been eroded with several changes that might have taken place over the time. Patton (2002) affirms this as he postulates that technological trends that are ever changing may change how people perceive things as life style also changes with the trend in technology.
Therefore, the researcher will be keen on the secondary sources of information since he understands that big time lag between current research times and when the source study was carried out may result to unreliable outcome.
Consistency of Information sources with others
Moreover, as Newman and Benz (1998) advice, the researcher will evaluate secondary sources by first assessing consistency in the information presented in them. For instance, in circumstances where two or more sources may present conflicting ideas on the same concept, the researcher will be tasked with the responsibility to determine among the source the most credible one.
This will be done to ensure that information materials used are consistent and that the resultant conclusions of the current research maintains consistency with others since the current research topic does not exist in a vacuum (Weinhardt, Stean & Jochen, 2008).
Areas where to find Secondary Research Materials
When conducting research using secondary research sources, it is at the discretion of the researcher to determine where he or she will find these secondary information materials for research. Nonetheless, according to Maxfield and Babbie (1995), there are several places at the disposal of the researcher where he or she may access these materials.
However, availability of these materials in these places is normally determined by the research topic. For instance, if the research topic is related to health, places to look for the secondary source materials will also be health related.
In relation to identification and provision for mathematically gifted and talented students, the researcher will be in a position to look for secondary research materials from educational institutions such as schools, colleges and universities.
These is so since these institutions are the ones responsible for nurturing these gifts and talents and they may be having guidelines and literature related to identification and provision for these aspects in mathematics.
In addition, the researcher will also explore resources from libraries which include school, academic and public libraries by scanning for any related books, journals, thesis and dissertations that may be in custody of these information centers.
Educational institutions such as universities are believed to be centers of research and therefore there are possibilities that several research studies that are closely related to the current topic under were carried out by other researchers. The researcher will therefore want to explore this pool of knowledge in order to come up with appropriate conclusion and recommendations for the subject.
Moreover, resource center are usually owned by professional organization such as those relating to psychology and mathematics. Therefore, the researcher will collaborate with these professional organization and other bodies that have resource centers that may contain material related to the topic of research.
Nonetheless, the researcher will closely collaborate with these institutions that are capable of providing secondary materials for research to facilitate smooth collection of information and data about the research subject. This will be done by using a variety of approaches which include seeking official permissions from authorities of these institutions
. In addition, the researcher will employ good interpersonal skills with all categories of people that he may interact with during the research process. For instance, the researcher will strive to have cordial relationship with librarians so that they can be willing to facilitate access of information materials.
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