As previously discussed, the education of gifted and talented students depends on the provision made by a school and within a classroom. However, there are additional support factors that should be considered. Three of these are presented in the following section: teachers, resources, and parents.
2.7.1 Teachers of the Gifted
It is an accepted understanding that teachers have a ‘significant’ influence on students. However extensive, reputable research on what makes an effective teacher of the gifted is limited. Clark and Zimmerman (2002) state that: “Most of what has been written about teachers for gifted students is ‘armchair speculation’ rather than the result of research” (p. 164). Teachers in Mingus and Grassl’s (1999) study acknowledged that working with gifted students was not an easy task. Gifted students often posed questions that they felt were beyond the parameters of the majority of the class and finding suitable material required considerable time and effort. Teachers are advised to plan and provide for suitable challenging work. This, McClure (2001) contested, is most difficult for teachers “who are not very confident in their own mathematical ability” (p. 43). An effective mathematics teacher is expected to have sound mathematics content (subject matter) and pedagogical content knowledge
(Ball, Lubienski, & Mewborn, 2001; Ma, 1999). McClure (2001) suggested that the most important issue was for teachers to understand what ‘greater depth’ means in the mathematical context as well as the appropriate vocabulary to use. Gifted students appreciated teachers who were “honest about their own mathematical abilities and were willing to learn alongside the students and demonstrate what it means to learn/explore mathematics” (Mingus & Grassl, 1999, p. 290).
In New Zealand, “many teachers have the willingness to cater for the needs of these students, but lack the knowledge and skills to be able to do so successfully” (Moltzen, 1998/99, p. 62). A key aspect in developing teacher knowledge in gifted education is professional development, although VanTassel-Baska (1986) writes that not all good teachers work effectively in gifted programmes, specifically accelerated programmes. On the other hand, teachers who may have the knowledge and skills to individualize programmes effectively to meet the needs of gifted students may be limited by school policy (Feldhusen et al., 2002). The Education Review Office (2008) found that many New Zealand schools “did not take a planned approach to building capability through professional development in gifted and talented education” (p. 12). This was seen as a “huge challenge” and schools also faced the ongoing issue of teachers with expertise leaving a school (p. 13).
The success of the Model Mathematics Program (MMP) (Miller & Mills, 1995) was attributed to the presence of highly motivated, knowledgeable teachers who were flexible in their thinking and instructional practices. Horn (2004) followed up on the ‘teacher expectation effect’ and through case studies found that high expectations, strong classroom practice, and intensive collaboration among mathematics teachers played a key role in supporting students’ long term successes. Teachers in Plunkett and Harvey’s (1999) Australian study acknowledged the need for professional development in the area of catering for gifted and talented students. Hansen and Feldhusen (1994) found, not surprisingly, that teachers with specialized training were more effective working with gifted and talented students than teachers without such training. This was supported by Plunkett and Harvey’s (1995) research when they found a considerable difference in the confidence of teachers who had some training in the area. The teachers (n=465) in Reis and Renzulli’s (1992) study on curriculum compacting confirmed the need for additional professional development—more
assistance for enrichment from gifted education specialists, and more training and assistance in locating and using appropriate enrichment materials. Subsequent research (Reis & Westberg, 1994) addressing this need, showed that staff development had a positive effect on teachers’ abilities to modify curriculum for gifted and talented students.
The National Association for Gifted Children in the United States published a position statement about the competencies needed by teachers of gifted and talented students in 1994. They stated that gifted children deserved to learn from highly qualified teachers who were aware of and could respond to the unique qualities and characteristics of gifted children. The specific roles, responsibilities, and competencies of key personnel working with gifted students were comprehensively addressed by Leppien and Westberg (2006) and built on reputable research in gifted education. Their extensive tables of competencies for teaching the gifted do not focus specifically on the learning domains of mathematics. The teacher of mathematically gifted students has not been examined in the New Zealand setting and is thus another area that is to be contributed to by this study.
2.7.2 Resources
Resources are a source of knowledge for students and teachers. They may be people resources or non-human such as print material, web sites, and computer games. Selecting resources suitable for gifted and talented learners can be a daunting process. Exemplary resources “foster student engagement when they are varied and closely linked to students’ reading levels, cognitive strengths, and interests” (Sak & Maker, 2006, p. 138). Unfortunately, there is limited research on the effectiveness of resources to enhance student learning and in particular the impact on gifted learners in mathematics.
Gifted and talented students in the upper primary and secondary school invariably work from textbooks in their mathematics schooling. These textbooks are usually written to reflect current syllabi. Mathematics textbooks commonly present mathematics in a particular sequence, suggest the content that teachers should teach, and include “excessive repetition of material [that] leads to shallow treatment of
(Reys, Reys, & Chávez, 2004, p. 62). The curriculum statement ‘Mathematics in the New Zealand Curriculum’ (Ministry of Education, 1992) stated that “teachers must realise that there are many dangers in adhering too closely to any particular textbook” (p. 13) and therefore supported no designated textbook. Accusations have been made that contemporary textbooks in the United States have been “dumbed down”, reflecting a decreasing level of difficulty (Reis & Renzulli, 1992, p. 52). Amit and Fried (2002) suggested that textbooks are “probably the most immediate determinant of practice” (p. 374) in mathematics. They also acknowledged the theoretical and practical problems associated with textbooks. Dowling (2001) raised questions regarding the basis upon which students’ learning was differentiated by the use of school mathematics textbooks and questioned whose ‘meaning’ students are intended to ‘get’ from such textbooks. Reis and Renzulli (1992) reported many of the brightest students were ‘rewarded’ by simply being given more pages of examples to complete as practice. Resources for gifted students, claimed Roberts and Roberts (2005), should help develop the process skills of knowledge, comprehension, application, analysis, synthesis, and evaluation as defined by Bloom’s Taxonomy (Bloom, 1956). They should also go further than this, according to Coleman (2001) who added another level to Bloom’s Taxonomy. She called this highest level, transformational application: “the use of knowledge to create new knowledge in an applied form─the ability to bring all of Bloom’s levels together to solve a problem, think a thought, design a product, or create a work” (p. 25).
Web sites are a rich resource, but one that has been found to be underused in gifted education classrooms (Siegle, 2005). However, there is little research regarding the appropriate use of web sites in programmes for the gifted. Although the Instructional Technology (IT) field has developed strategies for the use of web sites in class programmes, they are not specific to gifted education. Teachers who use IT strategies and tools incorporate computers, internet, software, multimedia, and web sites in their programmes. These strategies and tools can support stimulating learning environments and therefore, according to Besnoy (2006), should be included in gifted education programmes. This supports Tomlinson’s (1999) argument for the differentiated curriculum as previously described.
…gifted students must be exposed to authentic situations in which they are expected to synthesize multiple sources of information. By designing learning environments that utilize quality Web sites, teachers of the gifted provide their students with the opportunity to learn how to research information, compare it to prior knowledge, and create new ideas. Learning these practical, real-world skills empowers gifted students and increases their ability to maximise their potential.
(Besnoy, 2006, p. 30) As with all resources, teachers should evaluate them for quality, content, accuracy, and suitability. Not all educational web sites are adequate for the classroom as reported by Mioduser, Nachmias, Lahav, and Oren (2000) in a study of 436 educational web sites focusing on mathematics, science, and technology learning. The use of resources such as textbooks and web sites is an under-researched area; this use has not been specifically explored in relation to mathematically gifted students.
2.7.3 Parental Involvement
The literature on parental involvement in children’s and adolescents’ education supports the assertion that parental involvement benefits children’s learning (Eccles & Harold, 1993; Epstein, & Dauber, 1991; Fehrmann, Keith, & Reimers, 2001; Hoover-Dempsey, Bassler, & Brissie, 1992). Parents, as children’s first teachers, see the interests and advanced abilities displayed by their gifted children from early years and assume roles in their children’s education. According to Matthews and Foster (2005), parents can optimize learning experiences for gifted learners in a variety of ways. They “not only espouse the value of certain activities, fields or achievements, but they model attitudes and behaviours that foster achievement, direct the interests and activities of their child to these areas, model participation and achievement within the talent areas, and monitor and structure their children’s time and participation” (Kulieke & Olszewski-Kubilius, 1989, p. 42). From an early age, most parents have recognized their child’s mathematical talents and sought out additional support materials for their children (Lupkowski-Shoplik & Assouline, 1994).
Epstein and Dauber (1991) found that when teachers made parental involvement part of teaching practice, parents increased their interactions at home and felt more
positive about their abilities to help children. This study, using data from 171 teachers, reported that different parental involvement practices occurred across the curriculum areas. For example, reading and English used more homework practices than mathematics. Less information and guidance also occurred as students progressed beyond elementary school. The empowerment process in relation to the parent and the school was recognized as meaningful involvement of parents, teachers, and school administrators leading to improved student achievement (Cochran & Dean, 1991). This process was usually limited to traditional activities such as parent-teacher meetings, monitoring of homework, and reinforcement of school policies (for example, discipline). The authors advocated a redefining of the empowerment process as an “intentional and ongoing process centered in the local community, involving mutual respect, critical reflection, caring, and group participation, through which people lacking an equal share of valued resources gain greater access to and control over those resources” (p. 267). Instead of ‘one-way’ communication from school to home there should be a respectful partnership with both parties making a contribution. Schools also need to be aware that parents with a high efficacy7 are more likely to have increased levels of involvement (Hoover- Dempsey et al., 1992).
Parental involvement decreases as students move from primary to secondary school. The decrease in parent involvement may result from a decrease in parents’ feelings of efficacy as their children grow older (Eccles & Harold, 1993). As the schoolwork becomes more advanced and technical they feel less knowledgeable in some subject areas. Parents of high-achieving children may be more likely to participate in school governance and school activities than parents of lower-achieving children (Eccles & Harold, 1993). An ecological approach, reported by Comer and Haynes (1991), encouraged parent involvement at all levels of school life, through general support of schools’ educational programmes, active participation in daily activities, and in school planning and management. They found that parents provided useful perspectives on matters that served the best interests of children.
7 Defined as a set of beliefs that one is capable of achieving desired outcomes through one’s efforts
Using an extensive data base, Fehrmann, et al. (2001) examined the direct effect of perceived parental involvement on grades. Their study showed that parental involvement had an important direct effect on grades and additionally parental involvement led to increased time spent on homework. In a smaller study, conducted by Mingus and Grassl (1999), using data from seven cases, parents were viewed as the primary influence in the lives of the mathematically gifted students. Despite the students having more advanced mathematical abilities than their parents, the parents played a crucial role in providing the supportive framework—they encouraged them to work hard, provided stability, and encouragement.
Moon’s (1995) multiple-case study involved the families of 10 gifted and talented students who were participating in a withdrawal enrichment programme. The cases were selected as extreme cases across a continuum of most positive to most negative about their experiences in the programme, and there was one unique case (learning disabled but accelerated student). Parents indicated that their children were more likely to talk about the enrichment programme activities than any other school work. The programme sparked many of the conversations and is perceived to have enhanced family cohesion in positive ways. Participation in the programme reinforced parents’ perceptions that their children were gifted and talented, rather than changing those perceptions. One of the most important functions of the programme was to provide a link between home and school; the parents felt more connected to the school when their child was involved in the programme. Additional research focusing on exemplary programmes has also shown the need for increased support for talent development through sustained interactions with family and community (Briggs, Reis, Eckert, & Braun; 2006; Moon, 2003).
There are reported cases where parents have been dissatisfied with their children’s education and have advocated for alternative provisions. In a few Australian case studies reported by Vialle, Ashton, Carlon, and Rankin (2001), some of the parents had taken on an advocacy role in order for their children to be recognized as gifted and placed in an accelerated programme. These parents had considerable knowledge about appropriate educational options. Parents of children participating in research and programmes in various American universities for mathematically talented students have expressed frustrations of having children who do not fit into the system
(Lupkowski-Shoplik & Assouline, 1994). Parents often have to go through layers of official channels and wait months at the start of the school year before their children are appropriately recognized and challenged. Some have to repeat this in subsequent years and others seek outside help. Assouline and Lupkowski-Shoplik (2003) commented that parents are their children’s primary advocate and “in advocating for their children, parents are not “pushing” their children” (p. 19). They are merely responding to their child’s interests and abilities. “Parents are the #1 advocates for their children and therefore assume a prominent role in the home setting for rules, expectations for success, and quality of work” (Callard-Szulgit, 2003, p. 73). It is also suggested by Matthews and Foster (2005) that parents, in advocating for one child, may make a bigger difference than they realize. Parents may also advocate for increased professional development opportunities for teachers that will enable better recognition of, and provision for, gifted and talented students. Home-school partnership in gifted education has been recognized in New Zealand with the recent release by the Ministry of Education of Nurturing Gifted and Talented Children: A Parent-Teacher Partnership (Bevan-Brown & Taylor, 2008). This addresses questions commonly asked by families and provides information about identifying giftedness.
Homework
There appears to be variability in the research related to homework, with differing definitions and understandings as to what comprises homework, and what constitutes parental involvement and support. Many studies focused on homework at the higher levels of schooling, whereas Hoover-Dempsey, Bassler, and Burow (1995) focused specifically on the elementary years. They argued that parents have an important part to play in the early years in forming attitudes towards homework, patterns of strategy, and accomplishment. From a representative sample, the researchers found that parents’ involvement in their children’s homework was based on their understanding of children’s characteristics and their own abilities. As a group, they saw themselves as having an active role in structuring homework activities, motivating children, and working with them in relation to the tasks set, and interacting with the teacher about the homework.
Theoretical Frameworks
Parental involvement is by no means a unitary construct, but refers to substantially different types of involvement by parents. Most models for parental involvement were based on the assumption that student outcomes are influenced by parental involvement which, in turn, is influenced by factors such as socioeconomic variables or attitudes. These models, however, do not allow answers to the following question: In what way do parents become involved in their child’s education? Hoover- Dempsey and Sandler’s (1995) model provided a theoretical basis for examining parental involvement in children’s education. The focus is on variables most salient to the parent involvement process and therefore is potentially subject to specific intervention. In this model, the authors believe that parents become involved in their children’s education for three major reasons: “(1) their personal construction of the parental role; (2) their personal sense of efficacy for helping children succeed in school; and (3) their reaction to the opportunities and demand characteristics presented by both their children and their children’s schools” (p. 313). As a consequence of this role construction, parents select levels and forms of involvement in educationally-related activities both consciously or otherwise, in both the home and school setting. If they choose to become involved, that level of involvement is based on a variety of factors such as the parent’s specific skills and knowledge, total demands (which include family and work), and demands for involvement from children and school.
The role that parents play in terms of their children’s interest and development in mathematics learning is provided in Hoover-Dempsey and Sandler’s (1995) model. The essential elements of the model (in order from the bottom layer) are: (1) the parental involvement decision; (2) the parents’ choice of involvement forms; (3) the mechanisms through which parent involvement influences child/student outcomes; (4) tempering/medicating variables; and (5) child/student outcomes. The model (Figure 2.3) provides a theoretical framework for examining variables that are deemed to be of importance in parents’ decisions to become involved in their children’s education and the forms that involvement takes. The model suggests “specific points of entry into (or predictions about) the process of parental involvement and child outcomes for both research and practice” (p. 329).
Child/Student Outcomes
Skills and Knowledge Personal Sense of Efficacy for Doing Well in School Tempering/Mediating Variables Parents’ Use of Developmentally Appropriate Involvement Strategies
Fit between Parents’ Involvement Actions & School Expectations
Mechanisms through Which Parent Involvement Influences Child/Student Outcomes
Modeling Reinforcement Instruction
Closed- Ended
Open- Ended
Parents’ Choice of Involvement Forms
Influenced by: Specific Domains of Parents’ Skills & Knowledge
Mix of Demands on Total Time & Energy from:
Specific Invitations and Demands for Involvement from: Other Family Demands Employment Demands Children School/ Teacher(s)
Parent Involvement Decision
(The Parent’s Positive Decision to Become Involved) Influenced by:
Parent’s Construction of the Parental Role
Parent’s Sense for Helping Children Succeed in School
General Opportunities and Demands for Parental Involvement Presented by: Influenced by: Direct Experiences