Aiken, L.R. (1973) Ability and creativity in mathematics. Review of Educational Research, 43 (3), 405-432.

Considers how cognitive and affective variables combine to produce mathematical creativity and offers suggestions for teachers on developing creativity in maths.

 

Bartkovich, K.G. & George, W.C. (1980) Teaching the Gifted and Talented in the Mathematics Classroom. Washington: National Education Association. (510.71/B288T)

This short booklet covers identification, approaches, teaching strategies, evaluation, textbook selection and 'other accelerative options'.

 

Benbow, C.P. (1992) Academic achievement in mathematics and science of students between ages 13 and 23: Are there differences among students in the top one percent on mathematical ability? Journal of Educational Psychology, 84 (1), 51-61.

"Among students in the top 1% of ability, those with SAT-M scores in the top quarter, in comparison with those in the bottom quarter, achieved at much higher levels through high school, college, and graduate school. Of the 37 variables studied, 34 showed significant differences favoring the high SAT-M group, which were substantial. ... The predictive validity of the SAT-M for high-ability 7th and 8th graders was supported." (p.51)

 

Brown, I.C. (1992) The mathematical equivalent of the penalty shoot-out. Gifted Education International, 8 (2), 104-106.

"A description is given of a local mathematics competition that has been running for ten years among London's state schools. This article identifies some of the issues involved in setting questions which encourage children to take part and discusses types of questions which may be used to separate candidates who are almost equal. Examples of tie-breakers are given." (p.104)

 

Campbell, J.R. (1988) Secrets of award winning programs for the gifted in mathematics. Gifted Child Quarterly, 32 (4), 362-365.

"The key ingredients included the following: dynamic research-oriented math teachers, development of problem-centered courses that used no text or tests, active administrative support, active recruiting, and contact with nearby universities." (p.362)

 

Clarke, D. & McDonough, A. (1989) The problems of the problem solving classroom. The Australian Mathematics Teacher, 45 (3), 20-24.

"A problem solving environment consists of a wide variety of different problem solving situations. It might include short challenging tasks, puzzles, open-ended questions in familiar contexts, the application of practised skills to novel situations, or extended group investigations lasting days or weeks." (p. 21) Includes many examples of different kinds of problem.

 

Cramer, R.H. (1989) Attitudes of gifted boys and girls towards math: A qualitative study. Roeper Review, 11 (3), 128-131.

Found that 'Harmful stereotypical thinking regarding females and mathematics is much in evidence even as early as fourth grade.' (p. 128)

 

Cramer, J. & Oshima, T.C. (1992) Do gifted females attribute their math performance differently than other students? Journal for the Education of the Gifted, 16 (1), 18-35.

Compared the causal attributions of gifted and nongifted female and male students in grades 3, 6, and 9. "Gifted females evidenced self-defeating causal attributions for math performance relative to gifted males in the ninth grade only for six of the eight dependent variables. For the nongifted subjects, significant sex differences were not as pronounced as those for the gifted subjects. It was concluded that there was a need for developing appropriate intervention strategies for gifted females to remediate self-defeating causal attributions for math performance in the junior high school years.

 

de Vries, M.E. (1992) Thinking beyond the obvious boundaries in mathematics: An exploration of joyous discovery. Gifted Education International, 8 (3), 163-179.

"This article presents a collection of ideas for the development of creative explorations in mathematics. The writer provides numerous themes for curriculum extension and also provides sources for further reading. The major message is that of cooperative discovery-learning with the emphasis on enriched provision for all children providing them with opportunities to display their individual talents and insights in Mathematics." (p.163)

 

Dickens, M.N. & Cornell, D.G. (1993) Parent influences on the mathematics self-concept of high ability adolescent girls. Journal for the Education of the Gifted, 17 (1), 53-73.

"For both mothers and fathers, parent mathematics self-concept was related to parent expectations regardless of the degree of identification between parent and daughter. Parent expectations in turn linked to daughter mathematics self-concept. There was little evidence that degree of parent-daughter identification influenced the relations among parent mathematics self-concept, parent expectations, and adolescent mathematics self-concept." (p.53)

 

Gagen, T. (1987) Thoughts on mathematical education and some enrichment classes in North Sydney. The Australian Mathematics Teacher, 43 (4), 21-23.

"I want us to adopt a more humane, more uncomfortable attitude to our mathematics today. This would mean a less doctrinaire approach to the subject and to the dissemination of knowledge about it to the young. I would like a little less dogmatism, less pontification, less elegance, less finality about our mathematics of this level." (p.22) Discusses the different approach used at a weekly enrichment session after school for talented high school students in the North Sydney region.

 

Gallagher, S. et al. (1991) A community of scholars dedicated to exploration and discovery: The Illinois Mathematics and Science Academy. The Gifted Child Today, 14 (6), 16-21.

Outlines the development of the National Consortium for Specialized Secondary Schools of Mathematics, Science, and Technology (NCSSSMST) and how one consortium school, the Illinois Mathematics and Science Academy, "has set its course to systematically design our mission and our beliefs about scholarship, achievement, leadership, and interdisciplinary learning." (p.21)

 

Grandgenett, N. (1991) Roles of computer technology in the mathematics education of the gifted. The Gifted Child Today, 14 (1), 18-23.

Discusses computer technology as a tutor (Computer Assisted Instruction, Multimedia, Intelligent Computer Assisted Instruction), as a tool (numeric processing, symbolic processing, computer aided design packages) and as tutee (Logo, Hypercard, robotics).

 

Grumseit, D.H. & Hill, H.J. (1974) Enrichment Topics in Mathematics. Kareela: Sapphire Books. (510.76/G891E)

Has chapters on Topology, Picos and googolplexes, Handspans, cubits and footsteps, Sets, Numbers - past, present and future, Patterns, History and mystery, and Puzzles.

 

Hall, N. (1997) Teaching primary school students talented in mathematics. The Australasian Journal of Gifted Education, 6 (1), 21-26.

"The investigation reported here involved the teaching of children talented in mathematics through group work where the content was non-routine mathematics problems. The research focussed on student learning, examined the kinds of strategies that students developed and investigated the effectiveness of group learning. The results of this investigation demonstrated the ability of talented students to solve non-routine mathematical problems, the way in which talented students rise to a challenge, the ways in which problem solving in groups provided talented students with opportunities for talking, thinking and writing mathematically." (p.21)

 

Hébert, T.P. & Furner, J.M. (1997) Helping high ability students overcome math anxiety through bibliotherapy. Journal for Secondary Gifted Education, 8 (4), 164-178. [See under Counselling]

 

Hersberger, J. & Wheatley, G. (1980) A proposed model for a gifted elementary school mathematics program. Gifted Child Quarterly, 24 (1), 37-40.

"The gifted mathematics program presented here represents a necessary alternative to vertical acceleration and the traditional curriculum." (p.40)

 

 Hoeflinger, M. (1998) Developing mathematically promising students. Roeper Review, 20 (4), 244-247.

'This article describes the general characteristics of mathematically gifted students and how classroom teachers can identify, instruct, and assess students in question through observation, conversation, classroom activities, and individual testing, using true mathematical problems geared for the specific student. Cross curriculum indicators of talent are discussed as well as classroom structure and its role in differentiating instruction for mathematically talented students.' (p.244)

 

House, P.A. (Ed.) (1991) Providing Opportunities for the Mathematically Gifted, K-12. Reston: National Council of Teachers of Mathematics. (371.953/P969)

Includes sections on 'The psychology of mathematical giftedness', 'Mathematical content for the gifted', 'Sixteen essential components of programs for the gifted', 'Elementary school programs', 'Middle, junior, and senior high school programs', 'In-school alternatives for elementary pupils', 'Advanced curricula for secondary schools' and short policy statements on vertical acceleration and on provision for mathematically talented and gifted students.

 

Junge, M.E. & Dretzke, B.J. (1995) Mathematical self-efficacy gender differences in gifted/talented adolescents. Gifted Child Quarterly, 39 (1), 22-28. [See under Gender]

 

Kaiser, B. (1988) Explorations with tessellating polygons. Arithmetic Teacher, 36 (4), 19-24.

"This unit not only includes a review of two-dimensional shapes but also allows students to focus on relationships among the shapes. ... Many opportunities also arise for extension activities to enrich students' learning either as individuals, groups, or a class." (p.19)

 

Kajander, A. (1990) Measuring mathematical aptitude in exploratory computer environments. Roeper Review, 12 (4), 254-256.

"The ability to think in the abstract seems to be one of the most important characteristics of the mathematical gifted. To be truly gifted in mathematics, however, creative ability is also required. In a recent study of gifted tenth graders, mathematical creativity appears to be a special kind of creativity not necessarily related to divergent thinking ability." (p. 254)

 

Kolitch, E.R. & Brody, L.E. (1992) Mathematics acceleration of highly talented students: An evaluation. Gifted Child Quarterly, 36 (2), 78-86.

"This study strongly supports the position that highly talented students can do well in mathematics courses taken several years earlier than is typical. With few exceptions, these students performed extremely well in all of the courses, including college courses, they took in high school ...." (p.84)

 

Kulm, G. (1984) Team spirit: A computer math course for parents and gifted children. Teaching Exceptional Children, 16 (3), 168-171.

Describes "a college credit course for gifted junior high and high school students and their parents." (p.168)

 

Lamon, W.E. (Ed.) (1984) Focus on Learning Problems in Mathematics, 6 (3), 1-116.

A special issue on talent in maths, including articles on ''Education of mathematically gifted and talented children', 'Teaching the mathematically gifted in a regular classroom', 'Enrichment and acceleration in mathematics', 'Differentiating instruction in mathematics for talented and gifted youngsters', 'The mathematics learning problems of the gifted and/or talented in mathematics', 'Instructional strategy for the severely gifted' and 'Classroom activities for mathematically gifted elementary school students'.

 

Le Maistre, C. & Kanevsky, L. (1997) Factors influencing the realization of exceptional mathematical ability in girls: An analysis of the research. High Ability Studies, 8 (1), 31-46.

"It appears that a combination of strategies is needed: early identification of general and specific gifts; peer support groups; non-sexist classroom processes; counseling support; provision of female role models; and mentorship. Parents' expectations for their daughters must also be broadened to include school subjects and careers that have been considered male domains." (p.31)

 

Lerner, B.-T. & Crawford, C.G. (1984) Great expectations - challenging the interests of the gifted and talented junior high student. The Mathematics Teacher, 77 (1), 21-26.

Describes "courses taught by the Naval Academy's faculty to reach and inspire local gifted and talented junior high school students" (p.21), including group theory, transfinite numbers, and Eulerian circuits.

 

Lowrie, T. (1995) Visual and spatial problem-solving tasks to extend talented mathematicians within the regular classroom. Australasian Journal of Gifted Education, 4 (1), 12-15.

"Many activities designed to stimulate children who display potential in mathematics are often repetitive, with analytical content that challenges children for only a limited time. ... This paper argues that a more balanced curriculum, that places increasing importance on spatial and visual development, will allow most talented children to remain motivated and stimulated within the usual classroom setting." (p.12)

 

Lupkowski, A.E., Assouline, S.G. & Stanley, J.C. (1990) Applying a mentor model for young mathematically talented students. The Gifted Child Today, 13 (2), 15-19.

Discusses the Diagnostic Testing Prescriptive Instruction model.

 

Lupkowski, A.E., Assouline, S .G. & Vestal, J. (1992) Mentors in math. Gifted Child Today, 15 (3), 26-31. [See under Mentoring]

 

Lupkowski-Shoplik, A.E. & Assouline, S.G. (1994) Evidence of extreme mathematical precocity: Case studies of talented youths. Roeper Review, 16 (3), 144-151.

"Case studies of elementary students who are extremely talented in mathematics illustrate a series of principles for educating gifted youths." (p.144) The 11 principles include 'Objective data from standardized testing are helpful in the planning process', 'Most parents of talented students we encounter are responding to their child's interests and abilities, not pushing their child' and 'Talented students need to find an intellectual peer group'.

 

Lupkowski-Shoplik, A.E. & Kuhnel, A. (1995) Mathematics enrichment for talented elementary students. Gifted Child Today, 18 (4), 28-31, 42.

Describes aspects of the C-MITES summer enrichment program for third to sixth graders, at Carnegie Mellon University in the USA.

 

Miller, R. (1993) Discovering mathematical talent. Gifted, 80, 9-11.

Covers 'What should parents and teachers know to help them better recognise mathematical talent?', 'How can standardised test results help in recognising mathematical talent?', 'What systematic process can be used to identify mathematically talented students?' and 'What instructional approaches benefit mathematically talented students?'

 

Mottershead, L. (1977) Metamorphosis: A Source Book of Mathematical Discovery. Sydney: Wiley. (510.76/M922M)

Covers magic squares, topology, pastimes, Pascal's triangle, Fibonacci numbers, polyominoes, tessellations, number relationships, maths in nature and maths in art.

 

Niemi, D. (1996) A fraction is not a piece of pie: Assessing exceptional performance and deep understanding in elementary school mathematics. Gifted Child Quarterly, 40 (2), 70-80.

"The purpose of this study was to investigate how exceptional performance representing deep understanding of mathematical concepts might be assessed in the classroom or in larger scale assessment contexts. The study focused on several types of assessment based on cognitive analysis of fractions: problem solving, justification, and explanation tasks." (p.70)

 

Pletan, M.D., Robinson, N.M., Berninger, V.W. & Abbott, R.D. (1995) Parents' observations of kindergartners who are advanced in mathematical reasoning. Journal for the Education of the Gifted, 19 (1), 30-44. [See under Definition/Identification]

 

Rekdal, C.K. (1984) Guiding the gifted female through being aware: The math connection. G/C/T, 35, 10-12. [See under Underachievement - Gender]

 

Sirr, P.M. (1984) A proposed system for differentiating elementary mathematics for exceptionally able students. Gifted Child Quarterly, 28 (1), 40-44.

"The system presented here represents a viable means for differentiating the core elementary mathematics curriculum and articulating the topics at different levels from K-6. It allows for vertical acceleration in computational skills, while encouraging use of manipulative materials and the development of problem-solving skills, often in enjoyable game settings." (p.44)

 

Sowell, E.J. (1993) Programs for mathematically gifted students: A review of empirical research. Gifted Child Quarterly, 37 (3), 124-132.

"Much research has shown that accelerating the mathematics curriculum provides a very good program for precocious students. Organizational plans that place mathematically gifted students together for mathematics instruction also offer opportunities for these students to perform well. Although technology-based instruction also appears to provide an efficacious way of producing instruction for mathematically gifted elementary students, this method should be examined further with older students and in long-term studies. Research with enriched curricula and non-computer-based instruction provided inconclusive evidence of efficacy for mathematically gifted students." (p.124)

 

Stanley, J.C. (1988) Some characteristics of SMPY's 700-800 on SAT-M before age 13 group": Youths who reason extremely well mathematically. Gifted Child Quarterly, 32 (1), 205-209.

"The sex ratio is 12 boys per 1 girl. The group tends to be quite able verbally, but much more so mathematically. Most of their parents are well educated. Some of these young students are vastly more accelerated in school grade placement than are the majority of the group. Other relevant characteristics are also discussed." (p.205)

 

Swetz, F.J. (1984) Seeking relevance? Try the history of mathematics. The Mathematics Teacher, 77 (1), 54-62, 47.

"We frequently find ourselves concentrating on the teaching of 'mathematics' - the symbols, the mechanics, the answer-resulting procedures - without really teaching what mathematics is 'all about' - where it comes from, how it was labored on, how ideas were perceived, refined, and developed into useful theories - in brief, its social and human relevance." (p.54)

 

Taylor, H. (1992) Exciting mathematics with infants (5-7 years). Gifted Education International, 8 (3), 155-162.

Provides numerous examples of activities, many illustrated, including a 'mind map' of 'mathematics from a story' (using Leo Lionni's 'Pezzettino' as an example).

 

Taylor, M. (1992) How to stop girls getting M.A.D. Australasian Journal of Gifted Education, 1 (1), 15-19.

Describes a program designed to prevent girls in a Year 4 class at an independent girls' school from getting 'maths avoidance disease'. "The overall theme for the year was 'Mathematics is Everywhere!' In order to develop the theme and to enable students to see that mathematics is indeed all around us, a 'real world' problem was provided each term for the girls to solve." (p.17)

 

Trowell, J.M. (Ed.) (1990) Projects to Enrich School Mathematics. Reston: National Council of Teachers of Mathematics. (CR372.7/P9645)

"Each topic is composed of activities to be completed, along with some explanation or examples to facilitate independent work." (p.v) For Grades 4-6.

 

Useem, E.L. (1992) Getting on the fast track in mathematics: School organizational influences on math track assignment. American Journal of Education, 100 (3), 325-353.

"Data collected from interviews with school administrators in 26 school districts show that substantial variations exist among districts in students' opportunities to be placed in this track. Differences in district parental education levels as well as in beliefs among school administrators about the importance of and eligibility for accelerated math (especially calculus) help explain these variations." (p.325)

 

Wadlington, E. & Burns, J.M. (1993) Math instructional practices within preschool/kindergarten gifted programs. Journal for the Education of the Gifted, 17 (1), 41-52.

"Information was collected for a study that examined specific math practices utilized by teachers in gifted preschool/kindergarten programs within the United States. Results indicated that most respondents used unstructured activities (e.g., discovery learning, learning centers) in small groups when providing math instruction. Although the teachers exposed ther gifted children to concepts generally introduced to older students; they most frequently taught concepts found in traditional early childhood programs. Children were infrequently exposed to concepts/materials pertaining to time and measurement even though research has indicated that young gifted children often possess advanced capabilities in these areas." (p.41)

 

Wavrik, J.J. (1980) Mathematics education for the gifted elementary school student. Gifted Child Quarterly, 24 (4), 169-173.

 

Weatherly, M.S. (1984) Why probability? G/C/T, 35, 6-9.

Argues that "an understanding of probability will result in extending mathematical horizons for gifted students" (p.7) and includes details of ten activities to introduce basic ideas of probability "in an experiental, informal, hands-on approach." (p.7)

 

Wheatley, G.H. (1983) A mathematics curriculum for the gifted and talented. Gifted Child Quarterly, 27 (2), 77-80.

 

Wieczerkowski, W. & Prado, T.M. (1993) Programs and strategies for nurturing talents/gifts in mathematics. In K.A. Heller, F.J. Monks & A.H. Passow (Eds) International Handbook of Research and Development of Giftedness and Talent. Oxford: Pergamon. pp.443-451. (371.95/H477i)

Discusses the 'structure of mathematical abilities', 'mathematical excellence as a developing state of mind', and 'programs in advanced mathematics for the gifted'.

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