Welcome to another online addition of the Arizona Promising Practices forum. For those new to this service, each issue, which will now be sent to you on a regular basis, will focus on: (1) Recommended National Educational Websites; (2) A Local or Arizona Website/Practice of Importance; and (3) One promising practice article in condensed form. We welcome your recommendations for improvement to this forum or suggestions on future topics (these will be wide ranging to if nothing in this update interests you, hold on for future editions!) The Arizona Promising Practices Forum and website, www.azpromisingpractices.com is a FREE resource of the Arizona Department of Education.

Mary Urich, ACPE Director murich@mail1.ade.state.az.us

In this issue we focus on Promising Practice Research geared towards Assisting Special Needs and Gifted Students in the Math Classroom. With the emphasis in the No Child Left Behind Legislation on improving learning for all students, this research, brought to you by TeacherVision, outlines strategies that can be implemented in the classroom or structured around Staff Development.

But first:

National Website of Importance - The California Staff Development Consortia provides a series of online resources that can be used by schools, researchers, or State Department of Education Personnel to improve upon the learning for adults. Check them out at - http://www.cpdc.k12.ca.us/index.html

Promising Practice Research and Tips

What should be done to differentiate curriculum, instruction and assessment for the mathematically gifted in the regular classroom?

Historically there has been debate about the role of acceleration versus enrichment as the differentiation mode for mathematics. Most experts recommend a combination. The following are suggestions for differentiating for the mathematically gifted by using (1) assessment, (2) curriculum materials, (2) instructional techniques, and (4) grouping models. These opportunities should be made broadly available to any student with interest in taking advantage of them.

·        Give pre-assessments so that students who already know the material do not have to repeat it but may be provided with instruction and activities that are meaningful. In the elementary grades, gifted learners still need to know their basic facts. If they do not, don't hold them back from other more complex tasks, but continue to work concurrently on the basics.

·        Create assessments that allow for differences in understanding, creativity, and accomplishment; give students a chance to show what they have learned. Ask students to explain their reasoning both orally and in writing.

·        Choose textbooks that provide more enriched opportunities. Unfortunately, curriculum in this country is mainly driven by textbooks, which are used about 80% of the time (Lockwood, 1992). Math textbooks often repeat topics from year to year in the grades prior to algebra. Since most textbooks are written for the general population, they are not always appropriate for the gifted. Several series that hold promise for gifted learners have been developed recently under grants from the National Science Foundation; they emphasize constructivist learning and include concepts beyond the basics.

·        Use multiple resources. No single text will adequately meet the needs of these learners.

·        Be flexible in your expectations about pacing for different students. While some may be mastering basic skills, others may work on more advanced problems.

·        Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible.

·        Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions.

·        Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games.

·        Provide AP level courses in calculus, statistics, and computer science or encourage prepared students to take classes at local colleges if the supply of courses at the high school has been exhausted.

·        Differentiate assignments. It is not appropriate to give more problems of the same type to gifted students. You might give students a choice of a regular assignment; a different, more challenging one; or a task that is tailored to interests.

·        Expect high level products (e.g., writing, proofs, projects, solutions to challenging problems).

·        Provide opportunities to participate in contests such as Mathematical Olympiads for the Elementary School (grades 4-6), Math Counts (grades 7-8), and the American Junior High School Mathematics Exam (grades 7-8) or the American High School Mathematics Exam (grades 9-12). Give feedback to students on their solutions. After the contests, use some of the problems as the basis for classroom discussions.

·        Provide access to male and female mentors who represent diverse linguistic and cultural groups. They may be within the school system, volunteers from the community, or experts who agree to respond to questions by e-mail. Bring speakers into the classroom to explain how math has opened doors in their professions and careers.

·        Provide some activities that can be done independently or in groups based on student choice. Be aware that if gifted students always work independently, they are gaining no more than they could do at home. They also need appropriate instruction, interaction with other gifted students, and regular feedback from the teacher.

·        Provide useful concrete experiences. Even though gifted learners may be capable of abstraction and may move from concrete to abstract more rapidly, they still benefit from the use of manipulatives and "hands-on" activities.

How can technology support the needs of the gifted?

Technology can provide a tool, an inspiration, or an independent learning environment for any student, but for the gifted it is often a means to reach the appropriate depth and breadth of curriculum and advanced product opportunities. Calculators can be used as an exploration tool to solve complex and interesting problems.

Computer programming is a higher level skill that enhances problem solving abilities and promotes careful reasoning and creativity. The use of a database, spreadsheet, graphic calculator, or scientific calculator can facilitate powerful data analysis. The World Wide Web is a vast and exciting source of problems, contests, enrichment, teacher resources, and information about mathematical ideas that are not addressed in textbooks. Technology is an area in which disadvantaged gifted students may be left out because of lack of access or confidence. It is essential that students who do not have access at home get the exposure at school so that they will not fall behind the experiences of other students.

What is the responsibility of schools and teachers in developing giftedness in mathematics?

Classroom teachers and school districts share the responsibility of addressing the needs of gifted students.

·        Teachers need training and support in recognizing and addressing the needs of the mathematically gifted.

·        Teachers who teach mathematics to gifted learners need a strong background in mathematics content. If the school has only a few students with special needs and does not have such a teacher, a mentor from outside the school should be located to work with individuals.

·        A coordinated curriculum plan needs to be in place so that the mathematical experiences for students are not duplicated or interrupted from one year to the next.

·        The school should have an organized support system that includes resource books, technology, and human resources.

Regular mathematics classrooms that offer sufficiently challenging and broad experiences for gifted students have the potential to enrich the learning community as a whole since other students will be interested in attempting, perhaps with help, some of the more challenging tasks. If math classes offer diversity in assignments, products, and pacing and monitor student needs, all students will be able to work at their own challenge level.