Differentiating Curriculum

• 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. 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 a lot 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 email. 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.