Secondary School, Mathematics Curriculum

Ideal Mathematics Curriculum for Advanced Learners

The mathematically gifted or talented learner is different from other students. These students are different in the pace with which they learn, the depth of their understanding, and the interests they hold. As such, an appropriate mathematics curriculum for advanced learners is one that is challenging, provides opportunities for extension, and connects to other disciplines. It also allows for depth and complexity, focuses on problem solving and higher-order thinking skills, and incorporates abstraction.

Appropriate experiences for advanced learners in mathematics should include compacting and differentiating the curriculum. Opportunities for acceleration and enrichment should be present, where acceleration refers to the faster pace with which the curriculum is covered and enrichment refers to the deeper level with which the curriculum is covered. Ideally, advanced learners should experience acceleration and enrichment, not one or the other.

preassessment and diagnostic testing should be used for placement to ensure that advanced students have the opportunity to experience exciting and new curriculum. In addition, students should participate in regular, ongoing summative and formative assessments, some of which are authentic. Inquiry-based and open-ended problems should be incorporated that allow for multiple solutions and multiple methods of solution. Students should have the opportunity to integrate technology and manipulatives to enhance learning and support multiple representations. The type of secondary school mathematics curriculum described here is [Page 781]rich, deep, and accelerative. This curriculum, however, is not the reality for many advanced mathematics learners.

Mathematics Course-Taking Pipeline

The reality of the secondary school mathematics curriculum differs greatly from the idealized one described. Most secondary schools address the mathematics curriculum for advanced learners through acceleration only. Students experience advanced mathematics through honors courses, the Advanced Placement program, or the International Baccalaureate program. Although honors, Advanced Placement, and International Baccalaureate courses represent the only option in some schools, these programs are not specifically designed for gifted, creative, and talented mathematics learners. In other districts, particularly urban and rural districts, schools are unable to offer students a variety of advanced or accelerative mathematics options.

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