Mathematics, Curriculum

Curriculum Terms and Techniques

Some terms used within the existing research literature on curriculum relevant for this entry are (1) contest problem training, (2) curriculum compacting, (3) curriculum differentiation, (4) heterogeneous and/or homogeneous grouping, (5) radical acceleration, and (6) summer programs.

• 1.
  Contest problem training is used to refer to specific mathematical techniques from the areas of algebra, analysis, combinatorics, geometry, number theory, and so on, which are useful to solve a wide variety of contest problems.
• 2.
  Curriculum compacting simply means eliminating previously mastered work (typically involving routine computations and procedures) to condense the regular curriculum for gifted learners.
• 3.
  Curriculum differentiation, as defined by various theorists, means tailoring the curriculum to meet the specific needs of learners of varied abilities. Although this term was initially used to refer to the varied needs of gifted learners, it has mutated into meaning tailoring the curriculum and the classroom environment to create different learning experiences for all students.
• 4.
  Homogeneous grouping refers to the grouping of learners at the same ability level; whereas heterogeneous grouping allows for learners of mixed ability levels to work together on ongoing class activities, projects, and the like. Sometimes the term exclusive grouping is used to refer to homogeneous or same-ability grouping.
• 5.
  Radical acceleration refers to the practice of grade skipping and early university entrance for profoundly gifted learners. These learners typically have IQs over 180.
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• 6.
  Summer programs are typically 1 – to 4–week courses held on university campuses in which mathematically gifted students are exposed to new topics in mathematics as well as mathematics' far-reaching applicability and relevance to the everyday world.

Given the differences in mathematical abilities between mathematically gifted students and their peers, curriculum compacting, differentiation, and acceleration can be applied effectively to the mathematics curriculum to meet the needs of mathematically gifted students. Numerous studies have shown that acceleration is perhaps the most effective way of meeting gifted student programming needs. Mathematics, unlike any other discipline, lends itself to acceleration because of the sequential developmental nature of many elementary concepts. The very nature of acceleration suggests that the principles of curriculum compacting are applied to trim out the excessive amount of repetitive tasks. Differentiation occurs naturally because acceleration allows gifted students with the opportunity to get through the “typical” traditional high school curriculum of geometry–algebra2–precalculus–calculus much faster than the norm of 4 years.

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