Early in math instruction, students are informally introduced to areas of higher math, such as geometry, probability, and statistics. Children experience geometry in the form of basic shapes and figures, part/whole relationships, and basic patterns. Laws of probability and chance are presented through games with cards and dice. Activities involving collecting, organizing and classifying objects provide the foundation for statistics.
Background for the study of algebra begins in the early grades as well. The simple equation 4+2 =?, for example, uses the algebraic concept of an unknown (“?”) representing a quantity (in this case 6). Solving equations with fractions in middle grades represents another building block for algebra readiness.
As students move to areas of higher math, they will find that these areas are also related and interdependent. For example, core concepts in pre-calculus require background skills in advanced graphing, coordinate and space geometry, laws of probability, statistical procedures, and algebraic expressions.
The transition into the formal teaching of higher math typically occurs with the high-school core curriculum. Background material must be developed for students at each step along the way in early, middle, and even higher grades to prepare them for the more formal instruction to come.
Here are some suggestions for helping students progress in areas of higher math.
- Establish that students have the necessary background skills to move ahead to formal instruction in areas of higher math. For example, students who have not mastered factoring from Algebra I will have great difficulty simplifying rational expressions in Algebra II.
- Utilize computer software programs to help students explore areas of higher math. Programs exist for all levels and areas. Incorporate tutorial programs that are interactive and dynamic.
- Set up a “math mentor” for the student. This person may be a mathematics teacher, or a professional in the community who uses math in his/her work, e.g., a surveyor, an architect, a research scientist, an accountant, etc.
- Use real life problem solving to help students connect concepts in higher math. For example, when students are exploring the question of how a spacecraft stays in orbit around the earth they will use formulas for gravity, geometric concepts, proportion formulas, etc.