When it comes to learning math, concrete materials offer some important advantages over alternative topics. Although many curricula are centered around incorporating numbers, objects, and basic algebra, very little effort is devoted to teaching students how to calculate their concrete results. The most challenging obstacle, however, occurs when concrete is considered in the context of other units such as angles, surfaces, volumes, and time. In this regard, concrete math can be seen not as a separate subject but as a logical extension of the more traditional mathematics curriculum and courses such as Algebra, Trigonometry, Geometry, and Calculus. Click Here – website
How to find Concrete Materials?
Students learn to think in terms of concrete materials rather than objects and places. This encourages them to perceive objects in new ways and to be receptive to new abstractions such as fractions, ratios, symmetries, and cohomotography. These abstractions are the building blocks for the discipline of geometry and they allow the student to think in a fresh way about spatial relationships and the connections among different objects. When concrete materials are introduced into the general curriculum, they become a part of the language used to describe geometrical shapes, such as conic sections, polygon units, polyhedra, etc. Similarly, in higher mathematics, concrete mathematics refers to the connective lattice structures used in geometry and to the recurrence formulas of algebraic equations. The goal of mathematics is to solve problems by abstracting them from the underlying geometrical structures.
Given that the vast majority of high school and middle school students have little or no exposure to concrete materials, they typically perform poorly in mathematics. However, it is possible to help them develop an interest in and appreciation for these objects by integrating hands-on materials into the curriculum. A curriculum based on hands-on materials provides opportunities for learners to build rich, concrete understandings of algebraic concepts by developing a sense of abstraction and modeling. In addition, hands-on materials provide opportunities to apply these abstractions and modeling skills to real world problems.