For a student to progress in mathematics, several conceptual building blocks must be acquired. Such components include:
- the ability to form and use associations (as in number concepts and symbol use)
- a grasp of the language of Mathematics, from concepts such as measurement and money to the technical vocabulary of math such as parallelogram and denominator.
- an understanding of the relationships involved in numeric operations (such as the place value concept behind borrowing and carrying)
- the ability to make generalizations (as in the application of mathematical learning to everyday situations)
This chart describes important skills related to understanding math concepts:
|Student understands mathematical symbols and can visualize patterns, math concepts, and the parts of a problem in his/her head.
|Student has difficulty visualizing patterns or the parts of a math problem in his head. Student has difficulty associating math symbols with the concepts they represent.
|Student understands math vocabulary words and is able to build math knowledge through the use of math language.
|Student is not comfortable using mathematical language, or has difficulty with math vocabulary words.
|Student understands how concepts are related (as in the relationship between addition and subtraction, or between ratio and proportion).
|Student has difficulty seeing how concepts (such as addition and subtraction, or ratio and proportion) are related to each other.
|Student can see how math concepts (such as proportion or measurement ) apply to everyday life.
|Student has problems transferring concepts learned in the math classroom to real life situations.