In developing an awareness of mathematical concepts,
students must engage their nonverbal thinking skills. Nonverbal
thinking involves the use of spatial and visual processes to learn
or think about a problem or concept.
Nonverbal thinking may involve the use of symbols.
The numerals 6 and 26, for example, are symbols that represent
quantities. Students use and manipulate symbols when doing operations
ranging from basic addition to algebraic equations.
Nonverbal thinking also may involve visual or
spatial representations of math processes and relationships. Students
must be able to interpret visual and spatial information (as when
looking at a map, graph, or geometric shape), and to form and
understand visual and spatial concepts (as when translating graph
images into usable mathematical information, or describing attributes
Some concepts lend themselves to ‘visualization’,
creating a mental image to represent a mathematical relationship.
The concept of proportion is a good example. A student may have
a difficult time interpreting proportion through words and verbal
explanation, but being able to visualize the relationship (e.g.,
the number of boys to girls in the class, the ratio of eaten slices
in a pizza) may greatly enhance his/her understanding of proportion
as a concept.
Here are some strategies to help students develop
and strengthen their understanding of symbols and their abilities
- Integrate hands-on activities and verbal explanations
into the learning of spatially based concepts. For example,
have students use pattern blocks or geoboards to make geometric
shapes, then discuss and write down the characteristics of the
shapes, such as number of sides, types of angles, etc.
- Use examples of familiar situations, or analogies,
to talk and think about math concepts. This helps students link
the concepts to a visual image. For example, the concept of
ratio may be illustrated by asking students to imagine two brothers
sharing a pizza, and the amount of pizza left over after the
big brother takes his portion.
- Guide students in visualizing patterns. For
example, talk students through ‘seeing’ a geometric
shape in their minds, ‘picturing’ a math process
taking place, such as 1/3 of a pizza being taken away, and 2/3
of the pizza remaining, etc.