Math Relationships/Impact of Higher Order Cognition, Spatial and Sequential Ordering, and Memory

In order to understand the mathematical relationships occurring in a problem or equation, students must understand the broad concepts involved. Some math relationships are spatial, they involve physical objects and/or physical space (e.g., the relationship between an object’s weight and its size or mass). Other math relationships are sequential, the order in which steps occur or elements act on each other is most important (e.g., the relationship between the equations ‘10x+4=24’ and ‘10x=24-4’).

To work effectively with math relationships, students must have a flexible approach to each problem, knowing that quantities may be represented in a variety of ways. For example, understanding the concept of place value (e.g., that 30 is the same as 3 tens) enables students to more easily deal with problems concerning money, just as understanding the concept of units and subdivisions (or parts and wholes) helps students divide a single candy bar into equal parts to share.

Finally, students must be able to store and retrieve concepts from long term memory, and to hold several symbols and concepts in their minds. For example, a problem requiring plotting information on a graph may involve multiple concepts, including collecting and organizing information, setting up ratios, finding averages, using the coordinate system, etc.

Here are some strategies to help develop and strengthen students’ understanding of relationships in math.

Helpful Hints

  • Provide plenty of hands-on practice with concepts that are typically confused, such as weight and mass, capacity and volume, area and perimeter, etc.  
  • Use manipulables to help students explore mathematical relationships. For example, Connecting People (available from the Cuisenaire Company), are small, connectable figurines of different colors, sexes, and sizes. Activities can be built around the Connecting People figurines in which students build patterns, use math concepts in stories, organize and classify, use estimation, collect data, and explore units of measurement. (Welchman-Tischler, 1995).  
  • In addition to using manipulables and hands-on activities, have students develop charts and diagrams, or create note cards to define terms, show examples, etc. to explore how math terms are related.  
  • Have students use different representations to describe the same situation. For example, demonstrate how something can be shown using a table, a graph, written description, etc.  
  • Give students access to a dynamic or interactive computer software program that allows them to manipulate symbols, compare concepts, etc.