Academic areas such as mathematics depend a great deal on systems of rules (rules for computing numbers, rules for working with fractions, rules for solving equations, etc.). Rules provide a consistent structure for calculating and problem solving. As students are required to apply more and more rules in math, their abilities in memory and higher order cognition are called into play. When working through a math problem, students must remember which rules apply to the problem and which do not. In addition, they must hold aspects of the problem in mind while accessing and applying rules.

It is common for children to overuse a rule when they first begin to learn it. Through further practice, students learn when the rule does and does not apply, and are able to apply the rule more appropriately. This conditional knowledge of rules is a function of higher order thinking.

Here are some strategies to develop and strengthen students’ applications of rules during math.

Helpful Hints

  • Promote students’ recognition of math patterns to guide them in the use of rules. For example, teach students to ask themselves, “Have I seen this type of problem before’ What rule did I use’ Do I apply the same rule for this problem‘” etc.  
  • Encourage students to be monitor their own progress as they use rules, for example, stopping after completing each problem, or each line of problems, to ask themselves, “How am I doing so far’ Am I using the rule I need to‘” etc.  
  • Build students’ knowledge of when to apply rules and how rules are relevant using real life situations. For example, to teach the rules for rounding numbers, use items from a restaurant menu, “for sale” notices from classified ads, mileage on a map, etc. Have students talk about when it would be appropriate to use rounded numbers, and when the exact figure would be needed.