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.
- 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
- 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.