As students develop their mathematical awareness,
they begin to discover the rules that guide computation and problem
solving. Attention skills play an important role in the learning
and recognition of these rules. For example, recognizing basic
rules, e.g., that the ‘+’ sign means combine quantities,
or that a fraction is represented as the part over the whole,
etc., depends in part upon a student’s ability to concentrate
consistently, attend to detail, and connect new information to
what is already known.
Rules in math are based upon patterns. Students
must learn to recognize the patterns in different math situations
and the rules associated with each pattern.
Once a rule pattern has been learned, the student
can then store it in long-term memory, and access the rule when
the pattern occurs in a new situation. For example, once a student
learns the rules for regrouping (borrowing and carrying) in subtraction
problems, when faced with a new subtraction problem requiring
regrouping, he/she can recognize the pattern and call up the proper
rules to mind.
Here are some strategies that may help develop
and strengthen students’ abilities to learn and recognize
rules in math.
- Help students see how patterns and rules reflect
mathematical concepts. For example, first explain that the rules
for regrouping rise from the concept of place value, then show
the role regrouping plays in addition, subtraction, multiplication
and division. This allows students to focus on the reasoning
behind the rules. Moreover, instead of memorizing eight different
sets of rules, students memorize two processes (borrowing and
carrying) with variations.
- As students learn and practice rules, use
written cues to remind them how the rules work (for example,
printing the phrase: "big number goes on top" next
to subtraction problems serves as a reminder about the number
relationships in subtraction).
- Use concrete objects, drawings, check marks,
etc. to illustrate mathematic rules whenever possible, so students
can associate the abstract process with a visual image.
- Use color-coding to help students become aware
of how and when rules are in play (e.g. making the bigger numbers
in a group of subtraction problems green, the smaller numbers
in each problem blue, using highlighting or underlining to identify
plus or minus signs, etc.)
- When focusing on specific rules or procedures,
separate different types of problems on the page. As students
become more comfortable with the rules, gradually combine problems
of different types.
- Have students practice identifying rules
in problems without actually doing the related computations.
For example, a student given the problem ‘4 + 0’
might respond that the ‘+’ sign means to add, and
that adding zero to any number results in the original number.
Or, given the problem ‘3/4 X 1/3,’ a student might
respond that the ‘X’ sign means multiply, and the
rule for multiplying fractions is to multiply the top numbers
together and the bottom numbers together.
- Have students categorize related math problems
together as variations of a larger rule. (e.g., the steps for
4/5 = __%, and the steps for 80% = _/_ are different, but the
steps fall within the larger rule for converting fractions to
- Have students practice identifying math
problems that are examples of specific rules (e.g., by operation),
then have them create their own math problems where the rules