Recognizing Rules and Procedures/Impact of Attention and Memory

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.

Helpful Hints

  • 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 percentages).  
  • 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 apply.