BASIC FACTS - The Nemesis of Every Elementary Classroom Teacher
Mari Muri, Eastern 1 Regional Director
In your role as a math teacher leader who works primarily with elementary classroom teachers, you've heard this statement over and over, "These kids don't know their basic facts!" This phrase is familiar to you as a math consultant, coach, lead teacher, grade-level team leader, math specialist, or whatever title your district has assigned to you.
As a math leader you know that the NCTM Curriculum Focal Points for Pre-K through Grade 8 Mathematics (2006), and the relatively new Common Core State Standards for Mathematics (June 2, 2010) call for 'developing quick recall' of basic addition and subtraction facts by the end of grade 2. These documents also call for 'developing quick recall' of basic multiplication and division facts by the end of grade 4. These are realistic goals for students at these grade levels, but not all students learn at the same rate or in the same way. Thus saying, "These kids don't know their basic facts," can be misleading. Some students have surely developed the necessary quick recall, yet there may be some that are still lacking the quick recall of all facts. In either case, it would help the teacher to determine which understandings are still limited. Having these data available can assist in structuring interventions for those students needing extra help in the specifically identified weaknesses.
Since the inception of the NCTM Curriculum and Evaluation Standards (1989) and the ensuing NCTM Principles and Standards (2000), elementary math curricula have had a greater focus on the understanding of basic facts with an emphasis on building various strategies to help students become comfortable with the acquisition of basic facts. These strategies are designed to support not only a student's basic fact acquisition but also place value, number sense, mental math strategies, and basic computational skills involving multi-digit numbers.
You may want to work with teachers of struggling students in the early grades to develop (or select) resources that provide computational strategies to help these students gain confidence in their number sense and, thus, computational proficiency. At the primary level, 'making tens' using ten frames helps students to see that 7 + 8 is the same as 10 + 5 (take 2 from the 7 to add to the 8 to make a 10). Strategies such as 'counting up' or 'counting back' also support addition and subtraction of grade level appropriate numbers. With multi-digit numbers it often helps students to work from left to right, as they are used to doing in reading. This method reinforces the concept of place value and most often lessens the number of errors incurred when 'carrying 'or 'borrowing.' For example:
For students in the intermediate grades (3 and 4) some of the above strategies may need reinforcement. At this point, most likely, students may have difficulty with multiplication and related division facts. Once again, if the teacher can identify which facts are causing specific problems, resources can be made available to help students develop strategies beyond just having to memorize the facts. Understanding that multiplying any number by zero equals zero, and the result of multiplying any number by 1 (for example: 1 group of 12 equals 12) results in that same number. Remind students that multiplying by 2 is the same as doubling the number (this is the same as adding a number to itself).
Most problems occur when students face multi-digit multiplication. Once again, using the left-to-right method alleviates the cumbersome 'carrying' which does not promote the continued development of place value. For example:
In most other countries, division is tied much more closely to multiplication. In the U.S., students use one set of flash cards for multiplication and another set for division. By tying the two operations more closely together, students are able to better understand the meaning of division and use the multiplication skills already acquired. This sample shows a method becoming more widely used to develop a greater understanding of how multiplication does not have to follow the "Dirty Monkey Smells Bad," "Dad Mom Sister Brother," or the more current version "Dracula Must Suck Blood" mnemonic to memorize the sequence of Divide-Multiply-Subtract-Bring it down.
Only a few examples have been included here; there are many others that your teachers may want to explore. It is important to remember that the error in teaching students basic facts and computational algorithms is believing that drill and practice is a method of developing understanding. Drill and practice are still appropriate but only when the desired place value concepts have been meaningfully developed, and flexible and useful computational processes have been developed.
I invite you to share other ideas for developing basic fact acquisition and computational strategies.