While walking through classrooms during the beginning of the year, I see many students following step-by-step procedures to find answers. For example, some of the problems required students to make 10 circles in the ones place then move them to the tens place, then make 10 circles in the tens place and move them to the hundreds place. This procedure teaches a rule: you cannot have more than 10 in any one place. Isn’t it interesting that for one procedure we tell kids that when adding digits that equal more than 9, you have to move it to the place to the left? However, the exact opposite holds true when subtracting. These long lists of rules and procedures can be confusing to students and can often lead to frustration and errors.
Many students use procedures to solve “place value” problems. For example, teachers may ask, “What number goes in the ones place, tens place, hundreds place?” Does this type of work and questioning support place value or does it support number placement?
If we look at the number 245, does knowing what number is in the ones, tens, or hundreds place really explain the value? If we were to ask kids, “How many tens are in 245?” What might they say? Would they say 24? Better yet, would they say 24.5? What if we asked them how many ones are in 245? Would they say 245?
Are we teaching number procedures or are we teaching number sense?
National Council of Teachers of Mathematics Position: Procedural fluency builds on a foundation of conceptual understanding, strategic reasoning, and problem solving (NGA Center & CCSSO, 2010; NCTM, 2000, 2014). Research suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999). Therefore, the development of students’ conceptual understanding of procedures should precede and coincide with instruction on procedures.
#1 Consider how physically working with groups of 10 in your classroom can support knowledge of the base 10 number system and place value.
#2 Ten frames are typically introduced as early as kindergarten. How might ten frames provide continued number sense support in 1st grade through 5th grade?
#3How about encouraging demanding problem analysis/wait time before solving a problem? “What if we said, “Stop and think before you answer this problem. or Think of at least two ways to solve this problem.”, before we let students pick a pencil?
Let’s continue to teach our students number procedures, but let’s make sure it goes hand in hand with teaching number sense.
What are some ways you support number sense in your classroom?
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