The Franklin Press
Math Moments - April 2017
Learning Math Facts: Three Important Steps
Research has shown that students need to go through three phases to achieve mastery of basic math facts. Each phase is important. Students need to progress through each; none should be skipped. Fact mastery depends on developing reasoning strategies and understanding relationships between numbers. These reasoning strategies are essential to fact development. Jumping ahead to memorization without sufficient time with hands-on materials and understanding the relationships between numbers will limit comprehension.
Phase 1 - Concept Learning: This first stage is all about developing understanding and meaning. Students use concrete objects, fingers, pictures and charts. Much time is spent counting, joining and separating groups, comparing amounts. Children will build the same number many different ways. This is a critical stage in developing strong number sense which should not be rushed through or skipped.
Phase 2 - Fact Strategies: This is the very important, often neglected bridge between concept learning and memorization. The goals in this phase are for students to recognize facts that relate in certain ways and to understand those relationships.
Here are a few examples of strategies/number relationships children should understand and use to help on their path to fluency and memorization:
Addition
- Counting on +1, +2
- Double facts (6+6)
- Doubles +1 (I know 6+6 is 12, so 6+7 is 1 more: 13)
- Doubles +2 (I know 6+6 is 12, so 6+8 is 2 more: 14)
- Combinations of 10 (7+3, 8+2)
- +9 facts (add 10, take 1 away: 6+9, think 6+10=16 so 6+9 is 1 less: 15)
Subtraction
- Counting back -1, -2
- Think Addition (Use the known addition fact 12-7, think 7+_=12)
- Work back through 10 (15-6: think 15-5=10 minus 1 more = 9)
Phase 3 – Memorization: - Here the goal is for students to master sums and differences (or products and quotients) so they can recall them efficiently and accurately, and retain them over time.
When students count on their fingers, make marks in the margins or are verbally counting, they have not mastered their facts because they have not yet developed efficient methods of getting an answer based on number relationships and reasoning.
For addition and subtraction, most students should be working:
Phase 1: Constructing Meaning in Kindergarten and grade 1,
Phase 2: Reasoning Strategies in 1st and 2nd grades,
Phase 3: Working Toward Recall in grades 2 through 5.
Multiplication and division follows this track for most children:
Phase 1: Constructing Meaning - late 2nd and all of 3rd grade,
Phase 2: Reasoning Strategies in 3rd and 4th grades,
Phase 3: Working Toward Recall in grade 5 and 6.
Click here for more information about the process of learning math facts.
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